\documentclass{amsart}
    \advance\textheight by 1.75in
    \advance\textwidth by 2in
    \advance\topmargin by -1in
    \advance\oddsidemargin by -1in
    \advance\evensidemargin by -1in
    \usepackage{amssymb}
    \parindent0pt
    \begin{document}
    \textbf{SWV007+2.ax} Priority queue checker: system of lower bounds






$\neg\,\mbox{isnonempty\_slb}(\mbox{create\_slb})\qquad\mbox{fof}(\mbox{ax}_{18},\mbox{axiom})$

$\forall u,v,w{:}\;\mbox{isnonempty\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(v,w)))\qquad\mbox{fof}(\mbox{ax}_{19},\mbox{axiom})$

$\forall u{:}\;\neg\,\mbox{contains\_slb}(\mbox{create\_slb},u)\qquad\mbox{fof}(\mbox{ax}_{20},\mbox{axiom})$

$\forall u,v,w,x{:}\;( \mbox{contains\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(v,x)),w)\iff ( \mbox{contains\_slb}(u,w)\mbox{ or }v = w ) )\qquad\mbox{fof}(\mbox{ax}_{21},\mbox{axiom})$

$\forall u,v{:}\;\neg\,\mbox{pair\_in\_list}(\mbox{create\_slb},u,v)\qquad\mbox{fof}(\mbox{ax}_{22},\mbox{axiom})$

$\forall u,v,w,x,y{:}\;( \mbox{pair\_in\_list}(\mbox{insert\_slb}(u,\mbox{pair}(v,x)),w,y)\iff ( \mbox{pair\_in\_list}(u,w,y)\mbox{ or }( v = w\mbox{ and }x = y ) ) )\qquad\mbox{fof}(\mbox{ax}_{23},\mbox{axiom})$

$\forall u,v,w{:}\;\mbox{remove\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(v,w)),v) = u\qquad\mbox{fof}(\mbox{ax}_{24},\mbox{axiom})$

$\forall u,v,w,x{:}\;( ( v\ne w\mbox{ and }\mbox{contains\_slb}(u,w) ) \ \Rightarrow \ \mbox{remove\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(v,x)),w) = \mbox{insert\_slb}(\mbox{remove\_slb}(u,w),\mbox{pair}(v,x)) )\qquad\mbox{fof}(\mbox{ax}_{25},\mbox{axiom})$

$\forall u,v,w{:}\;\mbox{lookup\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(v,w)),v) = w\qquad\mbox{fof}(\mbox{ax}_{26},\mbox{axiom})$

$\forall u,v,w,x{:}\;( ( v\ne w\mbox{ and }\mbox{contains\_slb}(u,w) ) \ \Rightarrow \ \mbox{lookup\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(v,x)),w) = \mbox{lookup\_slb}(u,w) )\qquad\mbox{fof}(\mbox{ax}_{27},\mbox{axiom})$

$\forall u{:}\;\mbox{update\_slb}(\mbox{create\_slb},u) = \mbox{create\_slb}\qquad\mbox{fof}(\mbox{ax}_{28},\mbox{axiom})$

$\forall u,v,w,x{:}\;( \mbox{strictly\_less\_than}(x,w) \ \Rightarrow \ \mbox{update\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(v,x)),w) = \mbox{insert\_slb}(\mbox{update\_slb}(u,w),\mbox{pair}(v,w)) )\qquad\mbox{fof}(\mbox{ax}_{29},\mbox{axiom})$

$\forall u,v,w,x{:}\;( w < x \ \Rightarrow \ \mbox{update\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(v,x)),w) = \mbox{insert\_slb}(\mbox{update\_slb}(u,w),\mbox{pair}(v,x)) )\qquad\mbox{fof}(\mbox{ax}_{30},\mbox{axiom})$

\medskip\textbf{SWV007+4.ax} Priority queue checker: implementation function, Pi, Pi\#






$\forall u,v{:}\;i(\mbox{triple}(u,\mbox{create\_slb},v)) = \mbox{create\_pq}\qquad\mbox{fof}(\mbox{ax}_{54},\mbox{axiom})$

$\forall u,v,w,x,y{:}\;i(\mbox{triple}(u,\mbox{insert\_slb}(v,\mbox{pair}(x,y)),w)) = \mbox{insert\_pq}(i(\mbox{triple}(u,v,w)),x)\qquad\mbox{fof}(\mbox{ax}_{55},\mbox{axiom})$

$\forall u,v{:}\;( \mbox{pi\_sharp\_remove}(u,v)\iff \mbox{contains\_pq}(u,v) )\qquad\mbox{fof}(\mbox{ax}_{56},\mbox{axiom})$

$\forall u,v{:}\;( \mbox{pi\_remove}(u,v)\iff \mbox{pi\_sharp\_remove}(i(u),v) )\qquad\mbox{fof}(\mbox{ax}_{57},\mbox{axiom})$

$\forall u,v{:}\;( \mbox{pi\_sharp\_find\_min}(u,v)\iff ( \mbox{contains\_pq}(u,v)\mbox{ and }\mbox{issmallestelement\_pq}(u,v) ) )\qquad\mbox{fof}(\mbox{ax}_{58},\mbox{axiom})$

$\forall u{:}\;( \mbox{pi\_find\_min}(u)\iff \exists v{:}\;\mbox{pi\_sharp\_find\_min}(i(u),v) )\qquad\mbox{fof}(\mbox{ax}_{59},\mbox{axiom})$

$\forall u,v{:}\;( \mbox{pi\_sharp\_removemin}(u,v)\iff ( \mbox{contains\_pq}(u,v)\mbox{ and }\mbox{issmallestelement\_pq}(u,v) ) )\qquad\mbox{fof}(\mbox{ax}_{60},\mbox{axiom})$

$\forall u{:}\;( \mbox{pi\_removemin}(u)\iff \exists v{:}\;\mbox{pi\_sharp\_find\_min}(i(u),v) )\qquad\mbox{fof}(\mbox{ax}_{61},\mbox{axiom})$

$\forall u{:}\;( \mbox{phi}(u)\iff \exists v{:}\;( \mbox{succ\_cpq}(u,v)\mbox{ and }\mbox{ok}(v)\mbox{ and }\mbox{check\_cpq}(v) ) )\qquad\mbox{fof}(\mbox{ax}_{62},\mbox{axiom})$

\medskip\textbf{SWV010$\wedge$0.ax} Translation from Binder Logic (BL) to CS4






$\mbox{princ\_inj}{:}\;\mbox{individuals}\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{princ\_inj},\mbox{type})$

$\mbox{bl\_atom}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bl\_atom\_decl},\mbox{type})$

$\mbox{bl\_princ}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bl\_princ\_decl},\mbox{type})$

$\mbox{bl\_and}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to ( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bl\_and\_decl},\mbox{type})$

$\mbox{bl\_or}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to ( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bl\_or\_decl},\mbox{type})$

$\mbox{bl\_impl}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to ( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bl\_impl\_decl},\mbox{type})$

$\mbox{bl\_all}{:}\;( \mbox{individuals}\to \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bl\_all\_decl},\mbox{type})$

$\mbox{bl\_true}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bl\_true\_decl},\mbox{type})$

$\mbox{bl\_false}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bl\_false\_decl},\mbox{type})$

$\mbox{bl\_says}{:}\;\mbox{individuals}\to ( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bl\_says\_decl},\mbox{type})$

$\mbox{bl\_atom} = ( \lambda p{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{cs4\_atom}@ p ) )\qquad\mbox{thf}(\mbox{bl\_atom},\mbox{definition})$

$\mbox{bl\_princ} = ( \lambda p{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{cs4\_atom}@ p ) )\qquad\mbox{thf}(\mbox{bl\_princ},\mbox{definition})$

$\mbox{bl\_and} = ( \lambda a{:}\;\mbox{\$i}\to \mbox{\$o},b{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{cs4\_and}@ a@ b ) )\qquad\mbox{thf}(\mbox{bl\_and},\mbox{definition})$

$\mbox{bl\_or} = ( \lambda a{:}\;\mbox{\$i}\to \mbox{\$o},b{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{cs4\_or}@ a@ b ) )\qquad\mbox{thf}(\mbox{bl\_or},\mbox{definition})$

$\mbox{bl\_impl} = ( \lambda a{:}\;\mbox{\$i}\to \mbox{\$o},b{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{cs4\_impl}@ a@ b ) )\qquad\mbox{thf}(\mbox{bl\_impl},\mbox{definition})$

$\mbox{bl\_all} = ( \lambda a{:}\;\mbox{individuals}\to \mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{cs4\_all}@ a ) )\qquad\mbox{thf}(\mbox{bl\_all},\mbox{definition})$

$\mbox{bl\_true} = \mbox{cs4\_true}\qquad\mbox{thf}(\mbox{bl\_true},\mbox{definition})$

$\mbox{bl\_false} = \mbox{cs4\_false}\qquad\mbox{thf}(\mbox{bl\_false},\mbox{definition})$

$\mbox{bl\_says} = ( \lambda k{:}\;\mbox{individuals},a{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{cs4\_box}@ ( \mbox{cs4\_impl}@ ( \mbox{bl\_princ}@ ( \mbox{princ\_inj}@ k ) )@ a ) ) )\qquad\mbox{thf}(\mbox{bl\_says},\mbox{definition})$

$\mbox{bl\_valid}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bl\_valid\_decl},\mbox{type})$

$\mbox{bl\_valid} = \mbox{mvalid}\qquad\mbox{thf}(\mbox{bl\_valid\_def},\mbox{definition})$

$\mbox{loca}{:}\;\mbox{individuals}\qquad\mbox{thf}(\mbox{loca\_decl},\mbox{type})$

$\mbox{cs4\_valid}@ ( \mbox{cs4\_all}@ \lambda k{:}\;\mbox{individuals}{:}\;( \mbox{cs4\_impl}@ ( \mbox{princ\_inj}@ k )@ ( \mbox{princ\_inj}@ \mbox{loca} ) ) )\qquad\mbox{thf}(\mbox{loca\_strength},\mbox{axiom})$

\medskip\textbf{SWV001-0.ax} Program verification axioms






$\mbox{predecessor}(\mbox{successor}(x)) = x\qquad\mbox{cnf}(\mbox{predecessor\_successor},\mbox{axiom})$

$\mbox{successor}(\mbox{predecessor}(x)) = x\qquad\mbox{cnf}(\mbox{successor\_predecessor},\mbox{axiom})$

$\mbox{predecessor}(x) = \mbox{predecessor}(y) \ \Rightarrow \ x = y\qquad\mbox{cnf}(\mbox{well\_defined\_predecessor},\mbox{axiom})$

$\mbox{successor}(x) = \mbox{successor}(y) \ \Rightarrow \ x = y\qquad\mbox{cnf}(\mbox{well\_defined\_successor},\mbox{axiom})$

$\mbox{predecessor}(x) < x\qquad\mbox{cnf}(\mbox{predecessor\_less\_than},\mbox{axiom})$

$x < \mbox{successor}(x)\qquad\mbox{cnf}(\mbox{less\_than\_successor},\mbox{axiom})$

$( x < y\mbox{ and }y < z ) \ \Rightarrow \ x < z\qquad\mbox{cnf}(\mbox{transitivity\_of\_less\_than},\mbox{axiom})$

$x < y\mbox{ or }y < x\mbox{ or }x = y\qquad\mbox{cnf}(\mbox{all\_related},\mbox{axiom})$

$\neg\,x < x\qquad\mbox{cnf}(\mbox{x\_not\_less\_than\_x},\mbox{axiom})$

$x < y \ \Rightarrow \ \neg\,y < x\qquad\mbox{cnf}(\mbox{anti\_symmetry\_of\_less\_than},\mbox{axiom})$

$( x = y\mbox{ and }x < z ) \ \Rightarrow \ y < z\qquad\mbox{cnf}(\mbox{equal\_and\_less\_than\_transitivity}_1,\mbox{axiom})$

$( x = y\mbox{ and }z < x ) \ \Rightarrow \ z < y\qquad\mbox{cnf}(\mbox{equal\_and\_less\_than\_transitivity}_2,\mbox{axiom})$

\medskip\textbf{SWV007+3.ax} Priority queue checker: checked priority queues

This axiom set fully describes checked priority queues. Checked
 priority queues are defined as triples of a "priority queue
 pretender", a system of lower bounds and Boolean value that keep
 track of errors.




$\forall u{:}\;\mbox{succ\_cpq}(u,u)\qquad\mbox{fof}(\mbox{ax}_{31},\mbox{axiom})$

$\forall u,v,w{:}\;( \mbox{succ\_cpq}(u,v) \ \Rightarrow \ \mbox{succ\_cpq}(u,\mbox{insert\_cpq}(v,w)) )\qquad\mbox{fof}(\mbox{ax}_{32},\mbox{axiom})$

$\forall u,v,w{:}\;( \mbox{succ\_cpq}(u,v) \ \Rightarrow \ \mbox{succ\_cpq}(u,\mbox{remove\_cpq}(v,w)) )\qquad\mbox{fof}(\mbox{ax}_{33},\mbox{axiom})$

$\forall u,v{:}\;( \mbox{succ\_cpq}(u,v) \ \Rightarrow \ \mbox{succ\_cpq}(u,\mbox{findmin\_cpq\_eff}(v)) )\qquad\mbox{fof}(\mbox{ax}_{34},\mbox{axiom})$

$\forall u,v{:}\;( \mbox{succ\_cpq}(u,v) \ \Rightarrow \ \mbox{succ\_cpq}(u,\mbox{removemin\_cpq\_eff}(v)) )\qquad\mbox{fof}(\mbox{ax}_{35},\mbox{axiom})$

$\forall u,v{:}\;\mbox{check\_cpq}(\mbox{triple}(u,\mbox{create\_slb},v))\qquad\mbox{fof}(\mbox{ax}_{36},\mbox{axiom})$

$\forall u,v,w,x,y{:}\;( y < x \ \Rightarrow \ ( \mbox{check\_cpq}(\mbox{triple}(u,\mbox{insert\_slb}(v,\mbox{pair}(x,y)),w))\iff \mbox{check\_cpq}(\mbox{triple}(u,v,w)) ) )\qquad\mbox{fof}(\mbox{ax}_{37},\mbox{axiom})$

$\forall u,v,w,x,y{:}\;( \mbox{strictly\_less\_than}(x,y) \ \Rightarrow \ ( \mbox{check\_cpq}(\mbox{triple}(u,\mbox{insert\_slb}(v,\mbox{pair}(x,y)),w))\iff \mbox{\$false} ) )\qquad\mbox{fof}(\mbox{ax}_{38},\mbox{axiom})$

$\forall u,v,w,x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\iff \mbox{contains\_slb}(v,x) )\qquad\mbox{fof}(\mbox{ax}_{39},\mbox{axiom})$

$\forall u,v{:}\;( \mbox{ok}(\mbox{triple}(u,v,\mbox{bad}))\iff \mbox{\$false} )\qquad\mbox{fof}(\mbox{ax}_{40},\mbox{axiom})$

$\forall u,v,w{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ w = \mbox{bad} )\qquad\mbox{fof}(\mbox{ax}_{41},\mbox{axiom})$

$\forall u,v,w,x{:}\;\mbox{insert\_cpq}(\mbox{triple}(u,v,w),x) = \mbox{triple}(\mbox{insert\_pqp}(u,x),\mbox{insert\_slb}(v,\mbox{pair}(x,\mbox{bottom})),w)\qquad\mbox{fof}(\mbox{ax}_{42},\mbox{axiom})$

$\forall u,v,w,x{:}\;( \neg\,\mbox{contains\_slb}(v,x) \ \Rightarrow \ \mbox{remove\_cpq}(\mbox{triple}(u,v,w),x) = \mbox{triple}(u,v,\mbox{bad}) )\qquad\mbox{fof}(\mbox{ax}_{43},\mbox{axiom})$

$\forall u,v,w,x{:}\;( ( \mbox{contains\_slb}(v,x)\mbox{ and }\mbox{lookup\_slb}(v,x) < x ) \ \Rightarrow \ \mbox{remove\_cpq}(\mbox{triple}(u,v,w),x) = \mbox{triple}(\mbox{remove\_pqp}(u,x),\mbox{remove\_slb}(v,x),w) )\qquad\mbox{fof}(\mbox{ax}_{44},\mbox{axiom})$

$\forall u,v,w,x{:}\;( ( \mbox{contains\_slb}(v,x)\mbox{ and }\mbox{strictly\_less\_than}(x,\mbox{lookup\_slb}(v,x)) ) \ \Rightarrow \ \mbox{remove\_cpq}(\mbox{triple}(u,v,w),x) = \mbox{triple}(\mbox{remove\_pqp}(u,x),\mbox{remove\_slb}(v,x),\mbox{bad}) )\qquad\mbox{fof}(\mbox{ax}_{45},\mbox{axiom})$

$\forall u,v{:}\;\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,\mbox{create\_slb},v)) = \mbox{triple}(u,\mbox{create\_slb},\mbox{bad})\qquad\mbox{fof}(\mbox{ax}_{46},\mbox{axiom})$

$\forall u,v,w,x{:}\;( ( v\ne \mbox{create\_slb}\mbox{ and }\neg\,\mbox{contains\_slb}(v,\mbox{findmin\_pqp\_res}(u)) ) \ \Rightarrow \ \mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w)) = \mbox{triple}(u,\mbox{update\_slb}(v,\mbox{findmin\_pqp\_res}(u)),\mbox{bad}) )\qquad\mbox{fof}(\mbox{ax}_{47},\mbox{axiom})$

$\forall u,v,w,x{:}\;( ( v\ne \mbox{create\_slb}\mbox{ and }\mbox{contains\_slb}(v,\mbox{findmin\_pqp\_res}(u))\mbox{ and }\mbox{strictly\_less\_than}(\mbox{findmin\_pqp\_res}(u),\mbox{lookup\_slb}(v,\mbox{findmin\_pqp\_res}(u))) ) \ \Rightarrow \ \mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w)) = \mbox{triple}(u,\mbox{update\_slb}(v,\mbox{findmin\_pqp\_res}(u)),\mbox{bad}) )\qquad\mbox{fof}(\mbox{ax}_{48},\mbox{axiom})$

$\forall u,v,w,x{:}\;( ( v\ne \mbox{create\_slb}\mbox{ and }\mbox{contains\_slb}(v,\mbox{findmin\_pqp\_res}(u))\mbox{ and }\mbox{lookup\_slb}(v,\mbox{findmin\_pqp\_res}(u)) < \mbox{findmin\_pqp\_res}(u) ) \ \Rightarrow \ \mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w)) = \mbox{triple}(u,\mbox{update\_slb}(v,\mbox{findmin\_pqp\_res}(u)),w) )\qquad\mbox{fof}(\mbox{ax}_{49},\mbox{axiom})$

$\forall u,v{:}\;\mbox{findmin\_cpq\_res}(\mbox{triple}(u,\mbox{create\_slb},v)) = \mbox{bottom}\qquad\mbox{fof}(\mbox{ax}_{50},\mbox{axiom})$

$\forall u,v,w,x{:}\;( v\ne \mbox{create\_slb} \ \Rightarrow \ \mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w)) = \mbox{findmin\_pqp\_res}(u) )\qquad\mbox{fof}(\mbox{ax}_{51},\mbox{axiom})$

$\forall u{:}\;\mbox{removemin\_cpq\_eff}(u) = \mbox{remove\_cpq}(\mbox{findmin\_cpq\_eff}(u),\mbox{findmin\_cpq\_res}(u))\qquad\mbox{fof}(\mbox{ax}_{52},\mbox{axiom})$

$\forall u{:}\;\mbox{removemin\_cpq\_res}(u) = \mbox{findmin\_cpq\_res}(u)\qquad\mbox{fof}(\mbox{ax}_{53},\mbox{axiom})$

\medskip\textbf{SWV008$\wedge$0.ax} ICL logic based upon modal logic based upon simple type theory






$\mbox{rel}{:}\;\mbox{\$i}\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{rel\_type},\mbox{type})$

$\mbox{icl\_atom}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{icl\_atom\_type},\mbox{type})$

$\mbox{icl\_atom} = ( \lambda p{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{mbox}@ \mbox{rel}@ p ) )\qquad\mbox{thf}(\mbox{icl\_atom},\mbox{definition})$

$\mbox{icl\_princ}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{icl\_princ\_type},\mbox{type})$

$\mbox{icl\_princ} = ( \lambda p{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;p )\qquad\mbox{thf}(\mbox{icl\_princ},\mbox{definition})$

$\mbox{icl\_and}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to ( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{icl\_and\_type},\mbox{type})$

$\mbox{icl\_and} = ( \lambda a{:}\;\mbox{\$i}\to \mbox{\$o},b{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{mand}@ a@ b ) )\qquad\mbox{thf}(\mbox{icl\_and},\mbox{definition})$

$\mbox{icl\_or}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to ( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{icl\_or\_type},\mbox{type})$

$\mbox{icl\_or} = ( \lambda a{:}\;\mbox{\$i}\to \mbox{\$o},b{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{mor}@ a@ b ) )\qquad\mbox{thf}(\mbox{icl\_or},\mbox{definition})$

$\mbox{icl\_impl}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to ( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{icl\_impl\_type},\mbox{type})$

$\mbox{icl\_impl} = ( \lambda a{:}\;\mbox{\$i}\to \mbox{\$o},b{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{mbox}@ \mbox{rel}@ ( \mbox{mimpl}@ a@ b ) ) )\qquad\mbox{thf}(\mbox{icl\_impl},\mbox{definition})$

$\mbox{icl\_true}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{icl\_true\_type},\mbox{type})$

$\mbox{icl\_true} = \mbox{mtrue}\qquad\mbox{thf}(\mbox{icl\_true},\mbox{definition})$

$\mbox{icl\_false}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{icl\_false\_type},\mbox{type})$

$\mbox{icl\_false} = \mbox{mfalse}\qquad\mbox{thf}(\mbox{icl\_false},\mbox{definition})$

$\mbox{icl\_says}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to ( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{icl\_says\_type},\mbox{type})$

$\mbox{icl\_says} = ( \lambda a{:}\;\mbox{\$i}\to \mbox{\$o},s{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{mbox}@ \mbox{rel}@ ( \mbox{mor}@ a@ s ) ) )\qquad\mbox{thf}(\mbox{icl\_says},\mbox{definition})$

$\mbox{iclval}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$o}\qquad\mbox{thf}(\mbox{iclval\_decl\_type},\mbox{type})$

$\mbox{iclval} = ( \lambda x{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{mvalid}@ x ) )\qquad\mbox{thf}(\mbox{icl\_s4\_valid},\mbox{definition})$

\medskip\textbf{SWV013-0.ax} Lists in Separation Logic

Axioms for proving entailments between separation logic formulas
 with list predicates.




$\mbox{sep}(s,\mbox{sep}(t,\mbox{sigma})) = \mbox{sep}(t,\mbox{sep}(s,\mbox{sigma}))\qquad\mbox{cnf}(\mbox{associative\_commutative},\mbox{axiom})$

$\mbox{sep}(\mbox{lseg}(x,x),\mbox{sigma}) = \mbox{sigma}\qquad\mbox{cnf}(\mbox{normalization},\mbox{axiom})$

$\neg\,\mbox{heap}(\mbox{sep}(\mbox{next}(\mbox{nil},y),\mbox{sigma}))\qquad\mbox{cnf}(\mbox{wellformedness}_1,\mbox{axiom})$

$\mbox{heap}(\mbox{sep}(\mbox{lseg}(\mbox{nil},y),\mbox{sigma})) \ \Rightarrow \ y = \mbox{nil}\qquad\mbox{cnf}(\mbox{wellformedness}_2,\mbox{axiom})$

$\neg\,\mbox{heap}(\mbox{sep}(\mbox{next}(x,y),\mbox{sep}(\mbox{next}(x,z),\mbox{sigma})))\qquad\mbox{cnf}(\mbox{wellformedness}_3,\mbox{axiom})$

$\mbox{heap}(\mbox{sep}(\mbox{next}(x,y),\mbox{sep}(\mbox{lseg}(x,z),\mbox{sigma}))) \ \Rightarrow \ x = z\qquad\mbox{cnf}(\mbox{wellformedness}_4,\mbox{axiom})$

$\mbox{heap}(\mbox{sep}(\mbox{lseg}(x,y),\mbox{sep}(\mbox{lseg}(x,z),\mbox{sigma}))) \ \Rightarrow \ ( x = y\mbox{ or }x = z )\qquad\mbox{cnf}(\mbox{wellformedness}_5,\mbox{axiom})$

$\mbox{heap}(\mbox{sep}(\mbox{next}(x,y),\mbox{sep}(\mbox{lseg}(y,z),\mbox{sigma}))) \ \Rightarrow \ ( x = y\mbox{ or }\mbox{heap}(\mbox{sep}(\mbox{lseg}(x,z),\mbox{sigma})) )\qquad\mbox{cnf}(\mbox{unfolding}_2,\mbox{axiom})$

$\mbox{heap}(\mbox{sep}(\mbox{lseg}(x,y),\mbox{sep}(\mbox{lseg}(y,\mbox{nil}),\mbox{sigma}))) \ \Rightarrow \ \mbox{heap}(\mbox{sep}(\mbox{lseg}(x,\mbox{nil}),\mbox{sigma}))\qquad\mbox{cnf}(\mbox{unfolding}_3,\mbox{axiom})$

$\mbox{heap}(\mbox{sep}(\mbox{lseg}(x,y),\mbox{sep}(\mbox{lseg}(y,z),\mbox{sep}(\mbox{next}(z,w),\mbox{sigma})))) \ \Rightarrow \ \mbox{heap}(\mbox{sep}(\mbox{lseg}(x,z),\mbox{sep}(\mbox{next}(z,w),\mbox{sigma})))\qquad\mbox{cnf}(\mbox{unfolding}_4,\mbox{axiom})$

$\mbox{heap}(\mbox{sep}(\mbox{lseg}(x,y),\mbox{sep}(\mbox{lseg}(y,z),\mbox{sep}(\mbox{lseg}(z,w),\mbox{sigma})))) \ \Rightarrow \ ( z = w\mbox{ or }\mbox{heap}(\mbox{sep}(\mbox{lseg}(x,z),\mbox{sep}(\mbox{lseg}(z,w),\mbox{sigma}))) )\qquad\mbox{cnf}(\mbox{unfolding}_5,\mbox{axiom})$

\medskip\textbf{SWV008$\wedge$2.ax} ICL$\wedge$=$>$ logic based upon modal logic






$\mbox{icl\_impl\_princ}{:}\;( \mbox{\$i}\to \mbox{\$o} )\to ( \mbox{\$i}\to \mbox{\$o} )\to \mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{icl\_impl\_princ\_type},\mbox{type})$

$\mbox{icl\_impl\_princ} = ( \lambda a{:}\;\mbox{\$i}\to \mbox{\$o},b{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{mbox}@ \mbox{rel}@ ( \mbox{mimpl}@ a@ b ) ) )\qquad\mbox{thf}(\mbox{icl\_impl\_princ},\mbox{definition})$

\medskip\textbf{SWV007+0.ax} Priority queue checker: quasi-order set with bottom element






$\forall u,v,w{:}\;( ( u < v\mbox{ and }v < w ) \ \Rightarrow \ u < w )\qquad\mbox{fof}(\mbox{transitivity},\mbox{axiom})$

$\forall u,v{:}\;( u < v\mbox{ or }v < u )\qquad\mbox{fof}(\mbox{totality},\mbox{axiom})$

$\forall u{:}\;u < u\qquad\mbox{fof}(\mbox{reflexivity},\mbox{axiom})$

$\forall u,v{:}\;( \mbox{strictly\_less\_than}(u,v)\iff ( u < v\mbox{ and }\neg\,v < u ) )\qquad\mbox{fof}(\mbox{stricly\_smaller\_definition},\mbox{axiom})$

$\forall u{:}\;\mbox{bottom} < u\qquad\mbox{fof}(\mbox{bottom\_smallest},\mbox{axiom})$

\medskip\textbf{SWV007+1.ax} Priority queue checker: priority queues

Priority queues are inductively defined.




$\neg\,\mbox{isnonempty\_pq}(\mbox{create\_pq})\qquad\mbox{fof}(\mbox{ax}_6,\mbox{axiom})$

$\forall u,v{:}\;\mbox{isnonempty\_pq}(\mbox{insert\_pq}(u,v))\qquad\mbox{fof}(\mbox{ax}_7,\mbox{axiom})$

$\forall u{:}\;\neg\,\mbox{contains\_pq}(\mbox{create\_pq},u)\qquad\mbox{fof}(\mbox{ax}_8,\mbox{axiom})$

$\forall u,v,w{:}\;( \mbox{contains\_pq}(\mbox{insert\_pq}(u,v),w)\iff ( \mbox{contains\_pq}(u,w)\mbox{ or }v = w ) )\qquad\mbox{fof}(\mbox{ax}_9,\mbox{axiom})$

$\forall u,v{:}\;( \mbox{issmallestelement\_pq}(u,v)\iff \forall w{:}\;( \mbox{contains\_pq}(u,w) \ \Rightarrow \ v < w ) )\qquad\mbox{fof}(\mbox{ax}_{10},\mbox{axiom})$

$\forall u,v{:}\;\mbox{remove\_pq}(\mbox{insert\_pq}(u,v),v) = u\qquad\mbox{fof}(\mbox{ax}_{11},\mbox{axiom})$

$\forall u,v,w{:}\;( ( \mbox{contains\_pq}(u,w)\mbox{ and }v\ne w ) \ \Rightarrow \ \mbox{remove\_pq}(\mbox{insert\_pq}(u,v),w) = \mbox{insert\_pq}(\mbox{remove\_pq}(u,w),v) )\qquad\mbox{fof}(\mbox{ax}_{12},\mbox{axiom})$

$\forall u,v{:}\;( ( \mbox{contains\_pq}(u,v)\mbox{ and }\mbox{issmallestelement\_pq}(u,v) ) \ \Rightarrow \ \mbox{findmin\_pq\_eff}(u,v) = u )\qquad\mbox{fof}(\mbox{ax}_{13},\mbox{axiom})$

$\forall u,v{:}\;( ( \mbox{contains\_pq}(u,v)\mbox{ and }\mbox{issmallestelement\_pq}(u,v) ) \ \Rightarrow \ \mbox{findmin\_pq\_res}(u,v) = v )\qquad\mbox{fof}(\mbox{ax}_{14},\mbox{axiom})$

$\forall u,v{:}\;( ( \mbox{contains\_pq}(u,v)\mbox{ and }\mbox{issmallestelement\_pq}(u,v) ) \ \Rightarrow \ \mbox{removemin\_pq\_eff}(u,v) = \mbox{remove\_pq}(u,v) )\qquad\mbox{fof}(\mbox{ax}_{15},\mbox{axiom})$

$\forall u,v{:}\;( ( \mbox{contains\_pq}(u,v)\mbox{ and }\mbox{issmallestelement\_pq}(u,v) ) \ \Rightarrow \ \mbox{removemin\_pq\_res}(u,v) = v )\qquad\mbox{fof}(\mbox{ax}_{16},\mbox{axiom})$

$\forall u,v,w{:}\;\mbox{insert\_pq}(\mbox{insert\_pq}(u,v),w) = \mbox{insert\_pq}(\mbox{insert\_pq}(u,w),v)\qquad\mbox{fof}(\mbox{ax}_{17},\mbox{axiom})$

\medskip\textbf{SWV005-4.ax} Cryptographic protocol axioms for Yahalom, simplified






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OGets\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OSpy\_\_analz\_\_shrK}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ and }\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OSpy\_\_analz\_\_shrK}_1,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OSpy\_\_see\_\_shrK}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ and }\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OSpy\_\_see\_\_shrK}_1,\mbox{axiom})$

\medskip\textbf{SWV002-0.ax} Program verification axioms

These "clauses arose in a natural manner from work done
 in program verification" [MOW76] p.779.




$q_1(\mbox{vj},\mbox{vt},\mbox{vx}) \ \Rightarrow \ q_2(\mbox{vj},e(\mbox{vx},n_1),\mbox{vx})\qquad\mbox{cnf}(\mbox{clause}_1,\mbox{axiom})$

$q_2(\mbox{vj},\mbox{vt},\mbox{vx}) \ \Rightarrow \ q_3(\mbox{successor}(n_1),\mbox{vt},\mbox{vWhat})\qquad\mbox{cnf}(\mbox{clause}_2,\mbox{axiom})$

$( q_3(\mbox{vj},\mbox{vt},\mbox{vx})\mbox{ and }\mbox{vj} \leq n ) \ \Rightarrow \ q_4(\mbox{vj},\mbox{vt},\mbox{vx})\qquad\mbox{cnf}(\mbox{clause}_3,\mbox{axiom})$

$q_3(\mbox{vj},\mbox{vt},\mbox{vx}) \ \Rightarrow \ ( \mbox{vj} \leq n\mbox{ or }q_7(\mbox{vj},\mbox{vt},\mbox{vx}) )\qquad\mbox{cnf}(\mbox{clause}_4,\mbox{axiom})$

$( q_4(\mbox{vj},\mbox{vt},\mbox{vx})\mbox{ and }d(\mbox{vj})\mbox{ and }e(\mbox{vx},\mbox{vj}) \leq \mbox{vt} ) \ \Rightarrow \ q_6(\mbox{vj},\mbox{vt},\mbox{vx})\qquad\mbox{cnf}(\mbox{clause}_5,\mbox{axiom})$

$( q_4(\mbox{vj},\mbox{vt},\mbox{vx})\mbox{ and }d(\mbox{vj}) ) \ \Rightarrow \ ( e(\mbox{vx},\mbox{vj}) \leq \mbox{vt}\mbox{ or }q_5(\mbox{vj},\mbox{vt},\mbox{vx}) )\qquad\mbox{cnf}(\mbox{clause}_6,\mbox{axiom})$

$( q_5(\mbox{vj},\mbox{vt},\mbox{vx})\mbox{ and }d(\mbox{vj}) ) \ \Rightarrow \ q_6(\mbox{vj},e(\mbox{vx},\mbox{vj}),\mbox{vx})\qquad\mbox{cnf}(\mbox{clause}_7,\mbox{axiom})$

$q_6(\mbox{vj},\mbox{vt},\mbox{vx}) \ \Rightarrow \ q_3(\mbox{successor}(\mbox{vj}),\mbox{vt},\mbox{vx})\qquad\mbox{cnf}(\mbox{clause}_8,\mbox{axiom})$

$( n_1 \leq x\mbox{ and }x \leq n ) \ \Rightarrow \ d(x)\qquad\mbox{cnf}(\mbox{definition\_of\_d}_1,\mbox{axiom})$

$d(x) \ \Rightarrow \ \neg\,n_1 \leq x\qquad\mbox{cnf}(\mbox{definition\_of\_d}_2,\mbox{axiom})$

$d(x) \ \Rightarrow \ x \leq n\qquad\mbox{cnf}(\mbox{definition\_of\_d}_3,\mbox{axiom})$

$d(n_1)\qquad\mbox{cnf}(\mbox{one\_is\_d},\mbox{axiom})$

$d(n)\qquad\mbox{cnf}(\mbox{n\_is\_d},\mbox{axiom})$

$n_1 \leq n\qquad\mbox{cnf}(\mbox{clause}_9,\mbox{axiom})$

$( \mbox{ub}(w_1,x,y,z)\mbox{ and }w_1 \leq w_2 ) \ \Rightarrow \ \mbox{ub}(w_2,x,y,z)\qquad\mbox{cnf}(\mbox{clause}_{10},\mbox{axiom})$

$( \mbox{ub}(w,x,y,z_1)\mbox{ and }\mbox{successor}(z_1) = z_2\mbox{ and }d(z_2)\mbox{ and }e(x,z_2) \leq w ) \ \Rightarrow \ \mbox{ub}(w,x,y,z_2)\qquad\mbox{cnf}(\mbox{clause}_{11},\mbox{axiom})$

$\neg\,\mbox{successor}(x) \leq x\qquad\mbox{cnf}(\mbox{successor\_not\_less\_or\_equal},\mbox{axiom})$

$x \leq \mbox{successor}(x)\qquad\mbox{cnf}(\mbox{less\_or\_equal\_than\_successor},\mbox{axiom})$

$x \leq x\qquad\mbox{cnf}(\mbox{less\_or\_equal\_reflexivity},\mbox{axiom})$

$( x \leq y\mbox{ and }y \leq x ) \ \Rightarrow \ x = y\qquad\mbox{cnf}(\mbox{less\_or\_equal\_implies\_equal},\mbox{axiom})$

$( x \leq y\mbox{ and }y \leq z ) \ \Rightarrow \ x \leq z\qquad\mbox{cnf}(\mbox{transitivity\_of\_less\_or\_equal},\mbox{axiom})$

$x = y \ \Rightarrow \ x \leq y\qquad\mbox{cnf}(\mbox{equal\_implies\_less\_or\_equal},\mbox{axiom})$

\medskip\textbf{SWV008$\wedge$1.ax} ICL notions of validity wrt S4






$\forall a{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{mvalid}@ ( \mbox{mimpl}@ ( \mbox{mbox}@ \mbox{rel}@ a )@ a ) )\qquad\mbox{thf}(\mbox{refl\_axiom},\mbox{axiom})$

$\forall b{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{mvalid}@ ( \mbox{mimpl}@ ( \mbox{mbox}@ \mbox{rel}@ b )@ ( \mbox{mbox}@ \mbox{rel}@ ( \mbox{mbox}@ \mbox{rel}@ b ) ) ) )\qquad\mbox{thf}(\mbox{trans\_axiom},\mbox{axiom})$

\medskip\textbf{SWV293-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OCrypt\_\_imp\_\_OR1\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

\medskip\textbf{SWV445$\wedge$1.p} (K says K says A) =$>$ (K says A) in BL






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/LCL009\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV010\string^0.ax'})$

$\forall k{:}\;\mbox{individuals},a{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{bl\_valid}@ ( \mbox{bl\_impl}@ ( \mbox{bl\_says}@ k@ ( \mbox{bl\_says}@ k@ ( \mbox{bl\_atom}@ a ) ) )@ ( \mbox{bl\_says}@ k@ ( \mbox{bl\_atom}@ a ) ) ) )\qquad\mbox{thf}(\mbox{bl\_c}_4,\mbox{conjecture})$

\medskip\textbf{SWV010+1.p} Fact 1 of the Neumann-Stubblebine analysis






$\mbox{a\_holds}(\mbox{key}(\mbox{at},t))\qquad\mbox{fof}(\mbox{a\_holds\_key\_at\_for\_t},\mbox{axiom})$

$\mbox{party\_of\_protocol}(a)\qquad\mbox{fof}(\mbox{a\_is\_party\_of\_protocol},\mbox{axiom})$

$\mbox{message}(\mbox{sent}(a,b,\mbox{pair}(a,\mbox{an\_a\_nonce})))\qquad\mbox{fof}(\mbox{a\_sent\_message\_i\_to\_b},\mbox{axiom})$

$\mbox{a\_stored}(\mbox{pair}(b,\mbox{an\_a\_nonce}))\qquad\mbox{fof}(\mbox{a\_stored\_message\_i},\mbox{axiom})$

$\forall u,v,w,x,y,z{:}\;( ( \mbox{message}(\mbox{sent}(t,a,\mbox{triple}(\mbox{encrypt}(\mbox{quadruple}(y,z,w,v),\mbox{at}),x,u)))\mbox{ and }\mbox{a\_stored}(\mbox{pair}(y,z)) ) \ \Rightarrow \ ( \mbox{message}(\mbox{sent}(a,y,\mbox{pair}(x,\mbox{encrypt}(u,w))))\mbox{ and }\mbox{a\_holds}(\mbox{key}(w,y)) ) )\qquad\mbox{fof}(\mbox{a\_forwards\_secure},\mbox{axiom})$

$\mbox{b\_holds}(\mbox{key}(\mbox{bt},t))\qquad\mbox{fof}(\mbox{b\_hold\_key\_bt\_for\_t},\mbox{axiom})$

$\mbox{party\_of\_protocol}(b)\qquad\mbox{fof}(\mbox{b\_is\_party\_of\_protocol},\mbox{axiom})$

$\mbox{fresh\_to\_b}(\mbox{an\_a\_nonce})\qquad\mbox{fof}(\mbox{nonce\_a\_is\_fresh\_to\_b},\mbox{axiom})$

$\forall u,v{:}\;( ( \mbox{message}(\mbox{sent}(u,b,\mbox{pair}(u,v)))\mbox{ and }\mbox{fresh\_to\_b}(v) ) \ \Rightarrow \ ( \mbox{message}(\mbox{sent}(b,t,\mbox{triple}(b,\mbox{generate\_b\_nonce}(v),\mbox{encrypt}(\mbox{triple}(u,v,\mbox{generate\_expiration\_time}(v)),\mbox{bt}))))\mbox{ and }\mbox{b\_stored}(\mbox{pair}(u,v)) ) )\qquad\mbox{fof}(\mbox{b\_creates\_freash\_nonces\_in\_time},\mbox{axiom})$

$\forall v,x,y{:}\;( ( \mbox{message}(\mbox{sent}(x,b,\mbox{pair}(\mbox{encrypt}(\mbox{triple}(x,v,\mbox{generate\_expiration\_time}(y)),\mbox{bt}),\mbox{encrypt}(\mbox{generate\_b\_nonce}(y),v))))\mbox{ and }\mbox{b\_stored}(\mbox{pair}(x,y)) ) \ \Rightarrow \ \mbox{b\_holds}(\mbox{key}(v,x)) )\qquad\mbox{fof}(\mbox{b\_accepts\_secure\_session\_key},\mbox{axiom})$

$\mbox{t\_holds}(\mbox{key}(\mbox{at},a))\qquad\mbox{fof}(\mbox{t\_holds\_key\_at\_for\_a},\mbox{axiom})$

$\mbox{t\_holds}(\mbox{key}(\mbox{bt},b))\qquad\mbox{fof}(\mbox{t\_holds\_key\_bt\_for\_b},\mbox{axiom})$

$\mbox{party\_of\_protocol}(t)\qquad\mbox{fof}(\mbox{t\_is\_party\_of\_protocol},\mbox{axiom})$

$\forall u,v,w,x,y,z,x_1{:}\;( ( \mbox{message}(\mbox{sent}(u,t,\mbox{triple}(u,v,\mbox{encrypt}(\mbox{triple}(w,x,y),z))))\mbox{ and }\mbox{t\_holds}(\mbox{key}(z,u))\mbox{ and }\mbox{t\_holds}(\mbox{key}(x_1,w)) ) \ \Rightarrow \ \mbox{message}(\mbox{sent}(t,w,\mbox{triple}(\mbox{encrypt}(\mbox{quadruple}(u,x,\mbox{generate\_key}(x),y),x_1),\mbox{encrypt}(\mbox{triple}(w,\mbox{generate\_key}(x),y),z),v))) )\qquad\mbox{fof}(\mbox{server\_t\_generates\_key},\mbox{axiom})$

\medskip\textbf{SWV503-1.030.p} Store commutativity (t1\_pp\_nf\_ni\_00030)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),\mbox{sk}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})))\ne \mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10}),\mbox{sk}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})))\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV355-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_1,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_1),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_1,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_1,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_1)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV408+2.p} Priority queue checker: lemma\_not\_min\_elem\_pair






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v{:}\;( \mbox{contains\_slb}(u,v) \ \Rightarrow \ \exists w{:}\;\mbox{pair\_in\_list}(u,v,w) )\qquad\mbox{fof}(\mbox{l45\_li}_{4647},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(w,x) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,x) )\qquad\mbox{fof}(\mbox{l48\_li}_{3839},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }x < w ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,w) )\qquad\mbox{fof}(\mbox{l49\_li}_{3637},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{contains\_slb}(v,x)\mbox{ and }\mbox{strictly\_less\_than}(x,\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) ) \ \Rightarrow \ ( \mbox{pair\_in\_list}(\mbox{update\_slb}(v,\mbox{findmin\_pqp\_res}(u)),x,\mbox{findmin\_pqp\_res}(u))\mbox{ or }\exists y{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(v,\mbox{findmin\_pqp\_res}(u)),x,y)\mbox{ and }\mbox{findmin\_pqp\_res}(u) < y ) ) )\qquad\mbox{fof}(\mbox{l44\_co},\mbox{conjecture})$

\medskip\textbf{SWV340-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_Ka}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{v\_K} = \mbox{v\_Ka}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_analz}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OGets\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV273-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-1.ax'})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_increasing}_0,\mbox{axiom})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV395+1.p} Priority queue checker: tmp\_not\_check\_02\_2\_1 base






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(\mbox{create\_slb},w,x)\mbox{ and }\mbox{strictly\_less\_than}(w,x)\mbox{ and }\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,\mbox{create\_slb},v),w)) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{remove\_slb}(\mbox{create\_slb},w),w,x) )\qquad\mbox{fof}(\mbox{l31\_co},\mbox{conjecture})$

\medskip\textbf{SWV511-1.050.p} Store commutativity (t2\_np\_nf\_ni\_00050)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(a,i,\mbox{select}(a,i)) = a\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,e),i,f) = \mbox{store}(a,i,f)\qquad\mbox{cnf}(a_4,\mbox{axiom})$

$i = j\mbox{ or }\mbox{store}(\mbox{store}(a,i,e),j,f) = \mbox{store}(\mbox{store}(a,j,f),i,e)\qquad\mbox{cnf}(a_5,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),n_{31},e_{31}),n_{32},e_{32}),n_{33},e_{33}),n_{34},e_{34}),n_{35},e_{35}),n_{36},e_{36}),n_{37},e_{37}),n_{38},e_{38}),n_{39},e_{39}),n_{40},e_{40}),n_{41},e_{41}),n_{42},e_{42}),n_{43},e_{43}),n_{44},e_{44}),n_{45},e_{45}),n_{46},e_{46}),n_{47},e_{47}),n_{48},e_{48}),n_{49},e_{49}),n_{50},e_{50})\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{41},e_{41}),n_{30},e_{30}),n_{45},e_{45}),n_{43},e_{43}),n_{28},e_{28}),n_{19},e_{19}),n_{22},e_{22}),n_{39},e_{39}),n_{20},e_{20}),n_{40},e_{40}),n_{16},e_{16}),n_8,e_8),n_{49},e_{49}),n_{14},e_{14}),n_{13},e_{13}),n_6,e_6),n_{27},e_{27}),n_{15},e_{15}),n_7,e_7),n_{33},e_{33}),n_9,e_9),n_{17},e_{17}),n_{42},e_{42}),n_{47},e_{47}),n_{18},e_{18}),n_{26},e_{26}),n_{34},e_{34}),n_{11},e_{11}),n_{36},e_{36}),n_{44},e_{44}),n_{38},e_{38}),n_{23},e_{23}),n_{25},e_{25}),n_{46},e_{46}),n_{35},e_{35}),n_{50},e_{50}),n_2,e_2),n_{10},e_{10}),n_{48},e_{48}),n_{29},e_{29}),n_3,e_3),n_{37},e_{37}),n_{12},e_{12}),n_5,e_5),n_{32},e_{32}),n_4,e_4),n_{24},e_{24}),n_{21},e_{21}),n_{31},e_{31}),n_1,e_1)\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV246-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV004-0.ax'})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_synthD\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_least}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV495-1.050.p} Store commutativity (t1\_np\_nf\_ni\_00050)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),n_{31},e_{31}),n_{32},e_{32}),n_{33},e_{33}),n_{34},e_{34}),n_{35},e_{35}),n_{36},e_{36}),n_{37},e_{37}),n_{38},e_{38}),n_{39},e_{39}),n_{40},e_{40}),n_{41},e_{41}),n_{42},e_{42}),n_{43},e_{43}),n_{44},e_{44}),n_{45},e_{45}),n_{46},e_{46}),n_{47},e_{47}),n_{48},e_{48}),n_{49},e_{49}),n_{50},e_{50})\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{41},e_{41}),n_{30},e_{30}),n_{45},e_{45}),n_{43},e_{43}),n_{28},e_{28}),n_{19},e_{19}),n_{22},e_{22}),n_{39},e_{39}),n_{20},e_{20}),n_{40},e_{40}),n_{16},e_{16}),n_8,e_8),n_{49},e_{49}),n_{14},e_{14}),n_{13},e_{13}),n_6,e_6),n_{27},e_{27}),n_{15},e_{15}),n_7,e_7),n_{33},e_{33}),n_9,e_9),n_{17},e_{17}),n_{42},e_{42}),n_{47},e_{47}),n_{18},e_{18}),n_{26},e_{26}),n_{34},e_{34}),n_{11},e_{11}),n_{36},e_{36}),n_{44},e_{44}),n_{38},e_{38}),n_{23},e_{23}),n_{25},e_{25}),n_{46},e_{46}),n_{35},e_{35}),n_{50},e_{50}),n_2,e_2),n_{10},e_{10}),n_{48},e_{48}),n_{29},e_{29}),n_3,e_3),n_{37},e_{37}),n_{12},e_{12}),n_5,e_5),n_{32},e_{32}),n_4,e_4),n_{24},e_{24}),n_{21},e_{21}),n_{31},e_{31}),n_1,e_1)\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV554-1.004.p} Store inverse (t1\_pp\_nf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_1,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4)) = \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4))\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$\mbox{select}(a_1,\mbox{sk}(a_1,a_2))\ne \mbox{select}(a_2,\mbox{sk}(a_1,a_2))\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV486+2.p} Matrix is lower-triangular






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{lu}(k + c,k) ) )\mbox{ and }\forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k,k) = \mbox{real\_one} )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qil},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\qquad\mbox{fof}(\mbox{lt},\mbox{conjecture})$

\medskip\textbf{SWV135+1.p} Simplified proof obligation gauss\_array\_0005

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{s\_best}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_sworst}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_worst}_7)\mbox{ and }\mbox{leq}(n_2,\mbox{pv}_{1325})\mbox{ and }\mbox{leq}(\mbox{s\_best}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_sworst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_worst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{pv}_{1325},n_3) ) \ \Rightarrow \ \mbox{leq}(n_0,\mbox{pv}_{1325})\qquad\mbox{fof}(\mbox{gauss\_array}_{0005},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV271-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-1.ax'})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_increasing}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV360-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Aa},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_KAB},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Ba},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV272-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OCrypt\_\_synth}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_2,\mbox{axiom})$

\medskip\textbf{SWV534-1.004.p} Swap elements (t1\_np\_sf\_ai\_00004)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{418} = \mbox{store}(a_1,i_1,e_{417})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{419} = \mbox{store}(a_{418},i_1,e_{417})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{421} = \mbox{store}(a_{419},i_0,e_{420})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{423} = \mbox{store}(a_{421},i_3,e_{422})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{425} = \mbox{store}(a_{423},i_3,e_{424})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{427} = \mbox{store}(a_{425},i_2,e_{426})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{429} = \mbox{store}(a_{427},i_2,e_{428})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{431} = \mbox{store}(a_{429},i_0,e_{430})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{432} = \mbox{store}(a_{419},i_3,e_{422})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{433} = \mbox{store}(a_{432},i_0,e_{420})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{435} = \mbox{store}(a_{433},i_3,e_{434})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{437} = \mbox{store}(a_{435},i_2,e_{436})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{439} = \mbox{store}(a_{437},i_0,e_{438})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{441} = \mbox{store}(a_{439},i_3,e_{440})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{417} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{420} = \mbox{select}(a_{419},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{422} = \mbox{select}(a_{419},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{424} = \mbox{select}(a_{423},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{426} = \mbox{select}(a_{423},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{428} = \mbox{select}(a_{427},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{430} = \mbox{select}(a_{427},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{434} = \mbox{select}(a_{433},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{436} = \mbox{select}(a_{433},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{438} = \mbox{select}(a_{437},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{440} = \mbox{select}(a_{437},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{431}\ne a_{441}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV355-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_spies}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_1),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_1,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

\medskip\textbf{SWV283-2.p} Cryptographic protocol problem for public






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_msg},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_sko\_\_upX}(\mbox{v\_msg}),\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_\_Nonce\_\_supply}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_k},\mbox{tc\_nat}),\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_k},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oadd\_\_leE}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_k},\mbox{tc\_nat}),\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oadd\_\_leE}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_list}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_x},\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{v\_W},\mbox{v\_xd}(\mbox{v\_W}),\mbox{tc\_nat})\mbox{ or }\mbox{c\_lessequals}(\mbox{v\_U},\mbox{v\_xd}(\mbox{v\_U}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_xd}(\mbox{v\_X})),\mbox{c\_Event\_Oused}(\mbox{v\_list}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_xd}(\mbox{v\_X})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_xc},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_xd}(\mbox{v\_U})),\mbox{c\_Event\_Oused}(\mbox{v\_list}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_xd}(\mbox{v\_U})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_xc},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV277-2.p} Cryptographic protocol problem for events






$\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_OkeysFor}(\mbox{v\_G}),\mbox{c\_Message\_OkeysFor}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_nat}))\qquad\mbox{cnf}(\mbox{cls\_Message\_OkeysFor\_\_mono}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetD}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

\medskip\textbf{SWV433$\wedge$1.p} ICL$\wedge$=$>$ logic mapping to modal logic implies that Example 2 holds






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^2.ax'})$

$\mbox{admin}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{admin},\mbox{type})$

$\mbox{bob}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bob},\mbox{type})$

$\mbox{alice}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{alice},\mbox{type})$

$\mbox{deletefile}_1{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{deletfile}_1,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_1,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) ) )\qquad\mbox{thf}(\mbox{ax}_2,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ \mbox{alice} )@ ( \mbox{icl\_princ}@ \mbox{bob} ) ) )\qquad\mbox{thf}(\mbox{ax}_3,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{alice} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_4,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 )\qquad\mbox{thf}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV249-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-1.ax'})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_analz\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV233+1.p} Protocol attack problem






$\forall e_1,e_2{:}\;( ( \mbox{knows}(\mbox{encrypt}(e_1,e_2))\mbox{ and }\mbox{knows}(e_2') ) \ \Rightarrow \ \mbox{knows}(e_1) )\qquad\mbox{fof}(\mbox{encrypt\_equation},\mbox{axiom})$

$\forall e_1,e_2{:}\;( ( \mbox{knows}(\mbox{symmetric\_encrypt}(e_1,e_2))\mbox{ and }\mbox{knows}(e_2) ) \ \Rightarrow \ \mbox{knows}(e_1) )\qquad\mbox{fof}(\mbox{symmetric\_encrypt\_equation},\mbox{axiom})$

$\forall e,k{:}\;( ( \mbox{knows}(\mbox{sign}(e,k'))\mbox{ and }\mbox{knows}(k) ) \ \Rightarrow \ \mbox{knows}(e) )\qquad\mbox{fof}(\mbox{sign\_equation},\mbox{axiom})$

$\forall e_1,e_2{:}\;( ( \mbox{knows}(e_1)\mbox{ and }\mbox{knows}(e_2) ) \ \Rightarrow \ ( \mbox{knows}(\mbox{concatenate}(e_1,e_2))\mbox{ and }\mbox{knows}(\mbox{encrypt}(e_1,e_2))\mbox{ and }\mbox{knows}(\mbox{symmetric\_encrypt}(e_1,e_2))\mbox{ and }\mbox{knows}(\mbox{decrypt}(e_1,e_2))\mbox{ and }\mbox{knows}(\mbox{symmetric\_decrypt}(e_1,e_2))\mbox{ and }\mbox{knows}(\mbox{extract}(e_1,e_2))\mbox{ and }\mbox{knows}(\mbox{sign}(e_1,e_2)) ) )\qquad\mbox{fof}(\mbox{construct\_message}_1,\mbox{axiom})$

$\forall e_1,e_2{:}\;( \mbox{knows}(\mbox{concatenate}(e_1,e_2)) \ \Rightarrow \ ( \mbox{knows}(e_1)\mbox{ and }\mbox{knows}(e_2) ) )\qquad\mbox{fof}(\mbox{construct\_message}_2,\mbox{axiom})$

$\forall e{:}\;( \mbox{knows}(e) \ \Rightarrow \ ( \mbox{knows}(\mbox{head}(e))\mbox{ and }\mbox{knows}(\mbox{tail}(e))\mbox{ and }\mbox{knows}(\mbox{hash}(e)) ) )\qquad\mbox{fof}(\mbox{construct\_message}_3,\mbox{axiom})$

$\forall e,k{:}\;\mbox{decrypt}(\mbox{encrypt}(e,k),k') = e\qquad\mbox{fof}(\mbox{decrypt\_axiom},\mbox{axiom})$

$\forall e,k{:}\;\mbox{symmetric\_decrypt}(\mbox{symmetric\_encrypt}(e,k),k) = e\qquad\mbox{fof}(\mbox{symmetric\_decrypt\_axiom},\mbox{axiom})$

$\forall e,k{:}\;\mbox{extract}(\mbox{sign}(e,k'),k) = e\qquad\mbox{fof}(\mbox{sign\_axiom},\mbox{axiom})$

$\forall x,y{:}\;\mbox{head}(\mbox{concatenate}(x,y)) = x\qquad\mbox{fof}(\mbox{head\_axiom},\mbox{axiom})$

$\forall x,y{:}\;\mbox{tail}(\mbox{concatenate}(x,y)) = y\qquad\mbox{fof}(\mbox{tail\_axiom},\mbox{axiom})$

$\forall x{:}\;\mbox{first}(x) = \mbox{head}(x)\qquad\mbox{fof}(\mbox{first\_axiom},\mbox{axiom})$

$\forall x{:}\;\mbox{second}(x) = \mbox{head}(\mbox{tail}(x))\qquad\mbox{fof}(\mbox{second\_axiom},\mbox{axiom})$

$\forall x{:}\;\mbox{third}(x) = \mbox{head}(\mbox{tail}(\mbox{tail}(x)))\qquad\mbox{fof}(\mbox{third\_axiom},\mbox{axiom})$

$\forall x{:}\;\mbox{fourth}(x) = \mbox{head}(\mbox{tail}(\mbox{tail}(\mbox{tail}(x))))\qquad\mbox{fof}(\mbox{fourth\_axiom},\mbox{axiom})$

$\forall x,y{:}\;( ( \mbox{knows}(x)\mbox{ and }\mbox{knows}(y) ) \ \Rightarrow \ \mbox{knows}(\mbox{mac}(x,y)) )\qquad\mbox{fof}(\mbox{symmac\_axiom},\mbox{axiom})$

$\mbox{knows}(\mbox{k\_ca})\mbox{ and }\mbox{knows}(\mbox{k\_a}')\mbox{ and }\mbox{knows}(\mbox{k\_a})\qquad\mbox{fof}(\mbox{previous\_knowledge},\mbox{axiom})$

$\forall \mbox{init}_1,\mbox{init}_2,\mbox{init}_3,\mbox{resp}_1,\mbox{resp}_2{:}\;( \mbox{knows}(\mbox{concatenate}(n,\mbox{concatenate}(\mbox{k\_c},\mbox{sign}(\mbox{concatenate}(c,\mbox{concatenate}(\mbox{k\_c},\mbox{eol})),\mbox{k\_c}'))))\mbox{ and }( ( \mbox{knows}(\mbox{resp}_1)\mbox{ and }\mbox{knows}(\mbox{resp}_2)\mbox{ and }\mbox{first}(\mbox{extract}(\mbox{resp}_2,\mbox{k\_ca})) = s\mbox{ and }\mbox{second}(\mbox{extract}(\mbox{decrypt}(\mbox{resp}_1,\mbox{k\_c}'),\mbox{second}(\mbox{extract}(\mbox{resp}_2,\mbox{k\_ca})))) = n ) \ \Rightarrow \ \mbox{knows}(\mbox{symmetric\_encrypt}(\mbox{secret},\mbox{first}(\mbox{extract}(\mbox{decrypt}(\mbox{resp}_1,\mbox{k\_c}'),\mbox{second}(\mbox{extract}(\mbox{resp}_2,\mbox{k\_ca})))))) )\mbox{ and }( ( \mbox{knows}(\mbox{init}_1)\mbox{ and }\mbox{knows}(\mbox{init}_2)\mbox{ and }\mbox{knows}(\mbox{init}_3)\mbox{ and }\mbox{second}(\mbox{extract}(\mbox{init}_3,\mbox{init}_2)) = \mbox{init}_2 ) \ \Rightarrow \ \mbox{knows}(\mbox{concatenate}(\mbox{encrypt}(\mbox{sign}(\mbox{concatenate}(\mbox{kgen}(\mbox{init}_2),\mbox{concatenate}(\mbox{init}_1,\mbox{eol})),\mbox{k\_s}'),\mbox{init}_2),\mbox{sign}(\mbox{concatenate}(s,\mbox{concatenate}(\mbox{k\_s},\mbox{eol})),\mbox{k\_ca}'))) ) )\qquad\mbox{fof}(\mbox{protocol},\mbox{axiom})$

$\mbox{knows}(\mbox{secret})\qquad\mbox{fof}(\mbox{attack},\mbox{conjecture})$

\medskip\textbf{SWV428$\wedge$1.p} ICL logic mapping to modal logic K implies that Example 1 holds






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{admin}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{admin},\mbox{type})$

$\mbox{bob}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bob},\mbox{type})$

$\mbox{deletefile}_1{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{deletfile}_1,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_1,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) ) )\qquad\mbox{thf}(\mbox{ax}_2,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_3,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 )\qquad\mbox{thf}(\mbox{ex}_1,\mbox{conjecture})$

\medskip\textbf{SWV363-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Aa},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_KAB},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Aa},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV019-1.p} Maximal array element






$x_1 < a\mbox{ or }b < x_1\mbox{ or }\mbox{in\_array\_bounds}(\mbox{array},x_1)\qquad\mbox{cnf}(\mbox{in\_bounds},\mbox{axiom})$

$\mbox{successor}(x) < \mbox{successor}(y) \ \Rightarrow \ x < y\qquad\mbox{cnf}(\mbox{predecessor\_less},\mbox{axiom})$

$( x < y\mbox{ and }y < z ) \ \Rightarrow \ x < z\qquad\mbox{cnf}(\mbox{transitivity\_of\_less},\mbox{axiom})$

$x < \mbox{successor}(x)\qquad\mbox{cnf}(\mbox{successor\_greater},\mbox{axiom})$

$\mbox{in\_array\_bounds}(\mbox{array},\mbox{index\_of\_maximal}) \ \Rightarrow \ \mbox{maximal\_value} = \mbox{array\_value\_at}(\mbox{array},\mbox{index\_of\_maximal})\qquad\mbox{cnf}(\mbox{this\_is\_maximal},\mbox{axiom})$

$\mbox{index\_of\_maximal} < \mbox{an\_index}\qquad\mbox{cnf}(\mbox{maximal\_before\_somewhere},\mbox{axiom})$

$\neg\,\mbox{an\_index} < a\qquad\mbox{cnf}(\mbox{somewhere\_above\_lower\_bound},\mbox{axiom})$

$\neg\,b < \mbox{an\_index}\qquad\mbox{cnf}(\mbox{somewhere\_below\_upper\_bound},\mbox{axiom})$

$\neg\,\mbox{index\_of\_maximal} < a\qquad\mbox{cnf}(\mbox{maximal\_above\_lower\_bound},\mbox{axiom})$

$( \mbox{in\_array\_bounds}(\mbox{array},\mbox{an\_index})\mbox{ and }\mbox{index\_of\_maximal} < \mbox{successor}(\mbox{an\_index})\mbox{ and }\mbox{in\_array\_bounds}(\mbox{array},\mbox{index\_of\_maximal})\mbox{ and }\mbox{maximal\_value} = \mbox{array\_value\_at}(\mbox{array},\mbox{index\_of\_maximal}) ) \ \Rightarrow \ ( \mbox{successor}(\mbox{an\_index}) < a\mbox{ or }\mbox{successor}(b) < \mbox{successor}(\mbox{an\_index})\mbox{ or }\mbox{index\_of\_maximal} < a )\qquad\mbox{cnf}(\mbox{prove\_this},\mbox{negated\_conjecture})$

\medskip\textbf{SWV325-2.p} Cryptographic protocol problem for Otway Rees






$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_C})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{v\_B}\ne \mbox{v\_C}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_C})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{v\_B} = \mbox{v\_C}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OCrypt\_\_synth}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnE}_0,\mbox{axiom})$

\medskip\textbf{SWV331-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{v\_H}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Public\_OCrypt\_\_imp\_\_keysFor}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}))),\mbox{tc\_nat})\mbox{ and }\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\mbox{ and }\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_Onew\_\_keys\_\_not\_\_used}_0,\mbox{axiom})$

\medskip\textbf{SWV337-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-3.ax'})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{v\_A}\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_U},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_U}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_V}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_W}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_V}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_U}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV264-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OFst}_0,\mbox{axiom})$

\medskip\textbf{SWV314-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_Osecrecy\_\_lemma\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

\medskip\textbf{SWV073+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0014

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{35})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5)\mbox{ and }\mbox{leq}(\mbox{pv}_{35},-n_{135300}) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{35})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5)\mbox{ and }\mbox{leq}(\mbox{pv}_{35},-n_{135300}) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0014},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV540-1.004.p} Swap elements (t2\_np\_sf\_ai\_00004)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(a,i,\mbox{select}(a,i)) = a\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,e),i,f) = \mbox{store}(a,i,f)\qquad\mbox{cnf}(a_4,\mbox{axiom})$

$i = j\mbox{ or }\mbox{store}(\mbox{store}(a,i,e),j,f) = \mbox{store}(\mbox{store}(a,j,f),i,e)\qquad\mbox{cnf}(a_5,\mbox{axiom})$

$a_{417} = \mbox{store}(a_1,i_1,e_{416})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{418} = \mbox{store}(a_{417},i_1,e_{416})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{420} = \mbox{store}(a_{418},i_0,e_{419})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{422} = \mbox{store}(a_{420},i_3,e_{421})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{424} = \mbox{store}(a_{422},i_3,e_{423})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{426} = \mbox{store}(a_{424},i_2,e_{425})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{428} = \mbox{store}(a_{426},i_2,e_{427})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{430} = \mbox{store}(a_{428},i_0,e_{429})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{431} = \mbox{store}(a_{418},i_3,e_{421})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{432} = \mbox{store}(a_{431},i_0,e_{419})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{434} = \mbox{store}(a_{432},i_3,e_{433})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{436} = \mbox{store}(a_{434},i_2,e_{435})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{438} = \mbox{store}(a_{436},i_0,e_{437})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{440} = \mbox{store}(a_{438},i_2,e_{439})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{416} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{419} = \mbox{select}(a_{418},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{421} = \mbox{select}(a_{418},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{423} = \mbox{select}(a_{422},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{425} = \mbox{select}(a_{422},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{427} = \mbox{select}(a_{426},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{429} = \mbox{select}(a_{426},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{433} = \mbox{select}(a_{432},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{435} = \mbox{select}(a_{432},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{437} = \mbox{select}(a_{436},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{439} = \mbox{select}(a_{436},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{430}\ne a_{440}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV258-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_Oin\_\_parts\_\_UnE}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_idem}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_partsD\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV427$\wedge$2.p} ICL logic mapping to modal logic implies 'idem'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) ) )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) ) )\qquad\mbox{thf}(\mbox{idem},\mbox{conjecture})$

\medskip\textbf{SWV561-1.004.p} Store inverse (t3\_np\_sf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{17} = \mbox{store}(a_1,i_1,e_{16})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{19} = \mbox{store}(a_2,i_1,e_{18})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{21} = \mbox{store}(a_{17},i_2,e_{20})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{23} = \mbox{store}(a_{19},i_2,e_{22})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{25} = \mbox{store}(a_{21},i_3,e_{24})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{27} = \mbox{store}(a_{23},i_3,e_{26})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{29} = \mbox{store}(a_{25},i_4,e_{28})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{31} = \mbox{store}(a_{27},i_4,e_{30})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$e_{16} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$e_{18} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$e_{20} = \mbox{select}(a_{19},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$e_{22} = \mbox{select}(a_{17},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$e_{24} = \mbox{select}(a_{23},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$e_{26} = \mbox{select}(a_{21},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{28} = \mbox{select}(a_{27},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{30} = \mbox{select}(a_{25},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{29} = a_{31}\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV347-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Aa},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_KAB},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Aa},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV559-1.004.p} Store inverse (t3\_np\_nf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4)) = \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4))\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV456+1.p} Establishing that there cannot be two leaders, part i27\_p134






$\mbox{include}(\mbox{'Axioms/SWV011+0.ax'})$

$\forall v,w,x,y{:}\;( ( \forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \mbox{host}(\mbox{pid}_0)\ne \mbox{host}(z) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Halt}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_{20},\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Ack}(\mbox{pid}_0,z),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{leq}(\mbox{pid}_0,z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \mbox{pid}_0\ne z\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ or }\neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) ) )\mbox{ and }\forall z,\mbox{pid}_{30},\mbox{pid}_{20},\mbox{pid}_0{:}\;( ( \mbox{host}(\mbox{pid}_{20})\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(\mbox{pid}_{20},\mbox{alive})\mbox{ and }\mbox{host}(\mbox{pid}_{30}) = \mbox{host}(z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(\mbox{pid}_{20}) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z)))\mbox{ and }\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_{30}),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) )\mbox{ and }\forall z,\mbox{pid}_{30},\mbox{pid}_{20},\mbox{pid}_0{:}\;( ( \mbox{host}(\mbox{pid}_{20})\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(\mbox{pid}_{20},\mbox{alive})\mbox{ and }\mbox{host}(\mbox{pid}_{30}) = \mbox{host}(z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(\mbox{pid}_{20}) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z)))\mbox{ and }\mbox{setIn}(\mbox{host}(\mbox{pid}_{30}),\mbox{index}(\mbox{down},\mbox{host}(\mbox{pid}_{20}))) )\mbox{ and }\mbox{queue}(\mbox{host}(x)) = \mbox{cons}(\mbox{m\_Down}(y),v) ) \ \Rightarrow \ ( \mbox{setIn}(x,\mbox{alive}) \ \Rightarrow \ ( \neg\,\mbox{leq}(\mbox{host}(x),\mbox{host}(y)) \ \Rightarrow \ ( ( ( \mbox{index}(\mbox{ldr},\mbox{host}(x)) = \mbox{host}(y)\mbox{ and }\mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{norm} )\mbox{ or }( \mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{wait}\mbox{ and }\mbox{host}(y) = \mbox{host}(\mbox{index}(\mbox{elid},\mbox{host}(x))) ) ) \ \Rightarrow \ ( ( \forall z{:}\;( \mbox{host}(x) = \mbox{host}(z) \ \Rightarrow \ \mbox{leq}(z,w) )\mbox{ and }\neg\,\mbox{setIn}(w,\mbox{pids})\mbox{ and }\mbox{host}(x) = \mbox{host}(w) ) \ \Rightarrow \ ( \mbox{host}(w)\ne s(0) \ \Rightarrow \ \forall z{:}\;( \mbox{host}(x) = \mbox{host}(z) \ \Rightarrow \ \forall x_0,y_0{:}\;( \mbox{host}(w)\ne \mbox{host}(y_0) \ \Rightarrow \ ( \mbox{host}(x)\ne \mbox{host}(y_0) \ \Rightarrow \ \forall z_0{:}\;( ( ( ( z\ne x\mbox{ and }\mbox{setIn}(z,\mbox{alive}) )\mbox{ or }z = w )\mbox{ and }( ( y_0\ne x\mbox{ and }\mbox{setIn}(y_0,\mbox{alive}) )\mbox{ or }y_0 = w )\mbox{ and }\mbox{host}(y_0)\ne \mbox{host}(z)\mbox{ and }\mbox{host}(x_0) = \mbox{host}(z)\mbox{ and }\mbox{host}(z_0) = \mbox{host}(y_0) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(z_0),v)\mbox{ and }\mbox{setIn}(\mbox{host}(x_0),\mbox{index}(\mbox{down},\mbox{host}(y_0))) ) ) ) ) ) ) ) ) ) )\qquad\mbox{fof}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV348-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{10},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{v\_Aa}\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_Aa},\mbox{v\_Ba},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV400+1.p} Priority queue checker: tmp\_not\_check\_03\_2 base






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(\mbox{create\_slb},v,w)\mbox{ and }x < w ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(\mbox{create\_slb},x),v,w) )\qquad\mbox{fof}(\mbox{l36\_co},\mbox{conjecture})$

\medskip\textbf{SWV442$\wedge$1.p} A =$>$ A in BL






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/LCL009\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV010\string^0.ax'})$

$\forall a{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{bl\_valid}@ ( \mbox{bl\_impl}@ ( \mbox{bl\_atom}@ a )@ ( \mbox{bl\_atom}@ a ) ) )\qquad\mbox{thf}(\mbox{bl\_id},\mbox{conjecture})$

\medskip\textbf{SWV244-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV004-0.ax'})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_synthD\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_least}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV003-1.p} E2






$\mbox{include}(\mbox{'Axioms/SWV001-0.ax'})$

$\neg\,n < j\qquad\mbox{cnf}(\mbox{clause}_1,\mbox{negated\_conjecture})$

$k < j\qquad\mbox{cnf}(\mbox{clause}_2,\mbox{negated\_conjecture})$

$\neg\,k < i\qquad\mbox{cnf}(\mbox{clause}_3,\mbox{negated\_conjecture})$

$i < n\qquad\mbox{cnf}(\mbox{clause}_4,\mbox{negated\_conjecture})$

$a(j) < a(k)\qquad\mbox{cnf}(\mbox{clause}_5,\mbox{negated\_conjecture})$

$( x < j\mbox{ and }a(x) < a(k) ) \ \Rightarrow \ x < i\qquad\mbox{cnf}(\mbox{clause}_6,\mbox{negated\_conjecture})$

$( 1 < i\mbox{ and }a(x) < a(\mbox{predecessor}(i)) ) \ \Rightarrow \ ( x < i\mbox{ or }n < x )\qquad\mbox{cnf}(\mbox{clause}_7,\mbox{negated\_conjecture})$

$( 1 < x\mbox{ and }x < i ) \ \Rightarrow \ \neg\,a(x) < a(\mbox{predecessor}(x))\qquad\mbox{cnf}(\mbox{clause}_8,\mbox{negated\_conjecture})$

$j < i\qquad\mbox{cnf}(\mbox{clause}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV415+2.p} Priority queue checker: Formula (7)






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$( \forall u,v,w,x{:}\;i(\mbox{triple}(u,\mbox{create\_slb},w)) = i(\mbox{triple}(v,\mbox{create\_slb},x))\mbox{ and }\forall y{:}\;( \forall z,x_1,x_2,x_3{:}\;i(\mbox{triple}(z,y,x_2)) = i(\mbox{triple}(x_1,y,x_3)) \ \Rightarrow \ \forall x_4,x_5,x_6,x_7,x_8,x_9{:}\;i(\mbox{triple}(x_4,\mbox{insert\_slb}(y,\mbox{pair}(x_8,x_9)),x_6)) = i(\mbox{triple}(x_5,\mbox{insert\_slb}(y,\mbox{pair}(x_8,x_9)),x_7)) ) ) \ \Rightarrow \ \forall x_{10},x_{11},x_{12},x_{13},x_{14}{:}\;i(\mbox{triple}(x_{10},x_{12},x_{13})) = i(\mbox{triple}(x_{11},x_{12},x_{14}))\qquad\mbox{fof}(\mbox{big2\_induction},\mbox{axiom})$

$\forall u,v,w,x{:}\;i(\mbox{insert\_cpq}(\mbox{triple}(u,v,w),x)) = \mbox{insert\_pq}(i(\mbox{triple}(u,v,w)),x)\qquad\mbox{fof}(\mbox{co}_2,\mbox{conjecture})$

\medskip\textbf{SWV133+1.p} Simplified proof obligation gauss\_array\_0003

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \neg\,\mbox{leq}(\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{pv}_{1325}),\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{s\_worst}_7))\mbox{ and }\mbox{leq}(n_0,\mbox{s\_best}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_sworst}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_worst}_7)\mbox{ and }\mbox{leq}(n_2,\mbox{pv}_{1325})\mbox{ and }\mbox{leq}(\mbox{s\_best}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_sworst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_worst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{pv}_{1325},n_3)\mbox{ and }\mbox{leq}(\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{pv}_{1325}),\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{s\_best}_7)) ) \ \Rightarrow \ \mbox{leq}(n_0,\mbox{pv}_{1325})\qquad\mbox{fof}(\mbox{gauss\_array}_{0003},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV904-1.p} Hoare logic with procedures 450\_1

Completeness is taken relative to completeness of the underlying
 logic. Two versions of completeness proof: nested single recursion
 and simultaneous recursion in call rule.




$\mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\ne \mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_a\_H},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_option\_Osimps\_I2\_J}_0,\mbox{axiom})$

$\mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\ne \mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_y},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_not\_\_Some\_\_eq}_1,\mbox{axiom})$

$\mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_a\_H},\mbox{t\_a})\ne \mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_option\_Osimps\_I3\_J}_0,\mbox{axiom})$

$\mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_xa},\mbox{t\_a})\ne \mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_not\_\_None\_\_eq}_1,\mbox{axiom})$

$\mbox{c\_Com\_OWT}(\mbox{c\_Com\_Ocom\_OBODY}(\mbox{v\_pn}))\mbox{ or }\mbox{c\_Com\_Obody}(\mbox{v\_pn}) = \mbox{c\_Option\_Ooption\_ONone}(\mbox{tc\_Com\_Ocom})\qquad\mbox{cnf}(\mbox{cls\_WT\_OBody}_0,\mbox{axiom})$

$\mbox{c\_Com\_Ocom\_OBODY}(\mbox{v\_pname\_H})\ne \mbox{c\_Com\_Ocom\_OSKIP}\qquad\mbox{cnf}(\mbox{cls\_com\_Osimps\_I19\_J}_0,\mbox{axiom})$

$\mbox{c\_Com\_Ocom\_OBODY}(\mbox{v\_pname\_H})\ne \mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_com}_1,\mbox{v\_com}_2)\qquad\mbox{cnf}(\mbox{cls\_com\_Osimps\_I49\_J}_0,\mbox{axiom})$

$\mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_com}_1,\mbox{v\_com}_2)\ne \mbox{c\_Com\_Ocom\_OBODY}(\mbox{v\_pname\_H})\qquad\mbox{cnf}(\mbox{cls\_com\_Osimps\_I48\_J}_0,\mbox{axiom})$

$\mbox{c\_Com\_Ocom\_OBODY}(\mbox{v\_pname}) = \mbox{c\_Com\_Ocom\_OBODY}(\mbox{v\_pname\_H}) \ \Rightarrow \ \mbox{v\_pname} = \mbox{v\_pname\_H}\qquad\mbox{cnf}(\mbox{cls\_com\_Osimps\_I6\_J}_0,\mbox{axiom})$

$\mbox{c\_Com\_Ocom\_OSKIP}\ne \mbox{c\_Com\_Ocom\_OBODY}(\mbox{v\_pname\_H})\qquad\mbox{cnf}(\mbox{cls\_com\_Osimps\_I18\_J}_0,\mbox{axiom})$

$\mbox{c\_Com\_OWT}(\mbox{c\_Com\_Ocom\_OBODY}(\mbox{v\_P})) \ \Rightarrow \ \mbox{c\_Com\_Obody}(\mbox{v\_P}) = \mbox{c\_Option\_Ooption\_OSome}(\mbox{c\_Com\_Osko\_\_Com\_\_XWTs\_\_elim\_\_cases\_\_7\_}_1(\mbox{v\_P}),\mbox{tc\_Com\_Ocom})\qquad\mbox{cnf}(\mbox{cls\_WTs\_\_elim\_\_cases\_I7\_J}_0,\mbox{axiom})$

$\mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_com}_1,\mbox{v\_com}_2) = \mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_com1\_H},\mbox{v\_com2\_H}) \ \Rightarrow \ \mbox{v\_com}_2 = \mbox{v\_com2\_H}\qquad\mbox{cnf}(\mbox{cls\_com\_Osimps\_I3\_J}_1,\mbox{axiom})$

$\mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_com}_1,\mbox{v\_com}_2) = \mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_com1\_H},\mbox{v\_com2\_H}) \ \Rightarrow \ \mbox{v\_com}_1 = \mbox{v\_com1\_H}\qquad\mbox{cnf}(\mbox{cls\_com\_Osimps\_I3\_J}_0,\mbox{axiom})$

$\mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_a},\mbox{t\_a}) = \mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_a\_H},\mbox{t\_a}) \ \Rightarrow \ \mbox{v\_a} = \mbox{v\_a\_H}\qquad\mbox{cnf}(\mbox{cls\_option\_Oinject}_0,\mbox{axiom})$

$\mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_com1\_H},\mbox{v\_com2\_H})\ne \mbox{c\_Com\_Ocom\_OSKIP}\qquad\mbox{cnf}(\mbox{cls\_com\_Osimps\_I13\_J}_0,\mbox{axiom})$

$\mbox{c\_Com\_Ocom\_OSKIP}\ne \mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_com1\_H},\mbox{v\_com2\_H})\qquad\mbox{cnf}(\mbox{cls\_com\_Osimps\_I12\_J}_0,\mbox{axiom})$

$( \mbox{c\_Com\_Obody}(\mbox{v\_pn}) = \mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_b},\mbox{tc\_Com\_Ocom})\mbox{ and }\mbox{c\_Com\_OWT\_\_bodies} ) \ \Rightarrow \ \mbox{c\_Com\_OWT}(\mbox{v\_b})\qquad\mbox{cnf}(\mbox{cls\_WT\_\_bodiesD}_0,\mbox{axiom})$

$( \mbox{c\_Com\_OWT}(\mbox{v\_c}_1)\mbox{ and }\mbox{c\_Com\_OWT}(\mbox{v\_c}_0) ) \ \Rightarrow \ \mbox{c\_Com\_OWT}(\mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_c}_0,\mbox{v\_c}_1))\qquad\mbox{cnf}(\mbox{cls\_WT\_OSemi}_0,\mbox{axiom})$

$\mbox{c\_Com\_OWT}(\mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_c}_1,\mbox{v\_c}_2)) \ \Rightarrow \ \mbox{c\_Com\_OWT}(\mbox{v\_c}_1)\qquad\mbox{cnf}(\mbox{cls\_WTs\_\_elim\_\_cases\_I4\_J}_0,\mbox{axiom})$

$\mbox{c\_Com\_OWT}(\mbox{c\_Com\_Ocom\_OSemi}(\mbox{v\_c}_1,\mbox{v\_c}_2)) \ \Rightarrow \ \mbox{c\_Com\_OWT}(\mbox{v\_c}_2)\qquad\mbox{cnf}(\mbox{cls\_WTs\_\_elim\_\_cases\_I4\_J}_1,\mbox{axiom})$

$\mbox{v\_sko\_\_Hoare\_\_Mirabelle\_\_Xstate\_\_not\_\_singleton\_\_def\_\_raw\_}_1 = \mbox{v\_sko\_\_Hoare\_\_Mirabelle\_\_Xstate\_\_not\_\_singleton\_\_def\_\_raw\_}_2 \ \Rightarrow \ \neg\,\mbox{c\_Hoare\_\_Mirabelle\_Ostate\_\_not\_\_singleton}\qquad\mbox{cnf}(\mbox{cls\_state\_\_not\_\_singleton\_\_def\_\_raw}_0,\mbox{axiom})$

$\mbox{c\_Hoare\_\_Mirabelle\_Ostate\_\_not\_\_singleton}\mbox{ or }\mbox{v\_x} = \mbox{v\_xa}\qquad\mbox{cnf}(\mbox{cls\_state\_\_not\_\_singleton\_\_def}_1,\mbox{axiom})$

$\mbox{v\_sko\_\_Hoare\_\_Mirabelle\_\_Xsingle\_\_stateE\_}_1(\mbox{v\_t}) = \mbox{v\_t} \ \Rightarrow \ \neg\,\mbox{c\_Hoare\_\_Mirabelle\_Ostate\_\_not\_\_singleton}\qquad\mbox{cnf}(\mbox{cls\_single\_\_stateE}_0,\mbox{axiom})$

$\mbox{c\_Com\_OWT}(\mbox{c\_Com\_Ocom\_OSKIP})\qquad\mbox{cnf}(\mbox{cls\_WT\_OSkip}_0,\mbox{axiom})$

$\mbox{v\_sko\_\_Hoare\_\_Mirabelle\_\_Xstate\_\_not\_\_singleton\_\_def\_}_1 = \mbox{v\_sko\_\_Hoare\_\_Mirabelle\_\_Xstate\_\_not\_\_singleton\_\_def\_}_2 \ \Rightarrow \ \neg\,\mbox{c\_Hoare\_\_Mirabelle\_Ostate\_\_not\_\_singleton}\qquad\mbox{cnf}(\mbox{cls\_state\_\_not\_\_singleton\_\_def}_0,\mbox{axiom})$

$\mbox{c\_Hoare\_\_Mirabelle\_Ostate\_\_not\_\_singleton}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_Com\_OWT\_\_bodies}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_Com\_OWT}(\mbox{v\_c})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_Hoare\_\_Mirabelle\_Ostate\_\_not\_\_singleton}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

\medskip\textbf{SWV330-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-6.ax'})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_Xa},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$( \mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))) = \mbox{v\_X}\mbox{ and }\mbox{v\_B} = \mbox{v\_Ba} ) \ \Rightarrow \ \mbox{v\_A}\ne \mbox{c\_Message\_Oagent\_OSpy}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV320-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_sko\_\_usf}(\mbox{v\_B},\mbox{v\_X},\mbox{v\_evs}),\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OGets\_\_imp\_\_Says\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_analz\_\_shrK}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ and }\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_analz\_\_shrK}_1,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ and }\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV551-1.007.p} Store inverse (t1\_np\_sf\_ai\_00007)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{29} = \mbox{store}(a_1,i_1,e_{28})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{31} = \mbox{store}(a_2,i_1,e_{30})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{33} = \mbox{store}(a_{29},i_2,e_{32})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{35} = \mbox{store}(a_{31},i_2,e_{34})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{37} = \mbox{store}(a_{33},i_3,e_{36})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{39} = \mbox{store}(a_{35},i_3,e_{38})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{41} = \mbox{store}(a_{37},i_4,e_{40})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{43} = \mbox{store}(a_{39},i_4,e_{42})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{45} = \mbox{store}(a_{41},i_5,e_{44})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{47} = \mbox{store}(a_{43},i_5,e_{46})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{49} = \mbox{store}(a_{45},i_6,e_{48})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{51} = \mbox{store}(a_{47},i_6,e_{50})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{53} = \mbox{store}(a_{49},i_7,e_{52})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{55} = \mbox{store}(a_{51},i_7,e_{54})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{28} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{30} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{32} = \mbox{select}(a_{31},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{34} = \mbox{select}(a_{29},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{36} = \mbox{select}(a_{35},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{38} = \mbox{select}(a_{33},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{40} = \mbox{select}(a_{39},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{42} = \mbox{select}(a_{37},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{44} = \mbox{select}(a_{43},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{46} = \mbox{select}(a_{41},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{48} = \mbox{select}(a_{47},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{50} = \mbox{select}(a_{45},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{52} = \mbox{select}(a_{51},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{54} = \mbox{select}(a_{49},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$a_{53} = a_{55}\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV319-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_sko\_\_usf}(\mbox{v\_B},\mbox{v\_X},\mbox{v\_evs}),\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OGets\_\_imp\_\_Says\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_N},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{v\_c})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OOR2\_\_parts\_\_knows\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_Public\_OshrK}(\mbox{v\_A})\ne \mbox{v\_K}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_Public\_OshrK}(\mbox{v\_A}) = \mbox{v\_K}\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV434$\wedge$4.p} ICL$\wedge$B logic mapping to modal logic implies 'trust'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ \mbox{icl\_false}@ ( \mbox{icl\_atom}@ s ) )@ ( \mbox{icl\_atom}@ s ) )\qquad\mbox{thf}(\mbox{trust},\mbox{conjecture})$

\medskip\textbf{SWV538-1.007.p} Swap elements (t1\_pp\_sf\_ai\_00007)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{836} = \mbox{store}(a_1,i_4,e_{835})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{838} = \mbox{store}(a_{836},i_3,e_{837})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{840} = \mbox{store}(a_{838},i_2,e_{839})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{842} = \mbox{store}(a_{840},i_1,e_{841})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{844} = \mbox{store}(a_{842},i_0,e_{843})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{846} = \mbox{store}(a_{844},i_5,e_{845})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{848} = \mbox{store}(a_{846},i_2,e_{847})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{850} = \mbox{store}(a_{848},i_5,e_{849})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{852} = \mbox{store}(a_{850},i_1,e_{851})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{853} = \mbox{store}(a_{852},i_1,e_{851})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{855} = \mbox{store}(a_{853},i_5,e_{854})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{857} = \mbox{store}(a_{855},i_2,e_{856})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{859} = \mbox{store}(a_{857},i_5,e_{858})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{861} = \mbox{store}(a_{859},i_2,e_{860})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{862} = \mbox{store}(a_{838},i_1,e_{841})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{863} = \mbox{store}(a_{862},i_2,e_{839})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{865} = \mbox{store}(a_{863},i_5,e_{864})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{867} = \mbox{store}(a_{865},i_0,e_{866})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{869} = \mbox{store}(a_{867},i_5,e_{868})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{871} = \mbox{store}(a_{869},i_2,e_{870})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$a_{873} = \mbox{store}(a_{871},i_1,e_{872})\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$a_{874} = \mbox{store}(a_{873},i_1,e_{872})\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$a_{876} = \mbox{store}(a_{874},i_5,e_{875})\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$a_{878} = \mbox{store}(a_{876},i_2,e_{877})\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$a_{880} = \mbox{store}(a_{878},i_6,e_{879})\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{882} = \mbox{store}(a_{880},i_2,e_{881})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{835} = \mbox{select}(a_1,i_3)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{837} = \mbox{select}(a_1,i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{839} = \mbox{select}(a_{838},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{841} = \mbox{select}(a_{838},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{843} = \mbox{select}(a_{842},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{845} = \mbox{select}(a_{842},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{847} = \mbox{select}(a_{846},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{849} = \mbox{select}(a_{846},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{851} = \mbox{select}(a_{850},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{854} = \mbox{select}(a_{853},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{856} = \mbox{select}(a_{853},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{858} = \mbox{select}(a_{857},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{860} = \mbox{select}(a_{857},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{864} = \mbox{select}(a_{863},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{866} = \mbox{select}(a_{863},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{868} = \mbox{select}(a_{867},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$e_{870} = \mbox{select}(a_{867},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$e_{872} = \mbox{select}(a_{871},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{875} = \mbox{select}(a_{874},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{44},\mbox{hypothesis})$

$e_{877} = \mbox{select}(a_{874},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{45},\mbox{hypothesis})$

$e_{879} = \mbox{select}(a_{878},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{46},\mbox{hypothesis})$

$e_{881} = \mbox{select}(a_{878},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{47},\mbox{hypothesis})$

$e_{884} = \mbox{select}(a_{861},i_{883})\qquad\mbox{cnf}(\mbox{hyp}_{48},\mbox{hypothesis})$

$e_{885} = \mbox{select}(a_{882},i_{883})\qquad\mbox{cnf}(\mbox{hyp}_{49},\mbox{hypothesis})$

$i_{883} = \mbox{sk}(a_{861},a_{882})\qquad\mbox{cnf}(\mbox{hyp}_{50},\mbox{hypothesis})$

$e_{884}\ne e_{885}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV566-1.010.p} Store inverse (t3\_pp\_sf\_ai\_00010)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{44} = \mbox{store}(a_1,i_1,e_{43})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{46} = \mbox{store}(a_2,i_1,e_{45})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{48} = \mbox{store}(a_{44},i_2,e_{47})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{50} = \mbox{store}(a_{46},i_2,e_{49})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{52} = \mbox{store}(a_{48},i_3,e_{51})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{54} = \mbox{store}(a_{50},i_3,e_{53})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{56} = \mbox{store}(a_{52},i_4,e_{55})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{58} = \mbox{store}(a_{54},i_4,e_{57})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{60} = \mbox{store}(a_{56},i_5,e_{59})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{62} = \mbox{store}(a_{58},i_5,e_{61})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{64} = \mbox{store}(a_{60},i_6,e_{63})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{66} = \mbox{store}(a_{62},i_6,e_{65})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{68} = \mbox{store}(a_{64},i_7,e_{67})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{70} = \mbox{store}(a_{66},i_7,e_{69})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{72} = \mbox{store}(a_{68},i_8,e_{71})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{74} = \mbox{store}(a_{70},i_8,e_{73})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{76} = \mbox{store}(a_{72},i_9,e_{75})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{78} = \mbox{store}(a_{74},i_9,e_{77})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{80} = \mbox{store}(a_{76},i_1,e_{79})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{82} = \mbox{store}(a_{78},i_{10},e_{81})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{43} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{45} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{47} = \mbox{select}(a_{46},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{49} = \mbox{select}(a_{44},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{51} = \mbox{select}(a_{50},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{53} = \mbox{select}(a_{48},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{55} = \mbox{select}(a_{54},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{57} = \mbox{select}(a_{52},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{59} = \mbox{select}(a_{58},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{61} = \mbox{select}(a_{56},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{63} = \mbox{select}(a_{62},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{65} = \mbox{select}(a_{60},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{67} = \mbox{select}(a_{66},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{69} = \mbox{select}(a_{64},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{71} = \mbox{select}(a_{70},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{73} = \mbox{select}(a_{68},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{75} = \mbox{select}(a_{74},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{77} = \mbox{select}(a_{72},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{79} = \mbox{select}(a_{78},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{81} = \mbox{select}(a_{76},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{84} = \mbox{select}(a_1,i_{83})\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{85} = \mbox{select}(a_2,i_{83})\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$i_{83} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$a_{80} = a_{82}\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{84}\ne e_{85}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV426$\wedge$1.p} ICL logic mapping to modal logic implies 'cuc'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$t{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(t,\mbox{type})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_atom}@ s )@ ( \mbox{icl\_atom}@ t ) ) )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ t ) ) ) )\qquad\mbox{thf}(\mbox{cuc},\mbox{conjecture})$

\medskip\textbf{SWV553-1.004.p} Store inverse (t1\_pp\_nf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4)) = \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4))\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$\mbox{select}(a_1,\mbox{sk}(a_1,a_2))\ne \mbox{select}(a_2,\mbox{sk}(a_1,a_2))\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV275-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_OInj}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_a},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_a},\mbox{c\_insert}(\mbox{v\_b},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OinsertCI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_x},\mbox{c\_insert}(\mbox{v\_x},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OinsertCI}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_a},\mbox{c\_insert}(\mbox{v\_b},\mbox{v\_A},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_a},\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{v\_a} = \mbox{v\_b} )\qquad\mbox{cnf}(\mbox{cls\_Set\_OinsertE}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetD}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_1,\mbox{axiom})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{c\_Message\_Osynth}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV248-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV004-0.ax'})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_synthD\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_least}_0,\mbox{axiom})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV565-1.007.p} Store inverse (t3\_pp\_sf\_ai\_00007)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{32} = \mbox{store}(a_1,i_1,e_{31})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{34} = \mbox{store}(a_2,i_1,e_{33})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{36} = \mbox{store}(a_{32},i_2,e_{35})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{38} = \mbox{store}(a_{34},i_2,e_{37})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{40} = \mbox{store}(a_{36},i_3,e_{39})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{42} = \mbox{store}(a_{38},i_3,e_{41})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{44} = \mbox{store}(a_{40},i_4,e_{43})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{46} = \mbox{store}(a_{42},i_4,e_{45})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{48} = \mbox{store}(a_{44},i_5,e_{47})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{50} = \mbox{store}(a_{46},i_5,e_{49})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{52} = \mbox{store}(a_{48},i_6,e_{51})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{54} = \mbox{store}(a_{50},i_6,e_{53})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{56} = \mbox{store}(a_{52},i_7,e_{55})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{58} = \mbox{store}(a_{54},i_7,e_{57})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{31} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{33} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{35} = \mbox{select}(a_{34},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{37} = \mbox{select}(a_{32},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{39} = \mbox{select}(a_{38},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{41} = \mbox{select}(a_{36},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{43} = \mbox{select}(a_{42},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{45} = \mbox{select}(a_{40},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{47} = \mbox{select}(a_{46},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{49} = \mbox{select}(a_{44},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{51} = \mbox{select}(a_{50},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{53} = \mbox{select}(a_{48},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{55} = \mbox{select}(a_{54},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{57} = \mbox{select}(a_{52},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{60} = \mbox{select}(a_1,i_{59})\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{61} = \mbox{select}(a_2,i_{59})\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$i_{59} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$a_{56} = a_{58}\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{60}\ne e_{61}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV066+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0007

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{53})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300})\mbox{ and }\mbox{leq}(\mbox{pv}_{53},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{53})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300})\mbox{ and }\mbox{leq}(\mbox{pv}_{53},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0007},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV272-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-1.ax'})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_increasing}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV134+1.p} Simplified proof obligation gauss\_array\_0004

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \neg\,\mbox{leq}(\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{pv}_{1325}),\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{s\_worst}_7))\mbox{ and }\mbox{leq}(n_0,\mbox{s\_best}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_sworst}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_worst}_7)\mbox{ and }\mbox{leq}(n_2,\mbox{pv}_{1325})\mbox{ and }\mbox{leq}(\mbox{s\_best}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_sworst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_worst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{pv}_{1325},n_3)\mbox{ and }\mbox{leq}(\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{pv}_{1325}),\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{s\_best}_7))\mbox{ and }\mbox{leq}(\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{pv}_{1325}),\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{s\_sworst}_7)) ) \ \Rightarrow \ \mbox{leq}(n_0,\mbox{pv}_{1325})\qquad\mbox{fof}(\mbox{gauss\_array}_{0004},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV145+1.p} Simplified proof obligation gauss\_array\_0015

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\neg\,\mbox{leq}(\mbox{tptp\_float\_0}_{001},\mbox{tptp\_float\_0}_{001}) \ \Rightarrow \ \mbox{leq}(n_0,\mbox{s\_best}_7)\qquad\mbox{fof}(\mbox{gauss\_array}_{0015},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV496-1.030.p} Store commutativity (t1\_np\_nf\_ni\_00030)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_1,e_1)\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV518-1.050.p} Store commutativity (t3\_np\_nf\_ni\_00050)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),n_{31},e_{31}),n_{32},e_{32}),n_{33},e_{33}),n_{34},e_{34}),n_{35},e_{35}),n_{36},e_{36}),n_{37},e_{37}),n_{38},e_{38}),n_{39},e_{39}),n_{40},e_{40}),n_{41},e_{41}),n_{42},e_{42}),n_{43},e_{43}),n_{44},e_{44}),n_{45},e_{45}),n_{46},e_{46}),n_{47},e_{47}),n_{48},e_{48}),n_{49},e_{49}),n_1,e_1)\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{41},e_{41}),n_{30},e_{30}),n_{45},e_{45}),n_{43},e_{43}),n_{28},e_{28}),n_{19},e_{19}),n_{22},e_{22}),n_{39},e_{39}),n_{20},e_{20}),n_{40},e_{40}),n_{16},e_{16}),n_8,e_8),n_{49},e_{49}),n_{14},e_{14}),n_{13},e_{13}),n_6,e_6),n_{27},e_{27}),n_{15},e_{15}),n_7,e_7),n_{33},e_{33}),n_9,e_9),n_{17},e_{17}),n_{42},e_{42}),n_{47},e_{47}),n_{18},e_{18}),n_{26},e_{26}),n_{34},e_{34}),n_{11},e_{11}),n_{36},e_{36}),n_{44},e_{44}),n_{38},e_{38}),n_{23},e_{23}),n_{25},e_{25}),n_{46},e_{46}),n_{35},e_{35}),n_{50},e_{50}),n_2,e_2),n_{10},e_{10}),n_{48},e_{48}),n_{29},e_{29}),n_3,e_3),n_{37},e_{37}),n_{12},e_{12}),n_5,e_5),n_{32},e_{32}),n_4,e_4),n_{24},e_{24}),n_{21},e_{21}),n_{31},e_{31}),n_1,e_1)\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV138+1.p} Simplified proof obligation gauss\_array\_0008

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{s\_best}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_sworst}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_worst}_7)\mbox{ and }\mbox{leq}(n_2,\mbox{pv}_{1325})\mbox{ and }\mbox{leq}(\mbox{s\_best}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_sworst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_worst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{pv}_{1325},n_3)\mbox{ and }\mbox{gt}(\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{pv}_{1325}),\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{s\_best}_7)) ) \ \Rightarrow \ \mbox{leq}(n_0,\mbox{pv}_{1325})\qquad\mbox{fof}(\mbox{gauss\_array}_{0008},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV432$\wedge$1.p} ICL$\wedge$=$>$ logic mapping to modal logic implies 'handoff'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^2.ax'})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$b{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(b,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ b )@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ b ) ) )@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ b ) ) )\qquad\mbox{thf}(\mbox{handoff},\mbox{conjecture})$

\medskip\textbf{SWV357-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_2,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_2),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_Ba},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Ba},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV551-1.004.p} Store inverse (t1\_np\_sf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{17} = \mbox{store}(a_1,i_1,e_{16})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{19} = \mbox{store}(a_2,i_1,e_{18})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{21} = \mbox{store}(a_{17},i_2,e_{20})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{23} = \mbox{store}(a_{19},i_2,e_{22})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{25} = \mbox{store}(a_{21},i_3,e_{24})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{27} = \mbox{store}(a_{23},i_3,e_{26})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{29} = \mbox{store}(a_{25},i_4,e_{28})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{31} = \mbox{store}(a_{27},i_4,e_{30})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$e_{16} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$e_{18} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$e_{20} = \mbox{select}(a_{19},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$e_{22} = \mbox{select}(a_{17},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$e_{24} = \mbox{select}(a_{23},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$e_{26} = \mbox{select}(a_{21},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{28} = \mbox{select}(a_{27},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{30} = \mbox{select}(a_{25},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{29} = a_{31}\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV409+1.p} Priority queue checker: lemma\_contains\_update






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u,v{:}\;( \mbox{contains\_slb}(u,v) \ \Rightarrow \ \exists w{:}\;\mbox{pair\_in\_list}(u,v,w) )\qquad\mbox{fof}(\mbox{l45\_li}_{4647},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(v,x)\mbox{ and }\mbox{strictly\_less\_than}(w,x) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,x) )\qquad\mbox{fof}(\mbox{l45\_l}_{48},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(v,x)\mbox{ and }x < w ) \ \Rightarrow \ \exists y{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,y)\mbox{ and }x < y ) )\qquad\mbox{fof}(\mbox{l45\_l}_{49},\mbox{lemma})$

$\forall u,v,w{:}\;( ( \mbox{contains\_slb}(u,v)\mbox{ and }\mbox{strictly\_less\_than}(v,w) ) \ \Rightarrow \ ( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,w),v,w)\mbox{ or }\exists x{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,w),v,x)\mbox{ and }w < x ) ) )\qquad\mbox{fof}(\mbox{l45\_co},\mbox{conjecture})$

\medskip\textbf{SWV270-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_synth}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_2,\mbox{axiom})$

\medskip\textbf{SWV544-1.004.p} Swap elements (t3\_np\_sf\_ai\_00004)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{418} = \mbox{store}(a_1,i_1,e_{417})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{419} = \mbox{store}(a_{418},i_1,e_{417})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{421} = \mbox{store}(a_{419},i_0,e_{420})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{423} = \mbox{store}(a_{421},i_3,e_{422})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{425} = \mbox{store}(a_{423},i_3,e_{424})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{427} = \mbox{store}(a_{425},i_2,e_{426})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{429} = \mbox{store}(a_{427},i_2,e_{428})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{431} = \mbox{store}(a_{429},i_0,e_{430})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{432} = \mbox{store}(a_{419},i_3,e_{422})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{433} = \mbox{store}(a_{432},i_0,e_{420})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{435} = \mbox{store}(a_{433},i_3,e_{434})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{437} = \mbox{store}(a_{435},i_2,e_{436})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{439} = \mbox{store}(a_{437},i_0,e_{438})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{441} = \mbox{store}(a_{439},i_3,e_{440})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{417} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{420} = \mbox{select}(a_{419},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{422} = \mbox{select}(a_{419},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{424} = \mbox{select}(a_{423},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{426} = \mbox{select}(a_{423},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{428} = \mbox{select}(a_{427},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{430} = \mbox{select}(a_{427},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{434} = \mbox{select}(a_{433},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{436} = \mbox{select}(a_{433},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{438} = \mbox{select}(a_{437},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{440} = \mbox{select}(a_{437},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{431}\ne a_{441}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV020-1.p} Program verification axioms






$\mbox{include}(\mbox{'Axioms/SWV001-0.ax'})$

\medskip\textbf{SWV552-1.004.p} Store inverse (t1\_np\_sf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{17} = \mbox{store}(a_1,i_1,e_{16})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{19} = \mbox{store}(a_2,i_1,e_{18})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{21} = \mbox{store}(a_{17},i_2,e_{20})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{23} = \mbox{store}(a_{19},i_2,e_{22})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{25} = \mbox{store}(a_{21},i_3,e_{24})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{27} = \mbox{store}(a_{23},i_3,e_{26})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{29} = \mbox{store}(a_{25},i_1,e_{28})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{31} = \mbox{store}(a_{27},i_4,e_{30})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$e_{16} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$e_{18} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$e_{20} = \mbox{select}(a_{19},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$e_{22} = \mbox{select}(a_{17},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$e_{24} = \mbox{select}(a_{23},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$e_{26} = \mbox{select}(a_{21},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{28} = \mbox{select}(a_{27},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{30} = \mbox{select}(a_{25},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{29} = a_{31}\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV318-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_cut\_\_eq}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_sko\_\_usf}(\mbox{v\_B},\mbox{v\_X},\mbox{v\_evs}),\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OGets\_\_imp\_\_Says\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Public\_OSpy\_\_spies\_\_bad\_\_shrK}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_a},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_a},\mbox{c\_insert}(\mbox{v\_b},\mbox{v\_A},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_iff}_2,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV045+1.p} Unsimplified proof obligation cl5\_nebula\_norm\_0007

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{pv}_{76} = n_0 + -n_{135300}{=}\mbox{a\_select}_3(q,\mbox{pv}_{77},\mbox{pv}_{25})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{25})\mbox{ and }\mbox{leq}(\mbox{pv}_{25},-n_5) ) \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0007},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV302-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_x},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ or }\mbox{v\_NB} = \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{13},\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{16},\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_2),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV364-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{v\_Y}),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OGets\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV566-1.007.p} Store inverse (t3\_pp\_sf\_ai\_00007)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{32} = \mbox{store}(a_1,i_1,e_{31})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{34} = \mbox{store}(a_2,i_1,e_{33})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{36} = \mbox{store}(a_{32},i_2,e_{35})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{38} = \mbox{store}(a_{34},i_2,e_{37})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{40} = \mbox{store}(a_{36},i_3,e_{39})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{42} = \mbox{store}(a_{38},i_3,e_{41})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{44} = \mbox{store}(a_{40},i_4,e_{43})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{46} = \mbox{store}(a_{42},i_4,e_{45})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{48} = \mbox{store}(a_{44},i_5,e_{47})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{50} = \mbox{store}(a_{46},i_5,e_{49})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{52} = \mbox{store}(a_{48},i_6,e_{51})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{54} = \mbox{store}(a_{50},i_6,e_{53})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{56} = \mbox{store}(a_{52},i_1,e_{55})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{58} = \mbox{store}(a_{54},i_7,e_{57})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{31} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{33} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{35} = \mbox{select}(a_{34},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{37} = \mbox{select}(a_{32},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{39} = \mbox{select}(a_{38},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{41} = \mbox{select}(a_{36},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{43} = \mbox{select}(a_{42},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{45} = \mbox{select}(a_{40},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{47} = \mbox{select}(a_{46},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{49} = \mbox{select}(a_{44},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{51} = \mbox{select}(a_{50},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{53} = \mbox{select}(a_{48},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{55} = \mbox{select}(a_{54},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{57} = \mbox{select}(a_{52},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{60} = \mbox{select}(a_1,i_{59})\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{61} = \mbox{select}(a_2,i_{59})\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$i_{59} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$a_{56} = a_{58}\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{60}\ne e_{61}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV426$\wedge$3.p} ICL$\wedge$B logic mapping to modal logic implies 'cuc'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$b{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(b,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ b ) )@ ( \mbox{icl\_atom}@ s ) )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ b )@ ( \mbox{icl\_atom}@ s ) ) ) )\qquad\mbox{thf}(\mbox{cuc},\mbox{conjecture})$

\medskip\textbf{SWV432$\wedge$2.p} ICL$\wedge$=$>$ logic mapping to modal logic implies 'handoff'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^2.ax'})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$b{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(b,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ b )@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ b ) ) )@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ b ) ) )\qquad\mbox{thf}(\mbox{handoff},\mbox{conjecture})$

\medskip\textbf{SWV237+1.p} Visa Security Module (VSM) attack

This models the API of the Visa Security Module (VSM). The
 conjecture allows the discovery of Bond's attack.




$\forall u,v{:}\;\mbox{enc}(i(u),\mbox{enc}(u,v)) = v\qquad\mbox{fof}(\mbox{enc\_dec\_cancel},\mbox{axiom})$

$\forall u,v{:}\;\mbox{enc}(u,\mbox{enc}(i(u),v)) = v\qquad\mbox{fof}(\mbox{dec\_enc\_cancel},\mbox{axiom})$

$\forall u{:}\;i(i(u)) = u\qquad\mbox{fof}(\mbox{double\_inverse\_cancel},\mbox{axiom})$

$\forall u{:}\;( p(u) \ \Rightarrow \ p(i(u)) )\qquad\mbox{fof}(\mbox{keys\_are\_symmetric},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{tmk},\mbox{enc}(i(\mbox{enc}(i(\mbox{zcmk}),v)),u))) )\qquad\mbox{fof}(\mbox{key\_translate\_from\_ZCMK\_to\_TMK},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(i(\mbox{enc}(i(\mbox{zcmk}),v)),\mbox{enc}(i(\mbox{tmk}),u))) )\qquad\mbox{fof}(\mbox{key\_translate\_from\_TMK\_to\_ZCMK},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{wk},\mbox{enc}(i(\mbox{tmk}),u))) )\qquad\mbox{fof}(\mbox{receive\_working\_key\_from\_switch},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{tmk}),v),\mbox{enc}(i(\mbox{tmk}),u))) )\qquad\mbox{fof}(\mbox{encrypt\_a\_PIN\_derivation\_key\_under\_a\_TMK},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{tmk}),v),\mbox{enc}(i(\mbox{tc}),u))) )\qquad\mbox{fof}(\mbox{encrypt\_a\_stored\_comms\_key},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{tc},u)) )\qquad\mbox{fof}(\mbox{encrypt\_clear\_key\_as\_Tcomms\_key},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{tc}),u),v)) )\qquad\mbox{fof}(\mbox{data\_encrypt},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(i(\mbox{enc}(i(\mbox{tc}),u)),v)) )\qquad\mbox{fof}(\mbox{data\_decrypt},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{wk}),w),\mbox{enc}(i(\mbox{enc}(i(\mbox{tmk}),v)),u))) )\qquad\mbox{fof}(\mbox{data\_translate\_PIN\_from\_local\_to\_interchange\_key},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{wk}),w),\mbox{enc}(i(\mbox{enc}(i(\mbox{wk}),v)),u))) )\qquad\mbox{fof}(\mbox{data\_translate\_between\_interchange\_keys},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{wk}),v),\mbox{enc}(i(\mbox{lp}),u))) )\qquad\mbox{fof}(\mbox{data\_translate\_PIN\_from\_local\_storage\_to\_interchange\_key},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(u,v)) )\qquad\mbox{fof}(\mbox{attacker\_can\_encrypt},\mbox{axiom})$

$p(\mbox{enc}(\mbox{tmk},\mbox{pp}))\qquad\mbox{fof}(\mbox{intruder\_knows}_1,\mbox{axiom})$

$p(\mbox{enc}(\mbox{wk},w))\qquad\mbox{fof}(\mbox{intruder\_knows}_2,\mbox{axiom})$

$p(\mbox{enc}(w,t_1))\qquad\mbox{fof}(\mbox{intruder\_knows}_3,\mbox{axiom})$

$p(\mbox{enc}(\mbox{lp},t_2))\qquad\mbox{fof}(\mbox{intruder\_knows}_4,\mbox{axiom})$

$p(\mbox{enc}(\mbox{tc},k))\qquad\mbox{fof}(\mbox{intruder\_knows}_5,\mbox{axiom})$

$p(\mbox{kk})\qquad\mbox{fof}(\mbox{intruder\_knows}_6,\mbox{axiom})$

$p(i(\mbox{kk}))\qquad\mbox{fof}(\mbox{intruder\_knows}_7,\mbox{axiom})$

$p(a)\qquad\mbox{fof}(\mbox{intruder\_knows}_8,\mbox{axiom})$

$p(\mbox{enc}(\mbox{pp},a))\qquad\mbox{fof}(\mbox{co}_1,\mbox{conjecture})$

\medskip\textbf{SWV408+1.p} Priority queue checker: lemma\_not\_min\_elem\_pair






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( ( \mbox{contains\_slb}(u,v)\mbox{ and }\mbox{strictly\_less\_than}(v,w) ) \ \Rightarrow \ ( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,w),v,w)\mbox{ or }\exists x{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,w),v,x)\mbox{ and }w < x ) ) )\qquad\mbox{fof}(\mbox{l44\_l}_{45},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{contains\_slb}(v,x)\mbox{ and }\mbox{strictly\_less\_than}(x,\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) ) \ \Rightarrow \ ( \mbox{pair\_in\_list}(\mbox{update\_slb}(v,\mbox{findmin\_pqp\_res}(u)),x,\mbox{findmin\_pqp\_res}(u))\mbox{ or }\exists y{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(v,\mbox{findmin\_pqp\_res}(u)),x,y)\mbox{ and }\mbox{findmin\_pqp\_res}(u) < y ) ) )\qquad\mbox{fof}(\mbox{l44\_co},\mbox{conjecture})$

\medskip\textbf{SWV343-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb})))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{10},\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_analz}_0,\mbox{axiom})$

\medskip\textbf{SWV556-1.007.p} Store inverse (t1\_pp\_sf\_ai\_00007)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{32} = \mbox{store}(a_1,i_1,e_{31})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{34} = \mbox{store}(a_2,i_1,e_{33})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{36} = \mbox{store}(a_{32},i_2,e_{35})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{38} = \mbox{store}(a_{34},i_2,e_{37})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{40} = \mbox{store}(a_{36},i_3,e_{39})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{42} = \mbox{store}(a_{38},i_3,e_{41})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{44} = \mbox{store}(a_{40},i_4,e_{43})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{46} = \mbox{store}(a_{42},i_4,e_{45})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{48} = \mbox{store}(a_{44},i_5,e_{47})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{50} = \mbox{store}(a_{46},i_5,e_{49})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{52} = \mbox{store}(a_{48},i_6,e_{51})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{54} = \mbox{store}(a_{50},i_6,e_{53})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{56} = \mbox{store}(a_{52},i_1,e_{55})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{58} = \mbox{store}(a_{54},i_7,e_{57})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{31} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{33} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{35} = \mbox{select}(a_{34},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{37} = \mbox{select}(a_{32},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{39} = \mbox{select}(a_{38},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{41} = \mbox{select}(a_{36},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{43} = \mbox{select}(a_{42},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{45} = \mbox{select}(a_{40},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{47} = \mbox{select}(a_{46},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{49} = \mbox{select}(a_{44},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{51} = \mbox{select}(a_{50},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{53} = \mbox{select}(a_{48},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{55} = \mbox{select}(a_{54},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{57} = \mbox{select}(a_{52},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{60} = \mbox{select}(a_1,i_{59})\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{61} = \mbox{select}(a_2,i_{59})\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$i_{59} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$a_{56} = a_{58}\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{60}\ne e_{61}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV441$\wedge$1.p} (K says (A =$>$ B)) =$>$ (K says A) =$>$ (K says B) in BL






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/LCL009\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV010\string^0.ax'})$

$\forall k{:}\;\mbox{individuals},a{:}\;\mbox{\$i}\to \mbox{\$o},b{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{bl\_valid}@ ( \mbox{bl\_impl}@ ( \mbox{bl\_says}@ k@ ( \mbox{bl\_impl}@ a@ b ) )@ ( \mbox{bl\_impl}@ ( \mbox{bl\_says}@ k@ a )@ ( \mbox{bl\_says}@ k@ b ) ) ) )\qquad\mbox{thf}(\mbox{bl\_k},\mbox{conjecture})$

\medskip\textbf{SWV359-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_spies}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_analz}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OGets\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_nb\_H}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_Ono\_\_nonce\_\_YM1\_\_YM2}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV372+1.p} Priority queue checker: lemma\_contains\_cpq\_min\_elem






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w,x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\iff \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),x) )\qquad\mbox{fof}(\mbox{l8\_li}_{56},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{contains\_cpq}(\mbox{triple}(u,v,w),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l8\_l}_9,\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{phi}(\mbox{triple}(u,v,w)) )\qquad\mbox{fof}(\mbox{l8\_lX},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l8\_co},\mbox{conjecture})$

\medskip\textbf{SWV381+2.p} Priority queue checker: lemma\_min\_elem\_smallest






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w,x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\iff \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),x) )\qquad\mbox{fof}(\mbox{l17\_li}_{56},\mbox{lemma})$

$\forall u,v,w{:}\;( ( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w))\mbox{ or }\neg\,\mbox{ok}(\mbox{triple}(u,v,w)) ) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ ( \neg\,\mbox{ok}(\mbox{triple}(x,y,z))\mbox{ or }\neg\,\mbox{check\_cpq}(\mbox{triple}(x,y,z)) ) ) )\qquad\mbox{fof}(\mbox{l19\_l}_{20},\mbox{lemma})$

$\forall u,v{:}\;( \mbox{contains\_slb}(u,v) \ \Rightarrow \ \exists w{:}\;\mbox{pair\_in\_list}(u,v,w) )\qquad\mbox{fof}(\mbox{l45\_li}_{4647},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(v,x)\mbox{ and }\mbox{strictly\_less\_than}(w,x) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,x) )\qquad\mbox{fof}(\mbox{l45\_l}_{48},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(v,x)\mbox{ and }x < w ) \ \Rightarrow \ \exists y{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,y)\mbox{ and }x < y ) )\qquad\mbox{fof}(\mbox{l45\_l}_{49},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{check\_cpq}(\mbox{triple}(u,v,w))\iff \forall x,y{:}\;( \mbox{pair\_in\_list}(v,x,y) \ \Rightarrow \ y < x ) )\qquad\mbox{fof}(\mbox{l43\_li}_{4142},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \mbox{issmallestelement\_pq}(i(\mbox{triple}(u,v,w)),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l17\_co},\mbox{conjecture})$

\medskip\textbf{SWV084+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0025

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{67})\mbox{ and }\mbox{leq}(\mbox{pv}_{67},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{67})\mbox{ and }\mbox{leq}(\mbox{pv}_{67},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0025},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV007-1.p} E6






$\mbox{include}(\mbox{'Axioms/SWV001-0.ax'})$

$\neg\,n < k\qquad\mbox{cnf}(\mbox{clause}_1,\mbox{negated\_conjecture})$

$\neg\,k < i\qquad\mbox{cnf}(\mbox{clause}_2,\mbox{negated\_conjecture})$

$i < n\qquad\mbox{cnf}(\mbox{clause}_3,\mbox{negated\_conjecture})$

$\neg\,n < m\qquad\mbox{cnf}(\mbox{clause}_4,\mbox{negated\_conjecture})$

$i < m\qquad\mbox{cnf}(\mbox{clause}_5,\mbox{negated\_conjecture})$

$\neg\,i < 1\qquad\mbox{cnf}(\mbox{clause}_6,\mbox{negated\_conjecture})$

$k\ne m\qquad\mbox{cnf}(\mbox{clause}_7,\mbox{negated\_conjecture})$

$a(m) < a(k)\qquad\mbox{cnf}(\mbox{clause}_8,\mbox{negated\_conjecture})$

$( 1 < x\mbox{ and }x < i ) \ \Rightarrow \ \neg\,a(x) < a(\mbox{predecessor}(x))\qquad\mbox{cnf}(\mbox{clause}_9,\mbox{negated\_conjecture})$

$( 1 < x\mbox{ and }a(x) < a(\mbox{predecessor}(i)) ) \ \Rightarrow \ ( x < i\mbox{ or }n < x )\qquad\mbox{cnf}(\mbox{clause}_{10},\mbox{negated\_conjecture})$

$( x < \mbox{successor}(n)\mbox{ and }a(x) < a(k) ) \ \Rightarrow \ x < i\qquad\mbox{cnf}(\mbox{clause}_{11},\mbox{negated\_conjecture})$

\medskip\textbf{SWV562-1.010.p} Store inverse (t3\_np\_sf\_ai\_00010)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{41} = \mbox{store}(a_1,i_1,e_{40})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{43} = \mbox{store}(a_2,i_1,e_{42})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{45} = \mbox{store}(a_{41},i_2,e_{44})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{47} = \mbox{store}(a_{43},i_2,e_{46})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{49} = \mbox{store}(a_{45},i_3,e_{48})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{51} = \mbox{store}(a_{47},i_3,e_{50})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{53} = \mbox{store}(a_{49},i_4,e_{52})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{55} = \mbox{store}(a_{51},i_4,e_{54})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{57} = \mbox{store}(a_{53},i_5,e_{56})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{59} = \mbox{store}(a_{55},i_5,e_{58})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{61} = \mbox{store}(a_{57},i_6,e_{60})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{63} = \mbox{store}(a_{59},i_6,e_{62})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{65} = \mbox{store}(a_{61},i_7,e_{64})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{67} = \mbox{store}(a_{63},i_7,e_{66})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{69} = \mbox{store}(a_{65},i_8,e_{68})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{71} = \mbox{store}(a_{67},i_8,e_{70})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{73} = \mbox{store}(a_{69},i_9,e_{72})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{75} = \mbox{store}(a_{71},i_9,e_{74})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{77} = \mbox{store}(a_{73},i_1,e_{76})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{79} = \mbox{store}(a_{75},i_{10},e_{78})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{40} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{42} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{44} = \mbox{select}(a_{43},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{46} = \mbox{select}(a_{41},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{48} = \mbox{select}(a_{47},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{50} = \mbox{select}(a_{45},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{52} = \mbox{select}(a_{51},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{54} = \mbox{select}(a_{49},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{56} = \mbox{select}(a_{55},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{58} = \mbox{select}(a_{53},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{60} = \mbox{select}(a_{59},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{62} = \mbox{select}(a_{57},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{64} = \mbox{select}(a_{63},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{66} = \mbox{select}(a_{61},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{68} = \mbox{select}(a_{67},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{70} = \mbox{select}(a_{65},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{72} = \mbox{select}(a_{71},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{74} = \mbox{select}(a_{69},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{76} = \mbox{select}(a_{75},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{78} = \mbox{select}(a_{73},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$a_{77} = a_{79}\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV555-1.010.p} Store inverse (t1\_pp\_sf\_ai\_00010)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{44} = \mbox{store}(a_1,i_1,e_{43})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{46} = \mbox{store}(a_2,i_1,e_{45})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{48} = \mbox{store}(a_{44},i_2,e_{47})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{50} = \mbox{store}(a_{46},i_2,e_{49})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{52} = \mbox{store}(a_{48},i_3,e_{51})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{54} = \mbox{store}(a_{50},i_3,e_{53})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{56} = \mbox{store}(a_{52},i_4,e_{55})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{58} = \mbox{store}(a_{54},i_4,e_{57})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{60} = \mbox{store}(a_{56},i_5,e_{59})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{62} = \mbox{store}(a_{58},i_5,e_{61})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{64} = \mbox{store}(a_{60},i_6,e_{63})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{66} = \mbox{store}(a_{62},i_6,e_{65})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{68} = \mbox{store}(a_{64},i_7,e_{67})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{70} = \mbox{store}(a_{66},i_7,e_{69})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{72} = \mbox{store}(a_{68},i_8,e_{71})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{74} = \mbox{store}(a_{70},i_8,e_{73})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{76} = \mbox{store}(a_{72},i_9,e_{75})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{78} = \mbox{store}(a_{74},i_9,e_{77})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{80} = \mbox{store}(a_{76},i_{10},e_{79})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{82} = \mbox{store}(a_{78},i_{10},e_{81})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{43} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{45} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{47} = \mbox{select}(a_{46},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{49} = \mbox{select}(a_{44},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{51} = \mbox{select}(a_{50},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{53} = \mbox{select}(a_{48},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{55} = \mbox{select}(a_{54},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{57} = \mbox{select}(a_{52},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{59} = \mbox{select}(a_{58},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{61} = \mbox{select}(a_{56},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{63} = \mbox{select}(a_{62},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{65} = \mbox{select}(a_{60},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{67} = \mbox{select}(a_{66},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{69} = \mbox{select}(a_{64},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{71} = \mbox{select}(a_{70},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{73} = \mbox{select}(a_{68},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{75} = \mbox{select}(a_{74},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{77} = \mbox{select}(a_{72},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{79} = \mbox{select}(a_{78},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{81} = \mbox{select}(a_{76},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{84} = \mbox{select}(a_1,i_{83})\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{85} = \mbox{select}(a_2,i_{83})\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$i_{83} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$a_{80} = a_{82}\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{84}\ne e_{85}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV361-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_spies}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_analz}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OGets\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_nb\_H}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_Ono\_\_nonce\_\_YM1\_\_YM2}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV566-1.004.p} Store inverse (t3\_pp\_sf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{20} = \mbox{store}(a_1,i_1,e_{19})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{22} = \mbox{store}(a_2,i_1,e_{21})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{24} = \mbox{store}(a_{20},i_2,e_{23})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{26} = \mbox{store}(a_{22},i_2,e_{25})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{28} = \mbox{store}(a_{24},i_3,e_{27})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{30} = \mbox{store}(a_{26},i_3,e_{29})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{32} = \mbox{store}(a_{28},i_1,e_{31})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{34} = \mbox{store}(a_{30},i_4,e_{33})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$e_{19} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$e_{21} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$e_{23} = \mbox{select}(a_{22},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$e_{25} = \mbox{select}(a_{20},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$e_{27} = \mbox{select}(a_{26},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$e_{29} = \mbox{select}(a_{24},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{31} = \mbox{select}(a_{30},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{33} = \mbox{select}(a_{28},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{36} = \mbox{select}(a_1,i_{35})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{37} = \mbox{select}(a_2,i_{35})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$i_{35} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{32} = a_{34}\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{36}\ne e_{37}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV313-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_OInj}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_Osecrecy\_\_lemma\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV273-2.p} Cryptographic protocol problem for messages






$\neg\,\mbox{c\_lessequals}(\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_increasing}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_subset\_\_iff}_2,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_refl}_0,\mbox{axiom})$

\medskip\textbf{SWV009-1.p} A condition from Hoare's FIND program






$x \leq y\mbox{ or }\mbox{less}(y,x)\qquad\mbox{cnf}(\mbox{clause}_1,\mbox{negated\_conjecture})$

$\mbox{less}(j,i)\qquad\mbox{cnf}(\mbox{clause}_2,\mbox{negated\_conjecture})$

$m \leq p\qquad\mbox{cnf}(\mbox{clause}_3,\mbox{negated\_conjecture})$

$p \leq q\qquad\mbox{cnf}(\mbox{clause}_4,\mbox{negated\_conjecture})$

$q \leq n\qquad\mbox{cnf}(\mbox{clause}_5,\mbox{negated\_conjecture})$

$( m \leq x\mbox{ and }\mbox{less}(x,i)\mbox{ and }\mbox{less}(j,y)\mbox{ and }y \leq n ) \ \Rightarrow \ a(x) \leq a(y)\qquad\mbox{cnf}(\mbox{clause}_6,\mbox{negated\_conjecture})$

$( m \leq x\mbox{ and }x \leq y\mbox{ and }y \leq j ) \ \Rightarrow \ a(x) \leq a(y)\qquad\mbox{cnf}(\mbox{clause}_7,\mbox{negated\_conjecture})$

$( i \leq x\mbox{ and }x \leq y\mbox{ and }y \leq n ) \ \Rightarrow \ a(x) \leq a(y)\qquad\mbox{cnf}(\mbox{clause}_8,\mbox{negated\_conjecture})$

$\neg\,a(p) \leq a(q)\qquad\mbox{cnf}(\mbox{clause}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV351-2.p} Cryptographic protocol problem for Yahalom






$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_k}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV080+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0021

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{56})\mbox{ and }\mbox{leq}(\mbox{pv}_{56},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{56})\mbox{ and }\mbox{leq}(\mbox{pv}_{56},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0021},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV434$\wedge$3.p} ICL$\wedge$B logic mapping to modal logic implies 'trust'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ \mbox{icl\_false}@ ( \mbox{icl\_atom}@ s ) )@ ( \mbox{icl\_atom}@ s ) )\qquad\mbox{thf}(\mbox{trust},\mbox{conjecture})$

\medskip\textbf{SWV271-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_2,\mbox{axiom})$

\medskip\textbf{SWV918-1.p} Java type soundness 030\_39






$\mbox{c\_COMBI}(\mbox{v\_P},\mbox{t\_a}) = \mbox{v\_P}\qquad\mbox{cnf}(\mbox{cls\_COMBI\_\_def}_0,\mbox{axiom})$

$\mbox{c\_Conform\_Ohconf}(\mbox{v\_P},\mbox{v\_h},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_Exceptions\_Opreallocated}(\mbox{v\_h})\qquad\mbox{cnf}(\mbox{cls\_hconf\_\_def}_1,\mbox{axiom})$

$\mbox{c\_Conform\_Ohconf}(\mbox{v\_P},\mbox{v\_ha\_\_\_\_},\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Expr\_Oexp}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}))))\qquad\mbox{cnf}(\mbox{cls\_hconf}_0,\mbox{axiom})$

$\mbox{c\_COMBI}(\mbox{v\_P},\mbox{t\_a}) = \mbox{v\_P}\qquad\mbox{cnf}(\mbox{cls\_COMBI\_\_def\_\_raw}_0,\mbox{axiom})$

$\mbox{v\_h\_Ha\_\_\_\_} = \mbox{c\_Fun\_Ofun\_\_upd}(\mbox{v\_ha\_\_\_\_},\mbox{v\_a\_\_\_\_},\mbox{c\_Option\_Ooption\_OSome}(\mbox{c\_Pair}(\mbox{v\_C\_\_\_\_},\mbox{c\_Objects\_Oinit\_\_fields}(\mbox{v\_FDTs\_\_\_\_}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_fun}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Option\_Ooption}(\mbox{tc\_Value\_Oval}))),\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_fun}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Option\_Ooption}(\mbox{tc\_Value\_Oval})))),\mbox{tc\_nat},\mbox{tc\_Option\_Ooption}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_fun}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Option\_Ooption}(\mbox{tc\_Value\_Oval})))))\qquad\mbox{cnf}(\mbox{cls\_CHAINED}_0,\mbox{axiom})$

$\mbox{c\_Conform\_Ooconf}(\mbox{v\_P},\mbox{v\_ha\_\_\_\_},\mbox{c\_Pair}(\mbox{v\_C\_\_\_\_},\mbox{c\_Objects\_Oinit\_\_fields}(\mbox{v\_FDTs\_\_\_\_}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_fun}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Option\_Ooption}(\mbox{tc\_Value\_Oval}))),\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Expr\_Oexp}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}))))\qquad\mbox{cnf}(\mbox{cls\_CHAINED\_0}_{01},\mbox{axiom})$

$\mbox{hAPP}(\mbox{v\_ha\_\_\_\_},\mbox{v\_a\_\_\_\_}) = \mbox{c\_Option\_Ooption\_ONone}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_fun}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Option\_Ooption}(\mbox{tc\_Value\_Oval}))))\qquad\mbox{cnf}(\mbox{cls\_CHAINED\_0}_{02},\mbox{axiom})$

$\neg\,\mbox{c\_Conform\_Ohconf}(\mbox{v\_P},\mbox{v\_h\_Ha\_\_\_\_},\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Expr\_Oexp}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}))))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_fequal}(\mbox{v\_x},\mbox{v\_x},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_ATP\_\_Linkup\_Oequal\_\_imp\_\_fequal}_0,\mbox{axiom})$

$\mbox{c\_fequal}(\mbox{v\_X},\mbox{v\_Y},\mbox{t\_a}) \ \Rightarrow \ \mbox{v\_X} = \mbox{v\_Y}\qquad\mbox{cnf}(\mbox{cls\_ATP\_\_Linkup\_Ofequal\_\_imp\_\_equal}_0,\mbox{axiom})$

\medskip\textbf{SWV298-2.p} Cryptographic protocol problem for Otway Rees






$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_Aa},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba})))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{v\_U} = \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}) \ \Rightarrow \ \mbox{v\_B}\ne \mbox{v\_Ba}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_1,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_C})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{v\_B} = \mbox{v\_C} )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_Ounique\_\_NA\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV284-1.p} Cryptographic protocol problem for shared






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_msg},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_sko\_\_upX}(\mbox{v\_msg}),\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_\_Nonce\_\_supply}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_k},\mbox{tc\_nat}),\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_k},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oadd\_\_leE}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_k},\mbox{tc\_nat}),\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oadd\_\_leE}_1,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_N}),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_OinitState}(\mbox{v\_B})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Shared\_ONonce\_\_notin\_\_initState\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Shared\_OshrK}(\mbox{v\_A})),\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Shared\_OSpy\_\_knows\_\_Spy\_\_bad}_0,\mbox{axiom})$

$\mbox{c\_Shared\_OshrK}(\mbox{v\_x}) = \mbox{c\_Shared\_OshrK}(\mbox{v\_y}) \ \Rightarrow \ \mbox{v\_x} = \mbox{v\_y}\qquad\mbox{cnf}(\mbox{cls\_Shared\_O\_91\_124\_AshrK\_Ax\_A\_61\_AshrK\_Ay\_59\_Ax\_A\_61\_Ay\_A\_61\_61\_62\_AP\_A\_124\_93\_A\_61\_61\_62\_AP}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Shared\_Oanalz\_\_Decrypt\_H\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Shared\_OshrK}(\mbox{v\_A})),\mbox{c\_Event\_OinitState}(\mbox{v\_A}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Shared\_OshrK\_\_in\_\_initState}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Shared\_OshrK}(\mbox{v\_A})),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Shared\_OshrK\_\_in\_\_used}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_U},\mbox{v\_x}(\mbox{v\_U}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_list}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_N},\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_x}(\mbox{v\_U})),\mbox{c\_Event\_Oused}(\mbox{v\_list}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_x}(\mbox{v\_U})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_msg},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV346-2.p} Cryptographic protocol problem for Yahalom






$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na\_H},\mbox{v\_nb\_H})))),\mbox{v\_X\_H})),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb})))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{v\_na} = \mbox{v\_na\_H}\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_Ounique\_\_session\_\_keys\_\_dest}_2,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb})))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{v\_na}\ne \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV564-1.004.p} Store inverse (t3\_pp\_nf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_1,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4)) = \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4))\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$\mbox{select}(a_1,\mbox{sk}(a_1,a_2))\ne \mbox{select}(a_2,\mbox{sk}(a_1,a_2))\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV496-1.050.p} Store commutativity (t1\_np\_nf\_ni\_00050)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),n_{31},e_{31}),n_{32},e_{32}),n_{33},e_{33}),n_{34},e_{34}),n_{35},e_{35}),n_{36},e_{36}),n_{37},e_{37}),n_{38},e_{38}),n_{39},e_{39}),n_{40},e_{40}),n_{41},e_{41}),n_{42},e_{42}),n_{43},e_{43}),n_{44},e_{44}),n_{45},e_{45}),n_{46},e_{46}),n_{47},e_{47}),n_{48},e_{48}),n_{49},e_{49}),n_1,e_1)\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{41},e_{41}),n_{30},e_{30}),n_{45},e_{45}),n_{43},e_{43}),n_{28},e_{28}),n_{19},e_{19}),n_{22},e_{22}),n_{39},e_{39}),n_{20},e_{20}),n_{40},e_{40}),n_{16},e_{16}),n_8,e_8),n_{49},e_{49}),n_{14},e_{14}),n_{13},e_{13}),n_6,e_6),n_{27},e_{27}),n_{15},e_{15}),n_7,e_7),n_{33},e_{33}),n_9,e_9),n_{17},e_{17}),n_{42},e_{42}),n_{47},e_{47}),n_{18},e_{18}),n_{26},e_{26}),n_{34},e_{34}),n_{11},e_{11}),n_{36},e_{36}),n_{44},e_{44}),n_{38},e_{38}),n_{23},e_{23}),n_{25},e_{25}),n_{46},e_{46}),n_{35},e_{35}),n_{50},e_{50}),n_2,e_2),n_{10},e_{10}),n_{48},e_{48}),n_{29},e_{29}),n_3,e_3),n_{37},e_{37}),n_{12},e_{12}),n_5,e_5),n_{32},e_{32}),n_4,e_4),n_{24},e_{24}),n_{21},e_{21}),n_{31},e_{31}),n_1,e_1)\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV544-1.007.p} Swap elements (t3\_np\_sf\_ai\_00007)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{785} = \mbox{store}(a_1,i_4,e_{784})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{787} = \mbox{store}(a_{785},i_3,e_{786})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{789} = \mbox{store}(a_{787},i_2,e_{788})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{791} = \mbox{store}(a_{789},i_1,e_{790})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{793} = \mbox{store}(a_{791},i_0,e_{792})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{795} = \mbox{store}(a_{793},i_5,e_{794})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{797} = \mbox{store}(a_{795},i_2,e_{796})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{799} = \mbox{store}(a_{797},i_5,e_{798})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{801} = \mbox{store}(a_{799},i_1,e_{800})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{802} = \mbox{store}(a_{801},i_1,e_{800})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{804} = \mbox{store}(a_{802},i_5,e_{803})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{806} = \mbox{store}(a_{804},i_2,e_{805})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{808} = \mbox{store}(a_{806},i_5,e_{807})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{810} = \mbox{store}(a_{808},i_2,e_{809})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{811} = \mbox{store}(a_{787},i_1,e_{790})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{812} = \mbox{store}(a_{811},i_2,e_{788})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{814} = \mbox{store}(a_{812},i_5,e_{813})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{816} = \mbox{store}(a_{814},i_0,e_{815})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{818} = \mbox{store}(a_{816},i_5,e_{817})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{820} = \mbox{store}(a_{818},i_2,e_{819})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$a_{822} = \mbox{store}(a_{820},i_1,e_{821})\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$a_{823} = \mbox{store}(a_{822},i_1,e_{821})\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$a_{825} = \mbox{store}(a_{823},i_5,e_{824})\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$a_{827} = \mbox{store}(a_{825},i_2,e_{826})\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$a_{829} = \mbox{store}(a_{827},i_6,e_{828})\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{831} = \mbox{store}(a_{829},i_2,e_{830})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{784} = \mbox{select}(a_1,i_3)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{786} = \mbox{select}(a_1,i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{788} = \mbox{select}(a_{787},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{790} = \mbox{select}(a_{787},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{792} = \mbox{select}(a_{791},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{794} = \mbox{select}(a_{791},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{796} = \mbox{select}(a_{795},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{798} = \mbox{select}(a_{795},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{800} = \mbox{select}(a_{799},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{803} = \mbox{select}(a_{802},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{805} = \mbox{select}(a_{802},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{807} = \mbox{select}(a_{806},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{809} = \mbox{select}(a_{806},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{813} = \mbox{select}(a_{812},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{815} = \mbox{select}(a_{812},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{817} = \mbox{select}(a_{816},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$e_{819} = \mbox{select}(a_{816},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$e_{821} = \mbox{select}(a_{820},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{824} = \mbox{select}(a_{823},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{44},\mbox{hypothesis})$

$e_{826} = \mbox{select}(a_{823},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{45},\mbox{hypothesis})$

$e_{828} = \mbox{select}(a_{827},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{46},\mbox{hypothesis})$

$e_{830} = \mbox{select}(a_{827},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{47},\mbox{hypothesis})$

$a_{810}\ne a_{831}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV330-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_Xa},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV411+1.p} Priority queue checker: lemma\_contains\_pair step






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u{:}\;( \forall v{:}\;( \mbox{contains\_slb}(u,v) \ \Rightarrow \ \exists w{:}\;\mbox{pair\_in\_list}(u,v,w) ) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{contains\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(y,z)),x) \ \Rightarrow \ \exists x_1{:}\;\mbox{pair\_in\_list}(\mbox{insert\_slb}(u,\mbox{pair}(y,z)),x,x_1) ) )\qquad\mbox{fof}(\mbox{l47\_co},\mbox{conjecture})$

\medskip\textbf{SWV486+3.p} Matrix is lower-triangular






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{real\_zero} ) )\mbox{ and }\forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k,k) = \mbox{real\_one} )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qii},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\qquad\mbox{fof}(\mbox{lt},\mbox{conjecture})$

\medskip\textbf{SWV561-1.010.p} Store inverse (t3\_np\_sf\_ai\_00010)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{41} = \mbox{store}(a_1,i_1,e_{40})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{43} = \mbox{store}(a_2,i_1,e_{42})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{45} = \mbox{store}(a_{41},i_2,e_{44})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{47} = \mbox{store}(a_{43},i_2,e_{46})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{49} = \mbox{store}(a_{45},i_3,e_{48})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{51} = \mbox{store}(a_{47},i_3,e_{50})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{53} = \mbox{store}(a_{49},i_4,e_{52})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{55} = \mbox{store}(a_{51},i_4,e_{54})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{57} = \mbox{store}(a_{53},i_5,e_{56})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{59} = \mbox{store}(a_{55},i_5,e_{58})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{61} = \mbox{store}(a_{57},i_6,e_{60})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{63} = \mbox{store}(a_{59},i_6,e_{62})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{65} = \mbox{store}(a_{61},i_7,e_{64})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{67} = \mbox{store}(a_{63},i_7,e_{66})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{69} = \mbox{store}(a_{65},i_8,e_{68})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{71} = \mbox{store}(a_{67},i_8,e_{70})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{73} = \mbox{store}(a_{69},i_9,e_{72})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{75} = \mbox{store}(a_{71},i_9,e_{74})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{77} = \mbox{store}(a_{73},i_{10},e_{76})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{79} = \mbox{store}(a_{75},i_{10},e_{78})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{40} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{42} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{44} = \mbox{select}(a_{43},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{46} = \mbox{select}(a_{41},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{48} = \mbox{select}(a_{47},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{50} = \mbox{select}(a_{45},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{52} = \mbox{select}(a_{51},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{54} = \mbox{select}(a_{49},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{56} = \mbox{select}(a_{55},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{58} = \mbox{select}(a_{53},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{60} = \mbox{select}(a_{59},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{62} = \mbox{select}(a_{57},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{64} = \mbox{select}(a_{63},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{66} = \mbox{select}(a_{61},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{68} = \mbox{select}(a_{67},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{70} = \mbox{select}(a_{65},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{72} = \mbox{select}(a_{71},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{74} = \mbox{select}(a_{69},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{76} = \mbox{select}(a_{75},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{78} = \mbox{select}(a_{73},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$a_{77} = a_{79}\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV412+1.p} Priority queue checker: lemma\_contains\_update\_01






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(w,x) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,x) )\qquad\mbox{fof}(\mbox{l48\_li}_{3839},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(v,x)\mbox{ and }\mbox{strictly\_less\_than}(w,x) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,x) )\qquad\mbox{fof}(\mbox{l48\_co},\mbox{conjecture})$

\medskip\textbf{SWV415+1.p} Priority queue checker: Formula (7)






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w,x,y{:}\;i(\mbox{triple}(u,w,x)) = i(\mbox{triple}(v,w,y))\qquad\mbox{fof}(\mbox{main2\_l}_{12},\mbox{lemma})$

$\forall u,v,w,x{:}\;i(\mbox{insert\_cpq}(\mbox{triple}(u,v,w),x)) = \mbox{insert\_pq}(i(\mbox{triple}(u,v,w)),x)\qquad\mbox{fof}(\mbox{co}_2,\mbox{conjecture})$

\medskip\textbf{SWV552-1.010.p} Store inverse (t1\_np\_sf\_ai\_00010)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{41} = \mbox{store}(a_1,i_1,e_{40})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{43} = \mbox{store}(a_2,i_1,e_{42})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{45} = \mbox{store}(a_{41},i_2,e_{44})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{47} = \mbox{store}(a_{43},i_2,e_{46})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{49} = \mbox{store}(a_{45},i_3,e_{48})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{51} = \mbox{store}(a_{47},i_3,e_{50})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{53} = \mbox{store}(a_{49},i_4,e_{52})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{55} = \mbox{store}(a_{51},i_4,e_{54})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{57} = \mbox{store}(a_{53},i_5,e_{56})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{59} = \mbox{store}(a_{55},i_5,e_{58})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{61} = \mbox{store}(a_{57},i_6,e_{60})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{63} = \mbox{store}(a_{59},i_6,e_{62})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{65} = \mbox{store}(a_{61},i_7,e_{64})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{67} = \mbox{store}(a_{63},i_7,e_{66})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{69} = \mbox{store}(a_{65},i_8,e_{68})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{71} = \mbox{store}(a_{67},i_8,e_{70})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{73} = \mbox{store}(a_{69},i_9,e_{72})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{75} = \mbox{store}(a_{71},i_9,e_{74})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{77} = \mbox{store}(a_{73},i_1,e_{76})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{79} = \mbox{store}(a_{75},i_{10},e_{78})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{40} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{42} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{44} = \mbox{select}(a_{43},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{46} = \mbox{select}(a_{41},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{48} = \mbox{select}(a_{47},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{50} = \mbox{select}(a_{45},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{52} = \mbox{select}(a_{51},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{54} = \mbox{select}(a_{49},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{56} = \mbox{select}(a_{55},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{58} = \mbox{select}(a_{53},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{60} = \mbox{select}(a_{59},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{62} = \mbox{select}(a_{57},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{64} = \mbox{select}(a_{63},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{66} = \mbox{select}(a_{61},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{68} = \mbox{select}(a_{67},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{70} = \mbox{select}(a_{65},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{72} = \mbox{select}(a_{71},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{74} = \mbox{select}(a_{69},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{76} = \mbox{select}(a_{75},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{78} = \mbox{select}(a_{73},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$a_{77} = a_{79}\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV486+1.p} Matrix is lower-triangular






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{qr}(k + c,k) ) )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qih},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\qquad\mbox{fof}(\mbox{lt},\mbox{conjecture})$

\medskip\textbf{SWV425$\wedge$1.p} ICL logic mapping to modal logic implies 'unit'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_atom}@ s )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) ) )\qquad\mbox{thf}(\mbox{unit},\mbox{conjecture})$

\medskip\textbf{SWV251-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-1.ax'})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_analz\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_x},\mbox{c\_Message\_Oanalz}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_x},\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV973-1.p} Java type soundness 464\_31






$\mbox{c\_Value\_Oval\_OUnit}\ne \mbox{c\_Value\_Oval\_OAddr}(\mbox{v\_nat\_H})\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I10\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_OIntg}(\mbox{v\_int})\ne \mbox{c\_Value\_Oval\_OAddr}(\mbox{v\_nat\_H})\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I22\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_OAddr}(\mbox{v\_nat\_H})\ne \mbox{c\_Value\_Oval\_OIntg}(\mbox{v\_int})\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I23\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_OAddr}(\mbox{v\_nat\_H})\ne \mbox{c\_Value\_Oval\_OUnit}\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I11\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_OUnit}\ne \mbox{c\_Value\_Oval\_OIntg}(\mbox{v\_int\_H})\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I8\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_OAddr}(\mbox{v\_nat}) = \mbox{c\_Value\_Oval\_OAddr}(\mbox{v\_nat\_H}) \ \Rightarrow \ \mbox{v\_nat} = \mbox{v\_nat\_H}\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I3\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_OIntg}(\mbox{v\_int\_H})\ne \mbox{c\_Value\_Oval\_OUnit}\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I9\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_OIntg}(\mbox{v\_int}) = \mbox{c\_Value\_Oval\_OIntg}(\mbox{v\_int\_H}) \ \Rightarrow \ \mbox{v\_int} = \mbox{v\_int\_H}\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I2\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_ONull}\ne \mbox{c\_Value\_Oval\_OUnit}\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I5\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_OIntg}(\mbox{v\_int\_H})\ne \mbox{c\_Value\_Oval\_ONull}\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I15\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_OUnit}\ne \mbox{c\_Value\_Oval\_ONull}\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I4\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_ONull}\ne \mbox{c\_Value\_Oval\_OIntg}(\mbox{v\_int\_H})\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I14\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_OAddr}(\mbox{v\_nat\_H})\ne \mbox{c\_Value\_Oval\_ONull}\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I17\_J}_0,\mbox{axiom})$

$\mbox{c\_Value\_Oval\_ONull}\ne \mbox{c\_Value\_Oval\_OAddr}(\mbox{v\_nat\_H})\qquad\mbox{cnf}(\mbox{cls\_val\_Osimps\_I16\_J}_0,\mbox{axiom})$

$\mbox{c\_WellTypeRT\_OWTrt}(\mbox{v\_P},\mbox{v\_ha\_\_\_\_},\mbox{v\_E\_\_\_\_},\mbox{c\_Expr\_Oexp\_OVal}(\mbox{v\_v\_\_\_\_},\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{c\_Type\_Oty\_ONT})\qquad\mbox{cnf}(\mbox{cls\_CHAINED}_0,\mbox{axiom})$

$\mbox{v\_v\_\_\_\_}\ne \mbox{c\_Value\_Oval\_ONull}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV275-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV004-0.ax'})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_mono}_0,\mbox{axiom})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{c\_Message\_Osynth}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV241-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_OInj}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_trans}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_a},\mbox{c\_insert}(\mbox{v\_b},\mbox{v\_A},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_a},\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{v\_a} = \mbox{v\_b} )\qquad\mbox{cnf}(\mbox{cls\_Set\_OinsertE}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV011-1.p} Fact 2 of the Neumann-Stubblebine analysis






$\mbox{b\_holds}(\mbox{key}(\mbox{generate\_key}(\mbox{an\_a\_nonce}),a))\qquad\mbox{cnf}(\mbox{ax1}_{11},\mbox{axiom})$

$\mbox{a\_holds}(\mbox{key}(\mbox{generate\_key}(\mbox{an\_a\_nonce}),b))\qquad\mbox{cnf}(\mbox{ax3}_{13},\mbox{axiom})$

$\mbox{a\_holds}(\mbox{key}(a,b)) \ \Rightarrow \ \neg\,\mbox{b\_holds}(\mbox{key}(a,a))\qquad\mbox{cnf}(\mbox{co1}_{17},\mbox{negated\_conjecture})$

\medskip\textbf{SWV533-1.004.p} Swap elements (t1\_np\_sf\_ai\_00004)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{417} = \mbox{store}(a_1,i_1,e_{416})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{418} = \mbox{store}(a_{417},i_1,e_{416})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{420} = \mbox{store}(a_{418},i_0,e_{419})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{422} = \mbox{store}(a_{420},i_3,e_{421})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{424} = \mbox{store}(a_{422},i_3,e_{423})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{426} = \mbox{store}(a_{424},i_2,e_{425})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{428} = \mbox{store}(a_{426},i_2,e_{427})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{430} = \mbox{store}(a_{428},i_0,e_{429})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{431} = \mbox{store}(a_{418},i_3,e_{421})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{432} = \mbox{store}(a_{431},i_0,e_{419})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{434} = \mbox{store}(a_{432},i_3,e_{433})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{436} = \mbox{store}(a_{434},i_2,e_{435})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{438} = \mbox{store}(a_{436},i_0,e_{437})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{440} = \mbox{store}(a_{438},i_2,e_{439})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{416} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{419} = \mbox{select}(a_{418},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{421} = \mbox{select}(a_{418},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{423} = \mbox{select}(a_{422},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{425} = \mbox{select}(a_{422},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{427} = \mbox{select}(a_{426},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{429} = \mbox{select}(a_{426},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{433} = \mbox{select}(a_{432},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{435} = \mbox{select}(a_{432},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{437} = \mbox{select}(a_{436},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{439} = \mbox{select}(a_{436},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{430}\ne a_{440}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV054+1.p} Unsimplified proof obligation cl5\_nebula\_norm\_0034

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300}) ) \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0034},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV278-1.p} Cryptographic protocol problem for events






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_OkeysFor}(\mbox{v\_G}),\mbox{c\_Message\_OkeysFor}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_nat}))\qquad\mbox{cnf}(\mbox{cls\_Message\_OkeysFor\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_insert\_\_subset\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K\_H}))),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K\_H}),\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K\_H}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K\_H}),\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{v\_G})),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

\medskip\textbf{SWV060+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0001

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\mbox{true} \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0001},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV387+1.p} Priority queue checker: lemma\_not\_min\_elem\_not\_check\_ind\_steps 2






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w,x{:}\;( ( \mbox{check\_cpq}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x))\mbox{ and }\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) ) \ \Rightarrow \ \mbox{check\_cpq}(\mbox{triple}(u,v,w)) )\qquad\mbox{fof}(\mbox{l23\_l}_{027},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \forall x{:}\;( \neg\,\mbox{check\_cpq}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x))\mbox{ or }\neg\,\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) ) )\qquad\mbox{fof}(\mbox{l23\_co},\mbox{conjecture})$

\medskip\textbf{SWV085+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0026

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{68})\mbox{ and }\mbox{leq}(\mbox{pv}_{68},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{68})\mbox{ and }\mbox{leq}(\mbox{pv}_{68},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0026},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV426$\wedge$4.p} ICL$\wedge$B logic mapping to modal logic implies 'cuc'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$b{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(b,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ b ) )@ ( \mbox{icl\_atom}@ s ) )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ b )@ ( \mbox{icl\_atom}@ s ) ) ) )\qquad\mbox{thf}(\mbox{cuc},\mbox{conjecture})$

\medskip\textbf{SWV242-2.p} Cryptographic protocol problem for messages






$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oanalz}(\mbox{v\_G\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Oanalz}(\mbox{v\_H\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G\_H},\mbox{v\_H\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G\_H},\mbox{v\_H\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_A},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_upper1}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_B},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_upper2}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_trans}_0,\mbox{axiom})$

\medskip\textbf{SWV344-2.p} Cryptographic protocol problem for Yahalom






$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb})))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_analz}_0,\mbox{axiom})$

\medskip\textbf{SWV151+1.p} Simplified proof obligation cl5\_nebula\_norm\_0001

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\forall a{:}\;( ( \mbox{leq}(n_0,a)\mbox{ and }\mbox{leq}(a,\mbox{tptp\_minus}_1) ) \ \Rightarrow \ n_0 + n_4{=}\mbox{a\_select}_3(q,a,\mbox{tptp\_sum\_index}) = n_1 )\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0001},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV306-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_1,\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_1),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{v\_A} = \mbox{v\_Aa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{v\_NA} = \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{v\_A} = \mbox{v\_Aa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{v\_B} = \mbox{v\_Ba}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_1)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_1)),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_1)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV362-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Ba},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_KAB},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Aa},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV449+1.p} Establishing that there cannot be two leaders, part i26\_p30






$\mbox{include}(\mbox{'Axioms/SWV011+0.ax'})$

$\forall v,w,x,y{:}\;( ( \forall z,\mbox{pid}_0{:}\;( \mbox{setIn}(\mbox{pid}_0,\mbox{alive}) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \mbox{host}(\mbox{pid}_0)\ne \mbox{host}(z) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Halt}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_{20},\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Ack}(\mbox{pid}_0,z),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{leq}(\mbox{pid}_0,z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \mbox{pid}_0\ne z\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ or }\neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) ) )\mbox{ and }\forall z,\mbox{pid}_{30},\mbox{pid}_{20},\mbox{pid}_0{:}\;( ( \mbox{host}(\mbox{pid}_{20})\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(\mbox{pid}_{20},\mbox{alive})\mbox{ and }\mbox{host}(\mbox{pid}_{30}) = \mbox{host}(z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(\mbox{pid}_{20}) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z)))\mbox{ and }\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_{30}),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) )\mbox{ and }\mbox{queue}(\mbox{host}(x)) = \mbox{cons}(\mbox{m\_Ack}(w,y),v) ) \ \Rightarrow \ ( \mbox{setIn}(x,\mbox{alive}) \ \Rightarrow \ ( ( \mbox{index}(\mbox{elid},\mbox{host}(x)) = w\mbox{ and }\mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{elec}_2\mbox{ and }\mbox{host}(y) = \mbox{index}(\mbox{pendack},\mbox{host}(x)) ) \ \Rightarrow \ ( \mbox{leq}(\mbox{nbr\_proc},\mbox{index}(\mbox{pendack},\mbox{host}(x))) \ \Rightarrow \ \forall z{:}\;( ( \mbox{setIn}(\mbox{host}(z),\mbox{index}(\mbox{acks},\mbox{host}(x)))\mbox{ or }\mbox{host}(z) = \mbox{host}(y) ) \ \Rightarrow \ \forall v_0{:}\;( \mbox{host}(z) = \mbox{host}(v_0) \ \Rightarrow \ ( \mbox{host}(x) = \mbox{host}(v_0) \ \Rightarrow \ \forall w_0,x_0{:}\;( \mbox{host}(z)\ne \mbox{host}(x_0) \ \Rightarrow \ ( \mbox{host}(x)\ne \mbox{host}(x_0) \ \Rightarrow \ \forall y_0{:}\;( ( \mbox{host}(x_0)\ne \mbox{host}(v_0)\mbox{ and }\mbox{setIn}(v_0,\mbox{alive})\mbox{ and }\mbox{setIn}(x_0,\mbox{alive})\mbox{ and }\mbox{host}(w_0) = \mbox{host}(v_0)\mbox{ and }\mbox{host}(y_0) = \mbox{host}(x_0) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(w_0),\mbox{queue}(\mbox{host}(x_0)))\mbox{ and }\mbox{elem}(\mbox{m\_Down}(y_0),\mbox{snoc}(v,\mbox{m\_Ldr}(x))) ) ) ) ) ) ) ) ) ) )\qquad\mbox{fof}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV396+1.p} Priority queue checker: tmp\_not\_check\_02\_2\_1 step






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u{:}\;( \forall v,w,x,y{:}\;( ( \mbox{pair\_in\_list}(u,x,y)\mbox{ and }\mbox{strictly\_less\_than}(x,y)\mbox{ and }\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(v,u,w),x)) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{remove\_slb}(u,x),x,y) ) \ \Rightarrow \ \forall z,x_1,x_2,x_3,x_4,x_5{:}\;( ( \mbox{pair\_in\_list}(\mbox{insert\_slb}(u,\mbox{pair}(x_4,x_5)),x_2,x_3)\mbox{ and }\mbox{strictly\_less\_than}(x_2,x_3)\mbox{ and }\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(z,\mbox{insert\_slb}(u,\mbox{pair}(x_4,x_5)),x_1),x_2)) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{remove\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(x_4,x_5)),x_2),x_2,x_3) ) )\qquad\mbox{fof}(\mbox{l32\_co},\mbox{conjecture})$

\medskip\textbf{SWV362-2.p} Cryptographic protocol problem for Yahalom






$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_S\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X\_H},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA\_H}),\mbox{v\_nb}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_C},\mbox{v\_S},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{v\_nb}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_nb},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{v\_A\_H} = \mbox{v\_A} )\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OSays\_\_unique\_\_NB}_1,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Aa},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV083+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0024

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{66})\mbox{ and }\mbox{leq}(\mbox{pv}_{66},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{66})\mbox{ and }\mbox{leq}(\mbox{pv}_{66},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0024},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV818-1.p} Hoare logic with procedures 114\_1

Completeness is taken relative to completeness of the underlying
 logic. Two versions of completeness proof: nested single recursion
 and simultaneous recursion in call rule.




$\mbox{c\_Code\_\_Evaluation\_Otracing}(\mbox{v\_s},\mbox{v\_x},\mbox{t\_a}) = \mbox{v\_x}\qquad\mbox{cnf}(\mbox{cls\_tracing\_\_def}_0,\mbox{axiom})$

$\mbox{c\_Code\_\_Evaluation\_Otracing}(\mbox{v\_s},\mbox{v\_x},\mbox{t\_a}) = \mbox{v\_x}\qquad\mbox{cnf}(\mbox{cls\_tracing\_\_def\_\_raw}_0,\mbox{axiom})$

$\mbox{v\_s}\ne \mbox{v\_t}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{v\_s} = \mbox{v\_ta}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV365+1.p} Priority queue checker: lemma\_I\_s base






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,x,y{:}\;i(\mbox{triple}(u,\mbox{create\_slb},x)) = i(\mbox{triple}(v,\mbox{create\_slb},y))\qquad\mbox{fof}(\mbox{l1\_co},\mbox{conjecture})$

\medskip\textbf{SWV126+1.p} Unsimplified proof obligation thruster\_init\_0001

Proof obligation emerging from the init-safety verification for
 the thruster program. inuse-safety ensures that each sensor
 reading passed as an input to the Kalman filter algorithm is
 actually used during the computation of the output estimate.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\mbox{init} = \mbox{init}\qquad\mbox{fof}(\mbox{thruster\_init}_{0001},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV058+1.p} Unsimplified proof obligation cl5\_nebula\_norm\_0046

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\neg\,\mbox{geq}(\mbox{pv}_{72},\mbox{tptp\_float\_0}_{001}) \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0046},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV319-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_Public\_OshrK}(\mbox{v\_A}) = \mbox{v\_K}\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_conj\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV399+1.p} Priority queue checker: tmp\_not\_check\_03\_1






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }x < w ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,w) )\qquad\mbox{fof}(\mbox{l35\_li}_{3637},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(w,x) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,x) )\qquad\mbox{fof}(\mbox{l35\_li}_{3839},\mbox{lemma})$

$\forall u{:}\;( \exists v,w{:}\;( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(v,w) ) \ \Rightarrow \ \forall x{:}\;\exists y,z{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),y,z)\mbox{ and }\mbox{strictly\_less\_than}(y,z) ) )\qquad\mbox{fof}(\mbox{l35\_co},\mbox{conjecture})$

\medskip\textbf{SWV404+1.p} Priority queue checker: tmp\_not\_check\_04






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w,x{:}\;( ( \mbox{check\_cpq}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x))\mbox{ and }\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) ) \ \Rightarrow \ \mbox{check\_cpq}(\mbox{triple}(u,v,w)) )\qquad\mbox{fof}(\mbox{l40\_l}_{27},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{check\_cpq}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l40\_l}_{34},\mbox{lemma})$

$\forall u,v,w{:}\;( ( \mbox{check\_cpq}(\mbox{removemin\_cpq\_eff}(\mbox{triple}(u,v,w)))\mbox{ and }\mbox{ok}(\mbox{removemin\_cpq\_eff}(\mbox{triple}(u,v,w))) ) \ \Rightarrow \ \mbox{check\_cpq}(\mbox{triple}(u,v,w)) )\qquad\mbox{fof}(\mbox{l40\_co},\mbox{conjecture})$

\medskip\textbf{SWV557-1.004.p} Store inverse (t2\_np\_nf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(a,i,\mbox{select}(a,i)) = a\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,e),i,f) = \mbox{store}(a,i,f)\qquad\mbox{cnf}(a_4,\mbox{axiom})$

$i = j\mbox{ or }\mbox{store}(\mbox{store}(a,i,e),j,f) = \mbox{store}(\mbox{store}(a,j,f),i,e)\qquad\mbox{cnf}(a_5,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4)) = \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4))\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV374+1.p} Priority queue checker: lemma\_ok\_find\_min






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \mbox{ok}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ ( v\ne \mbox{create\_slb}\mbox{ and }\mbox{contains\_slb}(v,\mbox{findmin\_pqp\_res}(u))\mbox{ and }\mbox{lookup\_slb}(v,\mbox{findmin\_pqp\_res}(u)) < \mbox{findmin\_pqp\_res}(u) ) )\qquad\mbox{fof}(\mbox{l10\_co},\mbox{conjecture})$

\medskip\textbf{SWV254-2.p} Cryptographic protocol problem for messages






$( \mbox{class\_Orderings\_Oorder}(\mbox{t\_a})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_n},\mbox{v\_m},\mbox{t\_a}) ) \ \Rightarrow \ \mbox{c\_SetInterval\_OatLeastLessThan}(\mbox{v\_m},\mbox{v\_n},\mbox{t\_a}) = \mbox{c\_emptyset}\qquad\mbox{cnf}(\mbox{cls\_SetInterval\_OatLeastLessThan\_\_empty}_0,\mbox{axiom})$

$\mbox{c\_SetInterval\_OatLeastLessThan}(\mbox{v\_m},\mbox{c\_Suc}(\mbox{v\_m}),\mbox{tc\_nat}) = \mbox{c\_insert}(\mbox{v\_m},\mbox{c\_emptyset},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_SetInterval\_OatLeastLessThan\_\_singleton}_0,\mbox{axiom})$

$\mbox{c\_emptyset}\ne \mbox{c\_insert}(\mbox{v\_a},\mbox{v\_A},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_Oempty\_\_not\_\_insert}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_U},\mbox{v\_x}(\mbox{v\_U}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{v\_x}(\mbox{v\_U}) = \mbox{v\_nat}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{class\_Orderings\_Oorder}(\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{clsarity\_nat}_3,\mbox{axiom})$

\medskip\textbf{SWV413+1.p} Priority queue checker: lemma\_contains\_update\_02






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }x < w ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,w) )\qquad\mbox{fof}(\mbox{l49\_li}_{3637},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(v,x)\mbox{ and }x < w ) \ \Rightarrow \ \exists y{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,y)\mbox{ and }x < y ) )\qquad\mbox{fof}(\mbox{l49\_co},\mbox{conjecture})$

\medskip\textbf{SWV307-2.p} Cryptographic protocol problem for Otway Rees






$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_2),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{v\_NA} = \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV021-1.p} Show that the add function is commutative.

A proof obligation formulated as a satisfiability problem.
 Given the definition of "add" on successor-naturals, show
 that no two terms t1 and t2 can be found such that
 add(t1,t2) /= add(t2,t1). In other words, show that adding
 the negation of that as a clause is still consistent.




$n_0\ne s(x)\qquad\mbox{cnf}(\mbox{zero\_is\_not\_s},\mbox{axiom})$

$s(x) = s(y) \ \Rightarrow \ x = y\qquad\mbox{cnf}(\mbox{successor\_is\_injective},\mbox{axiom})$

$n_0 + y = y\qquad\mbox{cnf}(\mbox{definition\_add}_0,\mbox{axiom})$

$s(x) + y = s(x + y)\qquad\mbox{cnf}(\mbox{definition\_add\_s},\mbox{axiom})$

$x + y = y + x\qquad\mbox{cnf}(\mbox{consistency\_of\_add\_commutative},\mbox{negated\_conjecture})$

\medskip\textbf{SWV317-2.p} Cryptographic protocol problem for Otway Rees






$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_Public\_OshrK}(\mbox{v\_A}) = \mbox{v\_KAB}\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Public\_OshrK\_\_in\_\_used}_0,\mbox{axiom})$

\medskip\textbf{SWV072+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0013

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{21})\mbox{ and }\mbox{leq}(\mbox{pv}_{21},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{21})\mbox{ and }\mbox{leq}(\mbox{pv}_{21},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0013},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV006-1.p} E5






$\mbox{include}(\mbox{'Axioms/SWV001-0.ax'})$

$\neg\,n < m\qquad\mbox{cnf}(\mbox{clause}_1,\mbox{negated\_conjecture})$

$i < m\qquad\mbox{cnf}(\mbox{clause}_2,\mbox{negated\_conjecture})$

$i < n\qquad\mbox{cnf}(\mbox{clause}_3,\mbox{negated\_conjecture})$

$\neg\,i < 1\qquad\mbox{cnf}(\mbox{clause}_4,\mbox{negated\_conjecture})$

$a(i) < a(m)\qquad\mbox{cnf}(\mbox{clause}_5,\mbox{negated\_conjecture})$

$( x < \mbox{successor}(n)\mbox{ and }a(x) < a(m) ) \ \Rightarrow \ x < i\qquad\mbox{cnf}(\mbox{clause}_6,\mbox{negated\_conjecture})$

$( 1 < i\mbox{ and }a(x) < a(\mbox{predecessor}(i)) ) \ \Rightarrow \ ( x < i\mbox{ or }n < x )\qquad\mbox{cnf}(\mbox{clause}_7,\mbox{negated\_conjecture})$

$( 1 < x\mbox{ and }x < i ) \ \Rightarrow \ \neg\,a(x) < a(\mbox{predecessor}(x))\qquad\mbox{cnf}(\mbox{clause}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV367+1.p} Priority queue checker: lemma\_contains\_s\_I\_remove base






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w{:}\;( \mbox{contains\_pq}(i(\mbox{triple}(u,\mbox{create\_slb},v)),w) \ \Rightarrow \ i(\mbox{remove\_cpq}(\mbox{triple}(u,\mbox{create\_slb},v),w)) = \mbox{remove\_pq}(i(\mbox{triple}(u,\mbox{create\_slb},v)),w) )\qquad\mbox{fof}(\mbox{l3\_co},\mbox{conjecture})$

\medskip\textbf{SWV496-1.040.p} Store commutativity (t1\_np\_nf\_ni\_00040)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),n_{31},e_{31}),n_{32},e_{32}),n_{33},e_{33}),n_{34},e_{34}),n_{35},e_{35}),n_{36},e_{36}),n_{37},e_{37}),n_{38},e_{38}),n_{39},e_{39}),n_1,e_1)\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{16},e_{16}),n_{14},e_{14}),n_{24},e_{24}),n_{11},e_{11}),n_{25},e_{25}),n_{17},e_{17}),n_7,e_7),n_{32},e_{32}),n_6,e_6),n_{18},e_{18}),n_{37},e_{37}),n_{31},e_{31}),n_{13},e_{13}),n_{12},e_{12}),n_{36},e_{36}),n_{20},e_{20}),n_{35},e_{35}),n_{23},e_{23}),n_{26},e_{26}),n_{21},e_{21}),n_{27},e_{27}),n_{10},e_{10}),n_{22},e_{22}),n_8,e_8),n_{33},e_{33}),n_2,e_2),n_{40},e_{40}),n_{38},e_{38}),n_{39},e_{39}),n_1,e_1),n_9,e_9),n_3,e_3),n_5,e_5),n_4,e_4),n_{30},e_{30}),n_{15},e_{15}),n_{34},e_{34}),n_{28},e_{28}),n_{29},e_{29}),n_{19},e_{19})\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV376+1.p} Priority queue checker: lemma\_not\_ok\_persistence






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w,x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ ( \neg\,\mbox{ok}(\mbox{triple}(x,y,z)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{im\_succ\_cpq}(\mbox{triple}(x,y,z))) ) ) \ \Rightarrow \ \forall x_1,x_2,x_3{:}\;( \neg\,\mbox{ok}(\mbox{triple}(x_1,x_2,x_3)) \ \Rightarrow \ \forall x_4,x_5,x_6{:}\;( \mbox{succ\_cpq}(\mbox{triple}(x_1,x_2,x_3),\mbox{triple}(x_4,x_5,x_6)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{triple}(x_4,x_5,x_6)) ) )\qquad\mbox{fof}(\mbox{l12\_induction},\mbox{axiom})$

$\forall u,v,w{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{im\_succ\_cpq}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l12\_l}_{13},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{triple}(x,y,z)) ) )\qquad\mbox{fof}(\mbox{l12\_co},\mbox{conjecture})$

\medskip\textbf{SWV511-1.030.p} Store commutativity (t2\_np\_nf\_ni\_00030)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(a,i,\mbox{select}(a,i)) = a\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,e),i,f) = \mbox{store}(a,i,f)\qquad\mbox{cnf}(a_4,\mbox{axiom})$

$i = j\mbox{ or }\mbox{store}(\mbox{store}(a,i,e),j,f) = \mbox{store}(\mbox{store}(a,j,f),i,e)\qquad\mbox{cnf}(a_5,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30})\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV249-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_analz\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth\_\_Un}_0,\mbox{axiom})$

$\mbox{class\_Orderings\_Oorder}(\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_x},\mbox{v\_x},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Orderings\_Oorder\_\_class\_Oaxioms\_\_1}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{c\_minus}(\mbox{v\_B},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a})),\mbox{v\_A},\mbox{t\_a}) = \mbox{c\_union}(\mbox{v\_B},\mbox{v\_A},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_Diff\_\_cancel2}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{v\_A},\mbox{c\_minus}(\mbox{v\_B},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a})),\mbox{t\_a}) = \mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_Diff\_\_cancel}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{c\_insert}(\mbox{v\_a},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{t\_a}) = \mbox{c\_insert}(\mbox{v\_a},\mbox{c\_union}(\mbox{v\_B},\mbox{v\_C},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_insert\_\_left}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{v\_A},\mbox{c\_insert}(\mbox{v\_a},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) = \mbox{c\_insert}(\mbox{v\_a},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_insert\_\_right}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_subset\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_subset\_\_iff}_1,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_subset\_\_iff}_2,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_insert}(\mbox{v\_x},\mbox{v\_A},\mbox{t\_a}),\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_subset}_1,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_x},\mbox{v\_B},\mbox{t\_a})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_insert}(\mbox{v\_x},\mbox{v\_A},\mbox{t\_a}),\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_subset}_2,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{v\_A} = \mbox{v\_B}\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_antisym}_0,\mbox{axiom})$

$\mbox{class\_Orderings\_Oorder}(\mbox{tc\_set}(t_1))\qquad\mbox{cnf}(\mbox{clsarity\_set}_2,\mbox{axiom})$

\medskip\textbf{SWV490+3.p} Matrix is diagonal invertible






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{real\_zero} ) )\mbox{ and }\forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k,k) = \mbox{real\_one} )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qii},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( ( i\ne j \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\mbox{ and }( i = j \ \Rightarrow \ a(i,j)\ne \mbox{real\_zero} ) ) )\qquad\mbox{fof}(\mbox{di},\mbox{conjecture})$

\medskip\textbf{SWV081+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0022

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{57})\mbox{ and }\mbox{leq}(\mbox{pv}_{57},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{57})\mbox{ and }\mbox{leq}(\mbox{pv}_{57},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0022},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV389+1.p} Priority queue checker: lemma\_not\_min\_elem\_not\_check\_ind\_steps 4






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( ( \mbox{check\_cpq}(\mbox{removemin\_cpq\_eff}(\mbox{triple}(u,v,w)))\mbox{ and }\mbox{ok}(\mbox{removemin\_cpq\_eff}(\mbox{triple}(u,v,w))) ) \ \Rightarrow \ \mbox{check\_cpq}(\mbox{triple}(u,v,w)) )\qquad\mbox{fof}(\mbox{l25\_l}_{40},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ ( \neg\,\mbox{check\_cpq}(\mbox{removemin\_cpq\_eff}(\mbox{triple}(u,v,w)))\mbox{ or }\neg\,\mbox{ok}(\mbox{removemin\_cpq\_eff}(\mbox{triple}(u,v,w))) ) )\qquad\mbox{fof}(\mbox{l25\_co},\mbox{conjecture})$

\medskip\textbf{SWV336-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_U},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_U}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_V}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_W}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_V}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_U}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV340-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Event\_OkeysFor\_\_parts\_\_insert\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4))),\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{10},\mbox{negated\_conjecture})$

$\mbox{v\_A}\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Ka},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_Ka}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_insert}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_Ka},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{v\_K} = \mbox{v\_Ka}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV056+1.p} Unsimplified proof obligation cl5\_nebula\_norm\_0040

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{25})\mbox{ and }\mbox{leq}(\mbox{pv}_{25},-n_5) ) \ \Rightarrow \ ( n_0 = n_0 + -n_0{=}\mbox{a\_select}_3(q,\mbox{pv}_{77},\mbox{pv}_{25})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{25})\mbox{ and }\mbox{leq}(\mbox{pv}_{25},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0040},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV150+1.p} Simplified proof obligation gauss\_array\_0020

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\neg\,\mbox{leq}(\mbox{tptp\_float\_0}_{001},\mbox{tptp\_float\_0}_{001}) \ \Rightarrow \ \mbox{leq}(\mbox{s\_worst}_7,n_3)\qquad\mbox{fof}(\mbox{gauss\_array}_{0020},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV307-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_2,\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_2),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{v\_A\_H} = \mbox{v\_Aa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{v\_NA} = \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{v\_NA\_H} = \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{v\_A} = \mbox{v\_Ba}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV278-2.p} Cryptographic protocol problem for events






$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K\_H}))),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K\_H}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_conj\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_Message\_OinvKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_y})) = \mbox{v\_y}\qquad\mbox{cnf}(\mbox{cls\_Message\_OinvKey\_A\_IinvKey\_Ay\_J\_A\_61\_61\_Ay}_0,\mbox{axiom})$

\medskip\textbf{SWV565-1.004.p} Store inverse (t3\_pp\_sf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{20} = \mbox{store}(a_1,i_1,e_{19})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{22} = \mbox{store}(a_2,i_1,e_{21})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{24} = \mbox{store}(a_{20},i_2,e_{23})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{26} = \mbox{store}(a_{22},i_2,e_{25})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{28} = \mbox{store}(a_{24},i_3,e_{27})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{30} = \mbox{store}(a_{26},i_3,e_{29})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{32} = \mbox{store}(a_{28},i_4,e_{31})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{34} = \mbox{store}(a_{30},i_4,e_{33})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$e_{19} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$e_{21} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$e_{23} = \mbox{select}(a_{22},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$e_{25} = \mbox{select}(a_{20},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$e_{27} = \mbox{select}(a_{26},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$e_{29} = \mbox{select}(a_{24},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{31} = \mbox{select}(a_{30},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{33} = \mbox{select}(a_{28},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{36} = \mbox{select}(a_1,i_{35})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{37} = \mbox{select}(a_2,i_{35})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$i_{35} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{32} = a_{34}\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{36}\ne e_{37}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV324-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_Public\_OshrK}(\mbox{v\_A})\ne \mbox{v\_K}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_Public\_OshrK}(\mbox{v\_A}) = \mbox{v\_K}\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV263-2.p} Cryptographic protocol problem for messages






$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetD}_0,\mbox{axiom})$

\medskip\textbf{SWV260-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_a},\mbox{c\_insert}(\mbox{v\_b},\mbox{v\_A},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_a},\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{v\_a} = \mbox{v\_b} )\qquad\mbox{cnf}(\mbox{cls\_Set\_OinsertE}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_1,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_trans}_0,\mbox{axiom})$

\medskip\textbf{SWV378+1.p} Priority queue checker: lemma\_not\_ok\_persistence\_induction step 2






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w,x{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) )\qquad\mbox{fof}(\mbox{l14\_co},\mbox{conjecture})$

\medskip\textbf{SWV322-2.p} Cryptographic protocol problem for Otway Rees






$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_Public\_OshrK}(\mbox{v\_A}) = \mbox{v\_KAB}\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Public\_OshrK\_\_in\_\_used}_0,\mbox{axiom})$

\medskip\textbf{SWV358-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_spies}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_2),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV246-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnE}_0,\mbox{axiom})$

\medskip\textbf{SWV334-2.p} Cryptographic protocol problem for Yahalom






$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_Xa},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV377+1.p} Priority queue checker: lemma\_not\_ok\_persistence\_induction step 1






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w,x{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{insert\_cpq}(\mbox{triple}(u,v,w),x)) )\qquad\mbox{fof}(\mbox{l13\_co},\mbox{conjecture})$

\medskip\textbf{SWV336-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-3.ax'})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_KAB},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_U},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_U}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_V}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_W}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_V}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_U}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$( \mbox{v\_NB} = \mbox{v\_NBa}\mbox{ and }\mbox{v\_W} = \mbox{v\_NA}\mbox{ and }\mbox{v\_K} = \mbox{v\_KAB}\mbox{ and }\mbox{v\_V} = \mbox{v\_B} ) \ \Rightarrow \ \mbox{v\_U}\ne \mbox{v\_A}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV281-1.p} Cryptographic protocol problem for public






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{c\_lessequals}(\mbox{v\_n},\mbox{c\_plus}(\mbox{v\_n},\mbox{v\_m},\mbox{tc\_nat}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Ole\_\_add1}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_n},\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Ole\_\_add2}_0,\mbox{axiom})$

$\mbox{c\_less}(\mbox{v\_m},\mbox{c\_Suc}(\mbox{v\_n}),\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oless\_\_Suc\_\_eq\_\_le}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_less}(\mbox{v\_m},\mbox{c\_Suc}(\mbox{v\_n}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oless\_\_Suc\_\_eq\_\_le}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_sko\_\_urX}(\mbox{v\_evs}),\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Public\_ONonce\_\_supply\_\_lemma}_0,\mbox{axiom})$

$\mbox{v\_U} = \mbox{v\_V}\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_V}),\mbox{c\_Event\_Oused}(\mbox{v\_evs\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV354-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_insert}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$( \mbox{v\_U} = \mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})\mbox{ and }\mbox{v\_NA} = \mbox{v\_NAa} ) \ \Rightarrow \ \mbox{v\_NB}\ne \mbox{v\_NBa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV489+3.p} Matrix is diagonal






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{real\_zero} ) )\mbox{ and }\forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k,k) = \mbox{real\_one} )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qii},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n)\mbox{ and }i\ne j ) \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\qquad\mbox{fof}(d,\mbox{conjecture})$

\medskip\textbf{SWV352-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$( \mbox{v\_U} = \mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})\mbox{ and }\mbox{v\_NA} = \mbox{v\_NB} ) \ \Rightarrow \ \mbox{v\_NB}\ne \mbox{v\_NBa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV258-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_1,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_x},\mbox{v\_B},\mbox{t\_a})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_insert}(\mbox{v\_x},\mbox{v\_A},\mbox{t\_a}),\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_subset}_2,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_refl}_0,\mbox{axiom})$

\medskip\textbf{SWV372+2.p} Priority queue checker: lemma\_contains\_cpq\_min\_elem






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w,x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\iff \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),x) )\qquad\mbox{fof}(\mbox{l8\_li}_{56},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{ok}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ ( v\ne \mbox{create\_slb}\mbox{ and }\mbox{contains\_slb}(v,\mbox{findmin\_pqp\_res}(u))\mbox{ and }\mbox{lookup\_slb}(v,\mbox{findmin\_pqp\_res}(u)) < \mbox{findmin\_pqp\_res}(u) ) )\qquad\mbox{fof}(\mbox{l9\_l}_{10},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{triple}(x,y,z)) ) )\qquad\mbox{fof}(\mbox{l11\_l}_{12},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l8\_co},\mbox{conjecture})$

\medskip\textbf{SWV287-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B\_H},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B\_H},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_sko\_\_u8o}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_K},\mbox{v\_NA},\mbox{v\_evs}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OA\_\_trusts\_\_OR4\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_Osecrecy\_\_lemma\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV558-1.004.p} Store inverse (t2\_np\_sf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(a,i,\mbox{select}(a,i)) = a\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,e),i,f) = \mbox{store}(a,i,f)\qquad\mbox{cnf}(a_4,\mbox{axiom})$

$i = j\mbox{ or }\mbox{store}(\mbox{store}(a,i,e),j,f) = \mbox{store}(\mbox{store}(a,j,f),i,e)\qquad\mbox{cnf}(a_5,\mbox{axiom})$

$a_{17} = \mbox{store}(a_1,i_1,e_{16})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{19} = \mbox{store}(a_2,i_1,e_{18})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{21} = \mbox{store}(a_{17},i_2,e_{20})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{23} = \mbox{store}(a_{19},i_2,e_{22})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{25} = \mbox{store}(a_{21},i_3,e_{24})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{27} = \mbox{store}(a_{23},i_3,e_{26})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{29} = \mbox{store}(a_{25},i_4,e_{28})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{31} = \mbox{store}(a_{27},i_4,e_{30})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$e_{16} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$e_{18} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$e_{20} = \mbox{select}(a_{19},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$e_{22} = \mbox{select}(a_{17},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$e_{24} = \mbox{select}(a_{23},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$e_{26} = \mbox{select}(a_{21},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{28} = \mbox{select}(a_{27},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{30} = \mbox{select}(a_{25},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{29} = a_{31}\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV293-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OCrypt\_\_imp\_\_OR1\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_sko\_\_usf}(\mbox{v\_B},\mbox{v\_X},\mbox{v\_evs}),\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OGets\_\_imp\_\_Says\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV052+1.p} Unsimplified proof obligation cl5\_nebula\_norm\_0028

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{pv}_{86} = n_0 + -\mbox{pv}_{73}{=}\mbox{divide}(\mbox{abs}(-\mbox{a\_select}_2(\mbox{mu},\mbox{pv}_{87})),\mbox{abs}(\mbox{a\_select}_2(\mbox{mu},\mbox{pv}_{87})) + \mbox{abs}(\mbox{a\_select}_2(\mbox{muold},\mbox{pv}_{87})))\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{73})\mbox{ and }\mbox{leq}(\mbox{pv}_{73},-n_5) ) \ \Rightarrow \ \mbox{pv}_{86} + \mbox{divide}(\mbox{abs}(-\mbox{a\_select}_2(\mbox{mu},\mbox{pv}_{73})),\mbox{abs}(\mbox{a\_select}_2(\mbox{mu},\mbox{pv}_{73})) + \mbox{abs}(\mbox{a\_select}_2(\mbox{muold},\mbox{pv}_{73}))) = n_0 + -( n_1 + \mbox{pv}_{73} ){=}\mbox{divide}(\mbox{abs}(-\mbox{a\_select}_2(\mbox{mu},\mbox{pv}_{87})),\mbox{abs}(\mbox{a\_select}_2(\mbox{mu},\mbox{pv}_{87})) + \mbox{abs}(\mbox{a\_select}_2(\mbox{muold},\mbox{pv}_{87})))\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0028},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV329-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OCrypt\_\_synth\_\_eq}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_conj\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OSpy\_\_analz\_\_shrK}_0,\mbox{axiom})$

\medskip\textbf{SWV010-1.p} Fact 1 of the Neumann-Stubblebine analysis






$\mbox{message}(\mbox{sent}(a,b,\mbox{pair}(a,\mbox{an\_a\_nonce})))\qquad\mbox{cnf}(\mbox{a\_sent\_message\_i\_to\_b}_3,\mbox{axiom})$

$\mbox{a\_stored}(\mbox{pair}(b,\mbox{an\_a\_nonce}))\qquad\mbox{cnf}(\mbox{a\_stored\_message\_i}_4,\mbox{axiom})$

$( \mbox{a\_stored}(\mbox{pair}(a,b))\mbox{ and }\mbox{message}(\mbox{sent}(t,a,\mbox{triple}(\mbox{encrypt}(\mbox{quadruple}(a,b,c,d),\mbox{at}),e,f))) ) \ \Rightarrow \ \mbox{message}(\mbox{sent}(a,a,\mbox{pair}(e,\mbox{encrypt}(f,c))))\qquad\mbox{cnf}(\mbox{a\_forwards\_secure}_5,\mbox{axiom})$

$\mbox{fresh\_to\_b}(\mbox{an\_a\_nonce})\qquad\mbox{cnf}(\mbox{nonce\_a\_is\_fresh\_to\_b}_9,\mbox{axiom})$

$( \mbox{fresh\_to\_b}(b)\mbox{ and }\mbox{message}(\mbox{sent}(a,b,\mbox{pair}(a,b))) ) \ \Rightarrow \ \mbox{message}(\mbox{sent}(b,t,\mbox{triple}(b,\mbox{generate\_b\_nonce}(b),\mbox{encrypt}(\mbox{triple}(a,b,\mbox{generate\_expiration\_time}(b)),\mbox{bt}))))\qquad\mbox{cnf}(\mbox{b\_creates\_freash\_nonces\_in\_time}_{10},\mbox{axiom})$

$\mbox{t\_holds}(\mbox{key}(\mbox{at},a))\qquad\mbox{cnf}(\mbox{t\_holds\_key\_at\_for\_a}_{13},\mbox{axiom})$

$\mbox{t\_holds}(\mbox{key}(\mbox{bt},b))\qquad\mbox{cnf}(\mbox{t\_holds\_key\_bt\_for\_b}_{14},\mbox{axiom})$

$( \mbox{message}(\mbox{sent}(a,t,\mbox{triple}(a,b,\mbox{encrypt}(\mbox{triple}(c,d,e),f))))\mbox{ and }\mbox{t\_holds}(\mbox{key}(g,c))\mbox{ and }\mbox{t\_holds}(\mbox{key}(f,a)) ) \ \Rightarrow \ \mbox{message}(\mbox{sent}(t,c,\mbox{triple}(\mbox{encrypt}(\mbox{quadruple}(a,d,\mbox{generate\_key}(d),e),g),\mbox{encrypt}(\mbox{triple}(c,\mbox{generate\_key}(d),e),f),b)))\qquad\mbox{cnf}(\mbox{server\_t\_generates\_key}_{16},\mbox{axiom})$

\medskip\textbf{SWV277-1.p} Cryptographic protocol problem for events






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_OkeysFor}(\mbox{v\_G}),\mbox{c\_Message\_OkeysFor}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_nat}))\qquad\mbox{cnf}(\mbox{cls\_Message\_OkeysFor\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_insert\_\_subset\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{v\_G})),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

\medskip\textbf{SWV558-1.007.p} Store inverse (t2\_np\_sf\_ai\_00007)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(a,i,\mbox{select}(a,i)) = a\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,e),i,f) = \mbox{store}(a,i,f)\qquad\mbox{cnf}(a_4,\mbox{axiom})$

$i = j\mbox{ or }\mbox{store}(\mbox{store}(a,i,e),j,f) = \mbox{store}(\mbox{store}(a,j,f),i,e)\qquad\mbox{cnf}(a_5,\mbox{axiom})$

$a_{29} = \mbox{store}(a_1,i_1,e_{28})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{31} = \mbox{store}(a_2,i_1,e_{30})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{33} = \mbox{store}(a_{29},i_2,e_{32})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{35} = \mbox{store}(a_{31},i_2,e_{34})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{37} = \mbox{store}(a_{33},i_3,e_{36})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{39} = \mbox{store}(a_{35},i_3,e_{38})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{41} = \mbox{store}(a_{37},i_4,e_{40})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{43} = \mbox{store}(a_{39},i_4,e_{42})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{45} = \mbox{store}(a_{41},i_5,e_{44})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{47} = \mbox{store}(a_{43},i_5,e_{46})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{49} = \mbox{store}(a_{45},i_6,e_{48})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{51} = \mbox{store}(a_{47},i_6,e_{50})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{53} = \mbox{store}(a_{49},i_7,e_{52})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{55} = \mbox{store}(a_{51},i_7,e_{54})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{28} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{30} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{32} = \mbox{select}(a_{31},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{34} = \mbox{select}(a_{29},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{36} = \mbox{select}(a_{35},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{38} = \mbox{select}(a_{33},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{40} = \mbox{select}(a_{39},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{42} = \mbox{select}(a_{37},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{44} = \mbox{select}(a_{43},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{46} = \mbox{select}(a_{41},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{48} = \mbox{select}(a_{47},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{50} = \mbox{select}(a_{45},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{52} = \mbox{select}(a_{51},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{54} = \mbox{select}(a_{49},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$a_{53} = a_{55}\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV518-1.040.p} Store commutativity (t3\_np\_nf\_ni\_00040)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),n_{31},e_{31}),n_{32},e_{32}),n_{33},e_{33}),n_{34},e_{34}),n_{35},e_{35}),n_{36},e_{36}),n_{37},e_{37}),n_{38},e_{38}),n_{39},e_{39}),n_1,e_1)\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{16},e_{16}),n_{14},e_{14}),n_{24},e_{24}),n_{11},e_{11}),n_{25},e_{25}),n_{17},e_{17}),n_7,e_7),n_{32},e_{32}),n_6,e_6),n_{18},e_{18}),n_{37},e_{37}),n_{31},e_{31}),n_{13},e_{13}),n_{12},e_{12}),n_{36},e_{36}),n_{20},e_{20}),n_{35},e_{35}),n_{23},e_{23}),n_{26},e_{26}),n_{21},e_{21}),n_{27},e_{27}),n_{10},e_{10}),n_{22},e_{22}),n_8,e_8),n_{33},e_{33}),n_2,e_2),n_{40},e_{40}),n_{38},e_{38}),n_{39},e_{39}),n_1,e_1),n_9,e_9),n_3,e_3),n_5,e_5),n_4,e_4),n_{30},e_{30}),n_{15},e_{15}),n_{34},e_{34}),n_{28},e_{28}),n_{29},e_{29}),n_{19},e_{19})\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV165+1.p} Simplified proof obligation cl5\_nebula\_init\_0001

Proof obligation emerging from the init-safety verification for
 the cl5\_nebula program. init-safety ensures that each variable or
 individual array element has been assigned a defined value before
 it is used.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\forall a{:}\;( ( \mbox{leq}(n_0,a)\mbox{ and }\mbox{leq}(a,\mbox{tptp\_minus}_1) ) \ \Rightarrow \ \mbox{uninit} = \mbox{init} )\qquad\mbox{fof}(\mbox{cl5\_nebula\_init}_{0001},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV244-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnE}_0,\mbox{axiom})$

\medskip\textbf{SWV077+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0018

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5)\mbox{ and }( n_0\ne \mbox{pv}_{40} \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5) ) )\mbox{ and }( n_0 = \mbox{pv}_{40} \ \Rightarrow \ \mbox{true} ) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0018},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV250-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_x},\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_x},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_analz\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_2,\mbox{axiom})$

\medskip\textbf{SWV543-1.004.p} Swap elements (t3\_np\_sf\_ai\_00004)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{417} = \mbox{store}(a_1,i_1,e_{416})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{418} = \mbox{store}(a_{417},i_1,e_{416})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{420} = \mbox{store}(a_{418},i_0,e_{419})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{422} = \mbox{store}(a_{420},i_3,e_{421})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{424} = \mbox{store}(a_{422},i_3,e_{423})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{426} = \mbox{store}(a_{424},i_2,e_{425})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{428} = \mbox{store}(a_{426},i_2,e_{427})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{430} = \mbox{store}(a_{428},i_0,e_{429})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{431} = \mbox{store}(a_{418},i_3,e_{421})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{432} = \mbox{store}(a_{431},i_0,e_{419})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{434} = \mbox{store}(a_{432},i_3,e_{433})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{436} = \mbox{store}(a_{434},i_2,e_{435})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{438} = \mbox{store}(a_{436},i_0,e_{437})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{440} = \mbox{store}(a_{438},i_2,e_{439})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{416} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{419} = \mbox{select}(a_{418},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{421} = \mbox{select}(a_{418},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{423} = \mbox{select}(a_{422},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{425} = \mbox{select}(a_{422},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{427} = \mbox{select}(a_{426},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{429} = \mbox{select}(a_{426},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{433} = \mbox{select}(a_{432},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{435} = \mbox{select}(a_{432},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{437} = \mbox{select}(a_{436},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{439} = \mbox{select}(a_{436},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{430}\ne a_{440}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV011+1.p} Fact 2 of the Neumann-Stubblebine analysis






$\mbox{a\_holds}(\mbox{key}(\mbox{at},t))\qquad\mbox{fof}(\mbox{a\_holds\_key\_at\_for\_t},\mbox{axiom})$

$\mbox{party\_of\_protocol}(a)\qquad\mbox{fof}(\mbox{a\_is\_party\_of\_protocol},\mbox{axiom})$

$\mbox{message}(\mbox{sent}(a,b,\mbox{pair}(a,\mbox{an\_a\_nonce})))\qquad\mbox{fof}(\mbox{a\_sent\_message\_i\_to\_b},\mbox{axiom})$

$\mbox{a\_stored}(\mbox{pair}(b,\mbox{an\_a\_nonce}))\qquad\mbox{fof}(\mbox{a\_stored\_message\_i},\mbox{axiom})$

$\mbox{b\_holds}(\mbox{key}(\mbox{bt},t))\qquad\mbox{fof}(\mbox{b\_hold\_key\_bt\_for\_t},\mbox{axiom})$

$\mbox{party\_of\_protocol}(b)\qquad\mbox{fof}(\mbox{b\_is\_party\_of\_protocol},\mbox{axiom})$

$\mbox{fresh\_to\_b}(\mbox{an\_a\_nonce})\qquad\mbox{fof}(\mbox{nonce\_a\_is\_fresh\_to\_b},\mbox{axiom})$

$\mbox{t\_holds}(\mbox{key}(\mbox{at},a))\qquad\mbox{fof}(\mbox{t\_holds\_key\_at\_for\_a},\mbox{axiom})$

$\mbox{t\_holds}(\mbox{key}(\mbox{bt},b))\qquad\mbox{fof}(\mbox{t\_holds\_key\_bt\_for\_b},\mbox{axiom})$

$\mbox{party\_of\_protocol}(t)\qquad\mbox{fof}(\mbox{t\_is\_party\_of\_protocol},\mbox{axiom})$

$\mbox{b\_holds}(\mbox{key}(\mbox{generate\_key}(\mbox{an\_a\_nonce}),a))\qquad\mbox{fof}(\mbox{ax}_1,\mbox{axiom})$

$\mbox{message}(\mbox{sent}(a,b,\mbox{pair}(\mbox{encrypt}(\mbox{triple}(a,\mbox{generate\_key}(\mbox{an\_a\_nonce}),\mbox{generate\_expiration\_time}(\mbox{an\_a\_nonce})),\mbox{bt}),\mbox{encrypt}(\mbox{generate\_b\_nonce}(\mbox{an\_a\_nonce}),\mbox{generate\_key}(\mbox{an\_a\_nonce})))))\qquad\mbox{fof}(\mbox{ax}_2,\mbox{axiom})$

$\mbox{a\_holds}(\mbox{key}(\mbox{generate\_key}(\mbox{an\_a\_nonce}),b))\qquad\mbox{fof}(\mbox{ax}_3,\mbox{axiom})$

$\mbox{message}(\mbox{sent}(t,a,\mbox{triple}(\mbox{encrypt}(\mbox{quadruple}(b,\mbox{an\_a\_nonce},\mbox{generate\_key}(\mbox{an\_a\_nonce}),\mbox{generate\_expiration\_time}(\mbox{an\_a\_nonce})),\mbox{at}),\mbox{encrypt}(\mbox{triple}(a,\mbox{generate\_key}(\mbox{an\_a\_nonce}),\mbox{generate\_expiration\_time}(\mbox{an\_a\_nonce})),\mbox{bt}),\mbox{generate\_b\_nonce}(\mbox{an\_a\_nonce}))))\qquad\mbox{fof}(\mbox{ax}_4,\mbox{axiom})$

$\mbox{message}(\mbox{sent}(b,t,\mbox{triple}(b,\mbox{generate\_b\_nonce}(\mbox{an\_a\_nonce}),\mbox{encrypt}(\mbox{triple}(a,\mbox{an\_a\_nonce},\mbox{generate\_expiration\_time}(\mbox{an\_a\_nonce})),\mbox{bt}))))\qquad\mbox{fof}(\mbox{ax}_5,\mbox{axiom})$

$\mbox{b\_stored}(\mbox{pair}(a,\mbox{an\_a\_nonce}))\qquad\mbox{fof}(\mbox{ax}_6,\mbox{axiom})$

$\exists u{:}\;( \mbox{a\_holds}(\mbox{key}(u,b))\mbox{ and }\mbox{b\_holds}(\mbox{key}(u,a)) )\qquad\mbox{fof}(\mbox{co}_1,\mbox{conjecture})$

\medskip\textbf{SWV447$\wedge$1.p} Nipkow's simple map-cons problem






$\mbox{nil}{:}\;\mbox{\$i}\qquad\mbox{thf}(\mbox{nil\_type},\mbox{type})$

$\mbox{cons}{:}\;\mbox{\$i}\to \mbox{\$i}\to \mbox{\$i}\qquad\mbox{thf}(\mbox{cons\_type},\mbox{type})$

$\mbox{map}{:}\;( \mbox{\$i}\to \mbox{\$i} )\to \mbox{\$i}\to \mbox{\$i}\qquad\mbox{thf}(\mbox{map\_type},\mbox{type})$

$\forall f{:}\;\mbox{\$i}\to \mbox{\$i}{:}\;( \mbox{map}@ f@ \mbox{nil} ) = \mbox{nil}\qquad\mbox{thf}(\mbox{ax}_1,\mbox{axiom})$

$\forall f{:}\;\mbox{\$i}\to \mbox{\$i},x{:}\;\mbox{\$i},y{:}\;\mbox{\$i}{:}\;( \mbox{map}@ f@ ( \mbox{cons}@ x@ y ) ) = ( \mbox{cons}@ ( f@ x )@ ( \mbox{map}@ f@ y ) )\qquad\mbox{thf}(\mbox{ax}_2,\mbox{axiom})$

$\forall a{:}\;\mbox{\$i}{:}\;( \mbox{map}@ \lambda x{:}\;\mbox{\$i}{:}\;x@ ( \mbox{cons}@ a@ \mbox{nil} ) ) = ( \mbox{cons}@ a@ \mbox{nil} )\qquad\mbox{thf}(\mbox{test},\mbox{conjecture})$

\medskip\textbf{SWV239-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV004-0.ax'})$

$( \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\mbox{ and }\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_G\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G\_H},\mbox{v\_H\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_cong}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_synthD\_\_dest}_0,\mbox{axiom})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV308-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{v\_Ba}\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_Ba},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X\_H},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_Ba},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV382+1.p} Priority queue checker: lemma\_not\_min\_elem\_not\_phi






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ ( \neg\,\mbox{ok}(\mbox{triple}(x,y,z))\mbox{ or }\neg\,\mbox{check\_cpq}(\mbox{triple}(x,y,z)) ) ) )\qquad\mbox{fof}(\mbox{l18\_l}_{19},\mbox{lemma})$

$\forall u,v,w{:}\;( \exists x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\mbox{ and }\mbox{strictly\_less\_than}(x,\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) ) \ \Rightarrow \ \neg\,\mbox{check\_cpq}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l18\_l}_{43},\mbox{lemma})$

$\forall u,v,w{:}\;( \exists x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\mbox{ and }\mbox{strictly\_less\_than}(x,\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) ) \ \Rightarrow \ \neg\,\mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l18\_co},\mbox{conjecture})$

\medskip\textbf{SWV430$\wedge$2.p} ICL$\wedge$=$>$ logic mapping to modal logic implies 'trans'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^2.ax'})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$b{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(b,\mbox{type})$

$c{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(c,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ b ) )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ b )@ ( \mbox{icl\_princ}@ c ) )@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ c ) ) ) )\qquad\mbox{thf}(\mbox{trans},\mbox{conjecture})$

\medskip\textbf{SWV369+1.p} Priority queue checker: lemma\_contains\_s\_I base






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,\mbox{create\_slb},v),w)\iff \mbox{contains\_pq}(i(\mbox{triple}(u,\mbox{create\_slb},v)),w) )\qquad\mbox{fof}(\mbox{l5\_co},\mbox{conjecture})$

\medskip\textbf{SWV259-2.p} Cryptographic protocol problem for messages






$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_1,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_insert}(\mbox{v\_x},\mbox{v\_A},\mbox{t\_a}),\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_subset}_1,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_refl}_0,\mbox{axiom})$

\medskip\textbf{SWV324-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_Public\_OshrK}(\mbox{v\_A}) = \mbox{v\_K}\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV453+1.p} Establishing that there cannot be two leaders, part i26\_p217






$\mbox{include}(\mbox{'Axioms/SWV011+0.ax'})$

$\forall v,w,x,y{:}\;( ( \forall z,\mbox{pid}_0{:}\;( \mbox{setIn}(\mbox{pid}_0,\mbox{alive}) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \mbox{host}(\mbox{pid}_0)\ne \mbox{host}(z) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Halt}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_{20},\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Ack}(\mbox{pid}_0,z),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{leq}(\mbox{pid}_0,z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \mbox{pid}_0\ne z\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ or }\neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) ) )\mbox{ and }\forall z,\mbox{pid}_{30},\mbox{pid}_{20},\mbox{pid}_0{:}\;( ( \mbox{host}(\mbox{pid}_{20})\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(\mbox{pid}_{20},\mbox{alive})\mbox{ and }\mbox{host}(\mbox{pid}_{30}) = \mbox{host}(z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(\mbox{pid}_{20}) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z)))\mbox{ and }\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_{30}),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) )\mbox{ and }\mbox{queue}(\mbox{host}(x)) = \mbox{cons}(\mbox{m\_Down}(y),v) ) \ \Rightarrow \ ( \mbox{setIn}(x,\mbox{alive}) \ \Rightarrow \ ( \neg\,\mbox{leq}(\mbox{host}(x),\mbox{host}(y)) \ \Rightarrow \ ( ( ( \mbox{index}(\mbox{ldr},\mbox{host}(x)) = \mbox{host}(y)\mbox{ and }\mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{norm} )\mbox{ or }( \mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{wait}\mbox{ and }\mbox{host}(y) = \mbox{host}(\mbox{index}(\mbox{elid},\mbox{host}(x))) ) ) \ \Rightarrow \ ( ( \forall z{:}\;( \mbox{host}(x) = \mbox{host}(z) \ \Rightarrow \ \mbox{leq}(z,w) )\mbox{ and }\neg\,\mbox{setIn}(w,\mbox{pids})\mbox{ and }\mbox{host}(x) = \mbox{host}(w) ) \ \Rightarrow \ ( \mbox{host}(w)\ne s(0) \ \Rightarrow \ \forall z{:}\;( \mbox{host}(x)\ne \mbox{host}(z) \ \Rightarrow \ \forall x_0,y_0{:}\;( \mbox{host}(x) = \mbox{host}(y_0) \ \Rightarrow \ \forall z_0{:}\;( ( ( ( z\ne x\mbox{ and }\mbox{setIn}(z,\mbox{alive}) )\mbox{ or }z = w )\mbox{ and }( ( y_0\ne x\mbox{ and }\mbox{setIn}(y_0,\mbox{alive}) )\mbox{ or }y_0 = w )\mbox{ and }\mbox{host}(y_0)\ne \mbox{host}(z)\mbox{ and }\mbox{host}(x_0) = \mbox{host}(z)\mbox{ and }\mbox{host}(z_0) = \mbox{host}(y_0) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(x_0),v)\mbox{ and }\mbox{elem}(\mbox{m\_Down}(z_0),\mbox{queue}(\mbox{host}(z))) ) ) ) ) ) ) ) ) )\qquad\mbox{fof}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV299-2.p} Cryptographic protocol problem for Otway Rees






$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_Aaa},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A})))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_Ono\_\_nonce\_\_OR1\_\_OR2\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV040+1.p} Unsimplified proof obligation gauss\_init\_0073

Proof obligation emerging from the init-safety verification for
 the gauss program. init-safety ensures that each variable or
 individual array element has been assigned a defined value before
 it is used.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{1374})\mbox{ and }\mbox{leq}(\mbox{pv}_{1374},n_3)\mbox{ and }\forall a{:}\;( ( \mbox{leq}(n_0,a)\mbox{ and }\mbox{leq}(a,n_2) ) \ \Rightarrow \ \forall b{:}\;( ( \mbox{leq}(n_0,b)\mbox{ and }\mbox{leq}(b,-\mbox{pv}_{1374}) ) \ \Rightarrow \ \mbox{a\_select}_3(\mbox{simplex7\_init},b,a) = \mbox{init} ) ) ) \ \Rightarrow \ ( \mbox{init} = \mbox{init}\mbox{ and }\forall c{:}\;( ( \mbox{leq}(n_0,c)\mbox{ and }\mbox{leq}(c,n_2) ) \ \Rightarrow \ \forall d{:}\;( ( \mbox{leq}(n_0,d)\mbox{ and }\mbox{leq}(d,-( n_1 + \mbox{pv}_{1374} )) ) \ \Rightarrow \ \mbox{a\_select}_3(\mbox{tptp\_update}_3(\mbox{tptp\_update}_3(\mbox{tptp\_update}_3(\mbox{simplex7\_init},\mbox{pv}_{1374},n_0,\mbox{init}),\mbox{pv}_{1374},n_1,\mbox{init}),\mbox{pv}_{1374},n_2,\mbox{init}),d,c) = \mbox{init} ) ) )\qquad\mbox{fof}(\mbox{gauss\_init}_{0073},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV146+1.p} Simplified proof obligation gauss\_array\_0016

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\neg\,\mbox{leq}(\mbox{tptp\_float\_0}_{001},\mbox{tptp\_float\_0}_{001}) \ \Rightarrow \ \mbox{leq}(n_0,\mbox{s\_sworst}_7)\qquad\mbox{fof}(\mbox{gauss\_array}_{0016},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV996=1.p} Backward simplification: node deletion 2

A problem extracted from model checking a safety problem (no
 violation of mutual exclusion) for a parameterized system (a
 variant of the protocol due to Szymanski).




$z_1{:}\;\mbox{\$int}\qquad\mbox{tff}(\mbox{z1\_type},\mbox{type})$

$z_2{:}\;\mbox{\$int}\qquad\mbox{tff}(\mbox{z2\_type},\mbox{type})$

$z_3{:}\;\mbox{\$int}\qquad\mbox{tff}(\mbox{z3\_type},\mbox{type})$

$a{:}\;\mbox{\$int}\to \mbox{\$int}\qquad\mbox{tff}(\mbox{a\_type},\mbox{type})$

$b{:}\;\mbox{\$int}\to \mbox{\$int}\qquad\mbox{tff}(\mbox{b\_type},\mbox{type})$

$( \forall z_1{:}\;\mbox{\$int}{:}\;( \mbox{\$lesseq}(1,a(z_1))\mbox{ and }\mbox{\$lesseq}(a(z_1),12) )\mbox{ and }\forall z_1{:}\;\mbox{\$int}{:}\;( \mbox{\$lesseq}(1,b(z_1))\mbox{ and }\mbox{\$lesseq}(b(z_1),5) )\mbox{ and }\mbox{\$true}\mbox{ and }z_1\ne z_2\mbox{ and }z_1\ne z_3\mbox{ and }z_2\ne z_3\mbox{ and }\forall z_1{:}\;\mbox{\$int},z_2{:}\;\mbox{\$int}{:}\;\neg\,z_1\ne z_2\mbox{ and }a(z_1) = 10\mbox{ and }a(z_2) = 10 ) \ \Rightarrow \ \neg\,a(z_1) = 9\mbox{ and }a(z_2) = 10\mbox{ and }\mbox{\$less}(b(z_2),3)\mbox{ and }\mbox{\$less}(z_2,z_1)\qquad\mbox{tff}(0,\mbox{conjecture})$

\medskip\textbf{SWV525-1.030.p} Store commutativity (t3\_pp\_nf\_ni\_00030)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),\mbox{sk}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})))\ne \mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10}),\mbox{sk}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})))\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV517-1.050.p} Store commutativity (t3\_np\_nf\_ni\_00050)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),n_{31},e_{31}),n_{32},e_{32}),n_{33},e_{33}),n_{34},e_{34}),n_{35},e_{35}),n_{36},e_{36}),n_{37},e_{37}),n_{38},e_{38}),n_{39},e_{39}),n_{40},e_{40}),n_{41},e_{41}),n_{42},e_{42}),n_{43},e_{43}),n_{44},e_{44}),n_{45},e_{45}),n_{46},e_{46}),n_{47},e_{47}),n_{48},e_{48}),n_{49},e_{49}),n_{50},e_{50})\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{41},e_{41}),n_{30},e_{30}),n_{45},e_{45}),n_{43},e_{43}),n_{28},e_{28}),n_{19},e_{19}),n_{22},e_{22}),n_{39},e_{39}),n_{20},e_{20}),n_{40},e_{40}),n_{16},e_{16}),n_8,e_8),n_{49},e_{49}),n_{14},e_{14}),n_{13},e_{13}),n_6,e_6),n_{27},e_{27}),n_{15},e_{15}),n_7,e_7),n_{33},e_{33}),n_9,e_9),n_{17},e_{17}),n_{42},e_{42}),n_{47},e_{47}),n_{18},e_{18}),n_{26},e_{26}),n_{34},e_{34}),n_{11},e_{11}),n_{36},e_{36}),n_{44},e_{44}),n_{38},e_{38}),n_{23},e_{23}),n_{25},e_{25}),n_{46},e_{46}),n_{35},e_{35}),n_{50},e_{50}),n_2,e_2),n_{10},e_{10}),n_{48},e_{48}),n_{29},e_{29}),n_3,e_3),n_{37},e_{37}),n_{12},e_{12}),n_5,e_5),n_{32},e_{32}),n_4,e_4),n_{24},e_{24}),n_{21},e_{21}),n_{31},e_{31}),n_1,e_1)\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV356-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_2,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_2),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV070+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0011

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300}) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300}) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0011},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV410+1.p} Priority queue checker: lemma\_contains\_pair base






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u{:}\;( \mbox{contains\_slb}(\mbox{create\_slb},u) \ \Rightarrow \ \exists v{:}\;\mbox{pair\_in\_list}(\mbox{create\_slb},u,v) )\qquad\mbox{fof}(\mbox{l46\_co},\mbox{conjecture})$

\medskip\textbf{SWV276-2.p} Cryptographic protocol problem for events






$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_nat}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{v\_H}),\mbox{tc\_nat})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_sko\_\_uhi}(\mbox{v\_H},\mbox{v\_K})),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Event\_OkeysFor\_\_synth\_H}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_nat}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{v\_H}),\mbox{tc\_nat})\mbox{ or }\mbox{v\_K} = \mbox{c\_Message\_OinvKey}(\mbox{v\_sko\_\_uhi}(\mbox{v\_H},\mbox{v\_K})) )\qquad\mbox{cnf}(\mbox{cls\_Event\_OkeysFor\_\_synth\_H}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_conj\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_Message\_OinvKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_y})) = \mbox{v\_y}\qquad\mbox{cnf}(\mbox{cls\_Message\_OinvKey\_A\_IinvKey\_Ay\_J\_A\_61\_61\_Ay}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_OkeysFor}(\mbox{v\_G}),\mbox{c\_Message\_OkeysFor}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_nat}))\qquad\mbox{cnf}(\mbox{cls\_Message\_OkeysFor\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_Message\_OkeysFor}(\mbox{c\_union}(\mbox{v\_H},\mbox{v\_H\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_OkeysFor}(\mbox{v\_H}),\mbox{c\_Message\_OkeysFor}(\mbox{v\_H\_H}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Message\_OkeysFor\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_insert\_\_subset\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_Un}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetD}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_2,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

\medskip\textbf{SWV402+1.p} Priority queue checker: tmp\_not\_check\_03\_3 base






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u,v,w,x{:}\;( ( \mbox{pair\_in\_list}(\mbox{create\_slb},v,w)\mbox{ and }\mbox{strictly\_less\_than}(w,x) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(\mbox{create\_slb},x),v,x) )\qquad\mbox{fof}(\mbox{l38\_co},\mbox{conjecture})$

\medskip\textbf{SWV267-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_Oin\_\_parts\_\_UnE}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_idem}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_increasing}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_partsD\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_trans}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV427$\wedge$1.p} ICL logic mapping to modal logic implies 'idem'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) ) )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) ) )\qquad\mbox{thf}(\mbox{idem},\mbox{conjecture})$

\medskip\textbf{SWV327-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{v\_Ba}\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_Ba},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X\_H},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_Ba},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_C})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{v\_B}\ne \mbox{v\_C}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_C})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{v\_B} = \mbox{v\_C}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV357-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{v\_evs}_2,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_Ba},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OGets\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV397+1.p} Priority queue checker: tmp\_not\_check\_02\_3






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w,x{:}\;( \mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) \ \Rightarrow \ \mbox{contains\_slb}(v,x) )\qquad\mbox{fof}(\mbox{l33\_co},\mbox{conjecture})$

\medskip\textbf{SWV310-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_x},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV274-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_OInj}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_trans}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_a},\mbox{c\_insert}(\mbox{v\_b},\mbox{v\_A},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_a},\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{v\_a} = \mbox{v\_b} )\qquad\mbox{cnf}(\mbox{cls\_Set\_OinsertE}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Osynth}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV817-1.p} Hoare logic with procedures 112\_1

Completeness is taken relative to completeness of the underlying
 logic. Two versions of completeness proof: nested single recursion
 and simultaneous recursion in call rule.




$\mbox{c\_Fun\_Oid}(\mbox{v\_x},\mbox{t\_a}) = \mbox{v\_x}\qquad\mbox{cnf}(\mbox{cls\_id\_\_apply}_0,\mbox{axiom})$

$\mbox{c\_Fun\_Oid}(\mbox{v\_x},\mbox{t\_a}) = \mbox{v\_x}\qquad\mbox{cnf}(\mbox{cls\_id\_\_def}_0,\mbox{axiom})$

$\mbox{v\_sko\_\_Hoare\_\_Mirabelle\_\_Xstate\_\_not\_\_singleton\_\_def\_\_raw\_}_1 = \mbox{v\_sko\_\_Hoare\_\_Mirabelle\_\_Xstate\_\_not\_\_singleton\_\_def\_\_raw\_}_2 \ \Rightarrow \ \neg\,\mbox{c\_Hoare\_\_Mirabelle\_Ostate\_\_not\_\_singleton}\qquad\mbox{cnf}(\mbox{cls\_state\_\_not\_\_singleton\_\_def\_\_raw}_0,\mbox{axiom})$

$\mbox{c\_Hoare\_\_Mirabelle\_Ostate\_\_not\_\_singleton}\mbox{ or }\mbox{v\_x} = \mbox{v\_xa}\qquad\mbox{cnf}(\mbox{cls\_state\_\_not\_\_singleton\_\_def}_1,\mbox{axiom})$

$\mbox{v\_sko\_\_Hoare\_\_Mirabelle\_\_Xstate\_\_not\_\_singleton\_\_def\_}_1 = \mbox{v\_sko\_\_Hoare\_\_Mirabelle\_\_Xstate\_\_not\_\_singleton\_\_def\_}_2 \ \Rightarrow \ \neg\,\mbox{c\_Hoare\_\_Mirabelle\_Ostate\_\_not\_\_singleton}\qquad\mbox{cnf}(\mbox{cls\_state\_\_not\_\_singleton\_\_def}_0,\mbox{axiom})$

$\mbox{c\_Hoare\_\_Mirabelle\_Ostate\_\_not\_\_singleton}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{v\_s} = \mbox{v\_x}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV426$\wedge$2.p} ICL logic mapping to modal logic implies 'cuc'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$t{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(t,\mbox{type})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_atom}@ s )@ ( \mbox{icl\_atom}@ t ) ) )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ t ) ) ) )\qquad\mbox{thf}(\mbox{cuc},\mbox{conjecture})$

\medskip\textbf{SWV997=1.p} Fix-point check 20

A problem extracted from model checking a safety problem (no
 violation of mutual exclusion) for a parameterized system (a
 variant of the protocol due to Szymanski).




$z_1{:}\;\mbox{\$int}\qquad\mbox{tff}(\mbox{z1\_type},\mbox{type})$

$z_2{:}\;\mbox{\$int}\qquad\mbox{tff}(\mbox{z2\_type},\mbox{type})$

$z_3{:}\;\mbox{\$int}\qquad\mbox{tff}(\mbox{z3\_type},\mbox{type})$

$z_4{:}\;\mbox{\$int}\qquad\mbox{tff}(\mbox{z4\_type},\mbox{type})$

$a{:}\;\mbox{\$int}\to \mbox{\$int}\qquad\mbox{tff}(\mbox{a\_type},\mbox{type})$

$b{:}\;\mbox{\$int}\to \mbox{\$int}\qquad\mbox{tff}(\mbox{b\_type},\mbox{type})$

$( \forall z_1{:}\;\mbox{\$int}{:}\;( \mbox{\$lesseq}(1,a(z_1))\mbox{ and }\mbox{\$lesseq}(a(z_1),12) )\mbox{ and }\forall z_1{:}\;\mbox{\$int}{:}\;( \mbox{\$lesseq}(1,b(z_1))\mbox{ and }\mbox{\$lesseq}(b(z_1),5) )\mbox{ and }\mbox{\$true}\mbox{ and }z_1\ne z_2\mbox{ and }z_1\ne z_3\mbox{ and }z_1\ne z_4\mbox{ and }z_2\ne z_3\mbox{ and }z_2\ne z_4\mbox{ and }z_3\ne z_4\mbox{ and }\forall z_1{:}\;\mbox{\$int},z_2{:}\;\mbox{\$int}{:}\;\neg\,z_1\ne z_2\mbox{ and }a(z_1) = 10\mbox{ and }a(z_2) = 10\mbox{ and }\forall z_1{:}\;\mbox{\$int},z_2{:}\;\mbox{\$int}{:}\;\neg\,z_1\ne z_2\mbox{ and }a(z_1) = 9\mbox{ and }a(z_2) = 10\mbox{ and }\mbox{\$less}(b(z_2),3)\mbox{ and }\mbox{\$less}(z_2,z_1)\mbox{ and }\forall z_1{:}\;\mbox{\$int},z_2{:}\;\mbox{\$int}{:}\;\neg\,z_1\ne z_2\mbox{ and }a(z_1) = 8\mbox{ and }a(z_2) = 10\mbox{ and }\mbox{\$less}(b(z_2),3)\mbox{ and }\mbox{\$less}(z_2,z_1)\mbox{ and }\forall z_1{:}\;\mbox{\$int},z_2{:}\;\mbox{\$int},z_3{:}\;\mbox{\$int}{:}\;\neg\,z_1\ne z_2\mbox{ and }z_1\ne z_3\mbox{ and }z_2\ne z_3\mbox{ and }a(z_1) = 7\mbox{ and }a(z_2) = 10\mbox{ and }\mbox{\$less}(b(z_2),3)\mbox{ and }b(z_3) = 5\mbox{ and }\mbox{\$less}(z_2,z_1)\mbox{ and }\forall z_1{:}\;\mbox{\$int},z_2{:}\;\mbox{\$int},z_3{:}\;\mbox{\$int}{:}\;\neg\,z_1\ne z_2\mbox{ and }z_1\ne z_3\mbox{ and }z_2\ne z_3\mbox{ and }a(z_1) = 6\mbox{ and }a(z_2) = 10\mbox{ and }\mbox{\$less}(b(z_2),3)\mbox{ and }b(z_3) = 5\mbox{ and }\mbox{\$less}(z_2,z_1)\mbox{ and }\forall z_1{:}\;\mbox{\$int},z_2{:}\;\mbox{\$int},z_3{:}\;\mbox{\$int}{:}\;\neg\,z_1\ne z_2\mbox{ and }z_1\ne z_3\mbox{ and }z_2\ne z_3\mbox{ and }a(z_1) = 7\mbox{ and }a(z_2) = 10\mbox{ and }a(z_3) = 8\mbox{ and }\mbox{\$less}(b(z_2),3)\mbox{ and }\mbox{\$less}(z_2,z_1) ) \ \Rightarrow \ \neg\,a(z_1) = 6\mbox{ and }a(z_2) = 10\mbox{ and }a(z_3) = 1\mbox{ and }\mbox{\$less}(b(z_2),3)\mbox{ and }b(z_3) = 5\mbox{ and }\mbox{\$less}(z_2,z_1)\qquad\mbox{tff}(0,\mbox{conjecture})$

\medskip\textbf{SWV243-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-1.ax'})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_analz\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_Message\_Osynth}(\mbox{v\_H}))\ne \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV561-1.007.p} Store inverse (t3\_np\_sf\_ai\_00007)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{29} = \mbox{store}(a_1,i_1,e_{28})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{31} = \mbox{store}(a_2,i_1,e_{30})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{33} = \mbox{store}(a_{29},i_2,e_{32})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{35} = \mbox{store}(a_{31},i_2,e_{34})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{37} = \mbox{store}(a_{33},i_3,e_{36})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{39} = \mbox{store}(a_{35},i_3,e_{38})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{41} = \mbox{store}(a_{37},i_4,e_{40})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{43} = \mbox{store}(a_{39},i_4,e_{42})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{45} = \mbox{store}(a_{41},i_5,e_{44})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{47} = \mbox{store}(a_{43},i_5,e_{46})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{49} = \mbox{store}(a_{45},i_6,e_{48})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{51} = \mbox{store}(a_{47},i_6,e_{50})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{53} = \mbox{store}(a_{49},i_7,e_{52})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{55} = \mbox{store}(a_{51},i_7,e_{54})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{28} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{30} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{32} = \mbox{select}(a_{31},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{34} = \mbox{select}(a_{29},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{36} = \mbox{select}(a_{35},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{38} = \mbox{select}(a_{33},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{40} = \mbox{select}(a_{39},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{42} = \mbox{select}(a_{37},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{44} = \mbox{select}(a_{43},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{46} = \mbox{select}(a_{41},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{48} = \mbox{select}(a_{47},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{50} = \mbox{select}(a_{45},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{52} = \mbox{select}(a_{51},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{54} = \mbox{select}(a_{49},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$a_{53} = a_{55}\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV345-2.p} Cryptographic protocol problem for Yahalom






$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na\_H},\mbox{v\_nb\_H})))),\mbox{v\_X\_H})),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb})))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{v\_nb} = \mbox{v\_nb\_H}\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_Ounique\_\_session\_\_keys\_\_dest}_3,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb})))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{v\_nb}\ne \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV388+1.p} Priority queue checker: lemma\_not\_min\_elem\_not\_check\_ind\_steps 3






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{check\_cpq}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l24\_l}_{34},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ ( \neg\,\mbox{check\_cpq}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w)))\mbox{ or }\neg\,\mbox{ok}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) ) )\qquad\mbox{fof}(\mbox{l24\_co},\mbox{conjecture})$

\medskip\textbf{SWV917-1.p} Java type soundness 027\_36






$\mbox{v\_v} = \mbox{c\_Option\_Ooption\_OSome}(\mbox{c\_ATP\_\_Linkup\_Osko\_\_Option\_\_Xoption\_\_Xnchotomy\_\_1\_}_1(\mbox{v\_v},\mbox{t\_a}),\mbox{t\_a})\mbox{ or }\mbox{v\_v} = \mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_option\_Onchotomy}_0,\mbox{axiom})$

$\mbox{v\_x} = \mbox{c\_Option\_Ooption\_OSome}(\mbox{c\_ATP\_\_Linkup\_Osko\_\_Option\_\_Xnot\_\_None\_\_eq\_\_1\_}_1(\mbox{v\_x},\mbox{t\_a}),\mbox{t\_a})\mbox{ or }\mbox{v\_x} = \mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_not\_\_None\_\_eq}_0,\mbox{axiom})$

$\mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_a},\mbox{t\_a}) = \mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_a\_H},\mbox{t\_a}) \ \Rightarrow \ \mbox{v\_a} = \mbox{v\_a\_H}\qquad\mbox{cnf}(\mbox{cls\_option\_Oinject}_0,\mbox{axiom})$

$\neg\,\mbox{c\_Option\_Ois\_\_none}(\mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_x},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_is\_\_none\_\_code\_I2\_J}_0,\mbox{axiom})$

$\mbox{v\_x} = \mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\mbox{ or }\mbox{v\_x} = \mbox{c\_Option\_Ooption\_OSome}(\mbox{c\_ATP\_\_Linkup\_Osko\_\_Option\_\_Xnot\_\_Some\_\_eq\_\_1\_}_1(\mbox{v\_x},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_not\_\_Some\_\_eq}_0,\mbox{axiom})$

$\mbox{v\_y} = \mbox{c\_Option\_Ooption\_OSome}(\mbox{c\_ATP\_\_Linkup\_Osko\_\_Option\_\_Xoption\_\_Xexhaust\_\_1\_}_1(\mbox{v\_y},\mbox{t\_a}),\mbox{t\_a})\mbox{ or }\mbox{v\_y} = \mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_option\_Oexhaust}_0,\mbox{axiom})$

$\mbox{c\_Option\_Ois\_\_none}(\mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_is\_\_none\_\_def}_1,\mbox{axiom})$

$\mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_xa},\mbox{t\_a})\ne \mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_not\_\_None\_\_eq}_1,\mbox{axiom})$

$\mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_a\_H},\mbox{t\_a})\ne \mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_option\_Osimps\_I3\_J}_0,\mbox{axiom})$

$\mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\ne \mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_y},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_not\_\_Some\_\_eq}_1,\mbox{axiom})$

$\mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\ne \mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_a\_H},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_option\_Osimps\_I2\_J}_0,\mbox{axiom})$

$\mbox{c\_Option\_Ois\_\_none}(\mbox{v\_x},\mbox{t\_a}) \ \Rightarrow \ \mbox{v\_x} = \mbox{c\_Option\_Ooption\_ONone}(\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_is\_\_none\_\_def}_0,\mbox{axiom})$

$\mbox{c\_Objects\_Onew\_\_Addr}(\mbox{v\_ha\_\_\_\_}) = \mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_a\_\_\_\_},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_CHAINED}_0,\mbox{axiom})$

$\mbox{hAPP}(\mbox{v\_ha\_\_\_\_},\mbox{v\_a\_\_\_\_})\ne \mbox{c\_Option\_Ooption\_ONone}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_fun}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Option\_Ooption}(\mbox{tc\_Value\_Oval}))))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV321-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

\medskip\textbf{SWV259-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_Oin\_\_parts\_\_UnE}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_idem}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_partsD\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV353-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{v\_U} = \mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}) \ \Rightarrow \ \mbox{v\_NA}\ne \mbox{v\_NAa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_k},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb})))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OSays\_\_Server\_\_imp\_\_YM2}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_S\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X\_H},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA\_H}),\mbox{v\_nb}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_C},\mbox{v\_S},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{v\_nb}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_nb},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{v\_NA\_H} = \mbox{v\_NA} )\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OSays\_\_unique\_\_NB}_0,\mbox{axiom})$

\medskip\textbf{SWV381+4.p} Priority queue checker: lemma\_min\_elem\_smallest






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w,x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\iff \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),x) )\qquad\mbox{fof}(\mbox{l17\_li}_{56},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ ( \neg\,\mbox{ok}(\mbox{triple}(x,y,z))\mbox{ or }\neg\,\mbox{check\_cpq}(\mbox{triple}(x,y,z)) ) ) )\qquad\mbox{fof}(\mbox{l18\_l}_{19},\mbox{lemma})$

$\forall u,v,w{:}\;( \exists x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\mbox{ and }\mbox{strictly\_less\_than}(x,\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) ) \ \Rightarrow \ \neg\,\mbox{check\_cpq}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l18\_l}_{43},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \mbox{issmallestelement\_pq}(i(\mbox{triple}(u,v,w)),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l17\_co},\mbox{conjecture})$

\medskip\textbf{SWV435$\wedge$3.p} ICL$\wedge$B logic mapping to modal logic implies 'untrust'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$( \mbox{icl\_princ}@ a ) = \mbox{icl\_true}\qquad\mbox{thf}(\mbox{ax}_1,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ \mbox{icl\_false} )\qquad\mbox{thf}(\mbox{untrust},\mbox{conjecture})$

\medskip\textbf{SWV341-2.p} Cryptographic protocol problem for Yahalom






$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_conj\_\_parts}_0,\mbox{axiom})$

\medskip\textbf{SWV405+1.p} Priority queue checker: lemma\_check\_characterization base






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v{:}\;( \mbox{check\_cpq}(\mbox{triple}(u,\mbox{create\_slb},v))\iff \forall w,x{:}\;( \mbox{pair\_in\_list}(\mbox{create\_slb},w,x) \ \Rightarrow \ x < w ) )\qquad\mbox{fof}(\mbox{l41\_co},\mbox{conjecture})$

\medskip\textbf{SWV087+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0028

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\mbox{geq}(\mbox{pv}_{65},\mbox{tptp\_float\_0}_{001}) \ \Rightarrow \ ( ( \neg\,\mbox{gt}(n_1 + \mbox{loopcounter},n_1) \ \Rightarrow \ \mbox{true} )\mbox{ and }( \mbox{gt}(n_1 + \mbox{loopcounter},n_1) \ \Rightarrow \ \mbox{true} ) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0028},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV417+1.p} Priority queue checker: Formula (9)






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w{:}\;( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \mbox{pi\_sharp\_find\_min}(i(\mbox{triple}(u,v,w)),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{main4\_l}_7,\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{pi\_find\_min}(\mbox{triple}(u,v,w)) \ \Rightarrow \ ( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \exists x{:}\;( \mbox{pi\_sharp\_find\_min}(i(\mbox{triple}(u,v,w)),x)\mbox{ and }\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w)) = \mbox{findmin\_pq\_res}(i(\mbox{triple}(u,v,w)),x) ) ) )\qquad\mbox{fof}(\mbox{co}_4,\mbox{conjecture})$

\medskip\textbf{SWV337-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_U},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_U}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_V}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_W}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_V}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_U}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{v\_X}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Public\_OCrypt\_\_Spy\_\_analz\_\_bad}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb})))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OA\_\_trusts\_\_YM3}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OGets\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV239-2.p} Cryptographic protocol problem for messages






$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_analzD\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\mbox{ and }\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_G\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G\_H},\mbox{v\_H\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_cong}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_1,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_refl}_0,\mbox{axiom})$

\medskip\textbf{SWV284-2.p} Cryptographic protocol problem for shared






$\mbox{c\_lessequals}(\mbox{v\_U},\mbox{v\_x}(\mbox{v\_U}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_list}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_N},\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_x}(\mbox{v\_U})),\mbox{c\_Event\_Oused}(\mbox{v\_list}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_x}(\mbox{v\_U})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_msg},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_msg},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_sko\_\_upX}(\mbox{v\_msg}),\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_\_Nonce\_\_supply}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_k},\mbox{tc\_nat}),\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_k},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oadd\_\_leE}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_k},\mbox{tc\_nat}),\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oadd\_\_leE}_1,\mbox{axiom})$

\medskip\textbf{SWV047+1.p} Unsimplified proof obligation cl5\_nebula\_norm\_0013

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{pv}_{78} = n_0 + -n_{135300}{=}\mbox{a\_select}_3(q,\mbox{pv}_{79},\mbox{pv}_{35})\mbox{ and }\mbox{pv}_{82} = n_0 + -n_{135300}{=}\mbox{times}(-\mbox{a\_select}_2(x,\mbox{pv}_{83}),\mbox{times}(-\mbox{a\_select}_2(x,\mbox{pv}_{83}),\mbox{a\_select}_3(q,\mbox{pv}_{83},\mbox{pv}_{35})))\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{35})\mbox{ and }\mbox{leq}(\mbox{pv}_{35},-n_5) ) \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0013},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV256-2.p} Cryptographic protocol problem for messages






$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_1,\mbox{axiom})$

\medskip\textbf{SWV444$\wedge$1.p} (loca says A) =$>$ (K says A) in BL






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/LCL009\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV010\string^0.ax'})$

$\forall k{:}\;\mbox{individuals},a{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{bl\_valid}@ ( \mbox{bl\_impl}@ ( \mbox{bl\_says}@ \mbox{loca}@ ( \mbox{bl\_atom}@ a ) )@ ( \mbox{bl\_says}@ k@ ( \mbox{bl\_atom}@ a ) ) ) )\qquad\mbox{thf}(\mbox{bl\_strength},\mbox{conjecture})$

\medskip\textbf{SWV534-1.007.p} Swap elements (t1\_np\_sf\_ai\_00007)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{785} = \mbox{store}(a_1,i_4,e_{784})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{787} = \mbox{store}(a_{785},i_3,e_{786})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{789} = \mbox{store}(a_{787},i_2,e_{788})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{791} = \mbox{store}(a_{789},i_1,e_{790})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{793} = \mbox{store}(a_{791},i_0,e_{792})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{795} = \mbox{store}(a_{793},i_5,e_{794})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{797} = \mbox{store}(a_{795},i_2,e_{796})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{799} = \mbox{store}(a_{797},i_5,e_{798})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{801} = \mbox{store}(a_{799},i_1,e_{800})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{802} = \mbox{store}(a_{801},i_1,e_{800})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{804} = \mbox{store}(a_{802},i_5,e_{803})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{806} = \mbox{store}(a_{804},i_2,e_{805})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{808} = \mbox{store}(a_{806},i_5,e_{807})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{810} = \mbox{store}(a_{808},i_2,e_{809})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{811} = \mbox{store}(a_{787},i_1,e_{790})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{812} = \mbox{store}(a_{811},i_2,e_{788})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{814} = \mbox{store}(a_{812},i_5,e_{813})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{816} = \mbox{store}(a_{814},i_0,e_{815})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{818} = \mbox{store}(a_{816},i_5,e_{817})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{820} = \mbox{store}(a_{818},i_2,e_{819})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$a_{822} = \mbox{store}(a_{820},i_1,e_{821})\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$a_{823} = \mbox{store}(a_{822},i_1,e_{821})\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$a_{825} = \mbox{store}(a_{823},i_5,e_{824})\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$a_{827} = \mbox{store}(a_{825},i_2,e_{826})\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$a_{829} = \mbox{store}(a_{827},i_6,e_{828})\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{831} = \mbox{store}(a_{829},i_2,e_{830})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{784} = \mbox{select}(a_1,i_3)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{786} = \mbox{select}(a_1,i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{788} = \mbox{select}(a_{787},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{790} = \mbox{select}(a_{787},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{792} = \mbox{select}(a_{791},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{794} = \mbox{select}(a_{791},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{796} = \mbox{select}(a_{795},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{798} = \mbox{select}(a_{795},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{800} = \mbox{select}(a_{799},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{803} = \mbox{select}(a_{802},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{805} = \mbox{select}(a_{802},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{807} = \mbox{select}(a_{806},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{809} = \mbox{select}(a_{806},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{813} = \mbox{select}(a_{812},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{815} = \mbox{select}(a_{812},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{817} = \mbox{select}(a_{816},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$e_{819} = \mbox{select}(a_{816},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$e_{821} = \mbox{select}(a_{820},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{824} = \mbox{select}(a_{823},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{44},\mbox{hypothesis})$

$e_{826} = \mbox{select}(a_{823},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{45},\mbox{hypothesis})$

$e_{828} = \mbox{select}(a_{827},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{46},\mbox{hypothesis})$

$e_{830} = \mbox{select}(a_{827},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{47},\mbox{hypothesis})$

$a_{810}\ne a_{831}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV247-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OCrypt\_\_synth}_1,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_ODecrypt\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OKey\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnE}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

\medskip\textbf{SWV257-2.p} Cryptographic protocol problem for messages






$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_increasing}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

\medskip\textbf{SWV425$\wedge$2.p} ICL logic mapping to modal logic implies 'unit'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_atom}@ s )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) ) )\qquad\mbox{thf}(\mbox{unit},\mbox{conjecture})$

\medskip\textbf{SWV261-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_Un\_\_subset2}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_a},\mbox{c\_insert}(\mbox{v\_b},\mbox{v\_A},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_a},\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{v\_a} = \mbox{v\_b} )\qquad\mbox{cnf}(\mbox{cls\_Set\_OinsertE}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_1,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_trans}_0,\mbox{axiom})$

\medskip\textbf{SWV556-1.004.p} Store inverse (t1\_pp\_sf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{20} = \mbox{store}(a_1,i_1,e_{19})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{22} = \mbox{store}(a_2,i_1,e_{21})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{24} = \mbox{store}(a_{20},i_2,e_{23})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{26} = \mbox{store}(a_{22},i_2,e_{25})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{28} = \mbox{store}(a_{24},i_3,e_{27})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{30} = \mbox{store}(a_{26},i_3,e_{29})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{32} = \mbox{store}(a_{28},i_1,e_{31})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{34} = \mbox{store}(a_{30},i_4,e_{33})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$e_{19} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$e_{21} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$e_{23} = \mbox{select}(a_{22},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$e_{25} = \mbox{select}(a_{20},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$e_{27} = \mbox{select}(a_{26},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$e_{29} = \mbox{select}(a_{24},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{31} = \mbox{select}(a_{30},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{33} = \mbox{select}(a_{28},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{36} = \mbox{select}(a_1,i_{35})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{37} = \mbox{select}(a_2,i_{35})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$i_{35} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{32} = a_{34}\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{36}\ne e_{37}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV565-1.010.p} Store inverse (t3\_pp\_sf\_ai\_00010)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{44} = \mbox{store}(a_1,i_1,e_{43})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{46} = \mbox{store}(a_2,i_1,e_{45})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{48} = \mbox{store}(a_{44},i_2,e_{47})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{50} = \mbox{store}(a_{46},i_2,e_{49})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{52} = \mbox{store}(a_{48},i_3,e_{51})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{54} = \mbox{store}(a_{50},i_3,e_{53})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{56} = \mbox{store}(a_{52},i_4,e_{55})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{58} = \mbox{store}(a_{54},i_4,e_{57})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{60} = \mbox{store}(a_{56},i_5,e_{59})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{62} = \mbox{store}(a_{58},i_5,e_{61})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{64} = \mbox{store}(a_{60},i_6,e_{63})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{66} = \mbox{store}(a_{62},i_6,e_{65})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{68} = \mbox{store}(a_{64},i_7,e_{67})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{70} = \mbox{store}(a_{66},i_7,e_{69})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{72} = \mbox{store}(a_{68},i_8,e_{71})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{74} = \mbox{store}(a_{70},i_8,e_{73})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{76} = \mbox{store}(a_{72},i_9,e_{75})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{78} = \mbox{store}(a_{74},i_9,e_{77})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{80} = \mbox{store}(a_{76},i_{10},e_{79})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{82} = \mbox{store}(a_{78},i_{10},e_{81})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{43} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{45} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{47} = \mbox{select}(a_{46},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{49} = \mbox{select}(a_{44},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{51} = \mbox{select}(a_{50},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{53} = \mbox{select}(a_{48},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{55} = \mbox{select}(a_{54},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{57} = \mbox{select}(a_{52},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{59} = \mbox{select}(a_{58},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{61} = \mbox{select}(a_{56},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{63} = \mbox{select}(a_{62},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{65} = \mbox{select}(a_{60},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{67} = \mbox{select}(a_{66},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{69} = \mbox{select}(a_{64},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{71} = \mbox{select}(a_{70},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{73} = \mbox{select}(a_{68},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{75} = \mbox{select}(a_{74},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{77} = \mbox{select}(a_{72},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{79} = \mbox{select}(a_{78},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{81} = \mbox{select}(a_{76},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{84} = \mbox{select}(a_1,i_{83})\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{85} = \mbox{select}(a_2,i_{83})\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$i_{83} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$a_{80} = a_{82}\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{84}\ne e_{85}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV406+1.p} Priority queue checker: lemma\_check\_characterization step






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u{:}\;( \forall v,w{:}\;( \mbox{check\_cpq}(\mbox{triple}(v,u,w))\iff \forall x,y{:}\;( \mbox{pair\_in\_list}(u,x,y) \ \Rightarrow \ y < x ) ) \ \Rightarrow \ \forall z,x_1,x_2,x_3{:}\;( \mbox{check\_cpq}(\mbox{triple}(z,\mbox{insert\_slb}(u,\mbox{pair}(x_2,x_3)),x_1))\iff \forall x_4,x_5{:}\;( \mbox{pair\_in\_list}(\mbox{insert\_slb}(u,\mbox{pair}(x_2,x_3)),x_4,x_5) \ \Rightarrow \ x_5 < x_4 ) ) )\qquad\mbox{fof}(\mbox{l42\_co},\mbox{conjecture})$

\medskip\textbf{SWV401+1.p} Priority queue checker: tmp\_not\_check\_03\_2 step






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u{:}\;( \forall v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }x < w ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,w) ) \ \Rightarrow \ \forall y,z,x_1,x_2,x_3{:}\;( ( \mbox{pair\_in\_list}(\mbox{insert\_slb}(u,\mbox{pair}(x_2,x_3)),y,z)\mbox{ and }x_1 < z ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(x_2,x_3)),x_1),y,z) ) )\qquad\mbox{fof}(\mbox{l37\_co},\mbox{conjecture})$

\medskip\textbf{SWV255-2.p} Cryptographic protocol problem for messages






$\mbox{c\_lessequals}(\mbox{v\_U},\mbox{v\_xb}(\mbox{v\_U}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_msg}_1,\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_x},\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_msg}_2,\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_xa},\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_xb}(\mbox{v\_U})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_msg}_2,\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_xb}(\mbox{v\_U})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_msg}_1,\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_k},\mbox{tc\_nat}),\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_k},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oadd\_\_leE}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_k},\mbox{tc\_nat}),\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oadd\_\_leE}_1,\mbox{axiom})$

\medskip\textbf{SWV381+1.p} Priority queue checker: lemma\_min\_elem\_smallest






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w,x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\iff \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),x) )\qquad\mbox{fof}(\mbox{l17\_li}_{56},\mbox{lemma})$

$\forall u,v,w{:}\;( \exists x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\mbox{ and }\mbox{strictly\_less\_than}(x,\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) ) \ \Rightarrow \ \neg\,\mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l17\_l}_{18},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \mbox{issmallestelement\_pq}(i(\mbox{triple}(u,v,w)),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l17\_co},\mbox{conjecture})$

\medskip\textbf{SWV261-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV004-0.ax'})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_Un\_\_subset2}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_synthD\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_trans}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV414+1.p} Priority queue checker: Formula (12)






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u{:}\;i(\mbox{triple}(\mbox{create\_pqp},\mbox{create\_slb},u)) = \mbox{create\_pq}\qquad\mbox{fof}(\mbox{co}_1,\mbox{conjecture})$

\medskip\textbf{SWV349-2.p} Cryptographic protocol problem for Yahalom






$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_k}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV504-1.030.p} Store commutativity (t1\_pp\_nf\_ni\_00030)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_1,e_1),\mbox{sk}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_1,e_1),\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})))\ne \mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10}),\mbox{sk}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_1,e_1),\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})))\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV443$\wedge$1.p} (K says A) =$>$ (K says A) in BL






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/LCL009\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV010\string^0.ax'})$

$\forall k{:}\;\mbox{individuals},a{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{bl\_valid}@ ( \mbox{bl\_impl}@ ( \mbox{bl\_says}@ k@ ( \mbox{bl\_atom}@ a ) )@ ( \mbox{bl\_says}@ k@ ( \mbox{bl\_atom}@ a ) ) ) )\qquad\mbox{thf}(\mbox{bl\_id}_2,\mbox{conjecture})$

\medskip\textbf{SWV328-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-6.ax'})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$( \mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))) = \mbox{v\_X}\mbox{ and }\mbox{v\_B} = \mbox{v\_Ba} ) \ \Rightarrow \ \mbox{v\_A}\ne \mbox{c\_Message\_Oagent\_OSpy}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV342-2.p} Cryptographic protocol problem for Yahalom






$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{v\_nb})))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_analz}_0,\mbox{axiom})$

\medskip\textbf{SWV238+1.p} Visa Security Module (VSM) attack denied

This file models the API of the Visa Security Module (VSM). In
 this version, the command that Visa removed to try to prevent
 Bond's attack has been commented out. So the problem is now to
 prove the attack is not possible.




$\forall u,v{:}\;\mbox{enc}(i(u),\mbox{enc}(u,v)) = v\qquad\mbox{fof}(\mbox{enc\_dec\_cancel},\mbox{axiom})$

$\forall u,v{:}\;\mbox{enc}(u,\mbox{enc}(i(u),v)) = v\qquad\mbox{fof}(\mbox{dec\_enc\_cancel},\mbox{axiom})$

$\forall u{:}\;i(i(u)) = u\qquad\mbox{fof}(\mbox{double\_inverse\_cancel},\mbox{axiom})$

$\forall u{:}\;( p(u) \ \Rightarrow \ p(i(u)) )\qquad\mbox{fof}(\mbox{keys\_are\_symmetric},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{tmk},\mbox{enc}(i(\mbox{enc}(i(\mbox{zcmk}),v)),u))) )\qquad\mbox{fof}(\mbox{key\_translate\_from\_ZCMK\_to\_TMK},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(i(\mbox{enc}(i(\mbox{zcmk}),v)),\mbox{enc}(i(\mbox{tmk}),u))) )\qquad\mbox{fof}(\mbox{key\_translate\_from\_TMK\_to\_ZCMK},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{wk},\mbox{enc}(i(\mbox{tmk}),u))) )\qquad\mbox{fof}(\mbox{receive\_working\_key\_from\_switch},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{tmk}),v),\mbox{enc}(i(\mbox{tmk}),u))) )\qquad\mbox{fof}(\mbox{encrypt\_a\_PIN\_derivation\_key\_under\_a\_TMK},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{tmk}),v),\mbox{enc}(i(\mbox{tc}),u))) )\qquad\mbox{fof}(\mbox{encrypt\_a\_stored\_comms\_key},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{tc}),u),v)) )\qquad\mbox{fof}(\mbox{data\_encrypt},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(i(\mbox{enc}(i(\mbox{tc}),u)),v)) )\qquad\mbox{fof}(\mbox{data\_decrypt},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{wk}),w),\mbox{enc}(i(\mbox{enc}(i(\mbox{tmk}),v)),u))) )\qquad\mbox{fof}(\mbox{data\_translate\_PIN\_from\_local\_to\_interchange\_key},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{wk}),w),\mbox{enc}(i(\mbox{enc}(i(\mbox{wk}),v)),u))) )\qquad\mbox{fof}(\mbox{data\_translate\_between\_interchange\_keys},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(\mbox{enc}(i(\mbox{wk}),v),\mbox{enc}(i(\mbox{lp}),u))) )\qquad\mbox{fof}(\mbox{data\_translate\_PIN\_from\_local\_storage\_to\_interchange\_key},\mbox{axiom})$

$\forall u,v,w{:}\;( ( p(u)\mbox{ and }p(v)\mbox{ and }p(w) ) \ \Rightarrow \ p(\mbox{enc}(u,v)) )\qquad\mbox{fof}(\mbox{attacker\_can\_encrypt},\mbox{axiom})$

$p(\mbox{enc}(\mbox{tmk},\mbox{pp}))\qquad\mbox{fof}(\mbox{intruder\_knows}_1,\mbox{axiom})$

$p(\mbox{enc}(\mbox{wk},w))\qquad\mbox{fof}(\mbox{intruder\_knows}_2,\mbox{axiom})$

$p(\mbox{enc}(w,t_1))\qquad\mbox{fof}(\mbox{intruder\_knows}_3,\mbox{axiom})$

$p(\mbox{enc}(\mbox{lp},t_2))\qquad\mbox{fof}(\mbox{intruder\_knows}_4,\mbox{axiom})$

$p(\mbox{enc}(\mbox{tc},k))\qquad\mbox{fof}(\mbox{intruder\_knows}_5,\mbox{axiom})$

$p(\mbox{kk})\qquad\mbox{fof}(\mbox{intruder\_knows}_6,\mbox{axiom})$

$p(i(\mbox{kk}))\qquad\mbox{fof}(\mbox{intruder\_knows}_7,\mbox{axiom})$

$p(a)\qquad\mbox{fof}(\mbox{intruder\_knows}_8,\mbox{axiom})$

$p(\mbox{enc}(\mbox{pp},a))\qquad\mbox{fof}(\mbox{co}_1,\mbox{conjecture})$

\medskip\textbf{SWV488+3.p} Matrix has no zero on the diagonal






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{real\_zero} ) )\mbox{ and }\forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k,k) = \mbox{real\_one} )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qii},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,i)\mbox{ and }\mbox{int\_leq}(i,n) ) \ \Rightarrow \ ( i = j \ \Rightarrow \ a(i,j)\ne \mbox{real\_zero} ) )\qquad\mbox{fof}(\mbox{uti},\mbox{conjecture})$

\medskip\textbf{SWV338-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Event\_OkeysFor\_\_parts\_\_insert\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_y},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_Message\_OinvKey}(\mbox{v\_y}) = \mbox{v\_y}\qquad\mbox{cnf}(\mbox{cls\_Public\_OinvKey\_\_K}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{v\_y},\mbox{v\_y},\mbox{t\_a}) = \mbox{v\_y}\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_absorb}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV004-1.p} E3






$\mbox{include}(\mbox{'Axioms/SWV001-0.ax'})$

$\neg\,n < j\qquad\mbox{cnf}(\mbox{clause}_1,\mbox{negated\_conjecture})$

$k < j\qquad\mbox{cnf}(\mbox{clause}_{23},\mbox{negated\_conjecture})$

$\neg\,k < i\qquad\mbox{cnf}(\mbox{clause}_4,\mbox{negated\_conjecture})$

$i < n\qquad\mbox{cnf}(\mbox{clause}_5,\mbox{negated\_conjecture})$

$a(j) < a(k)\qquad\mbox{cnf}(\mbox{clause}_6,\mbox{negated\_conjecture})$

$a(q) < a(k)\qquad\mbox{cnf}(\mbox{clause}_7,\mbox{negated\_conjecture})$

$( x < j\mbox{ and }a(x) < a(k) ) \ \Rightarrow \ x < i\qquad\mbox{cnf}(\mbox{clause}_8,\mbox{negated\_conjecture})$

$( 1 < i\mbox{ and }a(x) < a(\mbox{predecessor}(i)) ) \ \Rightarrow \ ( x < i\mbox{ or }n < x )\qquad\mbox{cnf}(\mbox{clause}_9,\mbox{negated\_conjecture})$

$( 1 < x\mbox{ and }x < i ) \ \Rightarrow \ \neg\,a(x) < a(\mbox{predecessor}(x))\qquad\mbox{cnf}(\mbox{clause}_{10},\mbox{negated\_conjecture})$

$\neg\,q < i\qquad\mbox{cnf}(\mbox{clause}_{11},\mbox{negated\_conjecture})$

$\neg\,j < q\qquad\mbox{cnf}(\mbox{clause}_{12},\mbox{negated\_conjecture})$

\medskip\textbf{SWV245-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_synth}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnE}_0,\mbox{axiom})$

\medskip\textbf{SWV148+1.p} Simplified proof obligation gauss\_array\_0018

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\neg\,\mbox{leq}(\mbox{tptp\_float\_0}_{001},\mbox{tptp\_float\_0}_{001}) \ \Rightarrow \ \mbox{leq}(\mbox{s\_best}_7,n_3)\qquad\mbox{fof}(\mbox{gauss\_array}_{0018},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV390+1.p} Priority queue checker: tmp\_not\_check\_01






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \mbox{check\_cpq}(\mbox{triple}(u,v,w))\iff \forall x,y{:}\;( \mbox{pair\_in\_list}(v,x,y) \ \Rightarrow \ y < x ) )\qquad\mbox{fof}(\mbox{l26\_li}_{4142},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \forall x{:}\;\neg\,\mbox{check\_cpq}(\mbox{insert\_cpq}(\mbox{triple}(u,v,w),x)) )\qquad\mbox{fof}(\mbox{l26\_co},\mbox{conjecture})$

\medskip\textbf{SWV306-2.p} Cryptographic protocol problem for Otway Rees






$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_1),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{v\_NA} = \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_1)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV492+1.p} Matrix is lower-triangular and invertible






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{qr}(k + c,k) ) )\mbox{ and }\forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k,k) = \mbox{real\_one} )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qih},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\mbox{ and }\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(j,n)\mbox{ and }i = j ) \ \Rightarrow \ a(i,j)\ne \mbox{real\_zero} )\qquad\mbox{fof}(\mbox{lti},\mbox{conjecture})$

\medskip\textbf{SWV265-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OSnd}_0,\mbox{axiom})$

\medskip\textbf{SWV002-1.p} E1






$\mbox{include}(\mbox{'Axioms/SWV001-0.ax'})$

$\neg\,n < j\qquad\mbox{cnf}(\mbox{clause}_1,\mbox{negated\_conjecture})$

$k < j\qquad\mbox{cnf}(\mbox{clause}_2,\mbox{negated\_conjecture})$

$\neg\,k < i\qquad\mbox{cnf}(\mbox{clause}_3,\mbox{negated\_conjecture})$

$i < n\qquad\mbox{cnf}(\mbox{clause}_4,\mbox{negated\_conjecture})$

$a(j) < a(k)\qquad\mbox{cnf}(\mbox{clause}_5,\mbox{negated\_conjecture})$

$( x < j\mbox{ and }a(x) < a(k) ) \ \Rightarrow \ x < i\qquad\mbox{cnf}(\mbox{clause}_6,\mbox{negated\_conjecture})$

$( 1 < i\mbox{ and }a(x) < a(\mbox{predecessor}(i)) ) \ \Rightarrow \ ( x < i\mbox{ or }n < x )\qquad\mbox{cnf}(\mbox{clause}_7,\mbox{negated\_conjecture})$

$( 1 < x\mbox{ and }x < i ) \ \Rightarrow \ \neg\,a(x) < a(\mbox{predecessor}(x))\qquad\mbox{cnf}(\mbox{clause}_8,\mbox{negated\_conjecture})$

$\neg\,q < i\qquad\mbox{cnf}(\mbox{clause}_9,\mbox{negated\_conjecture})$

$\neg\,j < q\qquad\mbox{cnf}(\mbox{clause}_{10},\mbox{negated\_conjecture})$

$a(q) < a(j)\qquad\mbox{cnf}(\mbox{clause}_{11},\mbox{negated\_conjecture})$

\medskip\textbf{SWV548-1.007.p} Swap elements (t3\_pp\_sf\_ai\_00007)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{836} = \mbox{store}(a_1,i_4,e_{835})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{838} = \mbox{store}(a_{836},i_3,e_{837})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{840} = \mbox{store}(a_{838},i_2,e_{839})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{842} = \mbox{store}(a_{840},i_1,e_{841})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{844} = \mbox{store}(a_{842},i_0,e_{843})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{846} = \mbox{store}(a_{844},i_5,e_{845})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{848} = \mbox{store}(a_{846},i_2,e_{847})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{850} = \mbox{store}(a_{848},i_5,e_{849})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{852} = \mbox{store}(a_{850},i_1,e_{851})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{853} = \mbox{store}(a_{852},i_1,e_{851})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{855} = \mbox{store}(a_{853},i_5,e_{854})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{857} = \mbox{store}(a_{855},i_2,e_{856})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{859} = \mbox{store}(a_{857},i_5,e_{858})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{861} = \mbox{store}(a_{859},i_2,e_{860})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{862} = \mbox{store}(a_{838},i_1,e_{841})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{863} = \mbox{store}(a_{862},i_2,e_{839})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{865} = \mbox{store}(a_{863},i_5,e_{864})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{867} = \mbox{store}(a_{865},i_0,e_{866})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{869} = \mbox{store}(a_{867},i_5,e_{868})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{871} = \mbox{store}(a_{869},i_2,e_{870})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$a_{873} = \mbox{store}(a_{871},i_1,e_{872})\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$a_{874} = \mbox{store}(a_{873},i_1,e_{872})\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$a_{876} = \mbox{store}(a_{874},i_5,e_{875})\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$a_{878} = \mbox{store}(a_{876},i_2,e_{877})\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$a_{880} = \mbox{store}(a_{878},i_6,e_{879})\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{882} = \mbox{store}(a_{880},i_2,e_{881})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{835} = \mbox{select}(a_1,i_3)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{837} = \mbox{select}(a_1,i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{839} = \mbox{select}(a_{838},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{841} = \mbox{select}(a_{838},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{843} = \mbox{select}(a_{842},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{845} = \mbox{select}(a_{842},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{847} = \mbox{select}(a_{846},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{849} = \mbox{select}(a_{846},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{851} = \mbox{select}(a_{850},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{854} = \mbox{select}(a_{853},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{856} = \mbox{select}(a_{853},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{858} = \mbox{select}(a_{857},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{860} = \mbox{select}(a_{857},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{864} = \mbox{select}(a_{863},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{866} = \mbox{select}(a_{863},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{868} = \mbox{select}(a_{867},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$e_{870} = \mbox{select}(a_{867},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$e_{872} = \mbox{select}(a_{871},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{875} = \mbox{select}(a_{874},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{44},\mbox{hypothesis})$

$e_{877} = \mbox{select}(a_{874},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{45},\mbox{hypothesis})$

$e_{879} = \mbox{select}(a_{878},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{46},\mbox{hypothesis})$

$e_{881} = \mbox{select}(a_{878},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{47},\mbox{hypothesis})$

$e_{884} = \mbox{select}(a_{861},i_{883})\qquad\mbox{cnf}(\mbox{hyp}_{48},\mbox{hypothesis})$

$e_{885} = \mbox{select}(a_{882},i_{883})\qquad\mbox{cnf}(\mbox{hyp}_{49},\mbox{hypothesis})$

$i_{883} = \mbox{sk}(a_{861},a_{882})\qquad\mbox{cnf}(\mbox{hyp}_{50},\mbox{hypothesis})$

$e_{884}\ne e_{885}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV082+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0023

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{58})\mbox{ and }\mbox{leq}(\mbox{pv}_{58},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{58})\mbox{ and }\mbox{leq}(\mbox{pv}_{58},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0023},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV547-1.004.p} Swap elements (t3\_pp\_sf\_ai\_00004)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{466} = \mbox{store}(a_1,i_1,e_{465})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{467} = \mbox{store}(a_{466},i_1,e_{465})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{469} = \mbox{store}(a_{467},i_0,e_{468})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{471} = \mbox{store}(a_{469},i_3,e_{470})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{473} = \mbox{store}(a_{471},i_3,e_{472})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{475} = \mbox{store}(a_{473},i_2,e_{474})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{477} = \mbox{store}(a_{475},i_2,e_{476})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{479} = \mbox{store}(a_{477},i_0,e_{478})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{480} = \mbox{store}(a_{467},i_3,e_{470})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{481} = \mbox{store}(a_{480},i_0,e_{468})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{483} = \mbox{store}(a_{481},i_3,e_{482})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{485} = \mbox{store}(a_{483},i_2,e_{484})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{487} = \mbox{store}(a_{485},i_0,e_{486})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{489} = \mbox{store}(a_{487},i_2,e_{488})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{465} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{468} = \mbox{select}(a_{467},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{470} = \mbox{select}(a_{467},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{472} = \mbox{select}(a_{471},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{474} = \mbox{select}(a_{471},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{476} = \mbox{select}(a_{475},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{478} = \mbox{select}(a_{475},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{482} = \mbox{select}(a_{481},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{484} = \mbox{select}(a_{481},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{486} = \mbox{select}(a_{485},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{488} = \mbox{select}(a_{485},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{491} = \mbox{select}(a_{479},i_{490})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{492} = \mbox{select}(a_{489},i_{490})\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$i_{490} = \mbox{sk}(a_{479},a_{489})\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{491}\ne e_{492}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV450+1.p} Establishing that there cannot be two leaders, part i26\_p36






$\mbox{include}(\mbox{'Axioms/SWV011+0.ax'})$

$\forall v,w,x,y{:}\;( ( \forall z,\mbox{pid}_0{:}\;( \mbox{setIn}(\mbox{pid}_0,\mbox{alive}) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \mbox{host}(\mbox{pid}_0)\ne \mbox{host}(z) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Halt}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_{20},\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Ack}(\mbox{pid}_0,z),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{leq}(\mbox{pid}_0,z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \mbox{pid}_0\ne z\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ or }\neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) ) )\mbox{ and }\forall z,\mbox{pid}_{30},\mbox{pid}_{20},\mbox{pid}_0{:}\;( ( \mbox{host}(\mbox{pid}_{20})\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(\mbox{pid}_{20},\mbox{alive})\mbox{ and }\mbox{host}(\mbox{pid}_{30}) = \mbox{host}(z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(\mbox{pid}_{20}) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z)))\mbox{ and }\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_{30}),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) )\mbox{ and }\mbox{queue}(\mbox{host}(x)) = \mbox{cons}(\mbox{m\_Ack}(w,y),v) ) \ \Rightarrow \ ( \mbox{setIn}(x,\mbox{alive}) \ \Rightarrow \ ( ( \mbox{index}(\mbox{elid},\mbox{host}(x)) = w\mbox{ and }\mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{elec}_2\mbox{ and }\mbox{host}(y) = \mbox{index}(\mbox{pendack},\mbox{host}(x)) ) \ \Rightarrow \ ( \mbox{leq}(\mbox{nbr\_proc},\mbox{index}(\mbox{pendack},\mbox{host}(x))) \ \Rightarrow \ \forall z{:}\;( ( \mbox{setIn}(\mbox{host}(z),\mbox{index}(\mbox{acks},\mbox{host}(x)))\mbox{ or }\mbox{host}(z) = \mbox{host}(y) ) \ \Rightarrow \ \forall v_0{:}\;( \mbox{host}(z)\ne \mbox{host}(v_0) \ \Rightarrow \ ( \mbox{host}(x) = \mbox{host}(v_0) \ \Rightarrow \ \forall w_0,x_0{:}\;( \mbox{host}(z) = \mbox{host}(x_0) \ \Rightarrow \ ( \mbox{host}(x)\ne \mbox{host}(x_0) \ \Rightarrow \ \forall y_0{:}\;( ( \mbox{host}(x_0)\ne \mbox{host}(v_0)\mbox{ and }\mbox{setIn}(v_0,\mbox{alive})\mbox{ and }\mbox{setIn}(x_0,\mbox{alive})\mbox{ and }\mbox{host}(w_0) = \mbox{host}(v_0)\mbox{ and }\mbox{host}(y_0) = \mbox{host}(x_0) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(y_0),v)\mbox{ and }\mbox{elem}(\mbox{m\_Down}(w_0),\mbox{snoc}(\mbox{queue}(\mbox{host}(x_0)),\mbox{m\_Ldr}(x))) ) ) ) ) ) ) ) ) ) )\qquad\mbox{fof}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV517-1.030.p} Store commutativity (t3\_np\_nf\_ni\_00030)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30})\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV247-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV004-0.ax'})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_synthD\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_least}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

\medskip\textbf{SWV368+1.p} Priority queue checker: lemma\_contains\_s\_I\_remove induction






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w,x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\iff \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),x) )\qquad\mbox{fof}(\mbox{l3\_li}_{56},\mbox{lemma})$

$\forall u{:}\;( \forall v,w,x{:}\;( \mbox{contains\_pq}(i(\mbox{triple}(v,u,w)),x) \ \Rightarrow \ i(\mbox{remove\_cpq}(\mbox{triple}(v,u,w),x)) = \mbox{remove\_pq}(i(\mbox{triple}(v,u,w)),x) ) \ \Rightarrow \ \forall y,z,x_1,x_2,x_3{:}\;( \mbox{contains\_pq}(i(\mbox{triple}(y,\mbox{insert\_slb}(u,\mbox{pair}(x_2,x_3)),z)),x_1) \ \Rightarrow \ i(\mbox{remove\_cpq}(\mbox{triple}(y,\mbox{insert\_slb}(u,\mbox{pair}(x_2,x_3)),z),x_1)) = \mbox{remove\_pq}(i(\mbox{triple}(y,\mbox{insert\_slb}(u,\mbox{pair}(x_2,x_3)),z)),x_1) ) )\qquad\mbox{fof}(\mbox{l4\_co},\mbox{conjecture})$

\medskip\textbf{SWV022+1.p} Unsimplified proof obligation gauss\_init\_0001

Proof obligation emerging from the init-safety verification for
 the gauss program. init-safety ensures that each variable or
 individual array element has been assigned a defined value before
 it is used.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\mbox{init} = \mbox{init}\qquad\mbox{fof}(\mbox{gauss\_init}_{0001},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV269-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-1.ax'})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_increasing}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV314-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_Osecrecy\_\_lemma\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV495-1.030.p} Store commutativity (t1\_np\_nf\_ni\_00030)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30})\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV455+1.p} Establishing that there cannot be two leaders, part i26\_p257






$\mbox{include}(\mbox{'Axioms/SWV011+0.ax'})$

$\forall v,w,x,y{:}\;( ( \forall z,\mbox{pid}_0{:}\;( \mbox{setIn}(\mbox{pid}_0,\mbox{alive}) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \mbox{host}(\mbox{pid}_0)\ne \mbox{host}(z) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Halt}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_{20},\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Ack}(\mbox{pid}_0,z),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{leq}(\mbox{pid}_0,z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \mbox{pid}_0\ne z\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ or }\neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) ) )\mbox{ and }\forall z,\mbox{pid}_{30},\mbox{pid}_{20},\mbox{pid}_0{:}\;( ( \mbox{host}(\mbox{pid}_{20})\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(\mbox{pid}_{20},\mbox{alive})\mbox{ and }\mbox{host}(\mbox{pid}_{30}) = \mbox{host}(z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(\mbox{pid}_{20}) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z)))\mbox{ and }\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_{30}),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) )\mbox{ and }\mbox{queue}(\mbox{host}(x)) = \mbox{cons}(\mbox{m\_Down}(y),v) ) \ \Rightarrow \ ( \mbox{setIn}(x,\mbox{alive}) \ \Rightarrow \ ( \neg\,\mbox{leq}(\mbox{host}(x),\mbox{host}(y)) \ \Rightarrow \ ( \neg\,( \mbox{index}(\mbox{ldr},\mbox{host}(x)) = \mbox{host}(y)\mbox{ and }\mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{norm} )\mbox{ or }( \mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{wait}\mbox{ and }\mbox{host}(y) = \mbox{host}(\mbox{index}(\mbox{elid},\mbox{host}(x))) ) \ \Rightarrow \ ( \neg\,\forall z{:}\;( ( \neg\,\mbox{leq}(\mbox{host}(x),z)\mbox{ and }\mbox{leq}(s(0),z) ) \ \Rightarrow \ ( \mbox{setIn}(z,\mbox{index}(\mbox{down},\mbox{host}(x)))\mbox{ or }z = \mbox{host}(y) ) )\mbox{ and }\mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{elec}_1 \ \Rightarrow \ \forall z{:}\;( \mbox{host}(x)\ne \mbox{host}(z) \ \Rightarrow \ \forall w_0,x_0{:}\;( \mbox{host}(x) = \mbox{host}(x_0) \ \Rightarrow \ \forall y_0{:}\;( ( \mbox{host}(x_0)\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(x_0,\mbox{alive})\mbox{ and }\mbox{host}(w_0) = \mbox{host}(z)\mbox{ and }\mbox{host}(y_0) = \mbox{host}(x_0) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(w_0),v)\mbox{ and }\mbox{elem}(\mbox{m\_Down}(y_0),\mbox{queue}(\mbox{host}(z))) ) ) ) ) ) ) ) )\qquad\mbox{fof}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV454+1.p} Establishing that there cannot be two leaders, part i26\_p250






$\mbox{include}(\mbox{'Axioms/SWV011+0.ax'})$

$\forall v,w,x,y{:}\;( ( \forall z,\mbox{pid}_0{:}\;( \mbox{setIn}(\mbox{pid}_0,\mbox{alive}) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \mbox{host}(\mbox{pid}_0)\ne \mbox{host}(z) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Halt}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_{20},\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Ack}(\mbox{pid}_0,z),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{leq}(\mbox{pid}_0,z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \mbox{pid}_0\ne z\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ or }\neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) ) )\mbox{ and }\forall z,\mbox{pid}_{30},\mbox{pid}_{20},\mbox{pid}_0{:}\;( ( \mbox{host}(\mbox{pid}_{20})\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(\mbox{pid}_{20},\mbox{alive})\mbox{ and }\mbox{host}(\mbox{pid}_{30}) = \mbox{host}(z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(\mbox{pid}_{20}) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z)))\mbox{ and }\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_{30}),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) )\mbox{ and }\mbox{queue}(\mbox{host}(x)) = \mbox{cons}(\mbox{m\_Down}(y),v) ) \ \Rightarrow \ ( \mbox{setIn}(x,\mbox{alive}) \ \Rightarrow \ ( \neg\,\mbox{leq}(\mbox{host}(x),\mbox{host}(y)) \ \Rightarrow \ ( \neg\,( \mbox{index}(\mbox{ldr},\mbox{host}(x)) = \mbox{host}(y)\mbox{ and }\mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{norm} )\mbox{ or }( \mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{wait}\mbox{ and }\mbox{host}(y) = \mbox{host}(\mbox{index}(\mbox{elid},\mbox{host}(x))) ) \ \Rightarrow \ ( ( \forall z{:}\;( ( \neg\,\mbox{leq}(\mbox{host}(x),z)\mbox{ and }\mbox{leq}(s(0),z) ) \ \Rightarrow \ ( \mbox{setIn}(z,\mbox{index}(\mbox{down},\mbox{host}(x)))\mbox{ or }z = \mbox{host}(y) ) )\mbox{ and }\mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{elec}_1 ) \ \Rightarrow \ ( \neg\,\mbox{leq}(\mbox{nbr\_proc},\mbox{host}(x)) \ \Rightarrow \ \forall z{:}\;( s(\mbox{host}(x))\ne \mbox{host}(z) \ \Rightarrow \ ( \mbox{host}(x) = \mbox{host}(z) \ \Rightarrow \ \forall w_0,x_0{:}\;( s(\mbox{host}(x))\ne \mbox{host}(x_0) \ \Rightarrow \ ( \mbox{host}(x)\ne \mbox{host}(x_0) \ \Rightarrow \ \forall y_0{:}\;( ( \mbox{host}(x_0)\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(x_0,\mbox{alive})\mbox{ and }\mbox{host}(w_0) = \mbox{host}(z)\mbox{ and }\mbox{host}(y_0) = \mbox{host}(x_0) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(y_0),v)\mbox{ and }\mbox{elem}(\mbox{m\_Down}(w_0),\mbox{queue}(\mbox{host}(x_0))) ) ) ) ) ) ) ) ) ) ) )\qquad\mbox{fof}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV351-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$( \mbox{v\_U} = \mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})\mbox{ and }\mbox{v\_NA} = \mbox{v\_NAa} ) \ \Rightarrow \ \mbox{v\_NB}\ne \mbox{v\_NBa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{10},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_k}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_insert}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV495-1.040.p} Store commutativity (t1\_np\_nf\_ni\_00040)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),n_{31},e_{31}),n_{32},e_{32}),n_{33},e_{33}),n_{34},e_{34}),n_{35},e_{35}),n_{36},e_{36}),n_{37},e_{37}),n_{38},e_{38}),n_{39},e_{39}),n_{40},e_{40})\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{16},e_{16}),n_{14},e_{14}),n_{24},e_{24}),n_{11},e_{11}),n_{25},e_{25}),n_{17},e_{17}),n_7,e_7),n_{32},e_{32}),n_6,e_6),n_{18},e_{18}),n_{37},e_{37}),n_{31},e_{31}),n_{13},e_{13}),n_{12},e_{12}),n_{36},e_{36}),n_{20},e_{20}),n_{35},e_{35}),n_{23},e_{23}),n_{26},e_{26}),n_{21},e_{21}),n_{27},e_{27}),n_{10},e_{10}),n_{22},e_{22}),n_8,e_8),n_{33},e_{33}),n_2,e_2),n_{40},e_{40}),n_{38},e_{38}),n_{39},e_{39}),n_1,e_1),n_9,e_9),n_3,e_3),n_5,e_5),n_4,e_4),n_{30},e_{30}),n_{15},e_{15}),n_{34},e_{34}),n_{28},e_{28}),n_{29},e_{29}),n_{19},e_{19})\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV248-2.p} Cryptographic protocol problem for messages






$\neg\,\mbox{c\_lessequals}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_OInj}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnCI}_1,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_least}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_1,\mbox{axiom})$

\medskip\textbf{SWV398+1.p} Priority queue checker: tmp\_not\_check\_03






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \mbox{check\_cpq}(\mbox{triple}(u,v,w))\iff \forall x,y{:}\;( \mbox{pair\_in\_list}(v,x,y) \ \Rightarrow \ y < x ) )\qquad\mbox{fof}(\mbox{l26\_li}_{4142},\mbox{lemma})$

$\forall u{:}\;( \exists v,w{:}\;( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(v,w) ) \ \Rightarrow \ \forall x{:}\;\exists y,z{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),y,z)\mbox{ and }\mbox{strictly\_less\_than}(y,z) ) )\qquad\mbox{fof}(\mbox{l34\_l}_{35},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{check\_cpq}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l24\_co},\mbox{conjecture})$

\medskip\textbf{SWV428$\wedge$2.p} ICL logic mapping to modal logic S4 implies 'Ex1'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$\mbox{admin}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{admin},\mbox{type})$

$\mbox{bob}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bob},\mbox{type})$

$\mbox{deletefile}_1{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{deletfile}_1,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_1,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) ) )\qquad\mbox{thf}(\mbox{ax}_2,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_3,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 )\qquad\mbox{thf}(\mbox{ex}_1,\mbox{conjecture})$

\medskip\textbf{SWV315-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OKey\_\_synth\_\_eq}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_conj\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Public\_OSpy\_\_spies\_\_bad\_\_shrK}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_a},\mbox{v\_A},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_a},\mbox{c\_insert}(\mbox{v\_b},\mbox{v\_A},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_iff}_2,\mbox{axiom})$

\medskip\textbf{SWV075+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0016

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{37})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5)\mbox{ and }\mbox{leq}(\mbox{pv}_{37},-n_{135300}) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{37})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5)\mbox{ and }\mbox{leq}(\mbox{pv}_{37},-n_{135300}) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0016},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV234+2.p} 4758 typecast attack

Mike Bond's version of a model for the 4758 typecast attack.




$\forall u,v{:}\;( ( \mbox{public}(u)\mbox{ and }\mbox{public}(v) ) \ \Rightarrow \ \mbox{public}(\mbox{xor}(u,v)) )\qquad\mbox{fof}(\mbox{ability\_to\_xor},\mbox{axiom})$

$\forall u{:}\;( \mbox{public}(u) \ \Rightarrow \ \mbox{public}(\mbox{kp}(u)) )\qquad\mbox{fof}(\mbox{kp\_set},\mbox{axiom})$

$\forall u,v{:}\;( ( \mbox{public}(u)\mbox{ and }\mbox{public}(v) ) \ \Rightarrow \ \mbox{public}(\mbox{enc}(u,v)) )\qquad\mbox{fof}(\mbox{ability\_to\_encrypt},\mbox{axiom})$

$\forall u,v{:}\;( ( \mbox{public}(u)\mbox{ and }\mbox{public}(v) ) \ \Rightarrow \ \mbox{public}(\mbox{enc}(u^{-1},v)) )\qquad\mbox{fof}(\mbox{ability\_to\_decrypt},\mbox{axiom})$

$\forall u,v{:}\;( ( \mbox{public}(u)\mbox{ and }\mbox{public}(v) ) \ \Rightarrow \ \mbox{public}(\mbox{enc}(\mbox{enc}(\mbox{xor}(\mbox{data},\mbox{km})^{-1},u),v)) )\qquad\mbox{fof}(\mbox{encrypt\_data\_cmd},\mbox{axiom})$

$\forall u,v,w{:}\;( ( \mbox{public}(v)\mbox{ and }\mbox{public}(\mbox{enc}(\mbox{xor}(u,v),w))\mbox{ and }\mbox{public}(\mbox{enc}(\mbox{xor}(\mbox{km},\mbox{imp}),u)) ) \ \Rightarrow \ \mbox{public}(\mbox{enc}(\mbox{xor}(\mbox{km},v),w)) )\qquad\mbox{fof}(\mbox{key\_import\_cmd},\mbox{axiom})$

$\forall u,v,w{:}\;( ( \mbox{public}(\mbox{kp}(v))\mbox{ and }\mbox{public}(w)\mbox{ and }\mbox{public}(\mbox{enc}(\mbox{xor}(\mbox{km},\mbox{kp}(v)),u)) ) \ \Rightarrow \ \mbox{public}(\mbox{enc}(\mbox{xor}(\mbox{km},v),\mbox{xor}(u,w))) )\qquad\mbox{fof}(\mbox{key\_part\_import\_cmd},\mbox{axiom})$

$\forall u,v,w{:}\;\mbox{enc}(u,\mbox{enc}(u^{-1},v)) = v\qquad\mbox{fof}(\mbox{encrypt\_decrypt\_cancel},\mbox{axiom})$

$\forall u,v,w{:}\;\mbox{xor}(u,v) = \mbox{xor}(v,u)\qquad\mbox{fof}(\mbox{xor\_commutes},\mbox{axiom})$

$\forall u,v,w{:}\;\mbox{xor}(u,\mbox{xor}(v,w)) = \mbox{xor}(\mbox{xor}(u,v),w)\qquad\mbox{fof}(\mbox{xor\_assosciative},\mbox{axiom})$

$\forall u,v,w{:}\;\mbox{xor}(u,u) = z\qquad\mbox{fof}(\mbox{xor\_self\_cancel},\mbox{axiom})$

$\forall u,v,w{:}\;\mbox{xor}(u,z) = u\qquad\mbox{fof}(\mbox{xor\_zero},\mbox{axiom})$

$\mbox{public}(\mbox{imp})\qquad\mbox{fof}(\mbox{initial\_knowledge}_1,\mbox{axiom})$

$\mbox{public}(\mbox{data})\qquad\mbox{fof}(\mbox{initial\_knowledge}_2,\mbox{axiom})$

$\mbox{public}(z)\qquad\mbox{fof}(\mbox{initial\_knowledge}_3,\mbox{axiom})$

$\mbox{public}(\mbox{pin})\qquad\mbox{fof}(\mbox{initial\_knowledge}_4,\mbox{axiom})$

$\mbox{public}(\mbox{enc}(\mbox{xor}(\mbox{kek},\mbox{pin}),\mbox{pp}))\qquad\mbox{fof}(\mbox{initial\_knowledge}_5,\mbox{axiom})$

$\mbox{public}(k_3)\qquad\mbox{fof}(\mbox{initial\_knowledge}_6,\mbox{axiom})$

$\mbox{public}(\mbox{enc}(\mbox{xor}(\mbox{km},\mbox{kp}(\mbox{imp})),\mbox{xor}(\mbox{kek},k_3)))\qquad\mbox{fof}(\mbox{initial\_knowledge}_7,\mbox{axiom})$

$\mbox{public}(a)\qquad\mbox{fof}(\mbox{initial\_knowledge}_8,\mbox{axiom})$

$\mbox{public}(\mbox{enc}(\mbox{xor}(\mbox{km},\mbox{imp}),\mbox{xor}(\mbox{kek},\mbox{xor}(\mbox{pin},\mbox{data}))))\qquad\mbox{fof}(\mbox{initial\_knowledge}_9,\mbox{axiom})$

$\mbox{public}(\mbox{enc}(\mbox{pp},a))\qquad\mbox{fof}(\mbox{co}_1,\mbox{conjecture})$

\medskip\textbf{SWV555-1.004.p} Store inverse (t1\_pp\_sf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{20} = \mbox{store}(a_1,i_1,e_{19})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{22} = \mbox{store}(a_2,i_1,e_{21})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{24} = \mbox{store}(a_{20},i_2,e_{23})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{26} = \mbox{store}(a_{22},i_2,e_{25})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{28} = \mbox{store}(a_{24},i_3,e_{27})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{30} = \mbox{store}(a_{26},i_3,e_{29})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{32} = \mbox{store}(a_{28},i_4,e_{31})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{34} = \mbox{store}(a_{30},i_4,e_{33})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$e_{19} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$e_{21} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$e_{23} = \mbox{select}(a_{22},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$e_{25} = \mbox{select}(a_{20},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$e_{27} = \mbox{select}(a_{26},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$e_{29} = \mbox{select}(a_{24},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{31} = \mbox{select}(a_{30},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{33} = \mbox{select}(a_{28},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{36} = \mbox{select}(a_1,i_{35})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{37} = \mbox{select}(a_2,i_{35})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$i_{35} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{32} = a_{34}\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{36}\ne e_{37}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV431$\wedge$1.p} ICL$\wedge$=$>$ logic mapping to modal logic implies 'speaking\_for'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^2.ax'})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$b{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(b,\mbox{type})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ b ) )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ b )@ ( \mbox{icl\_atom}@ s ) ) ) )\qquad\mbox{thf}(\mbox{speaking\_for},\mbox{conjecture})$

\medskip\textbf{SWV551-1.010.p} Store inverse (t1\_np\_sf\_ai\_00010)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{41} = \mbox{store}(a_1,i_1,e_{40})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{43} = \mbox{store}(a_2,i_1,e_{42})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{45} = \mbox{store}(a_{41},i_2,e_{44})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{47} = \mbox{store}(a_{43},i_2,e_{46})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{49} = \mbox{store}(a_{45},i_3,e_{48})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{51} = \mbox{store}(a_{47},i_3,e_{50})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{53} = \mbox{store}(a_{49},i_4,e_{52})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{55} = \mbox{store}(a_{51},i_4,e_{54})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{57} = \mbox{store}(a_{53},i_5,e_{56})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{59} = \mbox{store}(a_{55},i_5,e_{58})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{61} = \mbox{store}(a_{57},i_6,e_{60})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{63} = \mbox{store}(a_{59},i_6,e_{62})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{65} = \mbox{store}(a_{61},i_7,e_{64})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{67} = \mbox{store}(a_{63},i_7,e_{66})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{69} = \mbox{store}(a_{65},i_8,e_{68})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{71} = \mbox{store}(a_{67},i_8,e_{70})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{73} = \mbox{store}(a_{69},i_9,e_{72})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{75} = \mbox{store}(a_{71},i_9,e_{74})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{77} = \mbox{store}(a_{73},i_{10},e_{76})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{79} = \mbox{store}(a_{75},i_{10},e_{78})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{40} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{42} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{44} = \mbox{select}(a_{43},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{46} = \mbox{select}(a_{41},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{48} = \mbox{select}(a_{47},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{50} = \mbox{select}(a_{45},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{52} = \mbox{select}(a_{51},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{54} = \mbox{select}(a_{49},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{56} = \mbox{select}(a_{55},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{58} = \mbox{select}(a_{53},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{60} = \mbox{select}(a_{59},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{62} = \mbox{select}(a_{57},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{64} = \mbox{select}(a_{63},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{66} = \mbox{select}(a_{61},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{68} = \mbox{select}(a_{67},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{70} = \mbox{select}(a_{65},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{72} = \mbox{select}(a_{71},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{74} = \mbox{select}(a_{69},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{76} = \mbox{select}(a_{75},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{78} = \mbox{select}(a_{73},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$a_{77} = a_{79}\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV320-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK}_0,\mbox{axiom})$

\medskip\textbf{SWV065+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0006

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{53})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300})\mbox{ and }\mbox{leq}(\mbox{pv}_{53},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,n_0)\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{53})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300})\mbox{ and }\mbox{leq}(\mbox{pv}_{53},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0006},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV394+1.p} Priority queue checker: tmp\_not\_check\_02\_2






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \mbox{check\_cpq}(\mbox{triple}(u,v,w))\iff \forall x,y{:}\;( \mbox{pair\_in\_list}(v,x,y) \ \Rightarrow \ y < x ) )\qquad\mbox{fof}(\mbox{l30\_li}_{4142},\mbox{lemma})$

$\forall u,v,w,x,y{:}\;( ( \mbox{pair\_in\_list}(v,x,y)\mbox{ and }\mbox{strictly\_less\_than}(x,y)\mbox{ and }\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{remove\_slb}(v,x),x,y) )\qquad\mbox{fof}(\mbox{l30\_li}_{3132},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{check\_cpq}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x))\mbox{ and }\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) ) \ \Rightarrow \ \forall y{:}\;( \mbox{pair\_in\_list}(v,x,y) \ \Rightarrow \ y < x ) )\qquad\mbox{fof}(\mbox{l30\_co},\mbox{conjecture})$

\medskip\textbf{SWV315-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_sko\_\_usf}(\mbox{v\_B},\mbox{v\_X},\mbox{v\_evs}),\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OGets\_\_imp\_\_Says\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_N},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{v\_c})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OOR2\_\_parts\_\_knows\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

\medskip\textbf{SWV353-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evso})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{v\_U} = \mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}) \ \Rightarrow \ \mbox{v\_NA}\ne \mbox{v\_NAa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV309-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_x},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

\medskip\textbf{SWV305-2.p} Cryptographic protocol problem for Otway Rees






$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OCrypt\_\_synth}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnE}_0,\mbox{axiom})$

\medskip\textbf{SWV555-1.007.p} Store inverse (t1\_pp\_sf\_ai\_00007)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{32} = \mbox{store}(a_1,i_1,e_{31})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{34} = \mbox{store}(a_2,i_1,e_{33})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{36} = \mbox{store}(a_{32},i_2,e_{35})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{38} = \mbox{store}(a_{34},i_2,e_{37})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{40} = \mbox{store}(a_{36},i_3,e_{39})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{42} = \mbox{store}(a_{38},i_3,e_{41})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{44} = \mbox{store}(a_{40},i_4,e_{43})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{46} = \mbox{store}(a_{42},i_4,e_{45})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{48} = \mbox{store}(a_{44},i_5,e_{47})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{50} = \mbox{store}(a_{46},i_5,e_{49})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{52} = \mbox{store}(a_{48},i_6,e_{51})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{54} = \mbox{store}(a_{50},i_6,e_{53})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{56} = \mbox{store}(a_{52},i_7,e_{55})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{58} = \mbox{store}(a_{54},i_7,e_{57})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{31} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{33} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{35} = \mbox{select}(a_{34},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{37} = \mbox{select}(a_{32},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{39} = \mbox{select}(a_{38},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{41} = \mbox{select}(a_{36},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{43} = \mbox{select}(a_{42},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{45} = \mbox{select}(a_{40},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{47} = \mbox{select}(a_{46},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{49} = \mbox{select}(a_{44},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{51} = \mbox{select}(a_{50},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{53} = \mbox{select}(a_{48},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{55} = \mbox{select}(a_{54},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{57} = \mbox{select}(a_{52},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{60} = \mbox{select}(a_1,i_{59})\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{61} = \mbox{select}(a_2,i_{59})\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$i_{59} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$a_{56} = a_{58}\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{60}\ne e_{61}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV086+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0027

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\neg\,\mbox{geq}(\mbox{pv}_{65},\mbox{tptp\_float\_0}_{001}) \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0027},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV333-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-6.ax'})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{v\_Aa}\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{10},\mbox{negated\_conjecture})$

$( \mbox{v\_U} = \mbox{v\_X}\mbox{ and }\mbox{v\_B} = \mbox{v\_Ba} ) \ \Rightarrow \ \mbox{v\_A}\ne \mbox{v\_Aa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_Aa},\mbox{v\_Ba},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_Xa},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV334-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-6.ax'})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{v\_Aa}\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{10},\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$( \mbox{v\_NB} = \mbox{v\_NBa}\mbox{ and }\mbox{v\_K} = \mbox{v\_Ka}\mbox{ and }\mbox{v\_U} = \mbox{v\_X}\mbox{ and }\mbox{v\_B} = \mbox{v\_Ba} ) \ \Rightarrow \ \mbox{v\_A}\ne \mbox{v\_Aa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{12},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Ka},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_Ka}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_Aa},\mbox{v\_Ba},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_Xa},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV251-2.p} Cryptographic protocol problem for messages






$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{c\_minus}(\mbox{v\_B},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a})),\mbox{v\_A},\mbox{t\_a}) = \mbox{c\_union}(\mbox{v\_B},\mbox{v\_A},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_Diff\_\_cancel2}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{v\_A},\mbox{c\_minus}(\mbox{v\_B},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a})),\mbox{t\_a}) = \mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_Diff\_\_cancel}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_subset\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_subset\_\_iff}_1,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_subset\_\_iff}_2,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_x},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_minus}(\mbox{c\_insert}(\mbox{v\_x},\mbox{v\_A},\mbox{t\_a}),\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) = \mbox{c\_minus}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_Diff1}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetD}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{v\_A} = \mbox{v\_B}\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_antisym}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_refl}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_x},\mbox{c\_Message\_Oanalz}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_x},\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV252-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_subset\_\_iff}_1,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_synth}_0,\mbox{axiom})$

$\mbox{class\_Orderings\_Oorder}(\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_x},\mbox{v\_x},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Orderings\_Oorder\_\_class\_Oaxioms\_\_1}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{c\_minus}(\mbox{v\_B},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a})),\mbox{v\_A},\mbox{t\_a}) = \mbox{c\_union}(\mbox{v\_B},\mbox{v\_A},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_Diff\_\_cancel2}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{v\_A},\mbox{c\_minus}(\mbox{v\_B},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a})),\mbox{t\_a}) = \mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_Diff\_\_cancel}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_subset\_\_iff}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_subset\_\_iff}_1,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_subset\_\_iff}_2,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_insert}(\mbox{v\_x},\mbox{v\_A},\mbox{t\_a}),\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_x},\mbox{v\_B},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_subset}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_insert}(\mbox{v\_x},\mbox{v\_A},\mbox{t\_a}),\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_subset}_1,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_x},\mbox{v\_B},\mbox{t\_a})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_insert}(\mbox{v\_x},\mbox{v\_A},\mbox{t\_a}),\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_subset}_2,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{v\_A} = \mbox{v\_B}\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_antisym}_0,\mbox{axiom})$

$\mbox{class\_Orderings\_Oorder}(\mbox{tc\_set}(t_1))\qquad\mbox{cnf}(\mbox{clsarity\_set}_2,\mbox{axiom})$

\medskip\textbf{SWV560-1.004.p} Store inverse (t3\_np\_nf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_1,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4)) = \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4))\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV429$\wedge$2.p} ICL$\wedge$=$>$ logic mapping to modal logic implies 'refl'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^2.ax'})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ a ) )\qquad\mbox{thf}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV268-2.p} Cryptographic protocol problem for messages






$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_idem}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

\medskip\textbf{SWV240-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV004-0.ax'})$

$( \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\mbox{ and }\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_G\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G\_H},\mbox{v\_H\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_cong}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_synthD\_\_dest}_0,\mbox{axiom})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV321-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OKey\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Public\_OSpy\_\_spies\_\_bad\_\_shrK}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnE}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_a},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_a},\mbox{c\_insert}(\mbox{v\_b},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OinsertCI}_0,\mbox{axiom})$

\medskip\textbf{SWV429$\wedge$1.p} ICL$\wedge$=$>$ logic mapping to modal logic implies 'refl'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^2.ax'})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ a ) )\qquad\mbox{thf}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV252-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-1.ax'})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_analz\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_insert\_\_subset\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV526-1.030.p} Store commutativity (t3\_pp\_nf\_ni\_00030)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_1,e_1),\mbox{sk}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_1,e_1),\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})))\ne \mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10}),\mbox{sk}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_1,e_1),\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})))\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV001-1.p} PV1

These "clauses arose in a natural manner from work done in
 program verification" [MOW76] p.779.




$( x{=}y\mbox{ and }\mbox{less\_or\_equalish}(x,z) ) \ \Rightarrow \ \mbox{less\_or\_equalish}(y,z)\qquad\mbox{cnf}(\mbox{less\_or\_equal\_substitution}_1,\mbox{axiom})$

$( x{=}y\mbox{ and }\mbox{less\_or\_equalish}(z,x) ) \ \Rightarrow \ \mbox{less\_or\_equalish}(z,y)\qquad\mbox{cnf}(\mbox{less\_or\_equal\_substitution}_2,\mbox{axiom})$

$( q_1(x,y,z)\mbox{ and }\mbox{less\_or\_equalish}(x,y) ) \ \Rightarrow \ q_2(x,y,z)\qquad\mbox{cnf}(\mbox{clause}_1,\mbox{axiom})$

$q_1(x,y,z) \ \Rightarrow \ ( \mbox{less\_or\_equalish}(x,y)\mbox{ or }q_3(x,y,z) )\qquad\mbox{cnf}(\mbox{clause}_2,\mbox{axiom})$

$q_2(x,y,z) \ \Rightarrow \ q_4(x,y,y)\qquad\mbox{cnf}(\mbox{clause}_3,\mbox{axiom})$

$q_3(x,y,z) \ \Rightarrow \ q_4(x,y,x)\qquad\mbox{cnf}(\mbox{clause}_4,\mbox{axiom})$

$\mbox{less\_or\_equalish}(x,x)\qquad\mbox{cnf}(\mbox{less\_or\_equal\_reflexivity},\mbox{axiom})$

$( \mbox{less\_or\_equalish}(x,y)\mbox{ and }\mbox{less\_or\_equalish}(y,x) ) \ \Rightarrow \ x{=}y\qquad\mbox{cnf}(\mbox{less\_or\_equal\_implies\_equal},\mbox{axiom})$

$( \mbox{less\_or\_equalish}(x,y)\mbox{ and }\mbox{less\_or\_equalish}(y,z) ) \ \Rightarrow \ \mbox{less\_or\_equalish}(x,z)\qquad\mbox{cnf}(\mbox{transitivity\_of\_less\_or\_equal},\mbox{axiom})$

$\mbox{less\_or\_equalish}(x,y)\mbox{ or }\mbox{less\_or\_equalish}(y,x)\qquad\mbox{cnf}(\mbox{all\_less\_or\_equal},\mbox{axiom})$

$x{=}y \ \Rightarrow \ \mbox{less\_or\_equalish}(x,y)\qquad\mbox{cnf}(\mbox{equal\_implies\_less\_or\_equal},\mbox{axiom})$

$q_1(a,b,c)\qquad\mbox{cnf}(\mbox{clause}_5,\mbox{negated\_conjecture})$

$( q_4(a,b,w)\mbox{ and }\mbox{less\_or\_equalish}(a,w)\mbox{ and }\mbox{less\_or\_equalish}(b,w) ) \ \Rightarrow \ \neg\,\mbox{less\_or\_equalish}(w,a)\qquad\mbox{cnf}(\mbox{clause}_6,\mbox{negated\_conjecture})$

$( q_4(a,b,w)\mbox{ and }\mbox{less\_or\_equalish}(a,w)\mbox{ and }\mbox{less\_or\_equalish}(b,w) ) \ \Rightarrow \ \neg\,\mbox{less\_or\_equalish}(w,b)\qquad\mbox{cnf}(\mbox{clause}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV517-1.040.p} Store commutativity (t3\_np\_nf\_ni\_00040)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),n_{31},e_{31}),n_{32},e_{32}),n_{33},e_{33}),n_{34},e_{34}),n_{35},e_{35}),n_{36},e_{36}),n_{37},e_{37}),n_{38},e_{38}),n_{39},e_{39}),n_{40},e_{40})\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{16},e_{16}),n_{14},e_{14}),n_{24},e_{24}),n_{11},e_{11}),n_{25},e_{25}),n_{17},e_{17}),n_7,e_7),n_{32},e_{32}),n_6,e_6),n_{18},e_{18}),n_{37},e_{37}),n_{31},e_{31}),n_{13},e_{13}),n_{12},e_{12}),n_{36},e_{36}),n_{20},e_{20}),n_{35},e_{35}),n_{23},e_{23}),n_{26},e_{26}),n_{21},e_{21}),n_{27},e_{27}),n_{10},e_{10}),n_{22},e_{22}),n_8,e_8),n_{33},e_{33}),n_2,e_2),n_{40},e_{40}),n_{38},e_{38}),n_{39},e_{39}),n_1,e_1),n_9,e_9),n_3,e_3),n_5,e_5),n_4,e_4),n_{30},e_{30}),n_{15},e_{15}),n_{34},e_{34}),n_{28},e_{28}),n_{29},e_{29}),n_{19},e_{19})\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV356-2.p} Cryptographic protocol problem for Yahalom






$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_2),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_conj\_\_parts}_0,\mbox{axiom})$

\medskip\textbf{SWV279-2.p} Cryptographic protocol problem for public






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Event\_Oused}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Event\_Oused}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Event\_Oused}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Public\_Oused\_\_parts\_\_subset\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_x},\mbox{c\_insert}(\mbox{v\_x},\mbox{v\_A},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_Oinsert\_\_iff}_1,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetD}_0,\mbox{axiom})$

\medskip\textbf{SWV276-1.p} Cryptographic protocol problem for events






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_OkeysFor}(\mbox{v\_G}),\mbox{c\_Message\_OkeysFor}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_nat}))\qquad\mbox{cnf}(\mbox{cls\_Message\_OkeysFor\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_insert\_\_subset\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

\medskip\textbf{SWV329-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-6.ax'})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$( \mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))) = \mbox{v\_X}\mbox{ and }\mbox{v\_B} = \mbox{v\_Ba} ) \ \Rightarrow \ \mbox{v\_A}\ne \mbox{c\_Message\_Oagent\_OSpy}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV245-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV004-0.ax'})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_synthD\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_least}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV270-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-1.ax'})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_increasing}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV335-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OCrypt\_\_synth}_1,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_n}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_n}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_ONonce\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnE}_0,\mbox{axiom})$

\medskip\textbf{SWV339-2.p} Cryptographic protocol problem for Yahalom






$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{v\_K} = \mbox{c\_Public\_OshrK}(\mbox{v\_B})\mbox{ or }\mbox{v\_K} = \mbox{c\_Public\_OshrK}(\mbox{v\_A})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Public\_OshrK\_\_in\_\_used}_0,\mbox{axiom})$

\medskip\textbf{SWV487+1.p} Matrix is upper triangular






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{real\_zero} ) )\mbox{ and }\forall c{:}\;( ( \mbox{int\_leq}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{lu}(k,k + c) ) ) ) )\qquad\mbox{fof}(\mbox{qiu},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_less}(j,i)\mbox{ and }\mbox{int\_leq}(i,n) ) \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\qquad\mbox{fof}(\mbox{ut},\mbox{conjecture})$

\medskip\textbf{SWV452+1.p} Establishing that there cannot be two leaders, part i26\_p216






$\mbox{include}(\mbox{'Axioms/SWV011+0.ax'})$

$\forall v,w,x,y{:}\;( ( \forall z,\mbox{pid}_0{:}\;( \mbox{setIn}(\mbox{pid}_0,\mbox{alive}) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \mbox{host}(\mbox{pid}_0)\ne \mbox{host}(z) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Halt}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_{20},\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Ack}(\mbox{pid}_0,z),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{leq}(\mbox{pid}_0,z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \mbox{pid}_0\ne z\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ or }\neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) ) )\mbox{ and }\forall z,\mbox{pid}_{30},\mbox{pid}_{20},\mbox{pid}_0{:}\;( ( \mbox{host}(\mbox{pid}_{20})\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(\mbox{pid}_{20},\mbox{alive})\mbox{ and }\mbox{host}(\mbox{pid}_{30}) = \mbox{host}(z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(\mbox{pid}_{20}) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z)))\mbox{ and }\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_{30}),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) )\mbox{ and }\mbox{queue}(\mbox{host}(x)) = \mbox{cons}(\mbox{m\_Down}(y),v) ) \ \Rightarrow \ ( \mbox{setIn}(x,\mbox{alive}) \ \Rightarrow \ ( \neg\,\mbox{leq}(\mbox{host}(x),\mbox{host}(y)) \ \Rightarrow \ ( ( ( \mbox{index}(\mbox{ldr},\mbox{host}(x)) = \mbox{host}(y)\mbox{ and }\mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{norm} )\mbox{ or }( \mbox{index}(\mbox{status},\mbox{host}(x)) = \mbox{wait}\mbox{ and }\mbox{host}(y) = \mbox{host}(\mbox{index}(\mbox{elid},\mbox{host}(x))) ) ) \ \Rightarrow \ ( ( \forall z{:}\;( \mbox{host}(x) = \mbox{host}(z) \ \Rightarrow \ \mbox{leq}(z,w) )\mbox{ and }\neg\,\mbox{setIn}(w,\mbox{pids})\mbox{ and }\mbox{host}(x) = \mbox{host}(w) ) \ \Rightarrow \ ( \mbox{host}(w)\ne s(0) \ \Rightarrow \ \forall z{:}\;( \mbox{host}(x) = \mbox{host}(z) \ \Rightarrow \ \forall x_0,y_0{:}\;( \mbox{host}(x)\ne \mbox{host}(y_0) \ \Rightarrow \ \forall z_0{:}\;( ( ( ( z\ne x\mbox{ and }\mbox{setIn}(z,\mbox{alive}) )\mbox{ or }z = w )\mbox{ and }( ( y_0\ne x\mbox{ and }\mbox{setIn}(y_0,\mbox{alive}) )\mbox{ or }y_0 = w )\mbox{ and }\mbox{host}(y_0)\ne \mbox{host}(z)\mbox{ and }\mbox{host}(x_0) = \mbox{host}(z)\mbox{ and }\mbox{host}(z_0) = \mbox{host}(y_0) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(z_0),v)\mbox{ and }\mbox{elem}(\mbox{m\_Down}(x_0),\mbox{queue}(\mbox{host}(y_0))) ) ) ) ) ) ) ) ) )\qquad\mbox{fof}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV043+1.p} Unsimplified proof obligation cl5\_nebula\_norm\_0001

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\mbox{true} \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0001},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV288-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B\_H},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_sko\_\_u7f}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_K},\mbox{v\_NA},\mbox{v\_evs}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_ONA\_\_Crypt\_\_imp\_\_Server\_\_msg}_0,\mbox{axiom})$

\medskip\textbf{SWV243-2.p} Cryptographic protocol problem for messages






$\mbox{c\_Message\_Oanalz}(\mbox{c\_Message\_Osynth}(\mbox{v\_H}))\ne \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{v\_y},\mbox{c\_emptyset},\mbox{t\_a}) = \mbox{v\_y}\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_empty\_\_right}_0,\mbox{axiom})$

\medskip\textbf{SWV088+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0029

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\mbox{geq}(-n_{135300},n_0) \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0029},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV280-1.p} Cryptographic protocol problem for public






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{c\_lessequals}(\mbox{v\_n},\mbox{c\_plus}(\mbox{v\_n},\mbox{v\_m},\mbox{tc\_nat}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Ole\_\_add1}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_n},\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Ole\_\_add2}_0,\mbox{axiom})$

$\mbox{c\_less}(\mbox{v\_m},\mbox{c\_Suc}(\mbox{v\_n}),\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oless\_\_Suc\_\_eq\_\_le}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_less}(\mbox{v\_m},\mbox{c\_Suc}(\mbox{v\_n}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oless\_\_Suc\_\_eq\_\_le}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_sko\_\_urX}(\mbox{v\_evs}),\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Public\_ONonce\_\_supply\_\_lemma}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV350-2.p} Cryptographic protocol problem for Yahalom






$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_k}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV266-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody}_0,\mbox{axiom})$

\medskip\textbf{SWV322-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_Public\_OshrK}(\mbox{v\_A})\ne \mbox{v\_KAB}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_Public\_OshrK}(\mbox{v\_A}) = \mbox{v\_KAB}\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV335-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-3.ax'})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_U},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_U}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_V}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_W}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_V}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_U}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

\medskip\textbf{SWV291-2.p} Cryptographic protocol problem for Otway Rees






$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OCrypt\_\_synth}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnE}_0,\mbox{axiom})$

\medskip\textbf{SWV537-1.004.p} Swap elements (t1\_pp\_sf\_ai\_00004)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{466} = \mbox{store}(a_1,i_1,e_{465})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{467} = \mbox{store}(a_{466},i_1,e_{465})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{469} = \mbox{store}(a_{467},i_0,e_{468})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{471} = \mbox{store}(a_{469},i_3,e_{470})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{473} = \mbox{store}(a_{471},i_3,e_{472})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{475} = \mbox{store}(a_{473},i_2,e_{474})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{477} = \mbox{store}(a_{475},i_2,e_{476})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{479} = \mbox{store}(a_{477},i_0,e_{478})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{480} = \mbox{store}(a_{467},i_3,e_{470})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{481} = \mbox{store}(a_{480},i_0,e_{468})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{483} = \mbox{store}(a_{481},i_3,e_{482})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{485} = \mbox{store}(a_{483},i_2,e_{484})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{487} = \mbox{store}(a_{485},i_0,e_{486})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{489} = \mbox{store}(a_{487},i_2,e_{488})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{465} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{468} = \mbox{select}(a_{467},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{470} = \mbox{select}(a_{467},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{472} = \mbox{select}(a_{471},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{474} = \mbox{select}(a_{471},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{476} = \mbox{select}(a_{475},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{478} = \mbox{select}(a_{475},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{482} = \mbox{select}(a_{481},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{484} = \mbox{select}(a_{481},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{486} = \mbox{select}(a_{485},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{488} = \mbox{select}(a_{485},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{491} = \mbox{select}(a_{479},i_{490})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{492} = \mbox{select}(a_{489},i_{490})\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$i_{490} = \mbox{sk}(a_{479},a_{489})\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{491}\ne e_{492}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV380+1.p} Priority queue checker: lemma\_not\_ok\_persistence\_induction step 4






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w,x{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) )\qquad\mbox{fof}(\mbox{l16\_l}_{14},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{removemin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l16\_co},\mbox{conjecture})$

\medskip\textbf{SWV240-2.p} Cryptographic protocol problem for messages






$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_OInj}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\mbox{ and }\mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_G\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G\_H},\mbox{v\_H\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_subset\_\_cong}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_A},\mbox{t\_a})\mbox{ or }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Main\_OsubsetI\_}_1(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_OsubsetI}_1,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_A},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_refl}_0,\mbox{axiom})$

\medskip\textbf{SWV451+1.p} Establishing that there cannot be two leaders, part i26\_p121






$\mbox{include}(\mbox{'Axioms/SWV011+0.ax'})$

$\forall v,w,x,y{:}\;( ( \forall z,\mbox{pid}_0{:}\;( \mbox{setIn}(\mbox{pid}_0,\mbox{alive}) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \mbox{host}(\mbox{pid}_0)\ne \mbox{host}(z) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Halt}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_{20},\mbox{pid}_0{:}\;( \mbox{elem}(\mbox{m\_Ack}(\mbox{pid}_0,z),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) \ \Rightarrow \ \neg\,\mbox{leq}(\mbox{host}(z),\mbox{host}(\mbox{pid}_0)) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{leq}(\mbox{pid}_0,z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ \neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) )\mbox{ and }\forall z,\mbox{pid}_0{:}\;( ( \mbox{pid}_0\ne z\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(z) ) \ \Rightarrow \ ( \neg\,\mbox{setIn}(z,\mbox{alive})\mbox{ or }\neg\,\mbox{setIn}(\mbox{pid}_0,\mbox{alive}) ) )\mbox{ and }\forall z,\mbox{pid}_{30},\mbox{pid}_{20},\mbox{pid}_0{:}\;( ( \mbox{host}(\mbox{pid}_{20})\ne \mbox{host}(z)\mbox{ and }\mbox{setIn}(z,\mbox{alive})\mbox{ and }\mbox{setIn}(\mbox{pid}_{20},\mbox{alive})\mbox{ and }\mbox{host}(\mbox{pid}_{30}) = \mbox{host}(z)\mbox{ and }\mbox{host}(\mbox{pid}_0) = \mbox{host}(\mbox{pid}_{20}) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_0),\mbox{queue}(\mbox{host}(z)))\mbox{ and }\mbox{elem}(\mbox{m\_Down}(\mbox{pid}_{30}),\mbox{queue}(\mbox{host}(\mbox{pid}_{20}))) )\mbox{ and }\mbox{queue}(\mbox{host}(y)) = \mbox{cons}(\mbox{m\_NotNorm}(x),v) ) \ \Rightarrow \ ( \mbox{setIn}(y,\mbox{alive}) \ \Rightarrow \ ( ( \mbox{index}(\mbox{ldr},\mbox{host}(y)) = \mbox{host}(y)\mbox{ and }\mbox{index}(\mbox{status},\mbox{host}(y)) = \mbox{norm}\mbox{ and }\mbox{index}(\mbox{elid},\mbox{host}(y)) = x ) \ \Rightarrow \ ( ( \forall z{:}\;( \mbox{host}(y) = \mbox{host}(z) \ \Rightarrow \ \mbox{leq}(z,w) )\mbox{ and }\neg\,\mbox{setIn}(w,\mbox{pids})\mbox{ and }\mbox{host}(y) = \mbox{host}(w) ) \ \Rightarrow \ ( \mbox{host}(w) = s(0) \ \Rightarrow \ ( \neg\,\mbox{leq}(\mbox{nbr\_proc},\mbox{host}(w)) \ \Rightarrow \ \forall z{:}\;( s(\mbox{host}(w)) = \mbox{host}(z) \ \Rightarrow \ ( \mbox{host}(y)\ne \mbox{host}(z) \ \Rightarrow \ \forall x_0,y_0{:}\;( s(\mbox{host}(w))\ne \mbox{host}(y_0) \ \Rightarrow \ ( \mbox{host}(y) = \mbox{host}(y_0) \ \Rightarrow \ \forall z_0{:}\;( ( ( ( z\ne y\mbox{ and }\mbox{setIn}(z,\mbox{alive}) )\mbox{ or }z = w )\mbox{ and }( ( y_0\ne y\mbox{ and }\mbox{setIn}(y_0,\mbox{alive}) )\mbox{ or }y_0 = w )\mbox{ and }\mbox{host}(y_0)\ne \mbox{host}(z)\mbox{ and }\mbox{host}(x_0) = \mbox{host}(z)\mbox{ and }\mbox{host}(z_0) = \mbox{host}(y_0) ) \ \Rightarrow \ \neg\,\mbox{elem}(\mbox{m\_Down}(x_0),v)\mbox{ and }\mbox{elem}(\mbox{m\_Down}(z_0),\mbox{snoc}(\mbox{queue}(\mbox{host}(z)),\mbox{m\_Halt}(w))) ) ) ) ) ) ) ) ) ) ) )\qquad\mbox{fof}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV436$\wedge$4.p} ICL$\wedge$B logic mapping to modal logic implies that Example 3 holds






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$\mbox{admin}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{admin},\mbox{type})$

$\mbox{bob}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bob},\mbox{type})$

$\mbox{deletefile}_1{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{deletfile}_1,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ \mbox{icl\_false} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_1,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ ( \mbox{icl\_says}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_princ}@ \mbox{admin} ) )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) ) )\qquad\mbox{thf}(\mbox{ax}_2,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_3,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 )\qquad\mbox{thf}(\mbox{ex}_3,\mbox{conjecture})$

\medskip\textbf{SWV373+1.p} Priority queue checker: lemma\_not\_contains\_min\_not\_ok






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \mbox{ok}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ ( v\ne \mbox{create\_slb}\mbox{ and }\mbox{contains\_slb}(v,\mbox{findmin\_pqp\_res}(u))\mbox{ and }\mbox{lookup\_slb}(v,\mbox{findmin\_pqp\_res}(u)) < \mbox{findmin\_pqp\_res}(u) ) )\qquad\mbox{fof}(\mbox{l9\_l}_{10},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{contains\_cpq}(\mbox{triple}(u,v,w),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l9\_co},\mbox{conjecture})$

\medskip\textbf{SWV331-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-6.ax'})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV366+1.p} Priority queue checker: lemma\_I\_s induction






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u{:}\;( \forall v,w,x,y{:}\;i(\mbox{triple}(v,u,x)) = i(\mbox{triple}(w,u,y)) \ \Rightarrow \ \forall z,x_1,x_2,x_3,x_4,x_5{:}\;i(\mbox{triple}(z,\mbox{insert\_slb}(u,\mbox{pair}(x_4,x_5)),x_2)) = i(\mbox{triple}(x_1,\mbox{insert\_slb}(u,\mbox{pair}(x_4,x_5)),x_3)) )\qquad\mbox{fof}(\mbox{l2\_co},\mbox{conjecture})$

\medskip\textbf{SWV280-2.p} Cryptographic protocol problem for public






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{v\_n},\mbox{c\_plus}(\mbox{v\_n},\mbox{v\_m},\mbox{tc\_nat}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Ole\_\_add1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_sko\_\_urX}(\mbox{v\_evs}),\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Public\_ONonce\_\_supply\_\_lemma}_0,\mbox{axiom})$

\medskip\textbf{SWV548-1.004.p} Swap elements (t3\_pp\_sf\_ai\_00004)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{469} = \mbox{store}(a_1,i_1,e_{468})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{470} = \mbox{store}(a_{469},i_1,e_{468})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{472} = \mbox{store}(a_{470},i_0,e_{471})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{474} = \mbox{store}(a_{472},i_3,e_{473})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{476} = \mbox{store}(a_{474},i_3,e_{475})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{478} = \mbox{store}(a_{476},i_2,e_{477})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{480} = \mbox{store}(a_{478},i_2,e_{479})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{482} = \mbox{store}(a_{480},i_0,e_{481})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{483} = \mbox{store}(a_{470},i_3,e_{473})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{484} = \mbox{store}(a_{483},i_0,e_{471})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{486} = \mbox{store}(a_{484},i_3,e_{485})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{488} = \mbox{store}(a_{486},i_2,e_{487})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{490} = \mbox{store}(a_{488},i_0,e_{489})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{492} = \mbox{store}(a_{490},i_3,e_{491})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{468} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{471} = \mbox{select}(a_{470},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{473} = \mbox{select}(a_{470},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{475} = \mbox{select}(a_{474},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{477} = \mbox{select}(a_{474},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{479} = \mbox{select}(a_{478},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{481} = \mbox{select}(a_{478},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{485} = \mbox{select}(a_{484},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{487} = \mbox{select}(a_{484},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{489} = \mbox{select}(a_{488},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{491} = \mbox{select}(a_{488},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{494} = \mbox{select}(a_{482},i_{493})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{495} = \mbox{select}(a_{492},i_{493})\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$i_{493} = \mbox{sk}(a_{482},a_{492})\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{494}\ne e_{495}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV562-1.004.p} Store inverse (t3\_np\_sf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{17} = \mbox{store}(a_1,i_1,e_{16})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{19} = \mbox{store}(a_2,i_1,e_{18})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{21} = \mbox{store}(a_{17},i_2,e_{20})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{23} = \mbox{store}(a_{19},i_2,e_{22})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{25} = \mbox{store}(a_{21},i_3,e_{24})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{27} = \mbox{store}(a_{23},i_3,e_{26})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{29} = \mbox{store}(a_{25},i_1,e_{28})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{31} = \mbox{store}(a_{27},i_4,e_{30})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$e_{16} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$e_{18} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$e_{20} = \mbox{select}(a_{19},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$e_{22} = \mbox{select}(a_{17},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$e_{24} = \mbox{select}(a_{23},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$e_{26} = \mbox{select}(a_{21},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{28} = \mbox{select}(a_{27},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{30} = \mbox{select}(a_{25},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{29} = a_{31}\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV347-2.p} Cryptographic protocol problem for Yahalom






$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_S\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X\_H},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA\_H}),\mbox{v\_nb}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_C},\mbox{v\_S},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{v\_nb}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_nb},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{v\_A\_H} = \mbox{v\_A} )\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OSays\_\_unique\_\_NB}_1,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Aa},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV295-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_1)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{12},\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_1),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{v\_NA} = \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

\medskip\textbf{SWV268-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_Oin\_\_parts\_\_UnE}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_idem}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_increasing}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oparts}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_partsD\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_trans}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

\medskip\textbf{SWV267-2.p} Cryptographic protocol problem for messages






$\mbox{c\_lessequals}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_lessequals}(\mbox{v\_H},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_increasing}_0,\mbox{axiom})$

$( \mbox{c\_lessequals}(\mbox{v\_B},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_B},\mbox{tc\_set}(\mbox{t\_a})) ) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_A},\mbox{v\_C},\mbox{tc\_set}(\mbox{t\_a}))\qquad\mbox{cnf}(\mbox{cls\_Set\_Osubset\_\_trans}_0,\mbox{axiom})$

\medskip\textbf{SWV281-2.p} Cryptographic protocol problem for public






$\mbox{v\_U} = \mbox{v\_V}\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_V}),\mbox{c\_Event\_Oused}(\mbox{v\_evs\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_List\_Olist\_ONil}\ne \mbox{c\_List\_Olist\_OCons}(\mbox{v\_a\_H},\mbox{v\_list\_H},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_List\_Olist\_Odistinct\_\_1}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_n},\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Ole\_\_add2}_0,\mbox{axiom})$

$\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_k},\mbox{tc\_nat}) = \mbox{c\_plus}(\mbox{v\_n},\mbox{v\_k},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{v\_m} = \mbox{v\_n}\qquad\mbox{cnf}(\mbox{cls\_Nat\_Onat\_\_add\_\_right\_\_cancel}_0,\mbox{axiom})$

$\mbox{c\_plus}(c_0,\mbox{v\_y},\mbox{tc\_nat}) = \mbox{v\_y}\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oop\_A\_L\_Oadd\_\_0}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_sko\_\_urX}(\mbox{v\_evs}),\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Public\_ONonce\_\_supply\_\_lemma}_0,\mbox{axiom})$

\medskip\textbf{SWV079+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0020

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{51})\mbox{ and }\mbox{leq}(\mbox{pv}_{51},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,n_0)\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{51})\mbox{ and }\mbox{leq}(n_0,\mbox{uniform\_int\_rnd}(n_1,-( -n_{135300} )))\mbox{ and }\mbox{leq}(\mbox{pv}_{51},-n_5)\mbox{ and }\mbox{leq}(\mbox{uniform\_int\_rnd}(n_1,-( -n_{135300} )),-n_{135300}) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0020},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV069+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0010

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300}) ) \ \Rightarrow \ ( \mbox{leq}(n_0,n_0)\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(n_0,-n_5)\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300}) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0010},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV393+1.p} Priority queue checker: tmp\_not\_check\_02\_1 step






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u{:}\;( \forall v,w{:}\;( \mbox{pair\_in\_list}(u,v,w) \ \Rightarrow \ \forall x{:}\;( \mbox{contains\_slb}(u,x) \ \Rightarrow \ ( \mbox{pair\_in\_list}(\mbox{remove\_slb}(u,x),v,w)\mbox{ or }v = x ) ) ) \ \Rightarrow \ \forall y,z,x_1,x_2{:}\;( \mbox{pair\_in\_list}(\mbox{insert\_slb}(u,\mbox{pair}(x_1,x_2)),y,z) \ \Rightarrow \ \forall x_1{:}\;( \mbox{contains\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(x_1,x_2)),x_1) \ \Rightarrow \ ( \mbox{pair\_in\_list}(\mbox{remove\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(x_1,x_2)),x_1),y,z)\mbox{ or }y = x_1 ) ) ) )\qquad\mbox{fof}(\mbox{l29\_co},\mbox{conjecture})$

\medskip\textbf{SWV269-2.p} Cryptographic protocol problem for messages






$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_2,\mbox{axiom})$

\medskip\textbf{SWV323-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{v\_B}\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X\_H},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV384+1.p} Priority queue checker: lemma\_not\_min\_elem\_not\_check\_induction






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w,x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ ( ( \neg\,\mbox{check\_cpq}(\mbox{triple}(x,y,z))\mbox{ or }\neg\,\mbox{ok}(\mbox{triple}(x,y,z)) ) \ \Rightarrow \ ( \neg\,\mbox{check\_cpq}(\mbox{im\_succ\_cpq}(\mbox{triple}(x,y,z)))\mbox{ or }\neg\,\mbox{ok}(\mbox{im\_succ\_cpq}(\mbox{triple}(x,y,z))) ) ) ) \ \Rightarrow \ \forall x_1,x_2,x_3{:}\;( ( \neg\,\mbox{check\_cpq}(\mbox{triple}(x_1,x_2,x_3))\mbox{ or }\neg\,\mbox{ok}(\mbox{triple}(x_1,x_2,x_3)) ) \ \Rightarrow \ \forall x_4,x_5,x_6{:}\;( \mbox{succ\_cpq}(\mbox{triple}(x_1,x_2,x_3),\mbox{triple}(x_4,x_5,x_6)) \ \Rightarrow \ ( \neg\,\mbox{ok}(\mbox{triple}(x_4,x_5,x_6))\mbox{ or }\neg\,\mbox{check\_cpq}(\mbox{triple}(x_4,x_5,x_6)) ) ) )\qquad\mbox{fof}(\mbox{l20\_induction},\mbox{axiom})$

$\forall u,v,w{:}\;( ( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w))\mbox{ or }\neg\,\mbox{ok}(\mbox{triple}(u,v,w)) ) \ \Rightarrow \ ( \neg\,\mbox{check\_cpq}(\mbox{im\_succ\_cpq}(\mbox{triple}(u,v,w)))\mbox{ or }\neg\,\mbox{ok}(\mbox{im\_succ\_cpq}(\mbox{triple}(u,v,w))) ) )\qquad\mbox{fof}(\mbox{l12\_l}_{13},\mbox{lemma})$

$\forall u,v,w{:}\;( ( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w))\mbox{ or }\neg\,\mbox{ok}(\mbox{triple}(u,v,w)) ) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ ( \neg\,\mbox{ok}(\mbox{triple}(x,y,z))\mbox{ or }\neg\,\mbox{check\_cpq}(\mbox{triple}(x,y,z)) ) ) )\qquad\mbox{fof}(\mbox{l20\_co},\mbox{conjecture})$

\medskip\textbf{SWV005-1.p} E4






$\mbox{include}(\mbox{'Axioms/SWV001-0.ax'})$

$\neg\,n < k\qquad\mbox{cnf}(\mbox{clause}_1,\mbox{negated\_conjecture})$

$\neg\,k < l\qquad\mbox{cnf}(\mbox{clause}_2,\mbox{negated\_conjecture})$

$\neg\,k < i\qquad\mbox{cnf}(\mbox{clause}_3,\mbox{negated\_conjecture})$

$l < n\qquad\mbox{cnf}(\mbox{clause}_4,\mbox{negated\_conjecture})$

$1 < l\qquad\mbox{cnf}(\mbox{clause}_5,\mbox{negated\_conjecture})$

$a(k) < a(\mbox{predecessor}(l))\qquad\mbox{cnf}(\mbox{clause}_6,\mbox{negated\_conjecture})$

$( x < \mbox{successor}(n)\mbox{ and }a(x) < a(k) ) \ \Rightarrow \ x < l\qquad\mbox{cnf}(\mbox{clause}_7,\mbox{negated\_conjecture})$

$( 1 < l\mbox{ and }a(x) < a(\mbox{predecessor}(l)) ) \ \Rightarrow \ ( x < l\mbox{ or }n < x )\qquad\mbox{cnf}(\mbox{clause}_8,\mbox{negated\_conjecture})$

$( 1 < x\mbox{ and }x < l ) \ \Rightarrow \ \neg\,a(x) < a(\mbox{predecessor}(x))\qquad\mbox{cnf}(\mbox{clause}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV436$\wedge$3.p} ICL$\wedge$B logic mapping to modal logic implies that Example 3 holds






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{admin}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{admin},\mbox{type})$

$\mbox{bob}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bob},\mbox{type})$

$\mbox{deletefile}_1{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{deletfile}_1,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ \mbox{icl\_false} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_1,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ ( \mbox{icl\_says}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_princ}@ \mbox{admin} ) )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) ) )\qquad\mbox{thf}(\mbox{ax}_2,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_3,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 )\qquad\mbox{thf}(\mbox{ex}_3,\mbox{conjecture})$

\medskip\textbf{SWV491+4.p} Matrix is identity






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{real\_zero} ) )\mbox{ and }\forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k,k) = \mbox{real\_one} )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qii},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( ( i\ne j \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\mbox{ and }( i = j \ \Rightarrow \ a(i,j) = \mbox{real\_one} ) ) )\qquad\mbox{fof}(\mbox{id},\mbox{conjecture})$

\medskip\textbf{SWV383+1.p} Priority queue checker: lemma\_not\_check\_not\_phi






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( ( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w))\mbox{ or }\neg\,\mbox{ok}(\mbox{triple}(u,v,w)) ) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ ( \neg\,\mbox{ok}(\mbox{triple}(x,y,z))\mbox{ or }\neg\,\mbox{check\_cpq}(\mbox{triple}(x,y,z)) ) ) )\qquad\mbox{fof}(\mbox{l19\_l}_{20},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ ( \neg\,\mbox{ok}(\mbox{triple}(x,y,z))\mbox{ or }\neg\,\mbox{check\_cpq}(\mbox{triple}(x,y,z)) ) ) )\qquad\mbox{fof}(\mbox{l19\_co},\mbox{conjecture})$

\medskip\textbf{SWV552-1.007.p} Store inverse (t1\_np\_sf\_ai\_00007)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{29} = \mbox{store}(a_1,i_1,e_{28})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{31} = \mbox{store}(a_2,i_1,e_{30})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{33} = \mbox{store}(a_{29},i_2,e_{32})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{35} = \mbox{store}(a_{31},i_2,e_{34})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{37} = \mbox{store}(a_{33},i_3,e_{36})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{39} = \mbox{store}(a_{35},i_3,e_{38})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{41} = \mbox{store}(a_{37},i_4,e_{40})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{43} = \mbox{store}(a_{39},i_4,e_{42})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{45} = \mbox{store}(a_{41},i_5,e_{44})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{47} = \mbox{store}(a_{43},i_5,e_{46})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{49} = \mbox{store}(a_{45},i_6,e_{48})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{51} = \mbox{store}(a_{47},i_6,e_{50})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{53} = \mbox{store}(a_{49},i_1,e_{52})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{55} = \mbox{store}(a_{51},i_7,e_{54})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{28} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{30} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{32} = \mbox{select}(a_{31},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{34} = \mbox{select}(a_{29},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{36} = \mbox{select}(a_{35},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{38} = \mbox{select}(a_{33},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{40} = \mbox{select}(a_{39},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{42} = \mbox{select}(a_{37},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{44} = \mbox{select}(a_{43},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{46} = \mbox{select}(a_{41},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{48} = \mbox{select}(a_{47},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{50} = \mbox{select}(a_{45},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{52} = \mbox{select}(a_{51},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{54} = \mbox{select}(a_{49},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$a_{53} = a_{55}\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV325-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_C})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{v\_B}\ne \mbox{v\_C}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_C})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{v\_B} = \mbox{v\_C}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV332-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-6.ax'})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{v\_Aa}\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{10},\mbox{negated\_conjecture})$

$( \mbox{v\_U} = \mbox{v\_X}\mbox{ and }\mbox{v\_B} = \mbox{v\_Ba} ) \ \Rightarrow \ \mbox{v\_A}\ne \mbox{v\_Aa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_Aa},\mbox{v\_Ba},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV333-2.p} Cryptographic protocol problem for Yahalom






$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{10},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_Xa},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV068+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0009

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300}) ) \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0009},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV152+1.p} Simplified proof obligation cl5\_nebula\_norm\_0002

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\forall a{:}\;( ( \mbox{leq}(n_0,a)\mbox{ and }\mbox{leq}(a,\mbox{tptp\_minus}_1) ) \ \Rightarrow \ n_0 + n_4{=}\mbox{a\_select}_3(q,a,\mbox{tptp\_sum\_index}) = n_1 )\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0002},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV538-1.004.p} Swap elements (t1\_pp\_sf\_ai\_00004)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{469} = \mbox{store}(a_1,i_1,e_{468})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{470} = \mbox{store}(a_{469},i_1,e_{468})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{472} = \mbox{store}(a_{470},i_0,e_{471})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{474} = \mbox{store}(a_{472},i_3,e_{473})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{476} = \mbox{store}(a_{474},i_3,e_{475})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{478} = \mbox{store}(a_{476},i_2,e_{477})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{480} = \mbox{store}(a_{478},i_2,e_{479})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{482} = \mbox{store}(a_{480},i_0,e_{481})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{483} = \mbox{store}(a_{470},i_3,e_{473})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{484} = \mbox{store}(a_{483},i_0,e_{471})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{486} = \mbox{store}(a_{484},i_3,e_{485})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{488} = \mbox{store}(a_{486},i_2,e_{487})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{490} = \mbox{store}(a_{488},i_0,e_{489})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{492} = \mbox{store}(a_{490},i_3,e_{491})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{468} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{471} = \mbox{select}(a_{470},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{473} = \mbox{select}(a_{470},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{475} = \mbox{select}(a_{474},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{477} = \mbox{select}(a_{474},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{479} = \mbox{select}(a_{478},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{481} = \mbox{select}(a_{478},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{485} = \mbox{select}(a_{484},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{487} = \mbox{select}(a_{484},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{489} = \mbox{select}(a_{488},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{491} = \mbox{select}(a_{488},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{494} = \mbox{select}(a_{482},i_{493})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{495} = \mbox{select}(a_{492},i_{493})\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$i_{493} = \mbox{sk}(a_{482},a_{492})\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{494}\ne e_{495}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV562-1.007.p} Store inverse (t3\_np\_sf\_ai\_00007)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{29} = \mbox{store}(a_1,i_1,e_{28})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{31} = \mbox{store}(a_2,i_1,e_{30})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{33} = \mbox{store}(a_{29},i_2,e_{32})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{35} = \mbox{store}(a_{31},i_2,e_{34})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{37} = \mbox{store}(a_{33},i_3,e_{36})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{39} = \mbox{store}(a_{35},i_3,e_{38})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{41} = \mbox{store}(a_{37},i_4,e_{40})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{43} = \mbox{store}(a_{39},i_4,e_{42})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{45} = \mbox{store}(a_{41},i_5,e_{44})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{47} = \mbox{store}(a_{43},i_5,e_{46})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{49} = \mbox{store}(a_{45},i_6,e_{48})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{51} = \mbox{store}(a_{47},i_6,e_{50})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{53} = \mbox{store}(a_{49},i_1,e_{52})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{55} = \mbox{store}(a_{51},i_7,e_{54})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$e_{28} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$e_{30} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$e_{32} = \mbox{select}(a_{31},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$e_{34} = \mbox{select}(a_{29},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$e_{36} = \mbox{select}(a_{35},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$e_{38} = \mbox{select}(a_{33},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{40} = \mbox{select}(a_{39},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{42} = \mbox{select}(a_{37},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{44} = \mbox{select}(a_{43},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{46} = \mbox{select}(a_{41},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{48} = \mbox{select}(a_{47},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{50} = \mbox{select}(a_{45},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{52} = \mbox{select}(a_{51},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{54} = \mbox{select}(a_{49},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$a_{53} = a_{55}\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV363-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_spies}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})) = \mbox{c\_Message\_Oparts}(\mbox{v\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_analz}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OGets\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_na},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_nb\_H}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_Ono\_\_nonce\_\_YM1\_\_YM2}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV563-1.004.p} Store inverse (t3\_pp\_nf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4)) = \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4))\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$\mbox{select}(a_1,\mbox{sk}(a_1,a_2))\ne \mbox{select}(a_2,\mbox{sk}(a_1,a_2))\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV313-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_Osecrecy\_\_lemma\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

\medskip\textbf{SWV920-1.p} Java type soundness 058\_5






$\mbox{c\_Objects\_Ohext}(\mbox{v\_h},\mbox{v\_h})\qquad\mbox{cnf}(\mbox{cls\_hext\_\_refl}_0,\mbox{axiom})$

$( \mbox{c\_Objects\_Ohext}(\mbox{v\_h\_H},\mbox{v\_h\_H\_H})\mbox{ and }\mbox{c\_Objects\_Ohext}(\mbox{v\_h},\mbox{v\_h\_H}) ) \ \Rightarrow \ \mbox{c\_Objects\_Ohext}(\mbox{v\_h},\mbox{v\_h\_H\_H})\qquad\mbox{cnf}(\mbox{cls\_hext\_\_trans}_0,\mbox{axiom})$

$\mbox{c\_COMBI}(\mbox{v\_P},\mbox{t\_a}) = \mbox{v\_P}\qquad\mbox{cnf}(\mbox{cls\_COMBI\_\_def}_0,\mbox{axiom})$

$\mbox{c\_Conform\_Olconf}(\mbox{v\_P},\mbox{v\_ha\_\_\_\_\_\_},\mbox{v\_la\_\_\_\_\_\_},\mbox{v\_E\_\_\_\_},\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Expr\_Oexp}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}))))\qquad\mbox{cnf}(\mbox{cls\_RedNew\_I5\_J}_0,\mbox{axiom})$

$( \mbox{c\_Objects\_Ohext}(\mbox{v\_h},\mbox{v\_h\_H})\mbox{ and }\mbox{c\_Conform\_Olconf}(\mbox{v\_P},\mbox{v\_h},\mbox{v\_l},\mbox{v\_E},\mbox{t\_a}) ) \ \Rightarrow \ \mbox{c\_Conform\_Olconf}(\mbox{v\_P},\mbox{v\_h\_H},\mbox{v\_l},\mbox{v\_E},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_lconf\_\_hext}_0,\mbox{axiom})$

$\mbox{c\_COMBI}(\mbox{v\_P},\mbox{t\_a}) = \mbox{v\_P}\qquad\mbox{cnf}(\mbox{cls\_COMBI\_\_def\_\_raw}_0,\mbox{axiom})$

$\mbox{c\_Conform\_Olconf}(\mbox{v\_P},\mbox{v\_ha\_\_\_\_\_\_},\mbox{v\_la\_\_\_\_\_\_},\mbox{v\_E\_\_\_\_},\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Expr\_Oexp}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}))))\qquad\mbox{cnf}(\mbox{cls\_CHAINED}_0,\mbox{axiom})$

$\mbox{c\_WellTypeRT\_OWTrt}(\mbox{v\_P},\mbox{v\_ha\_\_\_\_\_\_},\mbox{v\_E\_\_\_\_},\mbox{c\_Expr\_Oexp\_Onew}(\mbox{v\_C\_\_\_\_\_\_},\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{v\_T\_\_\_\_})\qquad\mbox{cnf}(\mbox{cls\_CHAINED\_0}_{01},\mbox{axiom})$

$\mbox{v\_h\_Ha\_\_\_\_\_\_} = \mbox{c\_Fun\_Ofun\_\_upd}(\mbox{v\_ha\_\_\_\_\_\_},\mbox{v\_a\_\_\_\_\_\_},\mbox{c\_Option\_Ooption\_OSome}(\mbox{c\_Pair}(\mbox{v\_C\_\_\_\_\_\_},\mbox{c\_Objects\_Oinit\_\_fields}(\mbox{v\_FDTs\_\_\_\_\_\_}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_fun}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Option\_Ooption}(\mbox{tc\_Value\_Oval}))),\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_fun}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Option\_Ooption}(\mbox{tc\_Value\_Oval})))),\mbox{tc\_nat},\mbox{tc\_Option\_Ooption}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_fun}(\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}),\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Option\_Ooption}(\mbox{tc\_Value\_Oval})))))\qquad\mbox{cnf}(\mbox{cls\_CHAINED\_0}_{02},\mbox{axiom})$

$\mbox{c\_TypeRel\_OFields}(\mbox{v\_P},\mbox{v\_C\_\_\_\_\_\_},\mbox{v\_FDTs\_\_\_\_\_\_},\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Expr\_Oexp}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}))))\qquad\mbox{cnf}(\mbox{cls\_CHAINED\_0}_{03},\mbox{axiom})$

$\mbox{c\_Objects\_Onew\_\_Addr}(\mbox{v\_ha\_\_\_\_\_\_}) = \mbox{c\_Option\_Ooption\_OSome}(\mbox{v\_a\_\_\_\_\_\_},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_CHAINED\_0}_{04},\mbox{axiom})$

$\neg\,\mbox{c\_Conform\_Olconf}(\mbox{v\_P},\mbox{v\_h\_Ha\_\_\_\_\_\_},\mbox{v\_la\_\_\_\_\_\_},\mbox{v\_E\_\_\_\_},\mbox{tc\_prod}(\mbox{tc\_List\_Olist}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar})),\mbox{tc\_Expr\_Oexp}(\mbox{tc\_List\_Olist}(\mbox{tc\_String\_Ochar}))))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_fequal}(\mbox{v\_x},\mbox{v\_x},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_ATP\_\_Linkup\_Oequal\_\_imp\_\_fequal}_0,\mbox{axiom})$

$\mbox{c\_fequal}(\mbox{v\_X},\mbox{v\_Y},\mbox{t\_a}) \ \Rightarrow \ \mbox{v\_X} = \mbox{v\_Y}\qquad\mbox{cnf}(\mbox{cls\_ATP\_\_Linkup\_Ofequal\_\_imp\_\_equal}_0,\mbox{axiom})$

\medskip\textbf{SWV511-1.040.p} Store commutativity (t2\_np\_nf\_ni\_00040)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(a,i,\mbox{select}(a,i)) = a\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,e),i,f) = \mbox{store}(a,i,f)\qquad\mbox{cnf}(a_4,\mbox{axiom})$

$i = j\mbox{ or }\mbox{store}(\mbox{store}(a,i,e),j,f) = \mbox{store}(\mbox{store}(a,j,f),i,e)\qquad\mbox{cnf}(a_5,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_{30},e_{30}),n_{31},e_{31}),n_{32},e_{32}),n_{33},e_{33}),n_{34},e_{34}),n_{35},e_{35}),n_{36},e_{36}),n_{37},e_{37}),n_{38},e_{38}),n_{39},e_{39}),n_{40},e_{40})\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{16},e_{16}),n_{14},e_{14}),n_{24},e_{24}),n_{11},e_{11}),n_{25},e_{25}),n_{17},e_{17}),n_7,e_7),n_{32},e_{32}),n_6,e_6),n_{18},e_{18}),n_{37},e_{37}),n_{31},e_{31}),n_{13},e_{13}),n_{12},e_{12}),n_{36},e_{36}),n_{20},e_{20}),n_{35},e_{35}),n_{23},e_{23}),n_{26},e_{26}),n_{21},e_{21}),n_{27},e_{27}),n_{10},e_{10}),n_{22},e_{22}),n_8,e_8),n_{33},e_{33}),n_2,e_2),n_{40},e_{40}),n_{38},e_{38}),n_{39},e_{39}),n_1,e_1),n_9,e_9),n_3,e_3),n_5,e_5),n_4,e_4),n_{30},e_{30}),n_{15},e_{15}),n_{34},e_{34}),n_{28},e_{28}),n_{29},e_{29}),n_{19},e_{19})\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV189+1.p} Simplified proof obligation cl5\_nebula\_init\_0121

Proof obligation emerging from the init-safety verification for
 the cl5\_nebula program. init-safety ensures that each variable or
 individual array element has been assigned a defined value before
 it is used.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\forall a{:}\;( ( \mbox{leq}(n_0,a)\mbox{ and }\mbox{leq}(a,n_4) ) \ \Rightarrow \ \mbox{a\_select}_3(\mbox{center\_init},a,n_0) = \mbox{init} ) \ \Rightarrow \ \forall b{:}\;( ( \mbox{leq}(n_0,b)\mbox{ and }\mbox{leq}(b,\mbox{tptp\_minus}_1) ) \ \Rightarrow \ \forall c{:}\;( ( \mbox{leq}(n_0,c)\mbox{ and }\mbox{leq}(c,n_4) ) \ \Rightarrow \ \mbox{a\_select}_3(\mbox{q\_init},b,c) = \mbox{init} ) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_init}_{0121},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV488+2.p} Matrix has no zero on the diagonal






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{lu}(k + c,k) ) )\mbox{ and }\forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k,k) = \mbox{real\_one} )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qil},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( i = j \ \Rightarrow \ a(i,j)\ne \mbox{real\_zero} ) )\qquad\mbox{fof}(\mbox{lti},\mbox{conjecture})$

\medskip\textbf{SWV533-1.007.p} Swap elements (t1\_np\_sf\_ai\_00007)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{783} = \mbox{store}(a_1,i_4,e_{782})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{785} = \mbox{store}(a_{783},i_3,e_{784})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{787} = \mbox{store}(a_{785},i_2,e_{786})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{789} = \mbox{store}(a_{787},i_1,e_{788})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{791} = \mbox{store}(a_{789},i_0,e_{790})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{793} = \mbox{store}(a_{791},i_5,e_{792})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{795} = \mbox{store}(a_{793},i_2,e_{794})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{797} = \mbox{store}(a_{795},i_5,e_{796})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{799} = \mbox{store}(a_{797},i_1,e_{798})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{800} = \mbox{store}(a_{799},i_1,e_{798})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{802} = \mbox{store}(a_{800},i_5,e_{801})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{804} = \mbox{store}(a_{802},i_2,e_{803})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{806} = \mbox{store}(a_{804},i_5,e_{805})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{808} = \mbox{store}(a_{806},i_2,e_{807})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{809} = \mbox{store}(a_{785},i_1,e_{788})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{810} = \mbox{store}(a_{809},i_2,e_{786})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{812} = \mbox{store}(a_{810},i_5,e_{811})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{814} = \mbox{store}(a_{812},i_0,e_{813})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{816} = \mbox{store}(a_{814},i_5,e_{815})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{818} = \mbox{store}(a_{816},i_2,e_{817})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$a_{820} = \mbox{store}(a_{818},i_1,e_{819})\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$a_{821} = \mbox{store}(a_{820},i_1,e_{819})\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$a_{823} = \mbox{store}(a_{821},i_5,e_{822})\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$a_{825} = \mbox{store}(a_{823},i_2,e_{824})\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$a_{827} = \mbox{store}(a_{825},i_5,e_{826})\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{829} = \mbox{store}(a_{827},i_2,e_{828})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{782} = \mbox{select}(a_1,i_3)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{784} = \mbox{select}(a_1,i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{786} = \mbox{select}(a_{785},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{788} = \mbox{select}(a_{785},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{790} = \mbox{select}(a_{789},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{792} = \mbox{select}(a_{789},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{794} = \mbox{select}(a_{793},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{796} = \mbox{select}(a_{793},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{798} = \mbox{select}(a_{797},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{801} = \mbox{select}(a_{800},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{803} = \mbox{select}(a_{800},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{805} = \mbox{select}(a_{804},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{807} = \mbox{select}(a_{804},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{811} = \mbox{select}(a_{810},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{813} = \mbox{select}(a_{810},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{815} = \mbox{select}(a_{814},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$e_{817} = \mbox{select}(a_{814},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$e_{819} = \mbox{select}(a_{818},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{822} = \mbox{select}(a_{821},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{44},\mbox{hypothesis})$

$e_{824} = \mbox{select}(a_{821},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{45},\mbox{hypothesis})$

$e_{826} = \mbox{select}(a_{825},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{46},\mbox{hypothesis})$

$e_{828} = \mbox{select}(a_{825},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{47},\mbox{hypothesis})$

$a_{808}\ne a_{829}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV540-1.007.p} Swap elements (t2\_np\_sf\_ai\_00007)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(a,i,\mbox{select}(a,i)) = a\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,e),i,f) = \mbox{store}(a,i,f)\qquad\mbox{cnf}(a_4,\mbox{axiom})$

$i = j\mbox{ or }\mbox{store}(\mbox{store}(a,i,e),j,f) = \mbox{store}(\mbox{store}(a,j,f),i,e)\qquad\mbox{cnf}(a_5,\mbox{axiom})$

$a_{783} = \mbox{store}(a_1,i_4,e_{782})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{785} = \mbox{store}(a_{783},i_3,e_{784})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{787} = \mbox{store}(a_{785},i_2,e_{786})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{789} = \mbox{store}(a_{787},i_1,e_{788})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{791} = \mbox{store}(a_{789},i_0,e_{790})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{793} = \mbox{store}(a_{791},i_5,e_{792})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{795} = \mbox{store}(a_{793},i_2,e_{794})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{797} = \mbox{store}(a_{795},i_5,e_{796})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{799} = \mbox{store}(a_{797},i_1,e_{798})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{800} = \mbox{store}(a_{799},i_1,e_{798})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{802} = \mbox{store}(a_{800},i_5,e_{801})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{804} = \mbox{store}(a_{802},i_2,e_{803})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{806} = \mbox{store}(a_{804},i_5,e_{805})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{808} = \mbox{store}(a_{806},i_2,e_{807})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{809} = \mbox{store}(a_{785},i_1,e_{788})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{810} = \mbox{store}(a_{809},i_2,e_{786})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{812} = \mbox{store}(a_{810},i_5,e_{811})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{814} = \mbox{store}(a_{812},i_0,e_{813})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{816} = \mbox{store}(a_{814},i_5,e_{815})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{818} = \mbox{store}(a_{816},i_2,e_{817})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$a_{820} = \mbox{store}(a_{818},i_1,e_{819})\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$a_{821} = \mbox{store}(a_{820},i_1,e_{819})\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$a_{823} = \mbox{store}(a_{821},i_5,e_{822})\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$a_{825} = \mbox{store}(a_{823},i_2,e_{824})\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$a_{827} = \mbox{store}(a_{825},i_5,e_{826})\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{829} = \mbox{store}(a_{827},i_2,e_{828})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{782} = \mbox{select}(a_1,i_3)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{784} = \mbox{select}(a_1,i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{786} = \mbox{select}(a_{785},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{788} = \mbox{select}(a_{785},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{790} = \mbox{select}(a_{789},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{792} = \mbox{select}(a_{789},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{794} = \mbox{select}(a_{793},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{796} = \mbox{select}(a_{793},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{798} = \mbox{select}(a_{797},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{801} = \mbox{select}(a_{800},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{803} = \mbox{select}(a_{800},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{805} = \mbox{select}(a_{804},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{807} = \mbox{select}(a_{804},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{811} = \mbox{select}(a_{810},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{813} = \mbox{select}(a_{810},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{815} = \mbox{select}(a_{814},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$e_{817} = \mbox{select}(a_{814},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$e_{819} = \mbox{select}(a_{818},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{822} = \mbox{select}(a_{821},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{44},\mbox{hypothesis})$

$e_{824} = \mbox{select}(a_{821},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{45},\mbox{hypothesis})$

$e_{826} = \mbox{select}(a_{825},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{46},\mbox{hypothesis})$

$e_{828} = \mbox{select}(a_{825},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{47},\mbox{hypothesis})$

$a_{808}\ne a_{829}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV291-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evsf},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$( \mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}))))))) = \mbox{v\_X}\mbox{ and }\mbox{v\_B} = \mbox{v\_Ba} ) \ \Rightarrow \ \mbox{v\_A}\ne \mbox{c\_Message\_Oagent\_OSpy}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV375+1.p} Priority queue checker: lemma\_not\_ok\_not\_phi






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{triple}(x,y,z)) ) )\qquad\mbox{fof}(\mbox{l11\_l}_{12},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{phi}(\mbox{triple}(u,v,w)) )\qquad\mbox{fof}(\mbox{l11\_co},\mbox{conjecture})$

\medskip\textbf{SWV288-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\mbox{ or }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_sko\_\_u7f}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_K},\mbox{v\_NA},\mbox{v\_evs}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) )\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_ONA\_\_Crypt\_\_imp\_\_Server\_\_msg}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B\_H},\mbox{v\_A},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

\medskip\textbf{SWV558-1.010.p} Store inverse (t2\_np\_sf\_ai\_00010)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(a,i,\mbox{select}(a,i)) = a\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,e),i,f) = \mbox{store}(a,i,f)\qquad\mbox{cnf}(a_4,\mbox{axiom})$

$i = j\mbox{ or }\mbox{store}(\mbox{store}(a,i,e),j,f) = \mbox{store}(\mbox{store}(a,j,f),i,e)\qquad\mbox{cnf}(a_5,\mbox{axiom})$

$a_{41} = \mbox{store}(a_1,i_1,e_{40})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{43} = \mbox{store}(a_2,i_1,e_{42})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{45} = \mbox{store}(a_{41},i_2,e_{44})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{47} = \mbox{store}(a_{43},i_2,e_{46})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{49} = \mbox{store}(a_{45},i_3,e_{48})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{51} = \mbox{store}(a_{47},i_3,e_{50})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{53} = \mbox{store}(a_{49},i_4,e_{52})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{55} = \mbox{store}(a_{51},i_4,e_{54})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{57} = \mbox{store}(a_{53},i_5,e_{56})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{59} = \mbox{store}(a_{55},i_5,e_{58})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{61} = \mbox{store}(a_{57},i_6,e_{60})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{63} = \mbox{store}(a_{59},i_6,e_{62})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{65} = \mbox{store}(a_{61},i_7,e_{64})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{67} = \mbox{store}(a_{63},i_7,e_{66})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{69} = \mbox{store}(a_{65},i_8,e_{68})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{71} = \mbox{store}(a_{67},i_8,e_{70})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{73} = \mbox{store}(a_{69},i_9,e_{72})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{75} = \mbox{store}(a_{71},i_9,e_{74})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{77} = \mbox{store}(a_{73},i_{10},e_{76})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{79} = \mbox{store}(a_{75},i_{10},e_{78})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{40} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{42} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{44} = \mbox{select}(a_{43},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{46} = \mbox{select}(a_{41},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{48} = \mbox{select}(a_{47},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{50} = \mbox{select}(a_{45},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{52} = \mbox{select}(a_{51},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{54} = \mbox{select}(a_{49},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{56} = \mbox{select}(a_{55},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{58} = \mbox{select}(a_{53},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{60} = \mbox{select}(a_{59},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{62} = \mbox{select}(a_{57},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{64} = \mbox{select}(a_{63},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{66} = \mbox{select}(a_{61},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{68} = \mbox{select}(a_{67},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{70} = \mbox{select}(a_{65},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{72} = \mbox{select}(a_{71},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{74} = \mbox{select}(a_{69},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{76} = \mbox{select}(a_{75},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{78} = \mbox{select}(a_{73},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$a_{77} = a_{79}\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV012-1.p} Fact 3 of the Neumann-Stubblebine analysis






$\mbox{party\_of\_protocol}(a)\qquad\mbox{cnf}(\mbox{a\_is\_party\_of\_protocol}_2,\mbox{axiom})$

$\mbox{message}(\mbox{sent}(a,b,\mbox{pair}(a,\mbox{an\_a\_nonce})))\qquad\mbox{cnf}(\mbox{a\_sent\_message\_i\_to\_b}_3,\mbox{axiom})$

$\mbox{a\_stored}(\mbox{pair}(b,\mbox{an\_a\_nonce}))\qquad\mbox{cnf}(\mbox{a\_stored\_message\_i}_4,\mbox{axiom})$

$( \mbox{a\_stored}(\mbox{pair}(a,b))\mbox{ and }\mbox{message}(\mbox{sent}(t,a,\mbox{triple}(\mbox{encrypt}(\mbox{quadruple}(a,b,c,d),\mbox{at}),e,f))) ) \ \Rightarrow \ \mbox{message}(\mbox{sent}(a,a,\mbox{pair}(e,\mbox{encrypt}(f,c))))\qquad\mbox{cnf}(\mbox{a\_forwards\_secure}_5,\mbox{axiom})$

$\mbox{party\_of\_protocol}(b)\qquad\mbox{cnf}(\mbox{b\_is\_party\_of\_protocol}_8,\mbox{axiom})$

$\mbox{fresh\_to\_b}(\mbox{an\_a\_nonce})\qquad\mbox{cnf}(\mbox{nonce\_a\_is\_fresh\_to\_b}_9,\mbox{axiom})$

$( \mbox{fresh\_to\_b}(b)\mbox{ and }\mbox{message}(\mbox{sent}(a,b,\mbox{pair}(a,b))) ) \ \Rightarrow \ \mbox{message}(\mbox{sent}(b,t,\mbox{triple}(b,\mbox{generate\_b\_nonce}(b),\mbox{encrypt}(\mbox{triple}(a,b,\mbox{generate\_expiration\_time}(b)),\mbox{bt}))))\qquad\mbox{cnf}(\mbox{b\_creates\_freash\_nonces\_in\_time}_{10},\mbox{axiom})$

$\mbox{t\_holds}(\mbox{key}(\mbox{at},a))\qquad\mbox{cnf}(\mbox{t\_holds\_key\_at\_for\_a}_{13},\mbox{axiom})$

$\mbox{t\_holds}(\mbox{key}(\mbox{bt},b))\qquad\mbox{cnf}(\mbox{t\_holds\_key\_bt\_for\_b}_{14},\mbox{axiom})$

$\mbox{party\_of\_protocol}(t)\qquad\mbox{cnf}(\mbox{t\_is\_party\_of\_protocol}_{15},\mbox{axiom})$

$( \mbox{message}(\mbox{sent}(a,t,\mbox{triple}(a,b,\mbox{encrypt}(\mbox{triple}(c,d,e),f))))\mbox{ and }\mbox{t\_holds}(\mbox{key}(g,c))\mbox{ and }\mbox{t\_holds}(\mbox{key}(f,a)) ) \ \Rightarrow \ \mbox{message}(\mbox{sent}(t,c,\mbox{triple}(\mbox{encrypt}(\mbox{quadruple}(a,d,\mbox{generate\_key}(d),e),g),\mbox{encrypt}(\mbox{triple}(c,\mbox{generate\_key}(d),e),f),b)))\qquad\mbox{cnf}(\mbox{server\_t\_generates\_key}_{16},\mbox{axiom})$

$\mbox{message}(\mbox{sent}(a,b,c)) \ \Rightarrow \ \mbox{intruder\_message}(c)\qquad\mbox{cnf}(\mbox{intruder\_can\_record}_{17},\mbox{axiom})$

$\mbox{intruder\_message}(\mbox{pair}(a,b)) \ \Rightarrow \ \mbox{intruder\_message}(a)\qquad\mbox{cnf}(\mbox{intruder\_decomposes\_pairs}_{18},\mbox{axiom})$

$\mbox{intruder\_message}(\mbox{pair}(a,b)) \ \Rightarrow \ \mbox{intruder\_message}(b)\qquad\mbox{cnf}(\mbox{intruder\_decomposes\_pairs}_{19},\mbox{axiom})$

$\mbox{intruder\_message}(\mbox{triple}(a,b,c)) \ \Rightarrow \ \mbox{intruder\_message}(a)\qquad\mbox{cnf}(\mbox{intruder\_decomposes\_triples}_{20},\mbox{axiom})$

$\mbox{intruder\_message}(\mbox{triple}(a,b,c)) \ \Rightarrow \ \mbox{intruder\_message}(b)\qquad\mbox{cnf}(\mbox{intruder\_decomposes\_triples}_{21},\mbox{axiom})$

$\mbox{intruder\_message}(\mbox{triple}(a,b,c)) \ \Rightarrow \ \mbox{intruder\_message}(c)\qquad\mbox{cnf}(\mbox{intruder\_decomposes\_triples}_{22},\mbox{axiom})$

$\mbox{intruder\_message}(\mbox{quadruple}(a,b,c,d)) \ \Rightarrow \ \mbox{intruder\_message}(a)\qquad\mbox{cnf}(\mbox{intruder\_decomposes\_quadruples}_{23},\mbox{axiom})$

$\mbox{intruder\_message}(\mbox{quadruple}(a,b,c,d)) \ \Rightarrow \ \mbox{intruder\_message}(b)\qquad\mbox{cnf}(\mbox{intruder\_decomposes\_quadruples}_{24},\mbox{axiom})$

$\mbox{intruder\_message}(\mbox{quadruple}(a,b,c,d)) \ \Rightarrow \ \mbox{intruder\_message}(c)\qquad\mbox{cnf}(\mbox{intruder\_decomposes\_quadruples}_{25},\mbox{axiom})$

$\mbox{intruder\_message}(\mbox{quadruple}(a,b,c,d)) \ \Rightarrow \ \mbox{intruder\_message}(d)\qquad\mbox{cnf}(\mbox{intruder\_decomposes\_quadruples}_{26},\mbox{axiom})$

$( \mbox{intruder\_message}(b)\mbox{ and }\mbox{intruder\_message}(a) ) \ \Rightarrow \ \mbox{intruder\_message}(\mbox{pair}(a,b))\qquad\mbox{cnf}(\mbox{intruder\_composes\_pairs}_{27},\mbox{axiom})$

$( \mbox{intruder\_message}(c)\mbox{ and }\mbox{intruder\_message}(b)\mbox{ and }\mbox{intruder\_message}(a) ) \ \Rightarrow \ \mbox{intruder\_message}(\mbox{triple}(a,b,c))\qquad\mbox{cnf}(\mbox{intruder\_composes\_triples}_{28},\mbox{axiom})$

$( \mbox{intruder\_message}(d)\mbox{ and }\mbox{intruder\_message}(c)\mbox{ and }\mbox{intruder\_message}(b)\mbox{ and }\mbox{intruder\_message}(a) ) \ \Rightarrow \ \mbox{intruder\_message}(\mbox{quadruple}(a,b,c,d))\qquad\mbox{cnf}(\mbox{intruder\_composes\_quadruples}_{29},\mbox{axiom})$

$( \mbox{intruder\_holds}(\mbox{key}(b,c))\mbox{ and }\mbox{intruder\_message}(\mbox{encrypt}(a,b))\mbox{ and }\mbox{party\_of\_protocol}(c) ) \ \Rightarrow \ \mbox{intruder\_message}(b)\qquad\mbox{cnf}(\mbox{intruder\_interception}_{30},\mbox{axiom})$

$( \mbox{intruder\_message}(a)\mbox{ and }\mbox{party\_of\_protocol}(c)\mbox{ and }\mbox{party\_of\_protocol}(b) ) \ \Rightarrow \ \mbox{message}(\mbox{sent}(b,c,a))\qquad\mbox{cnf}(\mbox{intruder\_message\_sent}_{31},\mbox{axiom})$

$( \mbox{intruder\_message}(a)\mbox{ and }\mbox{party\_of\_protocol}(b) ) \ \Rightarrow \ \mbox{intruder\_holds}(\mbox{key}(a,b))\qquad\mbox{cnf}(\mbox{intruder\_holds\_key}_{32},\mbox{axiom})$

$( \mbox{intruder\_holds}(\mbox{key}(b,c))\mbox{ and }\mbox{intruder\_message}(a)\mbox{ and }\mbox{party\_of\_protocol}(c) ) \ \Rightarrow \ \mbox{intruder\_message}(\mbox{encrypt}(a,b))\qquad\mbox{cnf}(\mbox{intruder\_message\_encrypted}_{33},\mbox{axiom})$

\medskip\textbf{SWV350-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_k}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{v\_U} = \mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}) \ \Rightarrow \ \mbox{v\_NA}\ne \mbox{v\_NAa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV074+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0015

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{36})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5)\mbox{ and }\mbox{leq}(\mbox{pv}_{36},-n_{135300}) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{36})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5)\mbox{ and }\mbox{leq}(\mbox{pv}_{36},-n_{135300}) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0015},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV137+1.p} Simplified proof obligation gauss\_array\_0007

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{s\_best}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_sworst}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_worst}_7)\mbox{ and }\mbox{leq}(n_2,\mbox{pv}_{1325})\mbox{ and }\mbox{leq}(\mbox{s\_best}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_sworst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_worst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{pv}_{1325},n_3)\mbox{ and }\mbox{leq}(\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{pv}_{1325}),\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{s\_best}_7))\mbox{ and }\mbox{leq}(\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{pv}_{1325}),\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{s\_worst}_7)) ) \ \Rightarrow \ \mbox{leq}(n_0,\mbox{pv}_{1325})\qquad\mbox{fof}(\mbox{gauss\_array}_{0007},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV253-2.p} Cryptographic protocol problem for messages






$\mbox{v\_K} = \mbox{v\_K\_H} \ \Rightarrow \ \mbox{c\_Message\_OinvKey}(\mbox{v\_K})\ne \mbox{c\_Message\_OinvKey}(\mbox{v\_K\_H})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_Message\_OinvKey}(\mbox{v\_K}) = \mbox{c\_Message\_OinvKey}(\mbox{v\_K\_H})\mbox{ or }\mbox{v\_K} = \mbox{v\_K\_H}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_Message\_OinvKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_y})) = \mbox{v\_y}\qquad\mbox{cnf}(\mbox{cls\_Message\_OinvKey\_A\_IinvKey\_Ay\_J\_A\_61\_61\_Ay}_0,\mbox{axiom})$

\medskip\textbf{SWV149+1.p} Simplified proof obligation gauss\_array\_0019

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\neg\,\mbox{leq}(\mbox{tptp\_float\_0}_{001},\mbox{tptp\_float\_0}_{001}) \ \Rightarrow \ \mbox{leq}(\mbox{s\_sworst}_7,n_3)\qquad\mbox{fof}(\mbox{gauss\_array}_{0019},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV547-1.007.p} Swap elements (t3\_pp\_sf\_ai\_00007)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{834} = \mbox{store}(a_1,i_4,e_{833})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{836} = \mbox{store}(a_{834},i_3,e_{835})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{838} = \mbox{store}(a_{836},i_2,e_{837})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{840} = \mbox{store}(a_{838},i_1,e_{839})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{842} = \mbox{store}(a_{840},i_0,e_{841})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{844} = \mbox{store}(a_{842},i_5,e_{843})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{846} = \mbox{store}(a_{844},i_2,e_{845})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{848} = \mbox{store}(a_{846},i_5,e_{847})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{850} = \mbox{store}(a_{848},i_1,e_{849})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{851} = \mbox{store}(a_{850},i_1,e_{849})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{853} = \mbox{store}(a_{851},i_5,e_{852})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{855} = \mbox{store}(a_{853},i_2,e_{854})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{857} = \mbox{store}(a_{855},i_5,e_{856})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{859} = \mbox{store}(a_{857},i_2,e_{858})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{860} = \mbox{store}(a_{836},i_1,e_{839})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{861} = \mbox{store}(a_{860},i_2,e_{837})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{863} = \mbox{store}(a_{861},i_5,e_{862})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{865} = \mbox{store}(a_{863},i_0,e_{864})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{867} = \mbox{store}(a_{865},i_5,e_{866})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{869} = \mbox{store}(a_{867},i_2,e_{868})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$a_{871} = \mbox{store}(a_{869},i_1,e_{870})\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$a_{872} = \mbox{store}(a_{871},i_1,e_{870})\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$a_{874} = \mbox{store}(a_{872},i_5,e_{873})\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$a_{876} = \mbox{store}(a_{874},i_2,e_{875})\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$a_{878} = \mbox{store}(a_{876},i_5,e_{877})\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{880} = \mbox{store}(a_{878},i_2,e_{879})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{833} = \mbox{select}(a_1,i_3)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{835} = \mbox{select}(a_1,i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{837} = \mbox{select}(a_{836},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{839} = \mbox{select}(a_{836},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{841} = \mbox{select}(a_{840},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{843} = \mbox{select}(a_{840},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{845} = \mbox{select}(a_{844},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{847} = \mbox{select}(a_{844},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{849} = \mbox{select}(a_{848},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{852} = \mbox{select}(a_{851},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{854} = \mbox{select}(a_{851},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{856} = \mbox{select}(a_{855},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{858} = \mbox{select}(a_{855},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{862} = \mbox{select}(a_{861},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{864} = \mbox{select}(a_{861},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{866} = \mbox{select}(a_{865},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$e_{868} = \mbox{select}(a_{865},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$e_{870} = \mbox{select}(a_{869},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{873} = \mbox{select}(a_{872},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{44},\mbox{hypothesis})$

$e_{875} = \mbox{select}(a_{872},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{45},\mbox{hypothesis})$

$e_{877} = \mbox{select}(a_{876},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{46},\mbox{hypothesis})$

$e_{879} = \mbox{select}(a_{876},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{47},\mbox{hypothesis})$

$e_{882} = \mbox{select}(a_{859},i_{881})\qquad\mbox{cnf}(\mbox{hyp}_{48},\mbox{hypothesis})$

$e_{883} = \mbox{select}(a_{880},i_{881})\qquad\mbox{cnf}(\mbox{hyp}_{49},\mbox{hypothesis})$

$i_{881} = \mbox{sk}(a_{859},a_{880})\qquad\mbox{cnf}(\mbox{hyp}_{50},\mbox{hypothesis})$

$e_{882}\ne e_{883}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV446$\wedge$1.p} K says ((K says A) =$>$ A) in BL






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/LCL009\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV010\string^0.ax'})$

$\forall k{:}\;\mbox{individuals},a{:}\;\mbox{\$i}\to \mbox{\$o}{:}\;( \mbox{bl\_valid}@ ( \mbox{bl\_says}@ k@ ( \mbox{bl\_impl}@ ( \mbox{bl\_says}@ k@ ( \mbox{bl\_atom}@ a ) )@ ( \mbox{bl\_atom}@ a ) ) ) )\qquad\mbox{thf}(\mbox{bl\_conceit},\mbox{conjecture})$

\medskip\textbf{SWV379+1.p} Priority queue checker: lemma\_not\_ok\_persistence\_induction step 3






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l15\_co},\mbox{conjecture})$

\medskip\textbf{SWV349-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evso},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_Aa},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa}))))),\mbox{v\_X})),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_k}))),\mbox{c\_List\_Oset}(\mbox{v\_evso},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$( \mbox{v\_U} = \mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})\mbox{ and }\mbox{v\_NA} = \mbox{v\_NB} ) \ \Rightarrow \ \mbox{v\_NB}\ne \mbox{v\_NBa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV381+3.p} Priority queue checker: lemma\_min\_elem\_smallest






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w,x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\iff \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),x) )\qquad\mbox{fof}(\mbox{l17\_li}_{56},\mbox{lemma})$

$\forall u,v,w{:}\;( ( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w))\mbox{ or }\neg\,\mbox{ok}(\mbox{triple}(u,v,w)) ) \ \Rightarrow \ \forall x,y,z{:}\;( \mbox{succ\_cpq}(\mbox{triple}(u,v,w),\mbox{triple}(x,y,z)) \ \Rightarrow \ ( \neg\,\mbox{ok}(\mbox{triple}(x,y,z))\mbox{ or }\neg\,\mbox{check\_cpq}(\mbox{triple}(x,y,z)) ) ) )\qquad\mbox{fof}(\mbox{l19\_l}_{20},\mbox{lemma})$

$\forall u,v,w{:}\;( ( \mbox{contains\_slb}(u,v)\mbox{ and }\mbox{strictly\_less\_than}(v,w) ) \ \Rightarrow \ ( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,w),v,w)\mbox{ or }\exists x{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(u,w),v,x)\mbox{ and }w < x ) ) )\qquad\mbox{fof}(\mbox{l44\_l}_{45},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{check\_cpq}(\mbox{triple}(u,v,w))\iff \forall x,y{:}\;( \mbox{pair\_in\_list}(v,x,y) \ \Rightarrow \ y < x ) )\qquad\mbox{fof}(\mbox{l43\_li}_{4142},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \mbox{issmallestelement\_pq}(i(\mbox{triple}(u,v,w)),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l17\_co},\mbox{conjecture})$

\medskip\textbf{SWV391+1.p} Priority queue checker: tmp\_not\_check\_02






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \mbox{check\_cpq}(\mbox{triple}(u,v,w))\iff \forall x,y{:}\;( \mbox{pair\_in\_list}(v,x,y) \ \Rightarrow \ y < x ) )\qquad\mbox{fof}(\mbox{l27\_li}_{4142},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{pair\_in\_list}(u,v,w) \ \Rightarrow \ \forall x{:}\;( \mbox{contains\_slb}(u,x) \ \Rightarrow \ ( \mbox{pair\_in\_list}(\mbox{remove\_slb}(u,x),v,w)\mbox{ or }v = x ) ) )\qquad\mbox{fof}(\mbox{l27\_li}_{2829},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{check\_cpq}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x))\mbox{ and }\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) ) \ \Rightarrow \ \forall y{:}\;( \mbox{pair\_in\_list}(v,x,y) \ \Rightarrow \ y < x ) )\qquad\mbox{fof}(\mbox{l27\_l}_{30},\mbox{lemma})$

$\forall u,v,w,x{:}\;( \mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) \ \Rightarrow \ \mbox{contains\_slb}(v,x) )\qquad\mbox{fof}(\mbox{l27\_l}_{33},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{check\_cpq}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x))\mbox{ and }\mbox{ok}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) ) \ \Rightarrow \ \mbox{check\_cpq}(\mbox{triple}(u,v,w)) )\qquad\mbox{fof}(\mbox{l27\_co},\mbox{conjecture})$

\medskip\textbf{SWV550-1.004.p} Store inverse (t1\_np\_nf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_1,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4)) = \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4))\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV433$\wedge$2.p} ICL$\wedge$=$>$ logic mapping to modal logic implies that Example 2 holds






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^2.ax'})$

$\mbox{admin}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{admin},\mbox{type})$

$\mbox{bob}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{bob},\mbox{type})$

$\mbox{alice}{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{alice},\mbox{type})$

$\mbox{deletefile}_1{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(\mbox{deletfile}_1,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_1,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{admin} )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) ) )\qquad\mbox{thf}(\mbox{ax}_2,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{bob} )@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ \mbox{alice} )@ ( \mbox{icl\_princ}@ \mbox{bob} ) ) )\qquad\mbox{thf}(\mbox{ax}_3,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ \mbox{alice} )@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 ) )\qquad\mbox{thf}(\mbox{ax}_4,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_atom}@ \mbox{deletefile}_1 )\qquad\mbox{thf}(\mbox{conj},\mbox{conjecture})$

\medskip\textbf{SWV371+1.p} Priority queue checker: lemma\_pi\_min\_elem






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w{:}\;( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l7\_l}_8,\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \mbox{issmallestelement\_pq}(i(\mbox{triple}(u,v,w)),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l7\_lX},\mbox{lemma})$

$\forall u,v,w{:}\;( \mbox{phi}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) \ \Rightarrow \ \mbox{pi\_sharp\_find\_min}(i(\mbox{triple}(u,v,w)),\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l7\_co},\mbox{conjecture})$

\medskip\textbf{SWV071+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0012

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{21})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{23})\mbox{ and }\mbox{leq}(\mbox{pv}_{21},-n_5)\mbox{ and }\mbox{leq}(\mbox{pv}_{23},-n_{135300}) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{21})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{23})\mbox{ and }\mbox{leq}(\mbox{pv}_{21},-n_5)\mbox{ and }\mbox{leq}(\mbox{pv}_{23},-n_{135300}) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0012},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV430$\wedge$1.p} ICL$\wedge$=$>$ logic mapping to modal logic implies 'trans'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^2.ax'})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$b{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(b,\mbox{type})$

$c{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(c,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ b ) )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ b )@ ( \mbox{icl\_princ}@ c ) )@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ c ) ) ) )\qquad\mbox{thf}(\mbox{trans},\mbox{conjecture})$

\medskip\textbf{SWV549-1.004.p} Store inverse (t1\_np\_nf\_ai\_00004)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4)) = \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3)),i_4,\mbox{select}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2,\mbox{select}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2)),i_3,\mbox{select}(\mbox{store}(\mbox{store}(a_2,i_1,\mbox{select}(a_1,i_1)),i_2,\mbox{select}(\mbox{store}(a_1,i_1,\mbox{select}(a_2,i_1)),i_2)),i_3)),i_4))\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_1\ne a_2\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV360-2.p} Cryptographic protocol problem for Yahalom






$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_S\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X\_H},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA\_H}),\mbox{v\_nb}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\mbox{ and }\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_C},\mbox{v\_S},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{v\_nb}))))),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_nb},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{v\_B\_H} = \mbox{v\_B} )\qquad\mbox{cnf}(\mbox{cls\_Yahalom\_OSays\_\_unique\_\_NB}_2,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Ba},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV339-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Event\_OkeysFor\_\_parts\_\_insert\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_KAB},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{v\_K}\ne \mbox{v\_KAB}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3))),\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{v\_K} = \mbox{c\_Public\_OshrK}(\mbox{v\_B})\mbox{ or }\mbox{v\_K} = \mbox{c\_Public\_OshrK}(\mbox{v\_A})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV416+1.p} Priority queue checker: Formula (8)






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u,v,w,x,y{:}\;i(\mbox{triple}(u,w,x)) = i(\mbox{triple}(v,w,y))\qquad\mbox{fof}(\mbox{main3\_li}_{12},\mbox{lemma})$

$\forall u,v,w,x{:}\;( \mbox{contains\_pq}(i(\mbox{triple}(u,v,w)),x) \ \Rightarrow \ i(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) = \mbox{remove\_pq}(i(\mbox{triple}(u,v,w)),x) )\qquad\mbox{fof}(\mbox{main3\_li}_{34},\mbox{lemma})$

$\forall u,v,w,x{:}\;( \mbox{pi\_remove}(\mbox{triple}(u,v,w),x) \ \Rightarrow \ ( \mbox{phi}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) \ \Rightarrow \ ( \mbox{pi\_sharp\_remove}(i(\mbox{triple}(u,v,w)),x)\mbox{ and }i(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) = \mbox{remove\_pq}(i(\mbox{triple}(u,v,w)),x) ) ) )\qquad\mbox{fof}(\mbox{co}_3,\mbox{conjecture})$

\medskip\textbf{SWV147+1.p} Simplified proof obligation gauss\_array\_0017

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\neg\,\mbox{leq}(\mbox{tptp\_float\_0}_{001},\mbox{tptp\_float\_0}_{001}) \ \Rightarrow \ \mbox{leq}(n_0,\mbox{s\_worst}_7)\qquad\mbox{fof}(\mbox{gauss\_array}_{0017},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV338-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Message\_OinvKey}(\mbox{v\_K})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Event\_OkeysFor\_\_parts\_\_insert\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg}))),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_K},\mbox{c\_Message\_OkeysFor}(\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Event\_Oused}(\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

\medskip\textbf{SWV487+3.p} Matrix is upper triangular






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{real\_zero} ) )\mbox{ and }\forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k,k) = \mbox{real\_one} )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qii},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_less}(j,i)\mbox{ and }\mbox{int\_leq}(i,n) ) \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\qquad\mbox{fof}(\mbox{ut},\mbox{conjecture})$

\medskip\textbf{SWV326-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_Oc\_A\_58\_Aparts\_A\_Iknows\_ASpy\_Aevs1\_J\_A\_61\_61\_62\_Ac\_A\_58\_Aused\_Aevs1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_parts}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_1),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_C})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_1)),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{v\_C} = \mbox{v\_Ba}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{21},\mbox{negated\_conjecture})$

$\mbox{v\_A} = \mbox{v\_Aa}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{v\_Ba} = \mbox{v\_C} \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_1)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{32},\mbox{negated\_conjecture})$

$\mbox{v\_NA} = \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

\medskip\textbf{SWV274-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV004-0.ax'})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_synthD\_\_dest}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_lessequals}(\mbox{v\_G},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_trans}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Osynth}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV300-2.p} Cryptographic protocol problem for Otway Rees






$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_4,\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_Aaa},\mbox{v\_Ba},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_Ka})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_4),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_A},\mbox{v\_B},\mbox{v\_X}),\mbox{c\_List\_Oset}(\mbox{v\_evs},\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Event\_OSays\_\_imp\_\_analz\_\_Spy\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OCrypt\_\_synth}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_analz}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OMPair\_\_synth\_\_analz\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_c},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_into\_\_parts\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_OInj}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUnE}_0,\mbox{axiom})$

\medskip\textbf{SWV328-2.p} Cryptographic protocol problem for Yahalom






$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}),\mbox{v\_H},\mbox{tc\_Message\_Omsg}) )\qquad\mbox{cnf}(\mbox{cls\_Message\_OCrypt\_\_synth\_\_eq}_0,\mbox{axiom})$

$( \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\mbox{ and }\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Z},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_OFake\_\_parts\_\_insert\_\_in\_\_Un\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_conj\_\_parts}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_c},\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{t\_a}) \ \Rightarrow \ ( \mbox{c\_in}(\mbox{v\_c},\mbox{v\_B},\mbox{t\_a})\mbox{ or }\mbox{c\_in}(\mbox{v\_c},\mbox{v\_A},\mbox{t\_a}) )\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_iff}_0,\mbox{axiom})$

\medskip\textbf{SWV061+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0002

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\mbox{true} \ \Rightarrow \ ( ( \neg\,\mbox{gt}(\mbox{loopcounter},n_1) \ \Rightarrow \ \mbox{true} )\mbox{ and }( \mbox{gt}(\mbox{loopcounter},n_1) \ \Rightarrow \ \mbox{true} ) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0002},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV305-1.p} Cryptographic protocol problem for Otway Rees






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV006-2.ax'})$

$( \mbox{c\_in}(\mbox{v\_evs},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\mbox{ and }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{c\_Public\_OshrK}(\mbox{v\_A})),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs})),\mbox{tc\_Message\_Omsg}) ) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_OtwayRees\_OSpy\_\_see\_\_shrK\_\_D\_\_dest}_0,\mbox{axiom})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evsf},\mbox{c\_OtwayRees\_Ootway},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}))),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf}),\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA\_H},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A\_H}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}))))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))),\mbox{c\_Message\_Oparts}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evsf})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

\medskip\textbf{SWV385+1.p} Priority queue checker: lemma\_not\_min\_elem\_not\_check\_induction02






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \neg\,\mbox{ok}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \neg\,\mbox{ok}(\mbox{im\_succ\_cpq}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l21\_li}_{1316},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ ( \neg\,\mbox{check\_cpq}(\mbox{im\_succ\_cpq}(\mbox{triple}(u,v,w)))\mbox{ or }\neg\,\mbox{ok}(\mbox{im\_succ\_cpq}(\mbox{triple}(u,v,w))) ) )\qquad\mbox{fof}(\mbox{l21\_li}_{2225},\mbox{lemma})$

$\forall u,v,w{:}\;( ( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w))\mbox{ or }\neg\,\mbox{ok}(\mbox{triple}(u,v,w)) ) \ \Rightarrow \ ( \neg\,\mbox{check\_cpq}(\mbox{im\_succ\_cpq}(\mbox{triple}(u,v,w)))\mbox{ or }\neg\,\mbox{ok}(\mbox{im\_succ\_cpq}(\mbox{triple}(u,v,w))) ) )\qquad\mbox{fof}(\mbox{l21\_co},\mbox{conjecture})$

\medskip\textbf{SWV435$\wedge$4.p} ICL$\wedge$B logic mapping to modal logic implies 'untrust'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$( \mbox{icl\_princ}@ a ) = \mbox{icl\_true}\qquad\mbox{thf}(\mbox{ax}_1,\mbox{axiom})$

$\mbox{iclval}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ \mbox{icl\_false} )\qquad\mbox{thf}(\mbox{untrust},\mbox{conjecture})$

\medskip\textbf{SWV312-2.p} Cryptographic protocol problem for Otway Rees






$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_U},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{c\_Message\_Oagent\_OServer},\mbox{v\_B},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K}))),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_K})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent}) \ \Rightarrow \ \mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_x},\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NA},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_NB},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B})))))))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_4,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

\medskip\textbf{SWV136+1.p} Simplified proof obligation gauss\_array\_0006

Proof obligation emerging from the array-safety verification for
 the gauss program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{s\_best}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_sworst}_7)\mbox{ and }\mbox{leq}(n_0,\mbox{s\_worst}_7)\mbox{ and }\mbox{leq}(n_2,\mbox{pv}_{1325})\mbox{ and }\mbox{leq}(\mbox{s\_best}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_sworst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{s\_worst}_7,n_3)\mbox{ and }\mbox{leq}(\mbox{pv}_{1325},n_3)\mbox{ and }\mbox{leq}(\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{pv}_{1325}),\mbox{a\_select}_2(\mbox{s\_values}_7,\mbox{s\_best}_7)) ) \ \Rightarrow \ \mbox{leq}(n_0,\mbox{pv}_{1325})\qquad\mbox{fof}(\mbox{gauss\_array}_{0006},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV370+1.p} Priority queue checker: lemma\_contains\_s\_I induction






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$\forall u{:}\;( \forall v,w,x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(v,u,w),x)\iff \mbox{contains\_pq}(i(\mbox{triple}(v,u,w)),x) ) \ \Rightarrow \ \forall y,z,x_1,x_2,x_3{:}\;( \mbox{contains\_cpq}(\mbox{triple}(y,\mbox{insert\_slb}(u,\mbox{pair}(x_1,x_2)),z),x_3)\iff \mbox{contains\_pq}(i(\mbox{triple}(y,\mbox{insert\_slb}(u,\mbox{pair}(x_1,x_2)),z)),x_3) ) )\qquad\mbox{fof}(\mbox{l6\_co},\mbox{conjecture})$

\medskip\textbf{SWV057+1.p} Unsimplified proof obligation cl5\_nebula\_norm\_0043

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{62})\mbox{ and }\mbox{leq}(\mbox{pv}_{62},-n_5) ) \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0043},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV518-1.030.p} Store commutativity (t3\_np\_nf\_ni\_00030)

The result of storing a set of elements in different positions 
 within an array is not acted by the relative order of the store 
 operations.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_1,e_1),n_2,e_2),n_3,e_3),n_4,e_4),n_5,e_5),n_6,e_6),n_7,e_7),n_8,e_8),n_9,e_9),n_{10},e_{10}),n_{11},e_{11}),n_{12},e_{12}),n_{13},e_{13}),n_{14},e_{14}),n_{15},e_{15}),n_{16},e_{16}),n_{17},e_{17}),n_{18},e_{18}),n_{19},e_{19}),n_{20},e_{20}),n_{21},e_{21}),n_{22},e_{22}),n_{23},e_{23}),n_{24},e_{24}),n_{25},e_{25}),n_{26},e_{26}),n_{27},e_{27}),n_{28},e_{28}),n_{29},e_{29}),n_1,e_1)\ne \mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(\mbox{store}(a_1,n_{13},e_{13}),n_1,e_1),n_{19},e_{19}),n_4,e_4),n_9,e_9),n_{30},e_{30}),n_2,e_2),n_{15},e_{15}),n_{25},e_{25}),n_{18},e_{18}),n_{20},e_{20}),n_8,e_8),n_{21},e_{21}),n_6,e_6),n_{11},e_{11}),n_{14},e_{14}),n_{29},e_{29}),n_5,e_5),n_{26},e_{26}),n_{22},e_{22}),n_{27},e_{27}),n_3,e_3),n_{12},e_{12}),n_{16},e_{16}),n_{28},e_{28}),n_{17},e_{17}),n_{23},e_{23}),n_{24},e_{24}),n_7,e_7),n_{10},e_{10})\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV543-1.007.p} Swap elements (t3\_np\_sf\_ai\_00007)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$\mbox{store}(\mbox{store}(a,i,\mbox{select}(a,j)),j,\mbox{select}(a,i)) = \mbox{store}(\mbox{store}(a,j,\mbox{select}(a,i)),i,\mbox{select}(a,j))\qquad\mbox{cnf}(a_3,\mbox{axiom})$

$a_{783} = \mbox{store}(a_1,i_4,e_{782})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{785} = \mbox{store}(a_{783},i_3,e_{784})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{787} = \mbox{store}(a_{785},i_2,e_{786})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{789} = \mbox{store}(a_{787},i_1,e_{788})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{791} = \mbox{store}(a_{789},i_0,e_{790})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{793} = \mbox{store}(a_{791},i_5,e_{792})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{795} = \mbox{store}(a_{793},i_2,e_{794})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{797} = \mbox{store}(a_{795},i_5,e_{796})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{799} = \mbox{store}(a_{797},i_1,e_{798})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{800} = \mbox{store}(a_{799},i_1,e_{798})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{802} = \mbox{store}(a_{800},i_5,e_{801})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{804} = \mbox{store}(a_{802},i_2,e_{803})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{806} = \mbox{store}(a_{804},i_5,e_{805})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{808} = \mbox{store}(a_{806},i_2,e_{807})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{809} = \mbox{store}(a_{785},i_1,e_{788})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{810} = \mbox{store}(a_{809},i_2,e_{786})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{812} = \mbox{store}(a_{810},i_5,e_{811})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{814} = \mbox{store}(a_{812},i_0,e_{813})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{816} = \mbox{store}(a_{814},i_5,e_{815})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{818} = \mbox{store}(a_{816},i_2,e_{817})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$a_{820} = \mbox{store}(a_{818},i_1,e_{819})\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$a_{821} = \mbox{store}(a_{820},i_1,e_{819})\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$a_{823} = \mbox{store}(a_{821},i_5,e_{822})\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$a_{825} = \mbox{store}(a_{823},i_2,e_{824})\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$a_{827} = \mbox{store}(a_{825},i_5,e_{826})\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{829} = \mbox{store}(a_{827},i_2,e_{828})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{782} = \mbox{select}(a_1,i_3)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{784} = \mbox{select}(a_1,i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{786} = \mbox{select}(a_{785},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{788} = \mbox{select}(a_{785},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{790} = \mbox{select}(a_{789},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{792} = \mbox{select}(a_{789},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{794} = \mbox{select}(a_{793},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{796} = \mbox{select}(a_{793},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{798} = \mbox{select}(a_{797},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{801} = \mbox{select}(a_{800},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{803} = \mbox{select}(a_{800},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{805} = \mbox{select}(a_{804},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{807} = \mbox{select}(a_{804},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{811} = \mbox{select}(a_{810},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{813} = \mbox{select}(a_{810},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{815} = \mbox{select}(a_{814},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$e_{817} = \mbox{select}(a_{814},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$e_{819} = \mbox{select}(a_{818},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{822} = \mbox{select}(a_{821},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{44},\mbox{hypothesis})$

$e_{824} = \mbox{select}(a_{821},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{45},\mbox{hypothesis})$

$e_{826} = \mbox{select}(a_{825},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{46},\mbox{hypothesis})$

$e_{828} = \mbox{select}(a_{825},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{47},\mbox{hypothesis})$

$a_{808}\ne a_{829}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV392+1.p} Priority queue checker: tmp\_not\_check\_02\_1 base






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u,v{:}\;( \mbox{pair\_in\_list}(\mbox{create\_slb},u,v) \ \Rightarrow \ \forall w{:}\;( \mbox{contains\_slb}(\mbox{create\_slb},w) \ \Rightarrow \ ( \mbox{pair\_in\_list}(\mbox{remove\_slb}(\mbox{create\_slb},w),u,v)\mbox{ or }u = w ) ) )\qquad\mbox{fof}(\mbox{l28\_co},\mbox{conjecture})$

\medskip\textbf{SWV386+1.p} Priority queue checker: lemma\_not\_min\_elem\_not\_check\_ind\_steps 1






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \forall x{:}\;\neg\,\mbox{check\_cpq}(\mbox{insert\_cpq}(\mbox{triple}(u,v,w),x)) )\qquad\mbox{fof}(\mbox{l22\_l}_{26},\mbox{lemma})$

$\forall u,v,w{:}\;( \neg\,\mbox{check\_cpq}(\mbox{triple}(u,v,w)) \ \Rightarrow \ \forall x{:}\;( \neg\,\mbox{check\_cpq}(\mbox{insert\_cpq}(\mbox{triple}(u,v,w),x))\mbox{ or }\neg\,\mbox{ok}(\mbox{insert\_cpq}(\mbox{triple}(u,v,w),x)) ) )\qquad\mbox{fof}(\mbox{l22\_co},\mbox{conjecture})$

\medskip\textbf{SWV008-1.p} E7






$\mbox{include}(\mbox{'Axioms/SWV001-0.ax'})$

$\neg\,n < l\qquad\mbox{cnf}(\mbox{clause}_1,\mbox{negated\_conjecture})$

$1 < l\qquad\mbox{cnf}(\mbox{clause}_2,\mbox{negated\_conjecture})$

$a(l) < a(\mbox{predecessor}(l))\qquad\mbox{cnf}(\mbox{clause}_3,\mbox{negated\_conjecture})$

$( 1 < n\mbox{ and }a(x) < a(\mbox{predecessor}(n)) ) \ \Rightarrow \ ( x < n\mbox{ or }n < x )\qquad\mbox{cnf}(\mbox{clause}_4,\mbox{negated\_conjecture})$

$( 1 < x\mbox{ and }x < n ) \ \Rightarrow \ \neg\,a(x) < a(\mbox{predecessor}(x))\qquad\mbox{cnf}(\mbox{clause}_5,\mbox{negated\_conjecture})$

\medskip\textbf{SWV537-1.007.p} Swap elements (t1\_pp\_sf\_ai\_00007)

Swapping an element at position i1 with an element at position 
 i2 is equivalent to swapping the element at position i2 with the
 element at position i1.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{834} = \mbox{store}(a_1,i_4,e_{833})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{836} = \mbox{store}(a_{834},i_3,e_{835})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{838} = \mbox{store}(a_{836},i_2,e_{837})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{840} = \mbox{store}(a_{838},i_1,e_{839})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{842} = \mbox{store}(a_{840},i_0,e_{841})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{844} = \mbox{store}(a_{842},i_5,e_{843})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{846} = \mbox{store}(a_{844},i_2,e_{845})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{848} = \mbox{store}(a_{846},i_5,e_{847})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{850} = \mbox{store}(a_{848},i_1,e_{849})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{851} = \mbox{store}(a_{850},i_1,e_{849})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{853} = \mbox{store}(a_{851},i_5,e_{852})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{855} = \mbox{store}(a_{853},i_2,e_{854})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{857} = \mbox{store}(a_{855},i_5,e_{856})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{859} = \mbox{store}(a_{857},i_2,e_{858})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{860} = \mbox{store}(a_{836},i_1,e_{839})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{861} = \mbox{store}(a_{860},i_2,e_{837})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{863} = \mbox{store}(a_{861},i_5,e_{862})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{865} = \mbox{store}(a_{863},i_0,e_{864})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{867} = \mbox{store}(a_{865},i_5,e_{866})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{869} = \mbox{store}(a_{867},i_2,e_{868})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$a_{871} = \mbox{store}(a_{869},i_1,e_{870})\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$a_{872} = \mbox{store}(a_{871},i_1,e_{870})\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$a_{874} = \mbox{store}(a_{872},i_5,e_{873})\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$a_{876} = \mbox{store}(a_{874},i_2,e_{875})\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$a_{878} = \mbox{store}(a_{876},i_5,e_{877})\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$a_{880} = \mbox{store}(a_{878},i_2,e_{879})\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{833} = \mbox{select}(a_1,i_3)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{835} = \mbox{select}(a_1,i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{837} = \mbox{select}(a_{836},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{839} = \mbox{select}(a_{836},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{841} = \mbox{select}(a_{840},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{843} = \mbox{select}(a_{840},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{845} = \mbox{select}(a_{844},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{847} = \mbox{select}(a_{844},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{849} = \mbox{select}(a_{848},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{852} = \mbox{select}(a_{851},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{854} = \mbox{select}(a_{851},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{856} = \mbox{select}(a_{855},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{858} = \mbox{select}(a_{855},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{862} = \mbox{select}(a_{861},i_0)\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{864} = \mbox{select}(a_{861},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{866} = \mbox{select}(a_{865},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$e_{868} = \mbox{select}(a_{865},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$e_{870} = \mbox{select}(a_{869},i_1)\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{873} = \mbox{select}(a_{872},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{44},\mbox{hypothesis})$

$e_{875} = \mbox{select}(a_{872},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{45},\mbox{hypothesis})$

$e_{877} = \mbox{select}(a_{876},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{46},\mbox{hypothesis})$

$e_{879} = \mbox{select}(a_{876},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{47},\mbox{hypothesis})$

$e_{882} = \mbox{select}(a_{859},i_{881})\qquad\mbox{cnf}(\mbox{hyp}_{48},\mbox{hypothesis})$

$e_{883} = \mbox{select}(a_{880},i_{881})\qquad\mbox{cnf}(\mbox{hyp}_{49},\mbox{hypothesis})$

$i_{881} = \mbox{sk}(a_{859},a_{880})\qquad\mbox{cnf}(\mbox{hyp}_{50},\mbox{hypothesis})$

$e_{882}\ne e_{883}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV556-1.010.p} Store inverse (t1\_pp\_sf\_ai\_00010)

If the arrays resulting from swapping elements of array a with
 the elements of array b occurring in the same positions are equal,
 then a and b must have been equal to begin with.




$\mbox{select}(\mbox{store}(a,i,e),i) = e\qquad\mbox{cnf}(a_1,\mbox{axiom})$

$i = j\mbox{ or }\mbox{select}(\mbox{store}(a,i,e),j) = \mbox{select}(a,j)\qquad\mbox{cnf}(a_2,\mbox{axiom})$

$a_{44} = \mbox{store}(a_1,i_1,e_{43})\qquad\mbox{cnf}(\mbox{hyp}_0,\mbox{hypothesis})$

$a_{46} = \mbox{store}(a_2,i_1,e_{45})\qquad\mbox{cnf}(\mbox{hyp}_1,\mbox{hypothesis})$

$a_{48} = \mbox{store}(a_{44},i_2,e_{47})\qquad\mbox{cnf}(\mbox{hyp}_2,\mbox{hypothesis})$

$a_{50} = \mbox{store}(a_{46},i_2,e_{49})\qquad\mbox{cnf}(\mbox{hyp}_3,\mbox{hypothesis})$

$a_{52} = \mbox{store}(a_{48},i_3,e_{51})\qquad\mbox{cnf}(\mbox{hyp}_4,\mbox{hypothesis})$

$a_{54} = \mbox{store}(a_{50},i_3,e_{53})\qquad\mbox{cnf}(\mbox{hyp}_5,\mbox{hypothesis})$

$a_{56} = \mbox{store}(a_{52},i_4,e_{55})\qquad\mbox{cnf}(\mbox{hyp}_6,\mbox{hypothesis})$

$a_{58} = \mbox{store}(a_{54},i_4,e_{57})\qquad\mbox{cnf}(\mbox{hyp}_7,\mbox{hypothesis})$

$a_{60} = \mbox{store}(a_{56},i_5,e_{59})\qquad\mbox{cnf}(\mbox{hyp}_8,\mbox{hypothesis})$

$a_{62} = \mbox{store}(a_{58},i_5,e_{61})\qquad\mbox{cnf}(\mbox{hyp}_9,\mbox{hypothesis})$

$a_{64} = \mbox{store}(a_{60},i_6,e_{63})\qquad\mbox{cnf}(\mbox{hyp}_{10},\mbox{hypothesis})$

$a_{66} = \mbox{store}(a_{62},i_6,e_{65})\qquad\mbox{cnf}(\mbox{hyp}_{11},\mbox{hypothesis})$

$a_{68} = \mbox{store}(a_{64},i_7,e_{67})\qquad\mbox{cnf}(\mbox{hyp}_{12},\mbox{hypothesis})$

$a_{70} = \mbox{store}(a_{66},i_7,e_{69})\qquad\mbox{cnf}(\mbox{hyp}_{13},\mbox{hypothesis})$

$a_{72} = \mbox{store}(a_{68},i_8,e_{71})\qquad\mbox{cnf}(\mbox{hyp}_{14},\mbox{hypothesis})$

$a_{74} = \mbox{store}(a_{70},i_8,e_{73})\qquad\mbox{cnf}(\mbox{hyp}_{15},\mbox{hypothesis})$

$a_{76} = \mbox{store}(a_{72},i_9,e_{75})\qquad\mbox{cnf}(\mbox{hyp}_{16},\mbox{hypothesis})$

$a_{78} = \mbox{store}(a_{74},i_9,e_{77})\qquad\mbox{cnf}(\mbox{hyp}_{17},\mbox{hypothesis})$

$a_{80} = \mbox{store}(a_{76},i_1,e_{79})\qquad\mbox{cnf}(\mbox{hyp}_{18},\mbox{hypothesis})$

$a_{82} = \mbox{store}(a_{78},i_{10},e_{81})\qquad\mbox{cnf}(\mbox{hyp}_{19},\mbox{hypothesis})$

$e_{43} = \mbox{select}(a_2,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{20},\mbox{hypothesis})$

$e_{45} = \mbox{select}(a_1,i_1)\qquad\mbox{cnf}(\mbox{hyp}_{21},\mbox{hypothesis})$

$e_{47} = \mbox{select}(a_{46},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{22},\mbox{hypothesis})$

$e_{49} = \mbox{select}(a_{44},i_2)\qquad\mbox{cnf}(\mbox{hyp}_{23},\mbox{hypothesis})$

$e_{51} = \mbox{select}(a_{50},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{24},\mbox{hypothesis})$

$e_{53} = \mbox{select}(a_{48},i_3)\qquad\mbox{cnf}(\mbox{hyp}_{25},\mbox{hypothesis})$

$e_{55} = \mbox{select}(a_{54},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{26},\mbox{hypothesis})$

$e_{57} = \mbox{select}(a_{52},i_4)\qquad\mbox{cnf}(\mbox{hyp}_{27},\mbox{hypothesis})$

$e_{59} = \mbox{select}(a_{58},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{28},\mbox{hypothesis})$

$e_{61} = \mbox{select}(a_{56},i_5)\qquad\mbox{cnf}(\mbox{hyp}_{29},\mbox{hypothesis})$

$e_{63} = \mbox{select}(a_{62},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{30},\mbox{hypothesis})$

$e_{65} = \mbox{select}(a_{60},i_6)\qquad\mbox{cnf}(\mbox{hyp}_{31},\mbox{hypothesis})$

$e_{67} = \mbox{select}(a_{66},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{32},\mbox{hypothesis})$

$e_{69} = \mbox{select}(a_{64},i_7)\qquad\mbox{cnf}(\mbox{hyp}_{33},\mbox{hypothesis})$

$e_{71} = \mbox{select}(a_{70},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{34},\mbox{hypothesis})$

$e_{73} = \mbox{select}(a_{68},i_8)\qquad\mbox{cnf}(\mbox{hyp}_{35},\mbox{hypothesis})$

$e_{75} = \mbox{select}(a_{74},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{36},\mbox{hypothesis})$

$e_{77} = \mbox{select}(a_{72},i_9)\qquad\mbox{cnf}(\mbox{hyp}_{37},\mbox{hypothesis})$

$e_{79} = \mbox{select}(a_{78},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{38},\mbox{hypothesis})$

$e_{81} = \mbox{select}(a_{76},i_{10})\qquad\mbox{cnf}(\mbox{hyp}_{39},\mbox{hypothesis})$

$e_{84} = \mbox{select}(a_1,i_{83})\qquad\mbox{cnf}(\mbox{hyp}_{40},\mbox{hypothesis})$

$e_{85} = \mbox{select}(a_2,i_{83})\qquad\mbox{cnf}(\mbox{hyp}_{41},\mbox{hypothesis})$

$i_{83} = \mbox{sk}(a_1,a_2)\qquad\mbox{cnf}(\mbox{hyp}_{42},\mbox{hypothesis})$

$a_{80} = a_{82}\qquad\mbox{cnf}(\mbox{hyp}_{43},\mbox{hypothesis})$

$e_{84}\ne e_{85}\qquad\mbox{cnf}(\mbox{goal},\mbox{negated\_conjecture})$

\medskip\textbf{SWV407+1.p} Priority queue checker: lemma\_not\_min\_elem\_not\_check






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\forall u,v,w{:}\;( \mbox{check\_cpq}(\mbox{triple}(u,v,w))\iff \forall x,y{:}\;( \mbox{pair\_in\_list}(v,x,y) \ \Rightarrow \ y < x ) )\qquad\mbox{fof}(\mbox{l43\_li}_{4142},\mbox{lemma})$

$\forall u,v,w,x{:}\;( ( \mbox{contains\_slb}(v,x)\mbox{ and }\mbox{strictly\_less\_than}(x,\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) ) \ \Rightarrow \ ( \mbox{pair\_in\_list}(\mbox{update\_slb}(v,\mbox{findmin\_pqp\_res}(u)),x,\mbox{findmin\_pqp\_res}(u))\mbox{ or }\exists y{:}\;( \mbox{pair\_in\_list}(\mbox{update\_slb}(v,\mbox{findmin\_pqp\_res}(u)),x,y)\mbox{ and }\mbox{findmin\_pqp\_res}(u) < y ) ) )\qquad\mbox{fof}(\mbox{l43\_l}_{44},\mbox{lemma})$

$\forall u,v,w{:}\;( \exists x{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,v,w),x)\mbox{ and }\mbox{strictly\_less\_than}(x,\mbox{findmin\_cpq\_res}(\mbox{triple}(u,v,w))) ) \ \Rightarrow \ \neg\,\mbox{check\_cpq}(\mbox{findmin\_cpq\_eff}(\mbox{triple}(u,v,w))) )\qquad\mbox{fof}(\mbox{l43\_co},\mbox{conjecture})$

\medskip\textbf{SWV282-1.p} Cryptographic protocol problem for public






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{c\_lessequals}(\mbox{v\_n},\mbox{c\_plus}(\mbox{v\_n},\mbox{v\_m},\mbox{tc\_nat}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Ole\_\_add1}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_n},\mbox{c\_plus}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Ole\_\_add2}_0,\mbox{axiom})$

$\mbox{c\_less}(\mbox{v\_m},\mbox{c\_Suc}(\mbox{v\_n}),\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oless\_\_Suc\_\_eq\_\_le}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_less}(\mbox{v\_m},\mbox{c\_Suc}(\mbox{v\_n}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oless\_\_Suc\_\_eq\_\_le}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_sko\_\_urX}(\mbox{v\_evs}),\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Public\_ONonce\_\_supply\_\_lemma}_0,\mbox{axiom})$

$\mbox{v\_U} = \mbox{v\_W}\mbox{ or }\mbox{v\_V} = \mbox{v\_W}\mbox{ or }\mbox{v\_U} = \mbox{v\_V}\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_W}),\mbox{c\_Event\_Oused}(\mbox{v\_evs\_H\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_V}),\mbox{c\_Event\_Oused}(\mbox{v\_evs\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip\textbf{SWV023+1.p} Unsimplified proof obligation gauss\_init\_0005

Proof obligation emerging from the init-safety verification for
 the gauss program. init-safety ensures that each variable or
 individual array element has been assigned a defined value before
 it is used.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{i0\_init} = \mbox{init}\mbox{ and }\mbox{sigma\_init} = \mbox{init}\mbox{ and }\forall a{:}\;( ( \mbox{leq}(n_0,a)\mbox{ and }\mbox{leq}(a,n_2) ) \ \Rightarrow \ \forall b{:}\;( ( \mbox{leq}(n_0,b)\mbox{ and }\mbox{leq}(b,n_3) ) \ \Rightarrow \ \mbox{a\_select}_3(\mbox{simplex7\_init},b,a) = \mbox{init} ) )\mbox{ and }\forall c{:}\;( ( \mbox{leq}(n_0,c)\mbox{ and }\mbox{leq}(c,n_3) ) \ \Rightarrow \ \mbox{a\_select}_2(\mbox{s\_values7\_init},c) = \mbox{init} ) ) \ \Rightarrow \ \mbox{true}\qquad\mbox{fof}(\mbox{gauss\_init}_{0005},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV359-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Aa},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_KAB},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Ba},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV263-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-2.ax'})$

$\mbox{c\_Message\_Oagent\_OServer}\ne \mbox{c\_Message\_Oagent\_OFriend}(\mbox{v\_nat\_H})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oagent\_Odistinct\_\_1\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oagent\_OFriend}(\mbox{v\_nat\_H})\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_Message\_Oagent\_Odistinct\_\_2\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oagent\_OServer}\ne \mbox{c\_Message\_Oagent\_OSpy}\qquad\mbox{cnf}(\mbox{cls\_Message\_Oagent\_Odistinct\_\_3\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oagent\_OSpy}\ne \mbox{c\_Message\_Oagent\_OServer}\qquad\mbox{cnf}(\mbox{cls\_Message\_Oagent\_Odistinct\_\_4\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oagent\_OFriend}(\mbox{v\_nat})\ne \mbox{c\_Message\_Oagent\_OSpy}\qquad\mbox{cnf}(\mbox{cls\_Message\_Oagent\_Odistinct\_\_5\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oagent\_OSpy}\ne \mbox{c\_Message\_Oagent\_OFriend}(\mbox{v\_nat})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oagent\_Odistinct\_\_6\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oagent\_OFriend}(\mbox{v\_nat}) = \mbox{c\_Message\_Oagent\_OFriend}(\mbox{v\_nat\_H}) \ \Rightarrow \ \mbox{v\_nat} = \mbox{v\_nat\_H}\qquad\mbox{cnf}(\mbox{cls\_Message\_Oagent\_Oinject\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_agent}) = \mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_agent\_H}) \ \Rightarrow \ \mbox{v\_agent} = \mbox{v\_agent\_H}\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_Oinject\_\_1\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Omsg\_ONumber}(\mbox{v\_nat}) = \mbox{c\_Message\_Omsg\_ONumber}(\mbox{v\_nat\_H}) \ \Rightarrow \ \mbox{v\_nat} = \mbox{v\_nat\_H}\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_Oinject\_\_2\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_nat}) = \mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_nat\_H}) \ \Rightarrow \ \mbox{v\_nat} = \mbox{v\_nat\_H}\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_Oinject\_\_3\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_nat}) = \mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_nat\_H}) \ \Rightarrow \ \mbox{v\_nat} = \mbox{v\_nat\_H}\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_Oinject\_\_4\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Omsg\_OHash}(\mbox{v\_msg}) = \mbox{c\_Message\_Omsg\_OHash}(\mbox{v\_msg\_H}) \ \Rightarrow \ \mbox{v\_msg} = \mbox{v\_msg\_H}\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_Oinject\_\_5\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_msg}_1,\mbox{v\_msg}_2) = \mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_msg1\_H},\mbox{v\_msg2\_H}) \ \Rightarrow \ \mbox{v\_msg}_1 = \mbox{v\_msg1\_H}\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_Oinject\_\_6\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_msg}_1,\mbox{v\_msg}_2) = \mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_msg1\_H},\mbox{v\_msg2\_H}) \ \Rightarrow \ \mbox{v\_msg}_2 = \mbox{v\_msg2\_H}\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_Oinject\_\_6\_\_iff1}_1,\mbox{axiom})$

$\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_nat},\mbox{v\_msg}) = \mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_nat\_H},\mbox{v\_msg\_H}) \ \Rightarrow \ \mbox{v\_nat} = \mbox{v\_nat\_H}\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_Oinject\_\_7\_\_iff1}_0,\mbox{axiom})$

$\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_nat},\mbox{v\_msg}) = \mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_nat\_H},\mbox{v\_msg\_H}) \ \Rightarrow \ \mbox{v\_msg} = \mbox{v\_msg\_H}\qquad\mbox{cnf}(\mbox{cls\_Message\_Omsg\_Oinject\_\_7\_\_iff1}_1,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OFst}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OInj}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OMPair}(\mbox{v\_X},\mbox{v\_Y}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_Y},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OSnd}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{v\_G},\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV985-1.p} Java type soundness 555\_24






$\mbox{c\_COMBI}(\mbox{v\_P},\mbox{t\_a}) = \mbox{v\_P}\qquad\mbox{cnf}(\mbox{cls\_COMBI\_\_def}_0,\mbox{axiom})$

$\mbox{c\_TypeSafe\_\_Mirabelle\_Osconf}(\mbox{v\_P},\mbox{v\_E},\mbox{v\_s\_H})\qquad\mbox{cnf}(\mbox{cls\_refl\_I2\_J}_0,\mbox{axiom})$

$\mbox{c\_WellTypeRT\_OWTrt}(\mbox{v\_P},\mbox{c\_State\_Ohp}(\mbox{v\_s\_H}),\mbox{v\_E},\mbox{v\_e\_H},\mbox{v\_T\_\_\_\_})\qquad\mbox{cnf}(\mbox{cls\_refl\_I1\_J}_0,\mbox{axiom})$

$\mbox{c\_COMBI}(\mbox{v\_P},\mbox{t\_a}) = \mbox{v\_P}\qquad\mbox{cnf}(\mbox{cls\_COMBI\_\_def\_\_raw}_0,\mbox{axiom})$

$\neg\,\mbox{c\_TypeSafe\_\_Mirabelle\_Osconf}(\mbox{v\_P},\mbox{v\_E},\mbox{v\_s\_H})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_fequal}(\mbox{v\_x},\mbox{v\_x},\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_ATP\_\_Linkup\_Oequal\_\_imp\_\_fequal}_0,\mbox{axiom})$

$\mbox{c\_fequal}(\mbox{v\_X},\mbox{v\_Y},\mbox{t\_a}) \ \Rightarrow \ \mbox{v\_X} = \mbox{v\_Y}\qquad\mbox{cnf}(\mbox{cls\_ATP\_\_Linkup\_Ofequal\_\_imp\_\_equal}_0,\mbox{axiom})$

\medskip\textbf{SWV403+1.p} Priority queue checker: tmp\_not\_check\_03\_3 step






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\forall u{:}\;( \forall v,w,x{:}\;( ( \mbox{pair\_in\_list}(u,v,w)\mbox{ and }\mbox{strictly\_less\_than}(w,x) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(u,x),v,x) ) \ \Rightarrow \ \forall y,z,x_1,x_2,x_3{:}\;( ( \mbox{pair\_in\_list}(\mbox{insert\_slb}(u,\mbox{pair}(x_2,x_3)),y,z)\mbox{ and }\mbox{strictly\_less\_than}(z,x_1) ) \ \Rightarrow \ \mbox{pair\_in\_list}(\mbox{update\_slb}(\mbox{insert\_slb}(u,\mbox{pair}(x_2,x_3)),x_1),y,x_1) ) )\qquad\mbox{fof}(\mbox{l39\_co},\mbox{conjecture})$

\medskip\textbf{SWV358-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_2,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_2),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{v\_Ba},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NAa}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_2)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_2,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Ba},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

\medskip\textbf{SWV416+2.p} Priority queue checker: Formula (8)






$\mbox{include}(\mbox{'Axioms/SWV007+0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV007+4.ax'})$

$( \forall u,v,w,x{:}\;i(\mbox{triple}(u,\mbox{create\_slb},w)) = i(\mbox{triple}(v,\mbox{create\_slb},x))\mbox{ and }\forall y{:}\;( \forall z,x_1,x_2,x_3{:}\;i(\mbox{triple}(z,y,x_2)) = i(\mbox{triple}(x_1,y,x_3)) \ \Rightarrow \ \forall x_4,x_5,x_6,x_7,x_8,x_9{:}\;i(\mbox{triple}(x_4,\mbox{insert\_slb}(y,\mbox{pair}(x_8,x_9)),x_6)) = i(\mbox{triple}(x_5,\mbox{insert\_slb}(y,\mbox{pair}(x_8,x_9)),x_7)) ) ) \ \Rightarrow \ \forall x_{10},x_{11},x_{12},x_{13},x_{14}{:}\;i(\mbox{triple}(x_{10},x_{12},x_{13})) = i(\mbox{triple}(x_{11},x_{12},x_{14}))\qquad\mbox{fof}(\mbox{big3\_induction}_1,\mbox{axiom})$

$( \forall u,v,w{:}\;( \mbox{contains\_pq}(i(\mbox{triple}(u,\mbox{create\_slb},v)),w) \ \Rightarrow \ i(\mbox{remove\_cpq}(\mbox{triple}(u,\mbox{create\_slb},v),w)) = \mbox{remove\_pq}(i(\mbox{triple}(u,\mbox{create\_slb},v)),w) )\mbox{ and }\forall x{:}\;( \forall y,z,x_1{:}\;( \mbox{contains\_pq}(i(\mbox{triple}(y,x,z)),x_1) \ \Rightarrow \ i(\mbox{remove\_cpq}(\mbox{triple}(y,x,z),x_1)) = \mbox{remove\_pq}(i(\mbox{triple}(y,x,z)),x_1) ) \ \Rightarrow \ \forall x_2,x_3,x_4,x_5,x_6{:}\;( \mbox{contains\_pq}(i(\mbox{triple}(x_2,\mbox{insert\_slb}(x,\mbox{pair}(x_5,x_6)),x_3)),x_4) \ \Rightarrow \ i(\mbox{remove\_cpq}(\mbox{triple}(x_2,\mbox{insert\_slb}(x,\mbox{pair}(x_5,x_6)),x_3),x_4)) = \mbox{remove\_pq}(i(\mbox{triple}(x_2,\mbox{insert\_slb}(x,\mbox{pair}(x_5,x_6)),x_3)),x_4) ) ) ) \ \Rightarrow \ \forall x_7,x_8,x_9,x_{10}{:}\;( \mbox{contains\_pq}(i(\mbox{triple}(x_7,x_8,x_9)),x_{10}) \ \Rightarrow \ i(\mbox{remove\_cpq}(\mbox{triple}(x_7,x_8,x_9),x_{10})) = \mbox{remove\_pq}(i(\mbox{triple}(x_7,x_8,x_9)),x_{10}) )\qquad\mbox{fof}(\mbox{big3\_induction}_2,\mbox{axiom})$

$( \forall u,v,w{:}\;( \mbox{contains\_cpq}(\mbox{triple}(u,\mbox{create\_slb},v),w)\iff \mbox{contains\_pq}(i(\mbox{triple}(u,\mbox{create\_slb},v)),w) )\mbox{ and }\forall x{:}\;( \forall y,z,x_1{:}\;( \mbox{contains\_cpq}(\mbox{triple}(y,x,z),x_1)\iff \mbox{contains\_pq}(i(\mbox{triple}(y,x,z)),x_1) ) \ \Rightarrow \ \forall x_2,x_3,x_4,x_5,x_6{:}\;( \mbox{contains\_cpq}(\mbox{triple}(x_2,\mbox{insert\_slb}(x,\mbox{pair}(x_4,x_5)),x_3),x_6)\iff \mbox{contains\_pq}(i(\mbox{triple}(x_2,\mbox{insert\_slb}(x,\mbox{pair}(x_4,x_5)),x_3)),x_6) ) ) ) \ \Rightarrow \ \forall x_7,x_8,x_9,x_{10}{:}\;( \mbox{contains\_cpq}(\mbox{triple}(x_7,x_8,x_9),x_{10})\iff \mbox{contains\_pq}(i(\mbox{triple}(x_7,x_8,x_9)),x_{10}) )\qquad\mbox{fof}(\mbox{big3\_induction}_3,\mbox{axiom})$

$\forall u,v,w,x{:}\;( \mbox{pi\_remove}(\mbox{triple}(u,v,w),x) \ \Rightarrow \ ( \mbox{phi}(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) \ \Rightarrow \ ( \mbox{pi\_sharp\_remove}(i(\mbox{triple}(u,v,w)),x)\mbox{ and }i(\mbox{remove\_cpq}(\mbox{triple}(u,v,w),x)) = \mbox{remove\_pq}(i(\mbox{triple}(u,v,w)),x) ) ) )\qquad\mbox{fof}(\mbox{co}_3,\mbox{conjecture})$

\medskip\textbf{SWV262-2.p} Cryptographic protocol problem for messages






$\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_insert}(\mbox{v\_Y},\mbox{v\_H},\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg}))\ne \mbox{c\_union}(\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_Y},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_G}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{c\_emptyset},\mbox{v\_y},\mbox{t\_a}) = \mbox{v\_y}\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_empty\_\_left}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{c\_insert}(\mbox{v\_a},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{t\_a}) = \mbox{c\_insert}(\mbox{v\_a},\mbox{c\_union}(\mbox{v\_B},\mbox{v\_C},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_insert\_\_left}_0,\mbox{axiom})$

\medskip\textbf{SWV282-2.p} Cryptographic protocol problem for public






$\mbox{v\_U} = \mbox{v\_W}\mbox{ or }\mbox{v\_V} = \mbox{v\_W}\mbox{ or }\mbox{v\_U} = \mbox{v\_V}\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_W}),\mbox{c\_Event\_Oused}(\mbox{v\_evs\_H\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_V}),\mbox{c\_Event\_Oused}(\mbox{v\_evs\_H}),\mbox{tc\_Message\_Omsg})\mbox{ or }\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_Binomial\_Obinomial}(\mbox{v\_y},\mbox{c\_Suc}(c_0)) = \mbox{v\_y}\qquad\mbox{cnf}(\mbox{cls\_Binomial\_Obinomial\_\_1}_0,\mbox{axiom})$

$\mbox{c\_Binomial\_Obinomial}(\mbox{c\_Suc}(\mbox{v\_n}),\mbox{c\_Suc}(\mbox{v\_k})) = \mbox{c\_plus}(\mbox{c\_Binomial\_Obinomial}(\mbox{v\_n},\mbox{v\_k}),\mbox{c\_Binomial\_Obinomial}(\mbox{v\_n},\mbox{c\_Suc}(\mbox{v\_k})),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Binomial\_Obinomial\_\_Suc\_\_Suc}_0,\mbox{axiom})$

$\mbox{c\_Binomial\_Obinomial}(\mbox{v\_n},c_0) = c_1\qquad\mbox{cnf}(\mbox{cls\_Binomial\_Obinomial\_\_n\_\_0}_0,\mbox{axiom})$

$c_1 = \mbox{c\_Suc}(c_0)\qquad\mbox{cnf}(\mbox{cls\_Nat\_OOne\_\_nat\_\_def}_0,\mbox{axiom})$

$\mbox{c\_minus}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat}) = c_0 \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Odiff\_\_is\_\_0\_\_eq}_0,\mbox{axiom})$

$\mbox{c\_minus}(\mbox{v\_m},\mbox{v\_m},\mbox{tc\_nat}) = c_0\qquad\mbox{cnf}(\mbox{cls\_Nat\_Odiff\_\_self\_\_eq\_\_0}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_n},\mbox{c\_plus}(\mbox{v\_n},\mbox{v\_m},\mbox{tc\_nat}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Ole\_\_add1}_0,\mbox{axiom})$

$\mbox{c\_less}(\mbox{v\_n},\mbox{c\_Suc}(\mbox{v\_n}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_OlessI}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_less}(\mbox{v\_m},\mbox{c\_Suc}(\mbox{v\_n}),\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Oless\_\_Suc\_\_eq\_\_le}_1,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{c\_plus}(\mbox{v\_k},\mbox{v\_m},\mbox{tc\_nat}),\mbox{c\_plus}(\mbox{v\_k},\mbox{v\_n},\mbox{tc\_nat}),\mbox{tc\_nat}) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{v\_m},\mbox{v\_n},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Onat\_\_add\_\_left\_\_cancel\_\_le}_0,\mbox{axiom})$

$\neg\,\mbox{c\_less}(\mbox{c\_plus}(\mbox{v\_j},\mbox{v\_i},\mbox{tc\_nat}),\mbox{v\_i},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Nat\_Onot\_\_add\_\_less2}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_U}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \neg\,\mbox{c\_lessequals}(\mbox{v\_sko\_\_urX}(\mbox{v\_evs}),\mbox{v\_U},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_Public\_ONonce\_\_supply\_\_lemma}_0,\mbox{axiom})$

$\mbox{c\_Finite\_\_Set\_Ocard}(\mbox{c\_SetInterval\_OatMost}(\mbox{v\_u},\mbox{tc\_nat}),\mbox{tc\_nat}) = \mbox{c\_Suc}(\mbox{v\_u})\qquad\mbox{cnf}(\mbox{cls\_SetInterval\_Ocard\_\_atMost}_0,\mbox{axiom})$

\medskip\textbf{SWV361-1.p} Cryptographic protocol problem for Yahalom






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-2.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-3.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-4.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-5.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-7.ax'})$

$\neg\,\mbox{c\_in}(\mbox{v\_A},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_B},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_Ba},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_{11},\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_evs}_3,\mbox{c\_Yahalom\_Oyahalom},\mbox{tc\_List\_Olist}(\mbox{tc\_Event\_Oevent}))\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OKey}(\mbox{v\_KAB}),\mbox{c\_Event\_Oused}(\mbox{v\_evs}_3),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_KAB},\mbox{c\_Message\_OsymKeys},\mbox{tc\_nat})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_4,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OGets}(\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_Ba}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_Aa}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NBa})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Event\_Oevent\_ONotes}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{v\_U}))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_6,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{c\_Event\_Oevent\_OSays}(\mbox{v\_B},\mbox{c\_Message\_Oagent\_OServer},\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{c\_Public\_OshrK}(\mbox{v\_B}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_OAgent}(\mbox{v\_A}),\mbox{c\_Message\_Omsg\_OMPair}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NA}),\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB})))))),\mbox{c\_List\_Oset}(\mbox{v\_evs}_3,\mbox{tc\_Event\_Oevent}),\mbox{tc\_Event\_Oevent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_7,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{c\_Message\_Omsg\_ONonce}(\mbox{v\_NB}),\mbox{c\_Message\_Oanalz}(\mbox{c\_Event\_Oknows}(\mbox{c\_Message\_Oagent\_OSpy},\mbox{v\_evs}_3)),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_8,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_Aa},\mbox{c\_Event\_Obad},\mbox{tc\_Message\_Oagent})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_9,\mbox{negated\_conjecture})$

\medskip\textbf{SWV076+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0017

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0017},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV250-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-1.ax'})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_analz\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G}),\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oanalz\_\_synth\_\_Un}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_Message\_Osynth}(\mbox{v\_H})) = \mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_synth}_0,\mbox{axiom})$

$\mbox{c\_lessequals}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_set}(\mbox{tc\_Message\_Omsg})) \ \Rightarrow \ \mbox{c\_lessequals}(\mbox{c\_Message\_Osynth}(\mbox{v\_G}),\mbox{c\_Message\_Osynth}(\mbox{v\_H}),\mbox{tc\_set}(\mbox{tc\_Message\_Omsg}))\qquad\mbox{cnf}(\mbox{cls\_Message\_Osynth\_\_mono}_0,\mbox{axiom})$

$\mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_x},\mbox{c\_Message\_Oanalz}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{c\_in}(\mbox{v\_x},\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

$\neg\,\mbox{c\_in}(\mbox{v\_x},\mbox{c\_union}(\mbox{c\_Message\_Osynth}(\mbox{c\_Message\_Oanalz}(\mbox{v\_G})),\mbox{c\_Message\_Oanalz}(\mbox{c\_union}(\mbox{v\_G},\mbox{v\_H},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_3,\mbox{negated\_conjecture})$

\medskip\textbf{SWV491+3.p} Matrix is identity






$\forall i,j{:}\;( \mbox{int\_leq}(i,j)\iff ( \mbox{int\_less}(i,j)\mbox{ or }i = j ) )\qquad\mbox{fof}(\mbox{int\_leq},\mbox{axiom})$

$\forall i,j,k{:}\;( ( \mbox{int\_less}(i,j)\mbox{ and }\mbox{int\_less}(j,k) ) \ \Rightarrow \ \mbox{int\_less}(i,k) )\qquad\mbox{fof}(\mbox{int\_less\_transitive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j) \ \Rightarrow \ i\ne j )\qquad\mbox{fof}(\mbox{int\_less\_irreflexive},\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\mbox{ or }\mbox{int\_leq}(j,i) )\qquad\mbox{fof}(\mbox{int\_less\_total},\mbox{axiom})$

$\mbox{int\_less}(\mbox{int\_zero},\mbox{int\_one})\qquad\mbox{fof}(\mbox{int\_zero\_one},\mbox{axiom})$

$\forall i,j{:}\;i + j = j + i\qquad\mbox{fof}(\mbox{plus\_commutative},\mbox{axiom})$

$\forall i{:}\;i + \mbox{int\_zero} = i\qquad\mbox{fof}(\mbox{plus\_zero},\mbox{axiom})$

$\forall i_1,j_1,i_2,j_2{:}\;( ( \mbox{int\_less}(i_1,j_1)\mbox{ and }\mbox{int\_leq}(i_2,j_2) ) \ \Rightarrow \ \mbox{int\_leq}(i_1 + i_2,j_1 + j_2) )\qquad\mbox{fof}(\mbox{plus\_and\_order}_1,\mbox{axiom})$

$\forall i,j{:}\;( \mbox{int\_less}(i,j)\iff \exists k{:}\;( i + k = j\mbox{ and }\mbox{int\_less}(\mbox{int\_zero},k) ) )\qquad\mbox{fof}(\mbox{plus\_and\_inverse},\mbox{axiom})$

$\forall i{:}\;( \mbox{int\_less}(\mbox{int\_zero},i)\iff \mbox{int\_leq}(\mbox{int\_one},i) )\qquad\mbox{fof}(\mbox{one\_successor\_of\_zero},\mbox{axiom})$

$\mbox{real\_zero}\ne \mbox{real\_one}\qquad\mbox{fof}(\mbox{real\_constants},\mbox{axiom})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( \forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }i = j + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k + c,k) = \mbox{real\_zero} ) )\mbox{ and }\forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,j) ) \ \Rightarrow \ a(k,k) = \mbox{real\_one} )\mbox{ and }\forall c{:}\;( ( \mbox{int\_less}(\mbox{int\_zero},c)\mbox{ and }j = i + c ) \ \Rightarrow \ \forall k{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},k)\mbox{ and }\mbox{int\_leq}(k,i) ) \ \Rightarrow \ a(k,k + c) = \mbox{real\_zero} ) ) ) )\qquad\mbox{fof}(\mbox{qih},\mbox{hypothesis})$

$\forall i,j{:}\;( ( \mbox{int\_leq}(\mbox{int\_one},i)\mbox{ and }\mbox{int\_leq}(i,n)\mbox{ and }\mbox{int\_leq}(\mbox{int\_one},j)\mbox{ and }\mbox{int\_leq}(j,n) ) \ \Rightarrow \ ( ( \mbox{int\_less}(i,j) \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\mbox{ and }( \mbox{int\_less}(j,i) \ \Rightarrow \ a(i,j) = \mbox{real\_zero} )\mbox{ and }( i = j \ \Rightarrow \ a(i,j) = \mbox{real\_one} ) ) )\qquad\mbox{fof}(\mbox{diag},\mbox{conjecture})$

\medskip\textbf{SWV431$\wedge$2.p} ICL$\wedge$=$>$ logic mapping to modal logic implies 'speaking\_for'






$\mbox{include}(\mbox{'Axioms/LCL008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^0.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV008\string^2.ax'})$

$a{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(a,\mbox{type})$

$b{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(b,\mbox{type})$

$s{:}\;\mbox{\$i}\to \mbox{\$o}\qquad\mbox{thf}(s,\mbox{type})$

$\mbox{iclval}@ ( \mbox{icl\_impl}@ ( \mbox{icl\_impl\_princ}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_princ}@ b ) )@ ( \mbox{icl\_impl}@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ a )@ ( \mbox{icl\_atom}@ s ) )@ ( \mbox{icl\_says}@ ( \mbox{icl\_princ}@ b )@ ( \mbox{icl\_atom}@ s ) ) ) )\qquad\mbox{thf}(\mbox{speaking\_for},\mbox{conjecture})$

\medskip\textbf{SWV063+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0004

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{43})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300})\mbox{ and }\mbox{leq}(\mbox{pv}_{43},-n_5) ) \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{10})\mbox{ and }\mbox{leq}(n_0,\mbox{pv}_{43})\mbox{ and }\mbox{leq}(\mbox{pv}_{10},-n_{135300})\mbox{ and }\mbox{leq}(\mbox{pv}_{43},-n_5) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0004},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_4)\qquad\mbox{fof}(\mbox{gt\_135300}_4,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_5)\qquad\mbox{fof}(\mbox{gt\_135300}_5,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_135300\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_0)\qquad\mbox{fof}(\mbox{gt\_135300}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_1)\qquad\mbox{fof}(\mbox{gt\_135300}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_2)\qquad\mbox{fof}(\mbox{gt\_135300}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\mbox{gt}(n_{135300},n_3)\qquad\mbox{fof}(\mbox{gt\_135300}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV059+1.p} Unsimplified proof obligation cl5\_nebula\_norm\_0049

Proof obligation emerging from the norm-safety verification for
 the cl5\_nebula program. norm-safety ensures that the contents of
 certain one-dimensional arrays add up to one.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$\mbox{geq}(\mbox{pv}_{72},\mbox{tptp\_float\_0}_{001}) \ \Rightarrow \ ( ( \neg\,\mbox{gt}(n_1 + \mbox{loopcounter},n_1) \ \Rightarrow \ \mbox{true} )\mbox{ and }( \mbox{gt}(n_1 + \mbox{loopcounter},n_1) \ \Rightarrow \ \mbox{true} ) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_norm}_{0049},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV078+1.p} Unsimplified proof obligation cl5\_nebula\_array\_0019

Proof obligation emerging from the array-safety verification for
 the cl5\_nebula program. array-safety ensures that each access to
 an array element is within the specified upper and lower bounds
 of the array.




$\mbox{include}(\mbox{'Axioms/SWV003+0.ax'})$

$( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5) ) \ \Rightarrow \ ( ( n_0\ne \mbox{pv}_{70} \ \Rightarrow \ ( \mbox{leq}(n_0,\mbox{pv}_{31})\mbox{ and }\mbox{leq}(\mbox{pv}_{31},-n_5) ) )\mbox{ and }( n_0 = \mbox{pv}_{70} \ \Rightarrow \ \mbox{true} ) )\qquad\mbox{fof}(\mbox{cl5\_nebula\_array}_{0019},\mbox{conjecture})$

$\mbox{gt}(n_5,n_4)\qquad\mbox{fof}(\mbox{gt\_5}_4,\mbox{axiom})$

$\mbox{gt}(n_4,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_4\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_5,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_5\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_0,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_0\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_1,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_1\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_2,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_2\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_3,\mbox{tptp\_minus}_1)\qquad\mbox{fof}(\mbox{gt\_3\_tptp\_minus}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_0)\qquad\mbox{fof}(\mbox{gt\_4}_0,\mbox{axiom})$

$\mbox{gt}(n_5,n_0)\qquad\mbox{fof}(\mbox{gt\_5}_0,\mbox{axiom})$

$\mbox{gt}(n_1,n_0)\qquad\mbox{fof}(\mbox{gt\_1}_0,\mbox{axiom})$

$\mbox{gt}(n_2,n_0)\qquad\mbox{fof}(\mbox{gt\_2}_0,\mbox{axiom})$

$\mbox{gt}(n_3,n_0)\qquad\mbox{fof}(\mbox{gt\_3}_0,\mbox{axiom})$

$\mbox{gt}(n_4,n_1)\qquad\mbox{fof}(\mbox{gt\_4}_1,\mbox{axiom})$

$\mbox{gt}(n_5,n_1)\qquad\mbox{fof}(\mbox{gt\_5}_1,\mbox{axiom})$

$\mbox{gt}(n_2,n_1)\qquad\mbox{fof}(\mbox{gt\_2}_1,\mbox{axiom})$

$\mbox{gt}(n_3,n_1)\qquad\mbox{fof}(\mbox{gt\_3}_1,\mbox{axiom})$

$\mbox{gt}(n_4,n_2)\qquad\mbox{fof}(\mbox{gt\_4}_2,\mbox{axiom})$

$\mbox{gt}(n_5,n_2)\qquad\mbox{fof}(\mbox{gt\_5}_2,\mbox{axiom})$

$\mbox{gt}(n_3,n_2)\qquad\mbox{fof}(\mbox{gt\_3}_2,\mbox{axiom})$

$\mbox{gt}(n_4,n_3)\qquad\mbox{fof}(\mbox{gt\_4}_3,\mbox{axiom})$

$\mbox{gt}(n_5,n_3)\qquad\mbox{fof}(\mbox{gt\_5}_3,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_4) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_5) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3\mbox{ or }x = n_4\mbox{ or }x = n_5 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_5,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_0) ) \ \Rightarrow \ x = n_0 )\qquad\mbox{fof}(\mbox{finite\_domain}_0,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_1) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_1,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_2) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_2,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{leq}(n_0,x)\mbox{ and }\mbox{leq}(x,n_3) ) \ \Rightarrow \ ( x = n_0\mbox{ or }x = n_1\mbox{ or }x = n_2\mbox{ or }x = n_3 ) )\qquad\mbox{fof}(\mbox{finite\_domain}_3,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0)))) = n_4\qquad\mbox{fof}(\mbox{successor}_4,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))))) = n_5\qquad\mbox{fof}(\mbox{successor}_5,\mbox{axiom})$

$\mbox{succ}(n_0) = n_1\qquad\mbox{fof}(\mbox{successor}_1,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(n_0)) = n_2\qquad\mbox{fof}(\mbox{successor}_2,\mbox{axiom})$

$\mbox{succ}(\mbox{succ}(\mbox{succ}(n_0))) = n_3\qquad\mbox{fof}(\mbox{successor}_3,\mbox{axiom})$

\medskip\textbf{SWV819-1.p} Hoare logic with procedures 116\_1

Completeness is taken relative to completeness of the underlying
 logic. Two versions of completeness proof: nested single recursion
 and simultaneous recursion in call rule.




$\mbox{c\_Code\_\_Evaluation\_Otracing}(\mbox{v\_s},\mbox{v\_x},\mbox{t\_a}) = \mbox{v\_x}\qquad\mbox{cnf}(\mbox{cls\_tracing\_\_def}_0,\mbox{axiom})$

$\mbox{c\_Code\_\_Evaluation\_Otracing}(\mbox{v\_s},\mbox{v\_x},\mbox{t\_a}) = \mbox{v\_x}\qquad\mbox{cnf}(\mbox{cls\_tracing\_\_def\_\_raw}_0,\mbox{axiom})$

$\mbox{v\_s}\ne \mbox{v\_t}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

$\mbox{v\_s} = \mbox{v\_ta}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_1,\mbox{negated\_conjecture})$

$\mbox{v\_ta}\ne \mbox{v\_t}\qquad\mbox{cnf}(\mbox{cls\_conjecture}_2,\mbox{negated\_conjecture})$

\medskip\textbf{SWV262-1.p} Cryptographic protocol problem for messages






$\mbox{include}(\mbox{'Axioms/MSC001-0.ax'})$

$\mbox{include}(\mbox{'Axioms/MSC001-1.ax'})$

$\mbox{include}(\mbox{'Axioms/SWV005-0.ax'})$

$\mbox{c\_in}(\mbox{c\_Message\_Omsg\_OCrypt}(\mbox{v\_K},\mbox{v\_X}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg}) \ \Rightarrow \ \mbox{c\_in}(\mbox{v\_X},\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_OBody\_\_dest}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{v\_H},\mbox{tc\_Message\_Omsg})) = \mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_Message\_Oparts\_\_insert}_0,\mbox{axiom})$

$\mbox{c\_union}(\mbox{c\_union}(\mbox{v\_A},\mbox{v\_B},\mbox{t\_a}),\mbox{v\_C},\mbox{t\_a}) = \mbox{c\_union}(\mbox{v\_A},\mbox{c\_union}(\mbox{v\_B},\mbox{v\_C},\mbox{t\_a}),\mbox{t\_a})\qquad\mbox{cnf}(\mbox{cls\_Set\_OUn\_\_assoc}_0,\mbox{axiom})$

$\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_insert}(\mbox{v\_Y},\mbox{v\_H},\mbox{tc\_Message\_Omsg}),\mbox{tc\_Message\_Omsg}))\ne \mbox{c\_union}(\mbox{c\_union}(\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_X},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{c\_Message\_Oparts}(\mbox{c\_insert}(\mbox{v\_Y},\mbox{c\_emptyset},\mbox{tc\_Message\_Omsg})),\mbox{tc\_Message\_Omsg}),\mbox{c\_Message\_Oparts}(\mbox{v\_H}),\mbox{tc\_Message\_Omsg})\qquad\mbox{cnf}(\mbox{cls\_conjecture}_0,\mbox{negated\_conjecture})$

\medskip
\end{document}