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    \textbf{SWB003+1.ax} RDFS Extensional axioms






$\forall p,c{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},p,c)\iff ( \mbox{ip}(p)\mbox{ and }\mbox{ic}(c)\mbox{ and }\forall x,y{:}\;( \mbox{iext}(p,x,y) \ \Rightarrow \ \mbox{icext}(c,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_domain},\mbox{axiom})$

$\forall p,c{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_range},p,c)\iff ( \mbox{ip}(p)\mbox{ and }\mbox{ip}(c)\mbox{ and }\forall x,y{:}\;( \mbox{iext}(p,x,y) \ \Rightarrow \ \mbox{icext}(c,y) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_range},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subClassOf},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x) \ \Rightarrow \ \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subclassof},\mbox{axiom})$

$\forall p_1,p_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},p_1,p_2)\iff ( \mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall x,y{:}\;( \mbox{iext}(p_1,x,y) \ \Rightarrow \ \mbox{iext}(p_2,x,y) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subpropertyof},\mbox{axiom})$

\medskip\textbf{SWB012+2.p} Template Class






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall p,c,x,y{:}\;( ( \mbox{iext}(\mbox{uri\_rdfs\_domain},p,c)\mbox{ and }\mbox{iext}(p,x,y) ) \ \Rightarrow \ \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_domain\_main},\mbox{axiom})$

$\forall z,s_1,c_1,s_2,c_2,s_3,c_3{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,c_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,c_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,s_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_3,c_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_3,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_intersectionOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\mbox{ic}(c_3)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff ( \mbox{icext}(c_1,x)\mbox{ and }\mbox{icext}(c_2,x)\mbox{ and }\mbox{icext}(c_3,x) ) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_bool\_intersectionof\_class}_{003},\mbox{axiom})$

$\forall z,p,a{:}\;( ( \mbox{iext}(\mbox{uri\_owl\_hasValue},z,a)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},z,p) ) \ \Rightarrow \ \forall x{:}\;( \mbox{icext}(z,x)\iff \mbox{iext}(p,x,a) ) )\qquad\mbox{fof}(\mbox{owl\_restrict\_hasvalue},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_name},\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_foaf\_Person})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_012\_Template\_Class},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3,\mbox{bNODE\_r}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_Person},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{uri\_ex\_PersonAttribute},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_owl\_DatatypeProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_3,\mbox{bNODE\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_r},\mbox{uri\_rdfs\_domain})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_hasValue},\mbox{bNODE\_r},\mbox{uri\_foaf\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_name},\mbox{uri\_ex\_PersonAttribute})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_name},\mbox{uri\_ex\_alice},\mbox{literal\_plain}(\mbox{dat\_str\_alice})) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_012\_Template\_Class},\mbox{axiom})$

\medskip\textbf{SWB023+3.p} Unique List Components






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_v})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_023\_Unique\_List\_Components},\mbox{conjecture})$

$\exists \mbox{bNODE\_o},\mbox{bNODE\_l}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_rdf\_first},\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{bNODE\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_o},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_o},\mbox{bNODE\_l})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_v})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_023\_Unique\_List\_Components},\mbox{axiom})$

\medskip\textbf{SWB033+1.p} Datatype Relationships






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

\medskip\textbf{SWB032+1.p} Datatype Relationships






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_xsd\_decimal},\mbox{uri\_xsd\_string})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_xsd\_integer},\mbox{uri\_xsd\_decimal})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_032\_Datatype\_Relationships},\mbox{conjecture})$

\medskip\textbf{SWB067+1.p} Double Inverse Property As Equivalence

Transitively related inverse properties are equivalent.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentProperty},\mbox{uri\_ex\_p}_3,\mbox{uri\_ex\_p}_1)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_inv\_trans},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{uri\_ex\_p}_3,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_p}_1)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_inv\_trans},\mbox{axiom})$

\medskip\textbf{SWB010+4.p} Negative Property Assertions






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_NegativePropertyAssertion})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sourceIndividual},\mbox{bNODE\_z},\mbox{uri\_ex\_s})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_assertionProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_targetIndividual},\mbox{bNODE\_z},\mbox{uri\_ex\_o}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_010\_Negative\_Property\_Assertions},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2,\mbox{bNODE\_x}_3,\mbox{bNODE\_x}_4{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{bNODE\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_x}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_allValuesFrom},\mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_x}_2,\mbox{bNODE\_x}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_3,\mbox{bNODE\_x}_4)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_x}_4,\mbox{uri\_ex\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_x}_4,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_010\_Negative\_Property\_Assertions},\mbox{axiom})$

\medskip\textbf{SWB001+4.p} Subgraph Entailment






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_r},\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_001\_Subgraph\_Entailment},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_r},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_r},\mbox{uri\_ex\_d})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_001\_Subgraph\_Entailment},\mbox{axiom})$

\medskip\textbf{SWB074+1.p} Universal Data Property Extensional Low

The extension of the vocabulary property owl:topDataProperty 
 equals the class product of OWL individuals and data values, and 
 thus subsumes that class product. See also 
 rdfbased-sem-prop-topdataproperty-ext-hi for a test case checking 
 the exact upper bounds of the domain and range.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_topDataProperty},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_prop\_topdataproperty\_ext\_lo},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_y},\mbox{uri\_rdfs\_Literal})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x},\mbox{uri\_owl\_Thing})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_prop\_topdataproperty\_ext\_lo},\mbox{axiom})$

\medskip\textbf{SWB005+3.p} Everything is a Resource






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_rdf\_Property})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_o},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_o},\mbox{uri\_owl\_Thing})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_005\_Everything\_is\_a\_Resource},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{uri\_ex\_o})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_005\_Everything\_is\_a\_Resource},\mbox{axiom})$

\medskip\textbf{SWB023+2.p} Unique List Components






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall z,s_1,a_1{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,a_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_oneOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff x = a_1 ) ) ) )\qquad\mbox{fof}(\mbox{owl\_enum\_class}_{001},\mbox{axiom})$

$\forall p{:}\;( \mbox{icext}(\mbox{uri\_owl\_FunctionalProperty},p)\iff ( \mbox{ip}(p)\mbox{ and }\forall x,y_1,y_2{:}\;( ( \mbox{iext}(p,x,y_1)\mbox{ and }\mbox{iext}(p,x,y_2) ) \ \Rightarrow \ y_1 = y_2 ) ) )\qquad\mbox{fof}(\mbox{owl\_char\_functional},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},x,y)\iff x = y )\qquad\mbox{fof}(\mbox{owl\_eqdis\_sameas},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_v})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_023\_Unique\_List\_Components},\mbox{conjecture})$

$\exists \mbox{bNODE\_o},\mbox{bNODE\_l}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_rdf\_first},\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{bNODE\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_o},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_o},\mbox{bNODE\_l})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_v})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_023\_Unique\_List\_Components},\mbox{axiom})$

\medskip\textbf{SWB005+2.p} Everything is a Resource






$\forall x{:}\;\mbox{ir}(x)\qquad\mbox{fof}(\mbox{simple\_ir},\mbox{axiom})$

$\forall s,p,o{:}\;( \mbox{iext}(p,s,o) \ \Rightarrow \ \mbox{ip}(p) )\qquad\mbox{fof}(\mbox{simple\_iext\_property},\mbox{axiom})$

$\forall p{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},p,\mbox{uri\_rdf\_Property})\iff \mbox{ip}(p) )\qquad\mbox{fof}(\mbox{rdf\_type\_ip},\mbox{axiom})$

$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall x{:}\;( \mbox{ir}(x)\iff \mbox{icext}(\mbox{uri\_rdfs\_Resource},x) )\qquad\mbox{fof}(\mbox{rdfs\_ir\_def},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_owl\_Thing},x)\iff \mbox{ir}(x) )\qquad\mbox{fof}(\mbox{owl\_class\_thing\_ext},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_owl\_ObjectProperty},x)\iff \mbox{ip}(x) )\qquad\mbox{fof}(\mbox{owl\_class\_objectproperty\_ext},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_rdf\_Property})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_o},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_o},\mbox{uri\_owl\_Thing})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_005\_Everything\_is\_a\_Resource},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{uri\_ex\_o})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_005\_Everything\_is\_a\_Resource},\mbox{axiom})$

\medskip\textbf{SWB056+1.p} Individual Enumeration Closed

If a class defines an enumeration class expression from two 
 individuals, and if an individual is an instance of the class but 
 is different from one of the two component individuals, then the 
 individual equals the remaining component individual.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_z},\mbox{uri\_ex\_y})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_enum\_inst\_closed},\mbox{conjecture})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_z},\mbox{uri\_ex\_e})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_z},\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_e},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_enum\_inst\_closed},\mbox{axiom})$

\medskip\textbf{SWB022+2.p} List Member Access






$\forall p,q{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},p,q) \ \Rightarrow \ ( \mbox{ip}(p)\mbox{ and }\mbox{ip}(q)\mbox{ and }\forall x,y{:}\;( \mbox{iext}(p,x,y) \ \Rightarrow \ \mbox{iext}(q,x,y) ) ) )\qquad\mbox{fof}(\mbox{rdfs\_subpropertyof\_main},\mbox{axiom})$

$\forall p,s_1,p_1,s_2,p_2{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,p_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,p_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},p,s_1)\iff ( \mbox{ip}(p)\mbox{ and }\mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall y_0,y_1,y_2{:}\;( ( \mbox{iext}(p_1,y_0,y_1)\mbox{ and }\mbox{iext}(p_2,y_1,y_2) ) \ \Rightarrow \ \mbox{iext}(p,y_0,y_2) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_chain}_{002},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_X})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_Y})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_Z})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_022\_List\_Member\_Access},\mbox{conjecture})$

$\exists \mbox{bNODE\_pL},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33}{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_memberList},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_skos\_member},\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_first})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{bNODE\_pL},\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_rest})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_skos\_OrderedCollection})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_memberList},\mbox{uri\_ex\_MyOrderedCollection},\mbox{bNODE\_l}_{31})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{31},\mbox{uri\_ex\_X})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{32},\mbox{uri\_ex\_Y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{33},\mbox{uri\_ex\_Z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{33},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_022\_List\_Member\_Access},\mbox{axiom})$

\medskip\textbf{SWB023+4.p} Unique List Components






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_v})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_023\_Unique\_List\_Components},\mbox{conjecture})$

$\exists \mbox{bNODE\_o},\mbox{bNODE\_l}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_rdf\_first},\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{bNODE\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_o},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_o},\mbox{bNODE\_l})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_v})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_023\_Unique\_List\_Components},\mbox{axiom})$

\medskip\textbf{SWB077+1.p} Property Range Sub-Property OWL

Every sub property of a given property with a given range also 
 has this range.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_c})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_rdfsext\_range\_subprop},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p}_2)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_rdfsext\_range\_subprop},\mbox{axiom})$

\medskip\textbf{SWB061+1.p} Disjoint Class Union As Union

If a class is defined by a disjoint-union axiom for two component 
 classes, then the class expresses the union of the two classes.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c}_3,x_0) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_eqdis\_disjointunion\_union},\mbox{conjecture})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_disjointUnionOf},\mbox{uri\_ex\_c}_3,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_eqdis\_disjointunion\_union},\mbox{axiom})$

\medskip\textbf{SWB076+1.p} Property Range Extensional OWL

If the extension of a given class is a range for the extension of 
 a given property, then the class is a range for the property.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_rdfsext\_range\_ext},\mbox{conjecture})$

$\exists x_0{:}\;( \mbox{iext}(\mbox{uri\_owl\_allValuesFrom},x_0,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},x_0,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_owl\_Thing},x_0) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_rdfsext\_range\_ext},\mbox{axiom})$

\medskip\textbf{SWB028+1.p} Inferred Property Characteristics III






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_InversesOfFunctionalProperties},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_028\_Inferred\_Property\_Characteristics\_III},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_InversesOfFunctionalProperties},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_owl\_inverseOf})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_z},\mbox{uri\_owl\_FunctionalProperty}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_028\_Inferred\_Property\_Characteristics\_III},\mbox{axiom})$

\medskip\textbf{SWB004+2.p} Axiomatic Triples






$\forall x{:}\;\mbox{ir}(x)\qquad\mbox{fof}(\mbox{simple\_ir},\mbox{axiom})$

$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall x{:}\;( \mbox{idc}(x) \ \Rightarrow \ \mbox{ic}(x) )\qquad\mbox{fof}(\mbox{owl\_parts\_idc\_cond\_set},\mbox{axiom})$

$\mbox{ic}(\mbox{uri\_owl\_Class})\qquad\mbox{fof}(\mbox{owl\_class\_classowl\_type},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_owl\_Class},x)\iff \mbox{ic}(x) )\qquad\mbox{fof}(\mbox{owl\_class\_classowl\_ext},\mbox{axiom})$

$\mbox{ic}(\mbox{uri\_rdfs\_Class})\qquad\mbox{fof}(\mbox{owl\_class\_classrdfs\_type},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_rdfs\_Class},x)\iff \mbox{ic}(x) )\qquad\mbox{fof}(\mbox{owl\_class\_classrdfs\_ext},\mbox{axiom})$

$\mbox{ic}(\mbox{uri\_rdfs\_Datatype})\qquad\mbox{fof}(\mbox{owl\_class\_datatype\_type},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_rdfs\_Datatype},x)\iff \mbox{idc}(x) )\qquad\mbox{fof}(\mbox{owl\_class\_datatype\_ext},\mbox{axiom})$

$\mbox{ic}(\mbox{uri\_owl\_Thing})\qquad\mbox{fof}(\mbox{owl\_class\_thing\_type},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_owl\_Thing},x)\iff \mbox{ir}(x) )\qquad\mbox{fof}(\mbox{owl\_class\_thing\_ext},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subClassOf},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x) \ \Rightarrow \ \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subclassof},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x)\iff \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_eqdis\_equivalentclass},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_owl\_Class},\mbox{uri\_rdfs\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_rdfs\_Datatype},\mbox{uri\_owl\_Class})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_004\_Axiomatic\_Triples},\mbox{conjecture})$

\medskip\textbf{SWB014+4.p} Harry belongs to some Species






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_harry},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_ex\_Species}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_014\_Harry\_belongs\_to\_some\_Species},\mbox{conjecture})$

$\exists \mbox{bNODE\_u},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Eagle},\mbox{uri\_ex\_Species})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Falcon},\mbox{uri\_ex\_Species})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_harry},\mbox{bNODE\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{bNODE\_u},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_Eagle})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_Falcon})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_014\_Harry\_belongs\_to\_some\_Species},\mbox{axiom})$

\medskip\textbf{SWB003+3.p} Blank Nodes for Literals






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_x})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_003\_Blank\_Nodes\_for\_Literals},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_003\_Blank\_Nodes\_for\_Literals},\mbox{axiom})$

\medskip\textbf{SWB038+1.p} Class De Morgan

The complement of the union of two classes is an equivalent class 
 to the intersection of the complements of the two classes.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_bool\_demorgan},\mbox{conjecture})$

$\exists x_1,x_4,x_0,x_2,x_5,x_3,x_6{:}\;( \mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{uri\_ex\_c}_2,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},x_1,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,x_4)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},x_5,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{uri\_ex\_c}_1,x_6)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_4,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_4,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},x_6,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,x_5)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_bool\_demorgan},\mbox{axiom})$

\medskip\textbf{SWB045+1.p} Functional Property Extensional

If the extension of a property is functional, then the property 
 itself is.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_FunctionalProperty})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_char\_functional\_ext},\mbox{conjecture})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_1) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_char\_functional\_ext},\mbox{axiom})$

\medskip\textbf{SWB009+2.p} Existential Restriction Entailments






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall z,p,c{:}\;( ( \mbox{iext}(\mbox{uri\_owl\_someValuesFrom},z,c)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},z,p) ) \ \Rightarrow \ \forall x{:}\;( \mbox{icext}(z,x)\iff \exists y{:}\;( \mbox{iext}(p,x,y)\mbox{ and }\mbox{icext}(c,y) ) ) )\qquad\mbox{fof}(\mbox{owl\_restrict\_somevaluesfrom},\mbox{axiom})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_ex\_c}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_009\_Existential\_Restriction\_Entailments},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_z},\mbox{uri\_ex\_c}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_009\_Existential\_Restriction\_Entailments},\mbox{axiom})$

\medskip\textbf{SWB015+1.p} Reflective Tautologies I






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_owl\_sameAs},\mbox{uri\_owl\_sameAs})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_015\_Reflective\_Tautologies\_I},\mbox{conjecture})$

\medskip\textbf{SWB105+1.p} Universal Existential Restriction Duality

Universal and existential restrictions are dual: The universal 
 restriction on property p to the complement of class c is 
 equivalent to the complement of the existential restriction on p 
 to c.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_nz}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_term\_sameall},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{uri\_ex\_nz}_2,\mbox{uri\_ex\_z}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{uri\_ex\_nc},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_allValuesFrom},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_nc})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_term\_sameall},\mbox{axiom})$

\medskip\textbf{SWB024+2.p} Cardinality Restrictions on Complex Properties






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall z,p{:}\;( ( \mbox{iext}(\mbox{uri\_owl\_minCardinality},z,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},z,p) ) \ \Rightarrow \ \forall x{:}\;( \mbox{icext}(z,x)\iff \exists y{:}\;\mbox{iext}(p,x,y) ) )\qquad\mbox{fof}(\mbox{owl\_restrict\_mincard}_{001},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subClassOf},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x) \ \Rightarrow \ \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subclassof},\mbox{axiom})$

$\forall p{:}\;( \mbox{icext}(\mbox{uri\_owl\_TransitiveProperty},p)\iff ( \mbox{ip}(p)\mbox{ and }\forall x,y,z{:}\;( ( \mbox{iext}(p,x,y)\mbox{ and }\mbox{iext}(p,y,z) ) \ \Rightarrow \ \mbox{iext}(p,x,z) ) ) )\qquad\mbox{fof}(\mbox{owl\_char\_transitive},\mbox{axiom})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_bob},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_alice},\mbox{bNODE\_x}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_024\_Cardinality\_Restrictions\_on\_Complex\_Properties},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_hasAncestor},\mbox{uri\_owl\_TransitiveProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_Person},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_hasAncestor})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_minCardinality},\mbox{bNODE\_z},\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_024\_Cardinality\_Restrictions\_on\_Complex\_Properties},\mbox{axiom})$

\medskip\textbf{SWB070+1.p} N-Ary Property Disjointness Extensional

For a group of mutually disjoint properties the corresponding 
 owl:AllDisjointProperties construct exists.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_1,x_0,x_3,x_2{:}\;( \mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_p}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},x_2,\mbox{uri\_owl\_AllDisjointProperties})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_members},x_2,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,x_0) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_ndis\_alldisjointproperties\_bw},\mbox{conjecture})$

$\exists x_2,x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_p}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_p}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_ndis\_alldisjointproperties\_bw},\mbox{axiom})$

\medskip\textbf{SWB013+3.p} Cliques






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_foaf\_knows},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_013\_Cliques},\mbox{conjecture})$

$\exists \mbox{bNODE\_r},\mbox{bNODE\_i},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Clique},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_sameCliqueAs},\mbox{uri\_owl\_sameAs})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_sameCliqueAs},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_Clique},\mbox{bNODE\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_r},\mbox{uri\_ex\_sameCliqueAs})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_r},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_knows},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_foaf\_knows},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_sameCliqueAs})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_3,\mbox{bNODE\_i})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_i},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_JoesGang},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_JoesGang})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_JoesGang}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_013\_Cliques},\mbox{axiom})$

\medskip\textbf{SWB002+2.p} Existential Blank Nodes






$\exists \mbox{bNODE\_x},\mbox{bNODE\_y}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{bNODE\_x},\mbox{bNODE\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_q},\mbox{bNODE\_y},\mbox{bNODE\_x}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_002\_Existential\_Blank\_Nodes},\mbox{conjecture})$

$\exists \mbox{bNODE\_o}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_q},\mbox{bNODE\_o},\mbox{uri\_ex\_s}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_002\_Existential\_Blank\_Nodes},\mbox{axiom})$

\medskip\textbf{SWB027+2.p} Inferred Property Characteristics II






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},x,y)\iff x = y )\qquad\mbox{fof}(\mbox{owl\_eqdis\_sameas},\mbox{axiom})$

$\forall p,s_1,p_1,s_2,p_2{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,p_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,p_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},p,s_1)\iff ( \mbox{ip}(p)\mbox{ and }\mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall y_0,y_1,y_2{:}\;( ( \mbox{iext}(p_1,y_0,y_1)\mbox{ and }\mbox{iext}(p_2,y_1,y_2) ) \ \Rightarrow \ \mbox{iext}(p,y_0,y_2) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_chain}_{002},\mbox{axiom})$

$\forall p{:}\;( \mbox{icext}(\mbox{uri\_owl\_InverseFunctionalProperty},p)\iff ( \mbox{ip}(p)\mbox{ and }\forall x_1,x_2,y{:}\;( ( \mbox{iext}(p,x_1,y)\mbox{ and }\mbox{iext}(p,x_2,y) ) \ \Rightarrow \ x_1 = x_2 ) ) )\qquad\mbox{fof}(\mbox{owl\_char\_inversefunctional},\mbox{axiom})$

$\forall p_1,p_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_inverseOf},p_1,p_2)\iff ( \mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall x,y{:}\;( \mbox{iext}(p_1,x,y)\iff \mbox{iext}(p_2,y,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_inv},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_027\_Inferred\_Property\_Characteristics\_II},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_v}{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_owl\_sameAs},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{bNODE\_v})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_v},\mbox{uri\_ex\_p}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_027\_Inferred\_Property\_Characteristics\_II},\mbox{axiom})$

\medskip\textbf{SWB030+3.p} Bad Class






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{uri\_ex\_c},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_x},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_hasSelf},\mbox{bNODE\_x},\mbox{literal\_typed}(\mbox{dat\_str\_true},\mbox{uri\_xsd\_boolean})) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_030\_Bad\_Class},\mbox{axiom})$

\medskip\textbf{SWB093+1.p} Min-QCR Comparison By Cardinality

A min-QCR for some cardinality on some property and to some class 
 is a subclass of another min-QCR on the same property to the same 
 class and for some smaller cardinality.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_minqcr\_cmp\_card},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_x}_2,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_x}_1,\mbox{literal\_typed}(\mbox{dat\_str}_2,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_minqcr\_cmp\_card},\mbox{axiom})$

\medskip\textbf{SWB025+3.p} Cyclic Dependencies between Complex Properties






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_ex\_hasUncle},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_charly})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasCousin},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_alice})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_025\_Cyclic\_Dependencies\_between\_Complex\_Properties},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_3{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_ex\_hasUncle},\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{uri\_ex\_hasCousin})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_ex\_hasFather})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_ex\_hasCousin},\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{uri\_ex\_hasUncle})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_l}_3,\mbox{uri\_ex\_hasFather})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasFather},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_dave})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasCousin},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasFather},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_charly})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasUncle},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_dave}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_025\_Cyclic\_Dependencies\_between\_Complex\_Properties},\mbox{axiom})$

\medskip\textbf{SWB024+1.p} Cardinality Restrictions on Complex Properties






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_bob},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_alice},\mbox{bNODE\_x}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_024\_Cardinality\_Restrictions\_on\_Complex\_Properties},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_hasAncestor},\mbox{uri\_owl\_TransitiveProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_Person},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_hasAncestor})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_minCardinality},\mbox{bNODE\_z},\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_024\_Cardinality\_Restrictions\_on\_Complex\_Properties},\mbox{axiom})$

\medskip\textbf{SWB037+1.p} Class Complement Extensional

If a class is an equivalent class to the complement of another 
 class, then the former class defines the complement of the other 
 class. This test checks that class complement is realized as an 
 iff-condition.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_bool\_complement\_ext},\mbox{conjecture})$

$\exists x_0{:}\;( \mbox{iext}(\mbox{uri\_owl\_complementOf},x_0,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_c}_1,x_0) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_bool\_complement\_ext},\mbox{axiom})$

\medskip\textbf{SWB026+1.p} Inferred Property Characteristics I






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_026\_Inferred\_Property\_Characteristics\_I},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2,\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p},\mbox{bNODE\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_1,\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{bNODE\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_2,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_026\_Inferred\_Property\_Characteristics\_I},\mbox{axiom})$

\medskip\textbf{SWB048+1.p} Irreflexive Property Extensional

If the extension of a property is irreflexive, then the property 
 itself is.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_IrreflexiveProperty})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_char\_irreflexive\_ext},\mbox{conjecture})$

$\exists x_0,x_3,x_1,x_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_1,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_3) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_char\_irreflexive\_ext},\mbox{axiom})$

\medskip\textbf{SWB018+1.p} Modified Logical Vocabulary Semantics






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_u},\mbox{uri\_ex\_Person})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_018\_Modified\_Logical\_Vocabulary\_Semantics},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_018\_Modified\_Logical\_Vocabulary\_Semantics},\mbox{axiom})$

\medskip\textbf{SWB019+1.p} Disjoint Annotation Properties






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_skos\_prefLabel},\mbox{uri\_owl\_AnnotationProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_prefLabel},\mbox{uri\_rdfs\_label})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_skos\_altLabel},\mbox{uri\_owl\_AnnotationProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_altLabel},\mbox{uri\_rdfs\_label})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_skos\_prefLabel},\mbox{uri\_skos\_altLabel})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_prefLabel},\mbox{uri\_ex\_foo},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_altLabel},\mbox{uri\_ex\_foo},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_019\_Disjoint\_Annotation\_Properties},\mbox{axiom})$

\medskip\textbf{SWB013+2.p} Cliques






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall z,p,c{:}\;( ( \mbox{iext}(\mbox{uri\_owl\_someValuesFrom},z,c)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},z,p) ) \ \Rightarrow \ \forall x{:}\;( \mbox{icext}(z,x)\iff \exists y{:}\;( \mbox{iext}(p,x,y)\mbox{ and }\mbox{icext}(c,y) ) ) )\qquad\mbox{fof}(\mbox{owl\_restrict\_somevaluesfrom},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subClassOf},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x) \ \Rightarrow \ \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subclassof},\mbox{axiom})$

$\forall p_1,p_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},p_1,p_2)\iff ( \mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall x,y{:}\;( \mbox{iext}(p_1,x,y) \ \Rightarrow \ \mbox{iext}(p_2,x,y) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subpropertyof},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},x,y)\iff x = y )\qquad\mbox{fof}(\mbox{owl\_eqdis\_sameas},\mbox{axiom})$

$\forall p,s_1,p_1,s_2,p_2,s_3,p_3{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,p_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,p_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,s_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_3,p_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_3,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},p,s_1)\iff ( \mbox{ip}(p)\mbox{ and }\mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\mbox{ip}(p_3)\mbox{ and }\forall y_0,y_1,y_2,y_3{:}\;( ( \mbox{iext}(p_1,y_0,y_1)\mbox{ and }\mbox{iext}(p_2,y_1,y_2)\mbox{ and }\mbox{iext}(p_3,y_2,y_3) ) \ \Rightarrow \ \mbox{iext}(p,y_0,y_3) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_chain}_{003},\mbox{axiom})$

$\forall p_1,p_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_inverseOf},p_1,p_2)\iff ( \mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall x,y{:}\;( \mbox{iext}(p_1,x,y)\iff \mbox{iext}(p_2,y,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_inv},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_foaf\_knows},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_013\_Cliques},\mbox{conjecture})$

$\exists \mbox{bNODE\_r},\mbox{bNODE\_i},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Clique},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_sameCliqueAs},\mbox{uri\_owl\_sameAs})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_sameCliqueAs},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_Clique},\mbox{bNODE\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_r},\mbox{uri\_ex\_sameCliqueAs})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_r},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_knows},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_foaf\_knows},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_sameCliqueAs})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_3,\mbox{bNODE\_i})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_i},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_JoesGang},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_JoesGang})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_JoesGang}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_013\_Cliques},\mbox{axiom})$

\medskip\textbf{SWB062+1.p} Property Disjointness Extensional

If the non-empty extensions of two properties are disjoint, then 
 the properties themselves are disjoint.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_eqdis\_disprop\_ext},\mbox{conjecture})$

$\exists x_1,x_2,x_0,x_3{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_y}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_s}_2,\mbox{uri\_ex\_o}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_y}_1,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_o}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_s}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_y}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_o}_1,\mbox{uri\_ex\_o}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_x}_1,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_y}_2,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_o}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_s}_1,\mbox{uri\_ex\_o}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_s}_1,\mbox{uri\_ex\_s}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_s}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_x}_2,x_1) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_eqdis\_disprop\_ext},\mbox{axiom})$

\medskip\textbf{SWB018+2.p} Modified Logical Vocabulary Semantics






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall p,c,x,y{:}\;( ( \mbox{iext}(\mbox{uri\_rdfs\_domain},p,c)\mbox{ and }\mbox{iext}(p,x,y) ) \ \Rightarrow \ \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_domain\_main},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},x,y)\iff x = y )\qquad\mbox{fof}(\mbox{owl\_eqdis\_sameas},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_u},\mbox{uri\_ex\_Person})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_018\_Modified\_Logical\_Vocabulary\_Semantics},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_018\_Modified\_Logical\_Vocabulary\_Semantics},\mbox{axiom})$

\medskip\textbf{SWB003+1.p} Blank Nodes for Literals






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_x})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_003\_Blank\_Nodes\_for\_Literals},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_003\_Blank\_Nodes\_for\_Literals},\mbox{axiom})$

\medskip\textbf{SWB011+1.p} Entity Types as Classes






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x},\mbox{uri\_owl\_ObjectProperty})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_011\_Entity\_Types\_as\_Classes},\mbox{axiom})$

\medskip\textbf{SWB041+1.p} Class Union Extensional

If a class is an equivalent class to the union of two other 
 classes, then the former class defines the union of the other 
 classes. This test checks that class union is realized as an 
 iff-condition.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c},x_0) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_bool\_union\_ext},\mbox{conjecture})$

$\exists x_2,x_1,x_0{:}\;( \mbox{iext}(\mbox{uri\_owl\_unionOf},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_c},x_0) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_bool\_union\_ext},\mbox{axiom})$

\medskip\textbf{SWB015+3.p} Reflective Tautologies I






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_owl\_sameAs},\mbox{uri\_owl\_sameAs})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_015\_Reflective\_Tautologies\_I},\mbox{conjecture})$

\medskip\textbf{SWB006+3.p} Literal Values represented by URIs and Blank Nodes






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_u},\mbox{uri\_ex\_w})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_006\_Literal\_Values\_represented\_by\_URIs\_and\_Blank\_Nodes},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_u},\mbox{literal\_plain}(\mbox{dat\_str\_abc}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{bNODE\_x},\mbox{literal\_plain}(\mbox{dat\_str\_abc}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{bNODE\_x},\mbox{uri\_ex\_w}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_006\_Literal\_Values\_represented\_by\_URIs\_and\_Blank\_Nodes},\mbox{axiom})$

\medskip\textbf{SWB086+1.p} Self-Restriction Comparison By Property

A self restriction on some property is a sub class of another 
 self restriction on a super property.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_hasself\_cmp\_prop},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_hasSelf},\mbox{uri\_ex\_x}_2,\mbox{literal\_typed}(\mbox{dat\_str\_true},\mbox{uri\_xsd\_boolean}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_hasSelf},\mbox{uri\_ex\_x}_1,\mbox{literal\_typed}(\mbox{dat\_str\_true},\mbox{uri\_xsd\_boolean}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p}_2)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_hasself\_cmp\_prop},\mbox{axiom})$

\medskip\textbf{SWB006+1.p} Literal Values represented by URIs and Blank Nodes






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_u},\mbox{uri\_ex\_w})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_006\_Literal\_Values\_represented\_by\_URIs\_and\_Blank\_Nodes},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_u},\mbox{literal\_plain}(\mbox{dat\_str\_abc}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{bNODE\_x},\mbox{literal\_plain}(\mbox{dat\_str\_abc}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{bNODE\_x},\mbox{uri\_ex\_w}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_006\_Literal\_Values\_represented\_by\_URIs\_and\_Blank\_Nodes},\mbox{axiom})$

\medskip\textbf{SWB075+1.p} Universal Data Property As Super-Property

Every data property is a sub property of the vocabulary property 
 owl:topDataProperty.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_p},\mbox{uri\_owl\_topDataProperty})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_prop\_topdataproperty\_term},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_DatatypeProperty})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_prop\_topdataproperty\_term},\mbox{axiom})$

\medskip\textbf{SWB017+4.p} Built-in Based Definitions






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_017\_Built\_in\_Based\_Definitions},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_ex\_notInstanceOf},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_notInstanceOf},\mbox{uri\_ex\_u},\mbox{uri\_ex\_c})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_017\_Built\_in\_Based\_Definitions},\mbox{axiom})$

\medskip\textbf{SWB016+3.p} Reflective Tautologies II






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_owl\_equivalentClass},\mbox{uri\_rdfs\_subClassOf})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_016\_Reflective\_Tautologies\_II},\mbox{conjecture})$

\medskip\textbf{SWB030+4.p} Bad Class






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{uri\_ex\_c},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_x},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_hasSelf},\mbox{bNODE\_x},\mbox{literal\_typed}(\mbox{dat\_str\_true},\mbox{uri\_xsd\_boolean})) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_030\_Bad\_Class},\mbox{axiom})$

\medskip\textbf{SWB031+2.p} Large Universe






$\forall x{:}\;\mbox{ir}(x)\qquad\mbox{fof}(\mbox{simple\_ir},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_owl\_Thing},x)\iff \mbox{ir}(x) )\qquad\mbox{fof}(\mbox{owl\_class\_thing\_ext},\mbox{axiom})$

$\forall x{:}\;\neg\,\mbox{icext}(\mbox{uri\_owl\_Nothing},x)\qquad\mbox{fof}(\mbox{owl\_class\_nothing\_ext},\mbox{axiom})$

$\forall z,s_1,a_1{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,a_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_oneOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff x = a_1 ) ) ) )\qquad\mbox{fof}(\mbox{owl\_enum\_class}_{001},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x)\iff \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_eqdis\_equivalentclass},\mbox{axiom})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_l}{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_owl\_Thing},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x},\mbox{bNODE\_l})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_031\_Large\_Universe},\mbox{axiom})$

\medskip\textbf{SWB001+2.p} Subgraph Entailment






$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_r},\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_001\_Subgraph\_Entailment},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_r},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_r},\mbox{uri\_ex\_d})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_001\_Subgraph\_Entailment},\mbox{axiom})$

\medskip\textbf{SWB057+1.p} Individual Difference Extensional

If two individuals are distinct, then the owl:differentFrom 
 relation holds between them.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_eqdis\_different\_ext},\mbox{conjecture})$

$\exists x_0{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_u},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},x_0,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_eqdis\_different\_ext},\mbox{axiom})$

\medskip\textbf{SWB002+4.p} Existential Blank Nodes






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_y}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{bNODE\_x},\mbox{bNODE\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_q},\mbox{bNODE\_y},\mbox{bNODE\_x}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_002\_Existential\_Blank\_Nodes},\mbox{conjecture})$

$\exists \mbox{bNODE\_o}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_q},\mbox{bNODE\_o},\mbox{uri\_ex\_s}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_002\_Existential\_Blank\_Nodes},\mbox{axiom})$

\medskip\textbf{SWB021+1.p} Composite Enumerations






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_c}_3,\mbox{uri\_ex\_c}_4)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_021\_Composite\_Enumerations},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33},\mbox{bNODE\_l}_{41},\mbox{bNODE\_l}_{42}{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_1,\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{uri\_ex\_w}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_2,\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_3,\mbox{bNODE\_l}_{31})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{31},\mbox{uri\_ex\_w}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{32},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{33},\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{33},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c}_4,\mbox{bNODE\_l}_{41})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{41},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{41},\mbox{bNODE\_l}_{42})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{42},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{42},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_021\_Composite\_Enumerations},\mbox{axiom})$

\medskip\textbf{SWB031+4.p} Large Universe






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_l}{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_owl\_Thing},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x},\mbox{bNODE\_l})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_031\_Large\_Universe},\mbox{axiom})$

\medskip\textbf{SWB079+1.p} Class Subsumption Extensional OWL

If the extension of a given class is subsumed by the extension of 
 a second class, then the first class is a subclass of the second 
 class.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_rdfsext\_subclass\_ext},\mbox{conjecture})$

$\exists x_0,x_1,x_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_2,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_1,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_rdfsext\_subclass\_ext},\mbox{axiom})$

\medskip\textbf{SWB010+1.p} Negative Property Assertions






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_NegativePropertyAssertion})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sourceIndividual},\mbox{bNODE\_z},\mbox{uri\_ex\_s})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_assertionProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_targetIndividual},\mbox{bNODE\_z},\mbox{uri\_ex\_o}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_010\_Negative\_Property\_Assertions},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2,\mbox{bNODE\_x}_3,\mbox{bNODE\_x}_4{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{bNODE\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_x}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_allValuesFrom},\mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_x}_2,\mbox{bNODE\_x}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_3,\mbox{bNODE\_x}_4)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_x}_4,\mbox{uri\_ex\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_x}_4,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_010\_Negative\_Property\_Assertions},\mbox{axiom})$

\medskip\textbf{SWB032+3.p} Datatype Relationships






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_xsd\_decimal},\mbox{uri\_xsd\_string})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_xsd\_integer},\mbox{uri\_xsd\_decimal})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_032\_Datatype\_Relationships},\mbox{conjecture})$

\medskip\textbf{SWB107+1.p} Has-Restriction As Existential Restriction

A has-value restriction for a value $\vee$ can be written as an 
 existential restriction to a singleton class containing v.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_z}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_term\_somehas},\mbox{conjecture})$

$\exists x_1,x_0{:}\;( \mbox{iext}(\mbox{uri\_owl\_hasValue},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_z}_1,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_term\_somehas},\mbox{axiom})$

\medskip\textbf{SWB080+1.p} Property Subsumption Extensional OWL

If the extension of a given property is subsumed by the extension 
 of a second property, then the first property is a subproperty of 
 the second property.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_rdfsext\_subprop\_ext},\mbox{conjecture})$

$\exists x_8,x_4,x_2,x_5,x_1,x_6,x_3,x_7,x_0{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p}_1,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p}_1,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_4,\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_4,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p}_2,x_5)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p}_2,x_6)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_1,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_7,\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_7,x_8)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_6,x_7)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_5,x_4)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_8,\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_8,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_w},\mbox{uri\_ex\_w}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_rdfsext\_subprop\_ext},\mbox{axiom})$

\medskip\textbf{SWB069+1.p} N-Ary Class Disjointness Extensional

For a group of mutually disjoint classes, the corresponding 
 owl:AllDisjointClasses construct exists.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_2,x_3,x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_c}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},x_2,\mbox{uri\_owl\_AllDisjointClasses})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_members},x_2,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,x_0) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_ndis\_alldisjointclasses\_bw},\mbox{conjecture})$

$\exists x_1,x_2,x_0{:}\;( \mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_ex\_c}_2,\mbox{uri\_ex\_c}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_c}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_ndis\_alldisjointclasses\_bw},\mbox{axiom})$

\medskip\textbf{SWB004+1.p} Axiomatic Triples






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_owl\_Class},\mbox{uri\_rdfs\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_rdfs\_Datatype},\mbox{uri\_owl\_Class})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_004\_Axiomatic\_Triples},\mbox{conjecture})$

\medskip\textbf{SWB001+1.p} Subgraph Entailment






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_r},\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_001\_Subgraph\_Entailment},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_r},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_r},\mbox{uri\_ex\_d})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_001\_Subgraph\_Entailment},\mbox{axiom})$

\medskip\textbf{SWB032+2.p} Datatype Relationships






$\mbox{idc}(\mbox{uri\_xsd\_string})\qquad\mbox{fof}(\mbox{owl\_dat\_dtype\_string\_type},\mbox{axiom})$

$\mbox{idc}(\mbox{uri\_xsd\_decimal})\qquad\mbox{fof}(\mbox{owl\_dat\_dtype\_decimal\_type},\mbox{axiom})$

$\mbox{idc}(\mbox{uri\_xsd\_integer})\qquad\mbox{fof}(\mbox{owl\_dat\_dtype\_integer\_type},\mbox{axiom})$

$\forall x{:}\;\neg\,\mbox{icext}(\mbox{uri\_rdf\_PlainLiteral},x)\mbox{ and }\mbox{icext}(\mbox{uri\_owl\_real},x)\qquad\mbox{fof}(\mbox{owl\_dat\_dtype\_relation\_disjoint\_plainliteral\_real},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_xsd\_string},x) \ \Rightarrow \ \mbox{icext}(\mbox{uri\_rdf\_PlainLiteral},x) )\qquad\mbox{fof}(\mbox{owl\_dat\_dtype\_relation\_subtype\_string\_plainliteral},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_owl\_rational},x) \ \Rightarrow \ \mbox{icext}(\mbox{uri\_owl\_real},x) )\qquad\mbox{fof}(\mbox{owl\_dat\_dtype\_relation\_subtype\_rational\_real},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_xsd\_decimal},x) \ \Rightarrow \ \mbox{icext}(\mbox{uri\_owl\_rational},x) )\qquad\mbox{fof}(\mbox{owl\_dat\_dtype\_relation\_subtype\_decimal\_rational},\mbox{axiom})$

$\forall x{:}\;( \mbox{icext}(\mbox{uri\_xsd\_integer},x) \ \Rightarrow \ \mbox{icext}(\mbox{uri\_xsd\_decimal},x) )\qquad\mbox{fof}(\mbox{owl\_dat\_dtype\_relation\_subtype\_integer\_decimal},\mbox{axiom})$

$\forall x{:}\;( \mbox{idc}(x) \ \Rightarrow \ \mbox{ic}(x) )\qquad\mbox{fof}(\mbox{owl\_parts\_idc\_cond\_set},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subClassOf},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x) \ \Rightarrow \ \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subclassof},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_disjointWith},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;\neg\,\mbox{icext}(c_1,x)\mbox{ and }\mbox{icext}(c_2,x) ) )\qquad\mbox{fof}(\mbox{owl\_eqdis\_disjointwith},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_xsd\_decimal},\mbox{uri\_xsd\_string})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_xsd\_integer},\mbox{uri\_xsd\_decimal})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_032\_Datatype\_Relationships},\mbox{conjecture})$

\medskip\textbf{SWB053+1.p} Empty Class As Sub-Class

Every OWL class is a super class of the vocabulary class 
 owl:Nothing.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_owl\_Nothing},\mbox{uri\_ex\_c})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_class\_nothing\_term},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Class})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_class\_nothing\_term},\mbox{axiom})$

\medskip\textbf{SWB024+3.p} Cardinality Restrictions on Complex Properties






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_bob},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_alice},\mbox{bNODE\_x}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_024\_Cardinality\_Restrictions\_on\_Complex\_Properties},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_hasAncestor},\mbox{uri\_owl\_TransitiveProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_Person},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_hasAncestor})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_minCardinality},\mbox{bNODE\_z},\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_024\_Cardinality\_Restrictions\_on\_Complex\_Properties},\mbox{axiom})$

\medskip\textbf{SWB011+4.p} Entity Types as Classes






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x},\mbox{uri\_owl\_ObjectProperty})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_011\_Entity\_Types\_as\_Classes},\mbox{axiom})$

\medskip\textbf{SWB029+2.p} Ex Falso Quodlibet






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall z,c{:}\;( \mbox{iext}(\mbox{uri\_owl\_complementOf},z,c) \ \Rightarrow \ ( \mbox{ic}(z)\mbox{ and }\mbox{ic}(c)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff \neg\,\mbox{icext}(c,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_bool\_complementof\_class},\mbox{axiom})$

$\forall z,s_1,c_1,s_2,c_2{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,c_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,c_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_intersectionOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff ( \mbox{icext}(c_1,x)\mbox{ and }\mbox{icext}(c_2,x) ) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_bool\_intersectionof\_class}_{002},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_B})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_029\_Ex\_Falso\_Quodlibet},\mbox{conjecture})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_y},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_A},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_B},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{bNODE\_x},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_A})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{bNODE\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_y},\mbox{uri\_ex\_A}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_029\_Ex\_Falso\_Quodlibet},\mbox{axiom})$

\medskip\textbf{SWB012+3.p} Template Class






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_name},\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_foaf\_Person})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_012\_Template\_Class},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3,\mbox{bNODE\_r}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_Person},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{uri\_ex\_PersonAttribute},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_owl\_DatatypeProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_3,\mbox{bNODE\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_r},\mbox{uri\_rdfs\_domain})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_hasValue},\mbox{bNODE\_r},\mbox{uri\_foaf\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_name},\mbox{uri\_ex\_PersonAttribute})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_name},\mbox{uri\_ex\_alice},\mbox{literal\_plain}(\mbox{dat\_str\_alice})) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_012\_Template\_Class},\mbox{axiom})$

\medskip\textbf{SWB020+3.p} Logical Complications






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_d},\mbox{uri\_ex\_c}_3)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_020\_Logical\_Complications},\mbox{conjecture})$

$\exists \mbox{bNODE\_xs},\mbox{bNODE\_xc},\mbox{bNODE\_lu}_1,\mbox{bNODE\_lu}_2,\mbox{bNODE\_lu}_3,\mbox{bNODE\_li}_1,\mbox{bNODE\_li}_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c},\mbox{bNODE\_lu}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_1,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_1,\mbox{bNODE\_lu}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_2,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_2,\mbox{bNODE\_lu}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_3,\mbox{uri\_ex\_c}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_ex\_d},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_d},\mbox{bNODE\_xs})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{bNODE\_xs},\mbox{bNODE\_li}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_li}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_li}_1,\mbox{bNODE\_li}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_li}_2,\mbox{bNODE\_xc})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_li}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_xc},\mbox{uri\_ex\_c}_2) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_020\_Logical\_Complications},\mbox{axiom})$

\medskip\textbf{SWB081+1.p} Universal Restriction Comparison By Class

A universal restriction on some property and some class is a sub 
 class of another universal restriction on the same property but 
 on a super class.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_allvalues\_cmp\_class},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_allValuesFrom},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_allValuesFrom},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_allvalues\_cmp\_class},\mbox{axiom})$

\medskip\textbf{SWB035+1.p} Datatype Relationships






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

\medskip\textbf{SWB013+4.p} Cliques






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_foaf\_knows},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_013\_Cliques},\mbox{conjecture})$

$\exists \mbox{bNODE\_r},\mbox{bNODE\_i},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Clique},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_sameCliqueAs},\mbox{uri\_owl\_sameAs})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_sameCliqueAs},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_Clique},\mbox{bNODE\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_r},\mbox{uri\_ex\_sameCliqueAs})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_r},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_knows},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_foaf\_knows},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_sameCliqueAs})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_3,\mbox{bNODE\_i})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_i},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_JoesGang},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_JoesGang})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_JoesGang}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_013\_Cliques},\mbox{axiom})$

\medskip\textbf{SWB027+1.p} Inferred Property Characteristics II






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_027\_Inferred\_Property\_Characteristics\_II},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_v}{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_owl\_sameAs},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{bNODE\_v})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_v},\mbox{uri\_ex\_p}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_027\_Inferred\_Property\_Characteristics\_II},\mbox{axiom})$

\medskip\textbf{SWB009+1.p} Existential Restriction Entailments






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_ex\_c}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_009\_Existential\_Restriction\_Entailments},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_z},\mbox{uri\_ex\_c}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_009\_Existential\_Restriction\_Entailments},\mbox{axiom})$

\medskip\textbf{SWB024+4.p} Cardinality Restrictions on Complex Properties






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_bob},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_alice},\mbox{bNODE\_x}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_024\_Cardinality\_Restrictions\_on\_Complex\_Properties},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_hasAncestor},\mbox{uri\_owl\_TransitiveProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_Person},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_hasAncestor})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_minCardinality},\mbox{bNODE\_z},\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasAncestor},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_024\_Cardinality\_Restrictions\_on\_Complex\_Properties},\mbox{axiom})$

\medskip\textbf{SWB013+1.p} Cliques






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_foaf\_knows},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_013\_Cliques},\mbox{conjecture})$

$\exists \mbox{bNODE\_r},\mbox{bNODE\_i},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Clique},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_sameCliqueAs},\mbox{uri\_owl\_sameAs})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_sameCliqueAs},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_Clique},\mbox{bNODE\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_r},\mbox{uri\_ex\_sameCliqueAs})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_r},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_knows},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_foaf\_knows},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_sameCliqueAs})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_3,\mbox{bNODE\_i})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_i},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_JoesGang},\mbox{uri\_ex\_Clique})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_JoesGang})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_JoesGang}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_013\_Cliques},\mbox{axiom})$

\medskip\textbf{SWB004+4.p} Axiomatic Triples






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_owl\_Class},\mbox{uri\_rdfs\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_rdfs\_Datatype},\mbox{uri\_owl\_Class})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_004\_Axiomatic\_Triples},\mbox{conjecture})$

\medskip\textbf{SWB021+2.p} Composite Enumerations






$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},x,y) \ \Rightarrow \ ( \mbox{ic}(x)\mbox{ and }\mbox{icext}(\mbox{uri\_rdf\_List},y) ) )\qquad\mbox{fof}(\mbox{owl\_prop\_oneof\_ext},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_unionOf},x,y) \ \Rightarrow \ ( \mbox{ic}(x)\mbox{ and }\mbox{icext}(\mbox{uri\_rdf\_List},y) ) )\qquad\mbox{fof}(\mbox{owl\_prop\_unionof\_ext},\mbox{axiom})$

$\forall z,s_1,c_1,s_2,c_2{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,c_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,c_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_unionOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff ( \mbox{icext}(c_1,x)\mbox{ or }\mbox{icext}(c_2,x) ) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_bool\_unionof\_class}_{002},\mbox{axiom})$

$\forall z,s_1,a_1,s_2,a_2{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,a_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,a_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_oneOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff ( x = a_1\mbox{ or }x = a_2 ) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_enum\_class}_{002},\mbox{axiom})$

$\forall z,s_1,a_1,s_2,a_2,s_3,a_3{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,a_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,a_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,s_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_3,a_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_3,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_oneOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff ( x = a_1\mbox{ or }x = a_2\mbox{ or }x = a_3 ) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_enum\_class}_{003},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x)\iff \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_eqdis\_equivalentclass},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_c}_3,\mbox{uri\_ex\_c}_4)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_021\_Composite\_Enumerations},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33},\mbox{bNODE\_l}_{41},\mbox{bNODE\_l}_{42}{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_1,\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{uri\_ex\_w}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_2,\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_3,\mbox{bNODE\_l}_{31})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{31},\mbox{uri\_ex\_w}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{32},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{33},\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{33},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c}_4,\mbox{bNODE\_l}_{41})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{41},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{41},\mbox{bNODE\_l}_{42})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{42},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{42},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_021\_Composite\_Enumerations},\mbox{axiom})$

\medskip\textbf{SWB066+1.p} Inverse Property Extensional

If the extensions of two properties are inverse, then the 
 properties themselves are.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{uri\_ex\_q},\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_inv\_ext},\mbox{conjecture})$

$\exists x_3,x_7,x_0,x_6,x_4,x_5,x_1,x_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p},x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_3,x_4)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_5,\mbox{uri\_ex\_s})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_5,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{uri\_ex\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_6,x_5)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_q},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_q},x_6)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_q},\mbox{uri\_ex\_o},\mbox{uri\_ex\_s})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_7,\mbox{uri\_ex\_s})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_7,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_4,\mbox{uri\_ex\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_4,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_2,x_7) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_inv\_ext},\mbox{axiom})$

\medskip\textbf{SWB039+1.p} Class Intersection Extensional

If a class is an equivalent class to the intersection of other 
 classes, then the former class defines the intersection of the 
 other classes. This test checks that class intersection is 
 realized as an iff-condition.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_1,x_0{:}\;( \mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{uri\_ex\_c},x_0) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_bool\_intersection\_ext},\mbox{conjecture})$

$\exists x_0,x_1,x_2{:}\;( \mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},x_1,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_c},x_1) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_bool\_intersection\_ext},\mbox{axiom})$

\medskip\textbf{SWB012+4.p} Template Class






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_name},\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_foaf\_Person})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_012\_Template\_Class},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3,\mbox{bNODE\_r}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_Person},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{uri\_ex\_PersonAttribute},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_owl\_DatatypeProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_3,\mbox{bNODE\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_r},\mbox{uri\_rdfs\_domain})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_hasValue},\mbox{bNODE\_r},\mbox{uri\_foaf\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_name},\mbox{uri\_ex\_PersonAttribute})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_name},\mbox{uri\_ex\_alice},\mbox{literal\_plain}(\mbox{dat\_str\_alice})) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_012\_Template\_Class},\mbox{axiom})$

\medskip\textbf{SWB008+4.p} Inverse Functional Data Properties






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_robert})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_008\_Inverse\_Functional\_Data\_Properties},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_owl\_DatatypeProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_owl\_InverseFunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_ex\_bob},\mbox{literal\_plain}(\mbox{dat\_str\_xyz}))\mbox{ and }\mbox{iext}(\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_ex\_robert},\mbox{literal\_plain}(\mbox{dat\_str\_xyz}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_008\_Inverse\_Functional\_Data\_Properties},\mbox{axiom})$

\medskip\textbf{SWB103+1.p} Exact-QCR As Min-QCR Max-QCR Intersection

The intersection of a min- and a max-QCR for the same 
 cardinality, property and class is equivalent to an exact-QCR for 
 the same cardinality, property and class.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_z}_4,\mbox{uri\_ex\_z}_1)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_term\_minmaxexact},\mbox{conjecture})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_z}_2,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_z}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_maxQualifiedCardinality},\mbox{uri\_ex\_z}_3,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_3,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z}_3,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_z}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_qualifiedCardinality},\mbox{uri\_ex\_z}_1,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{uri\_ex\_z}_4,x_1) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_term\_minmaxexact},\mbox{axiom})$

\medskip\textbf{SWB008+3.p} Inverse Functional Data Properties






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_robert})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_008\_Inverse\_Functional\_Data\_Properties},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_owl\_DatatypeProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_owl\_InverseFunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_ex\_bob},\mbox{literal\_plain}(\mbox{dat\_str\_xyz}))\mbox{ and }\mbox{iext}(\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_ex\_robert},\mbox{literal\_plain}(\mbox{dat\_str\_xyz}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_008\_Inverse\_Functional\_Data\_Properties},\mbox{axiom})$

\medskip\textbf{SWB025+2.p} Cyclic Dependencies between Complex Properties






$\forall p,s_1,p_1,s_2,p_2{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,p_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,p_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},p,s_1)\iff ( \mbox{ip}(p)\mbox{ and }\mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall y_0,y_1,y_2{:}\;( ( \mbox{iext}(p_1,y_0,y_1)\mbox{ and }\mbox{iext}(p_2,y_1,y_2) ) \ \Rightarrow \ \mbox{iext}(p,y_0,y_2) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_chain}_{002},\mbox{axiom})$

$\forall p_1,p_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_inverseOf},p_1,p_2)\iff ( \mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall x,y{:}\;( \mbox{iext}(p_1,x,y)\iff \mbox{iext}(p_2,y,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_inv},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_ex\_hasUncle},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_charly})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasCousin},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_alice})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_025\_Cyclic\_Dependencies\_between\_Complex\_Properties},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_3{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_ex\_hasUncle},\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{uri\_ex\_hasCousin})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_ex\_hasFather})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_ex\_hasCousin},\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{uri\_ex\_hasUncle})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_l}_3,\mbox{uri\_ex\_hasFather})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasFather},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_dave})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasCousin},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasFather},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_charly})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasUncle},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_dave}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_025\_Cyclic\_Dependencies\_between\_Complex\_Properties},\mbox{axiom})$

\medskip\textbf{SWB054+1.p} Universal Class As Super-Class

Every OWL class is a sub class of the vocabulary class owl:Thing.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Thing})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_class\_thing\_term},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Class})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_class\_thing\_term},\mbox{axiom})$

\medskip\textbf{SWB104+1.p} Universal Class As Min-QCR Max-QCR Union

The union of a min- and a max-QCR for the same cardinality, 
 property and class covers the whole universe.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_z}_3,\mbox{uri\_owl\_Thing})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_term\_minmaxthing},\mbox{conjecture})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_maxQualifiedCardinality},\mbox{uri\_ex\_z}_2,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_z}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_z}_3,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_z}_1,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_z}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,x_0) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_term\_minmaxthing},\mbox{axiom})$

\medskip\textbf{SWB004+3.p} Axiomatic Triples






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_owl\_Class},\mbox{uri\_rdfs\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_rdfs\_Datatype},\mbox{uri\_owl\_Class})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_004\_Axiomatic\_Triples},\mbox{conjecture})$

\medskip\textbf{SWB017+3.p} Built-in Based Definitions






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_017\_Built\_in\_Based\_Definitions},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_ex\_notInstanceOf},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_notInstanceOf},\mbox{uri\_ex\_u},\mbox{uri\_ex\_c})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_017\_Built\_in\_Based\_Definitions},\mbox{axiom})$

\medskip\textbf{SWB016+2.p} Reflective Tautologies II






$\forall p{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},p,\mbox{uri\_rdf\_Property})\iff \mbox{ip}(p) )\qquad\mbox{fof}(\mbox{rdf\_type\_ip},\mbox{axiom})$

$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall p,c,x,y{:}\;( ( \mbox{iext}(\mbox{uri\_rdfs\_domain},p,c)\mbox{ and }\mbox{iext}(p,x,y) ) \ \Rightarrow \ \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_domain\_main},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_rdfs\_domain},\mbox{uri\_rdf\_Property})\qquad\mbox{fof}(\mbox{rdfs\_domain\_domain},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_rdfs\_Class})\qquad\mbox{fof}(\mbox{rdfs\_subclassof\_domain},\mbox{axiom})$

$\mbox{ip}(\mbox{uri\_owl\_equivalentClass})\qquad\mbox{fof}(\mbox{owl\_prop\_equivalentclass\_type},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},x,y) \ \Rightarrow \ ( \mbox{ic}(x)\mbox{ and }\mbox{ic}(y) ) )\qquad\mbox{fof}(\mbox{owl\_prop\_equivalentclass\_ext},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subClassOf},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x) \ \Rightarrow \ \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subclassof},\mbox{axiom})$

$\forall p_1,p_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},p_1,p_2)\iff ( \mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall x,y{:}\;( \mbox{iext}(p_1,x,y) \ \Rightarrow \ \mbox{iext}(p_2,x,y) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subpropertyof},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x)\iff \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_eqdis\_equivalentclass},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_owl\_equivalentClass},\mbox{uri\_rdfs\_subClassOf})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_016\_Reflective\_Tautologies\_II},\mbox{conjecture})$

\medskip\textbf{SWB015+2.p} Reflective Tautologies I






$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},x,y)\iff x = y )\qquad\mbox{fof}(\mbox{owl\_eqdis\_sameas},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_owl\_sameAs},\mbox{uri\_owl\_sameAs})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_015\_Reflective\_Tautologies\_I},\mbox{conjecture})$

\medskip\textbf{SWB017+2.p} Built-in Based Definitions






$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_differentFrom},x,y)\iff x\ne y )\qquad\mbox{fof}(\mbox{owl\_eqdis\_differentfrom},\mbox{axiom})$

$\forall p_1,p_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},p_1,p_2)\iff ( \mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall x,y{:}\;\neg\,\mbox{iext}(p_1,x,y)\mbox{ and }\mbox{iext}(p_2,x,y) ) )\qquad\mbox{fof}(\mbox{owl\_eqdis\_propertydisjointwith},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_017\_Built\_in\_Based\_Definitions},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_ex\_notInstanceOf},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_notInstanceOf},\mbox{uri\_ex\_u},\mbox{uri\_ex\_c})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_017\_Built\_in\_Based\_Definitions},\mbox{axiom})$

\medskip\textbf{SWB029+4.p} Ex Falso Quodlibet






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_B})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_029\_Ex\_Falso\_Quodlibet},\mbox{conjecture})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_y},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_A},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_B},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{bNODE\_x},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_A})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{bNODE\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_y},\mbox{uri\_ex\_A}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_029\_Ex\_Falso\_Quodlibet},\mbox{axiom})$

\medskip\textbf{SWB099+1.p} Existential Restriction Comparison By Property

An existential restriction on some property and some class is a 
 sub class of another existential restriction on the same class 
 but on a super property.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_somevalues\_cmp\_prop},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p}_2)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_somevalues\_cmp\_prop},\mbox{axiom})$

\medskip\textbf{SWB005+4.p} Everything is a Resource






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_rdf\_Property})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_o},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_o},\mbox{uri\_owl\_Thing})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_005\_Everything\_is\_a\_Resource},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{uri\_ex\_o})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_005\_Everything\_is\_a\_Resource},\mbox{axiom})$

\medskip\textbf{SWB009+3.p} Existential Restriction Entailments






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_ex\_c}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_009\_Existential\_Restriction\_Entailments},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_z},\mbox{uri\_ex\_c}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_009\_Existential\_Restriction\_Entailments},\mbox{axiom})$

\medskip\textbf{SWB016+1.p} Reflective Tautologies II






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_owl\_equivalentClass},\mbox{uri\_rdfs\_subClassOf})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_016\_Reflective\_Tautologies\_II},\mbox{conjecture})$

\medskip\textbf{SWB073+1.p} Empty Data Property As Sub-Property

Every data property is a super property of the vocabulary 
 property owl:bottomDataProperty.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_owl\_bottomDataProperty},\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_prop\_bottomdataproperty\_term},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_DatatypeProperty})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_prop\_bottomdataproperty\_term},\mbox{axiom})$

\medskip\textbf{SWB028+3.p} Inferred Property Characteristics III






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_InversesOfFunctionalProperties},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_028\_Inferred\_Property\_Characteristics\_III},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_InversesOfFunctionalProperties},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_owl\_inverseOf})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_z},\mbox{uri\_owl\_FunctionalProperty}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_028\_Inferred\_Property\_Characteristics\_III},\mbox{axiom})$

\medskip\textbf{SWB051+1.p} Transitive Property Extensional

If the extension of a property is transitive, then the property 
 itself is.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_TransitiveProperty})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_char\_transitive\_ext},\mbox{conjecture})$

$\exists x_5,x_0,x_3,x_1,x_2,x_4{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_x},\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_4,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_4,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_5,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_5,x_4)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_y},\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_y},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_2,x_5) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_char\_transitive\_ext},\mbox{axiom})$

\medskip\textbf{SWB015+4.p} Reflective Tautologies I






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_owl\_sameAs},\mbox{uri\_owl\_sameAs})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_015\_Reflective\_Tautologies\_I},\mbox{conjecture})$

\medskip\textbf{SWB022+4.p} List Member Access






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_X})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_Y})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_Z})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_022\_List\_Member\_Access},\mbox{conjecture})$

$\exists \mbox{bNODE\_pL},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33}{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_memberList},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_skos\_member},\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_first})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{bNODE\_pL},\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_rest})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_skos\_OrderedCollection})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_memberList},\mbox{uri\_ex\_MyOrderedCollection},\mbox{bNODE\_l}_{31})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{31},\mbox{uri\_ex\_X})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{32},\mbox{uri\_ex\_Y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{33},\mbox{uri\_ex\_Z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{33},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_022\_List\_Member\_Access},\mbox{axiom})$

\medskip\textbf{SWB068+1.p} N-Ary Individual Difference Extensional

For a group of mutually different individuals, the corresponding 
 owl:AllDifferent construct exist.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_2,x_0,x_1,x_3{:}\;( \mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_w}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},x_3,\mbox{uri\_owl\_AllDifferent})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_members},x_3,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_ndis\_alldifferent\_bw},\mbox{conjecture})$

$\exists x_0,x_2,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_w}_1,\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_w}_1,\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_w}_2,\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_w}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,x_1) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_ndis\_alldifferent\_bw},\mbox{axiom})$

\medskip\textbf{SWB050+1.p} Symmetric Property Extensional

If the extension of a property is symmetric, then the property 
 itself is.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_SymmetricProperty})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_char\_symmetric\_ext},\mbox{conjecture})$

$\exists x_0,x_2,x_3,x_5,x_1,x_4{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_1,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_x},\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,x_4)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_5,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_5,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_y},\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_y},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_4,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_4,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,x_5) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_char\_symmetric\_ext},\mbox{axiom})$

\medskip\textbf{SWB034+1.p} Datatype Relationships






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

\medskip\textbf{SWB028+2.p} Inferred Property Characteristics III






$\mbox{ic}(\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{owl\_class\_inversefunctionalproperty\_type},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_inverseOf},x,y) \ \Rightarrow \ ( \mbox{ip}(x)\mbox{ and }\mbox{ip}(y) ) )\qquad\mbox{fof}(\mbox{owl\_prop\_inverseof\_ext},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},x,y) \ \Rightarrow \ ( \mbox{ic}(x)\mbox{ and }\mbox{ic}(y) ) )\qquad\mbox{fof}(\mbox{owl\_prop\_equivalentclass\_ext},\mbox{axiom})$

$\forall p{:}\;( \mbox{icext}(\mbox{uri\_owl\_FunctionalProperty},p)\iff ( \mbox{ip}(p)\mbox{ and }\forall x,y_1,y_2{:}\;( ( \mbox{iext}(p,x,y_1)\mbox{ and }\mbox{iext}(p,x,y_2) ) \ \Rightarrow \ y_1 = y_2 ) ) )\qquad\mbox{fof}(\mbox{owl\_char\_functional},\mbox{axiom})$

$\forall p{:}\;( \mbox{icext}(\mbox{uri\_owl\_InverseFunctionalProperty},p)\iff ( \mbox{ip}(p)\mbox{ and }\forall x_1,x_2,y{:}\;( ( \mbox{iext}(p,x_1,y)\mbox{ and }\mbox{iext}(p,x_2,y) ) \ \Rightarrow \ x_1 = x_2 ) ) )\qquad\mbox{fof}(\mbox{owl\_char\_inversefunctional},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subClassOf},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x) \ \Rightarrow \ \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subclassof},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x)\iff \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_eqdis\_equivalentclass},\mbox{axiom})$

$\forall z,p,c{:}\;( ( \mbox{iext}(\mbox{uri\_owl\_someValuesFrom},z,c)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},z,p) ) \ \Rightarrow \ \forall x{:}\;( \mbox{icext}(z,x)\iff \exists y{:}\;( \mbox{iext}(p,x,y)\mbox{ and }\mbox{icext}(c,y) ) ) )\qquad\mbox{fof}(\mbox{owl\_restrict\_somevaluesfrom},\mbox{axiom})$

$\forall p_1,p_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_inverseOf},p_1,p_2)\iff ( \mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall x,y{:}\;( \mbox{iext}(p_1,x,y)\iff \mbox{iext}(p_2,y,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_inv},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_InversesOfFunctionalProperties},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_028\_Inferred\_Property\_Characteristics\_III},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_InversesOfFunctionalProperties},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_owl\_inverseOf})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_z},\mbox{uri\_owl\_FunctionalProperty}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_028\_Inferred\_Property\_Characteristics\_III},\mbox{axiom})$

\medskip\textbf{SWB090+1.p} Max-QCR Comparison By Property

A max-QCR for some cardinality on some property and to some class 
 is a subclass of another max-QCR for the same cardinality to the 
 same class and on a sub property.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_maxqcr\_cmp\_prop},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_maxQualifiedCardinality},\mbox{uri\_ex\_x}_2,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_maxQualifiedCardinality},\mbox{uri\_ex\_x}_1,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_p}_1)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_maxqcr\_cmp\_prop},\mbox{axiom})$

\medskip\textbf{SWB001+3.p} Subgraph Entailment






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_r},\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_001\_Subgraph\_Entailment},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_r},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_r},\mbox{uri\_ex\_d})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_001\_Subgraph\_Entailment},\mbox{axiom})$

\medskip\textbf{SWB019+2.p} Disjoint Annotation Properties






$\forall p_1,p_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},p_1,p_2)\iff ( \mbox{ip}(p_1)\mbox{ and }\mbox{ip}(p_2)\mbox{ and }\forall x,y{:}\;\neg\,\mbox{iext}(p_1,x,y)\mbox{ and }\mbox{iext}(p_2,x,y) ) )\qquad\mbox{fof}(\mbox{owl\_eqdis\_propertydisjointwith},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_skos\_prefLabel},\mbox{uri\_owl\_AnnotationProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_prefLabel},\mbox{uri\_rdfs\_label})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_skos\_altLabel},\mbox{uri\_owl\_AnnotationProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_altLabel},\mbox{uri\_rdfs\_label})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_skos\_prefLabel},\mbox{uri\_skos\_altLabel})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_prefLabel},\mbox{uri\_ex\_foo},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_altLabel},\mbox{uri\_ex\_foo},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_019\_Disjoint\_Annotation\_Properties},\mbox{axiom})$

\medskip\textbf{SWB108+1.p} Existential Restriction As Min-QCR

An existential restriction can be written as a min-1-QCR.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_z}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_term\_someqcr},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_z}_2,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_term\_someqcr},\mbox{axiom})$

\medskip\textbf{SWB044+1.p} Asymmetric Property Extensional

If the extension of a property is asymmetric, then the property 
 itself is.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_AsymmetricProperty})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_char\_asymmetric\_ext},\mbox{conjecture})$

$\exists x_2,x_3,x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p},x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_2,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_char\_asymmetric\_ext},\mbox{axiom})$

\medskip\textbf{SWB072+1.p} Empty Data Property Extensional Low

The extension of the vocabulary property owl:bottomDataProperty 
 is empty. See also rdfbased-sem-prop-bottomdataproperty-ext-hi 
 for a weaker variant of this test case.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_owl\_bottomDataProperty},\mbox{uri\_owl\_Nothing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_owl\_bottomDataProperty},\mbox{uri\_owl\_Nothing})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_prop\_bottomdataproperty\_ext\_lo},\mbox{conjecture})$

$\mbox{tautology}\mbox{ or }\neg\,\mbox{tautology}\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_prop\_bottomdataproperty\_ext\_lo},\mbox{axiom})$

\medskip\textbf{SWB031+3.p} Large Universe






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_l}{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_owl\_Thing},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x},\mbox{bNODE\_l})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_031\_Large\_Universe},\mbox{axiom})$

\medskip\textbf{SWB043+1.p} Singleton Property Chain As Subsumption

A sub property chain axiom with a single chain property 
 corresponds to a sub property axiom.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_chain\_subprop},\mbox{conjecture})$

$\exists x_0{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_ex\_p},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_chain\_subprop},\mbox{axiom})$

\medskip\textbf{SWB029+1.p} Ex Falso Quodlibet






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_B})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_029\_Ex\_Falso\_Quodlibet},\mbox{conjecture})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_y},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_A},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_B},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{bNODE\_x},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_A})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{bNODE\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_y},\mbox{uri\_ex\_A}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_029\_Ex\_Falso\_Quodlibet},\mbox{axiom})$

\medskip\textbf{SWB010+2.p} Negative Property Assertions






$\forall x{:}\;\mbox{ir}(x)\qquad\mbox{fof}(\mbox{simple\_ir},\mbox{axiom})$

$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_sourceIndividual},x,y) \ \Rightarrow \ ( \mbox{icext}(\mbox{uri\_owl\_NegativePropertyAssertion},x)\mbox{ and }\mbox{ir}(y) ) )\qquad\mbox{fof}(\mbox{owl\_prop\_sourceindividual\_ext},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_onProperty},x,y) \ \Rightarrow \ ( \mbox{icext}(\mbox{uri\_owl\_Restriction},x)\mbox{ and }\mbox{ip}(y) ) )\qquad\mbox{fof}(\mbox{owl\_prop\_onproperty\_ext},\mbox{axiom})$

$\forall z,c{:}\;( \mbox{iext}(\mbox{uri\_owl\_complementOf},z,c) \ \Rightarrow \ ( \mbox{ic}(z)\mbox{ and }\mbox{ic}(c)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff \neg\,\mbox{icext}(c,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_bool\_complementof\_class},\mbox{axiom})$

$\forall z,s_1,a_1{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,a_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_oneOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff x = a_1 ) ) ) )\qquad\mbox{fof}(\mbox{owl\_enum\_class}_{001},\mbox{axiom})$

$\forall z,p,c{:}\;( ( \mbox{iext}(\mbox{uri\_owl\_allValuesFrom},z,c)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},z,p) ) \ \Rightarrow \ \forall x{:}\;( \mbox{icext}(z,x)\iff \forall y{:}\;( \mbox{iext}(p,x,y) \ \Rightarrow \ \mbox{icext}(c,y) ) ) )\qquad\mbox{fof}(\mbox{owl\_restrict\_allvaluesfrom},\mbox{axiom})$

$\forall p,a_1,a_2{:}\;( ( \mbox{ir}(a_1)\mbox{ and }\mbox{ip}(p)\mbox{ and }\mbox{ir}(a_2)\mbox{ and }\neg\,\mbox{iext}(p,a_1,a_2) ) \ \Rightarrow \ \exists z{:}\;( \mbox{iext}(\mbox{uri\_owl\_sourceIndividual},z,a_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_assertionProperty},z,p)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_targetIndividual},z,a_2) ) )\qquad\mbox{fof}(\mbox{owl\_npa\_object\_fi},\mbox{axiom})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_NegativePropertyAssertion})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sourceIndividual},\mbox{bNODE\_z},\mbox{uri\_ex\_s})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_assertionProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_targetIndividual},\mbox{bNODE\_z},\mbox{uri\_ex\_o}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_010\_Negative\_Property\_Assertions},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2,\mbox{bNODE\_x}_3,\mbox{bNODE\_x}_4{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{bNODE\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_x}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_allValuesFrom},\mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_x}_2,\mbox{bNODE\_x}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_3,\mbox{bNODE\_x}_4)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_x}_4,\mbox{uri\_ex\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_x}_4,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_010\_Negative\_Property\_Assertions},\mbox{axiom})$

\medskip\textbf{SWB003+4.p} Blank Nodes for Literals






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_x})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_003\_Blank\_Nodes\_for\_Literals},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_003\_Blank\_Nodes\_for\_Literals},\mbox{axiom})$

\medskip\textbf{SWB040+1.p} Class Modus Tollens

If a class is subsumed by another class, then the complement of 
 the latter class is subsumed by the complement of the former 
 class.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_n}_2,\mbox{uri\_ex\_n}_1)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_bool\_tollens},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{uri\_ex\_n}_2,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{uri\_ex\_n}_1,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_bool\_tollens},\mbox{axiom})$

\medskip\textbf{SWB007+3.p} Equal Classes






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_007\_Equal\_Classes},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c}_1)\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_007\_Equal\_Classes},\mbox{axiom})$

\medskip\textbf{SWB028+4.p} Inferred Property Characteristics III






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_InversesOfFunctionalProperties},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_028\_Inferred\_Property\_Characteristics\_III},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_InversesOfFunctionalProperties},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_owl\_inverseOf})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_z},\mbox{uri\_owl\_FunctionalProperty}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_028\_Inferred\_Property\_Characteristics\_III},\mbox{axiom})$

\medskip\textbf{SWB007+4.p} Equal Classes






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_007\_Equal\_Classes},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c}_1)\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_007\_Equal\_Classes},\mbox{axiom})$

\medskip\textbf{SWB023+1.p} Unique List Components






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_v})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_023\_Unique\_List\_Components},\mbox{conjecture})$

$\exists \mbox{bNODE\_o},\mbox{bNODE\_l}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_rdf\_first},\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{bNODE\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_o},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_o},\mbox{bNODE\_l})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_v})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_023\_Unique\_List\_Components},\mbox{axiom})$

\medskip\textbf{SWB055+1.p} Individual Enumeration Extensional

If a class is an equivalent class to the enumeration of two 
 individuals, then the class defines the enumeration of the two 
 individuals. This test checks that enumeration is realized as an 
 iff-condition.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_e},x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,x_0) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_enum\_ext},\mbox{conjecture})$

$\exists x_0,x_2,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_e},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_enum\_ext},\mbox{axiom})$

\medskip\textbf{SWB092+1.p} Max-0-QCR Extensional

For an individual w, if there is no triple w p x, with x being an 
 instance of class c, then w is an instance of the max-0-QCR on p 
 to c.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_z})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_maxqcr\_inst\_subj\_zero},\mbox{conjecture})$

$\exists x_2,x_4,x_0,x_3,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_complementOf},x_0,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_maxQualifiedCardinality},\mbox{uri\_ex\_z},\mbox{literal\_typed}(\mbox{dat\_str}_0,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_1,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},x_4,\mbox{uri\_owl\_NegativePropertyAssertion})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sourceIndividual},x_4,\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_assertionProperty},x_4,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_targetIndividual},x_4,\mbox{uri\_ex\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},\mbox{uri\_ex\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x}_2,x_0) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_maxqcr\_inst\_subj\_zero},\mbox{axiom})$

\medskip\textbf{SWB003+2.p} Blank Nodes for Literals






$\exists \mbox{bNODE\_x}{:}\;\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_x})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_003\_Blank\_Nodes\_for\_Literals},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_003\_Blank\_Nodes\_for\_Literals},\mbox{axiom})$

\medskip\textbf{SWB100+1.p} Existential Restriction Intensional

If an individual w is an instance of the existential restriction 
 on property p and class c, then an individual x exists with w p x 
 and x in c.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_0{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x_0,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},x_0) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_somevalues\_inst\_obj},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_z},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_z})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_somevalues\_inst\_obj},\mbox{axiom})$

\medskip\textbf{SWB026+4.p} Inferred Property Characteristics I






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_026\_Inferred\_Property\_Characteristics\_I},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2,\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p},\mbox{bNODE\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_1,\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{bNODE\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_2,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_026\_Inferred\_Property\_Characteristics\_I},\mbox{axiom})$

\medskip\textbf{SWB102+1.p} Data-QCR As Object-QCR

An object-QCR on a data property to a datatype is a data-QCR. 
 Also, every data-QCR is an object-QCR.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_z}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_term\_dataqcr},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_DatatypeProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_qualifiedCardinality},\mbox{uri\_ex\_z}_2,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onDataRange},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_d})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_d},\mbox{uri\_rdfs\_Datatype})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_qualifiedCardinality},\mbox{uri\_ex\_z}_1,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_d})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_term\_dataqcr},\mbox{axiom})$

\medskip\textbf{SWB083+1.p} Universal Restriction Extensional

If the range of property p is defined to be class c, then every 
 individual is an instance of the universal restriction on p to c.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_z})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_allvalues\_inst\_subj},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_allValuesFrom},\mbox{uri\_ex\_z},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_owl\_Thing})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_allvalues\_inst\_subj},\mbox{axiom})$

\medskip\textbf{SWB018+4.p} Modified Logical Vocabulary Semantics






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_u},\mbox{uri\_ex\_Person})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_018\_Modified\_Logical\_Vocabulary\_Semantics},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_018\_Modified\_Logical\_Vocabulary\_Semantics},\mbox{axiom})$

\medskip\textbf{SWB064+1.p} Property Equivalence Extensional

If the extensions of two properties are equal, then the 
 properties themselves are equivalent.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentProperty},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_eqdis\_eqprop\_ext},\mbox{conjecture})$

$\exists x_1,x_0{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_s},\mbox{uri\_ex\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_s},\mbox{uri\_ex\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_x},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_s})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_y},x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_eqdis\_eqprop\_ext},\mbox{axiom})$

\medskip\textbf{SWB010+3.p} Negative Property Assertions






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_NegativePropertyAssertion})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sourceIndividual},\mbox{bNODE\_z},\mbox{uri\_ex\_s})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_assertionProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_targetIndividual},\mbox{bNODE\_z},\mbox{uri\_ex\_o}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_010\_Negative\_Property\_Assertions},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2,\mbox{bNODE\_x}_3,\mbox{bNODE\_x}_4{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{bNODE\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_x}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_allValuesFrom},\mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_x}_2,\mbox{bNODE\_x}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_3,\mbox{bNODE\_x}_4)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_x}_4,\mbox{uri\_ex\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_x}_4,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_010\_Negative\_Property\_Assertions},\mbox{axiom})$

\medskip\textbf{SWB087+1.p} Self-Restriction Extensional

For a triple w p w, the individual w is an instance of the self 
 restriction on p.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_z})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_hasself\_inst\_subj},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_hasSelf},\mbox{uri\_ex\_z},\mbox{literal\_typed}(\mbox{dat\_str\_true},\mbox{uri\_xsd\_boolean}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},\mbox{uri\_ex\_w})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_hasself\_inst\_subj},\mbox{axiom})$

\medskip\textbf{SWB049+1.p} Reflexive Property Extensional

If the extension of a property is reflexive, then the property 
 itself is. Note that reflexivity is globally defined on the whole 
 universe, which has infinite cardinality under the RDF-Based 
 Semantics. Therefore, instead of explicitly defining the 
 extension of some custom property, the extension of the built-in 
 property owl:topObjectProperty is referred to.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ReflexiveProperty})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_char\_reflexive\_ext},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentProperty},\mbox{uri\_ex\_p},\mbox{uri\_owl\_topObjectProperty})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_char\_reflexive\_ext},\mbox{axiom})$

\medskip\textbf{SWB019+4.p} Disjoint Annotation Properties






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_skos\_prefLabel},\mbox{uri\_owl\_AnnotationProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_prefLabel},\mbox{uri\_rdfs\_label})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_skos\_altLabel},\mbox{uri\_owl\_AnnotationProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_altLabel},\mbox{uri\_rdfs\_label})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_skos\_prefLabel},\mbox{uri\_skos\_altLabel})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_prefLabel},\mbox{uri\_ex\_foo},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_altLabel},\mbox{uri\_ex\_foo},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_019\_Disjoint\_Annotation\_Properties},\mbox{axiom})$

\medskip\textbf{SWB020+1.p} Logical Complications






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_d},\mbox{uri\_ex\_c}_3)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_020\_Logical\_Complications},\mbox{conjecture})$

$\exists \mbox{bNODE\_xs},\mbox{bNODE\_xc},\mbox{bNODE\_lu}_1,\mbox{bNODE\_lu}_2,\mbox{bNODE\_lu}_3,\mbox{bNODE\_li}_1,\mbox{bNODE\_li}_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c},\mbox{bNODE\_lu}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_1,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_1,\mbox{bNODE\_lu}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_2,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_2,\mbox{bNODE\_lu}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_3,\mbox{uri\_ex\_c}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_ex\_d},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_d},\mbox{bNODE\_xs})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{bNODE\_xs},\mbox{bNODE\_li}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_li}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_li}_1,\mbox{bNODE\_li}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_li}_2,\mbox{bNODE\_xc})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_li}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_xc},\mbox{uri\_ex\_c}_2) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_020\_Logical\_Complications},\mbox{axiom})$

\medskip\textbf{SWB029+3.p} Ex Falso Quodlibet






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_B})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_029\_Ex\_Falso\_Quodlibet},\mbox{conjecture})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_y},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_A},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_B},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{bNODE\_x},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_A})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{bNODE\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_y},\mbox{uri\_ex\_A}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_029\_Ex\_Falso\_Quodlibet},\mbox{axiom})$

\medskip\textbf{SWB025+4.p} Cyclic Dependencies between Complex Properties






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_ex\_hasUncle},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_charly})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasCousin},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_alice})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_025\_Cyclic\_Dependencies\_between\_Complex\_Properties},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_3{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_ex\_hasUncle},\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{uri\_ex\_hasCousin})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_ex\_hasFather})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_ex\_hasCousin},\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{uri\_ex\_hasUncle})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_l}_3,\mbox{uri\_ex\_hasFather})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasFather},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_dave})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasCousin},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasFather},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_charly})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasUncle},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_dave}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_025\_Cyclic\_Dependencies\_between\_Complex\_Properties},\mbox{axiom})$

\medskip\textbf{SWB008+1.p} Inverse Functional Data Properties






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_robert})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_008\_Inverse\_Functional\_Data\_Properties},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_owl\_DatatypeProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_owl\_InverseFunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_ex\_bob},\mbox{literal\_plain}(\mbox{dat\_str\_xyz}))\mbox{ and }\mbox{iext}(\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_ex\_robert},\mbox{literal\_plain}(\mbox{dat\_str\_xyz}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_008\_Inverse\_Functional\_Data\_Properties},\mbox{axiom})$

\medskip\textbf{SWB021+4.p} Composite Enumerations






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_c}_3,\mbox{uri\_ex\_c}_4)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_021\_Composite\_Enumerations},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33},\mbox{bNODE\_l}_{41},\mbox{bNODE\_l}_{42}{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_1,\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{uri\_ex\_w}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_2,\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_3,\mbox{bNODE\_l}_{31})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{31},\mbox{uri\_ex\_w}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{32},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{33},\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{33},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c}_4,\mbox{bNODE\_l}_{41})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{41},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{41},\mbox{bNODE\_l}_{42})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{42},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{42},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_021\_Composite\_Enumerations},\mbox{axiom})$

\medskip\textbf{SWB020+2.p} Logical Complications






$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_disjointWith},x,y) \ \Rightarrow \ ( \mbox{ic}(x)\mbox{ and }\mbox{ic}(y) ) )\qquad\mbox{fof}(\mbox{owl\_prop\_disjointwith\_ext},\mbox{axiom})$

$\forall z,c{:}\;( \mbox{iext}(\mbox{uri\_owl\_complementOf},z,c) \ \Rightarrow \ ( \mbox{ic}(z)\mbox{ and }\mbox{ic}(c)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff \neg\,\mbox{icext}(c,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_bool\_complementof\_class},\mbox{axiom})$

$\forall z,s_1,c_1,s_2,c_2{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,c_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,c_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_intersectionOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff ( \mbox{icext}(c_1,x)\mbox{ and }\mbox{icext}(c_2,x) ) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_bool\_intersectionof\_class}_{002},\mbox{axiom})$

$\forall z,s_1,c_1,s_2,c_2,s_3,c_3{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,c_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,c_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,s_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_3,c_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_3,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_unionOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\mbox{ic}(c_3)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff ( \mbox{icext}(c_1,x)\mbox{ or }\mbox{icext}(c_2,x)\mbox{ or }\mbox{icext}(c_3,x) ) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_bool\_unionof\_class}_{003},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subClassOf},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(c_1,x) \ \Rightarrow \ \mbox{icext}(c_2,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_rdfsext\_subclassof},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_disjointWith},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;\neg\,\mbox{icext}(c_1,x)\mbox{ and }\mbox{icext}(c_2,x) ) )\qquad\mbox{fof}(\mbox{owl\_eqdis\_disjointwith},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_d},\mbox{uri\_ex\_c}_3)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_020\_Logical\_Complications},\mbox{conjecture})$

$\exists \mbox{bNODE\_xs},\mbox{bNODE\_xc},\mbox{bNODE\_lu}_1,\mbox{bNODE\_lu}_2,\mbox{bNODE\_lu}_3,\mbox{bNODE\_li}_1,\mbox{bNODE\_li}_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c},\mbox{bNODE\_lu}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_1,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_1,\mbox{bNODE\_lu}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_2,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_2,\mbox{bNODE\_lu}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_3,\mbox{uri\_ex\_c}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_ex\_d},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_d},\mbox{bNODE\_xs})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{bNODE\_xs},\mbox{bNODE\_li}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_li}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_li}_1,\mbox{bNODE\_li}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_li}_2,\mbox{bNODE\_xc})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_li}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_xc},\mbox{uri\_ex\_c}_2) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_020\_Logical\_Complications},\mbox{axiom})$

\medskip\textbf{SWB058+1.p} Class Disjointness Extensional

If the non-empty extensions of two classes are disjoint, then the 
 classes themselves are disjoint.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_eqdis\_disclass\_ext},\mbox{conjecture})$

$\exists x_1,x_0{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_2,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_1,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_eqdis\_disclass\_ext},\mbox{axiom})$

\medskip\textbf{SWB031+1.p} Large Universe






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_l}{:}\;( \mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_owl\_Thing},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x},\mbox{bNODE\_l})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l},\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_031\_Large\_Universe},\mbox{axiom})$

\medskip\textbf{SWB022+1.p} List Member Access






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_X})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_Y})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_Z})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_022\_List\_Member\_Access},\mbox{conjecture})$

$\exists \mbox{bNODE\_pL},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33}{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_memberList},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_skos\_member},\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_first})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{bNODE\_pL},\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_rest})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_skos\_OrderedCollection})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_memberList},\mbox{uri\_ex\_MyOrderedCollection},\mbox{bNODE\_l}_{31})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{31},\mbox{uri\_ex\_X})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{32},\mbox{uri\_ex\_Y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{33},\mbox{uri\_ex\_Z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{33},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_022\_List\_Member\_Access},\mbox{axiom})$

\medskip\textbf{SWB002+3.p} Existential Blank Nodes






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_y}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{bNODE\_x},\mbox{bNODE\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_q},\mbox{bNODE\_y},\mbox{bNODE\_x}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_002\_Existential\_Blank\_Nodes},\mbox{conjecture})$

$\exists \mbox{bNODE\_o}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_q},\mbox{bNODE\_o},\mbox{uri\_ex\_s}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_002\_Existential\_Blank\_Nodes},\mbox{axiom})$

\medskip\textbf{SWB089+1.p} Max-QCR Comparison By Class

A max-QCR for some cardinality on some property and to some class 
 is a subclass of another max-QCR for the same cardinality on the 
 same property and to some sub class.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_maxqcr\_cmp\_class},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_maxQualifiedCardinality},\mbox{uri\_ex\_x}_2,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c}_2,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_maxQualifiedCardinality},\mbox{uri\_ex\_x}_1,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c}_1)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_maxqcr\_cmp\_class},\mbox{axiom})$

\medskip\textbf{SWB011+2.p} Entity Types as Classes






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall c_1,c_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_disjointWith},c_1,c_2)\iff ( \mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;\neg\,\mbox{icext}(c_1,x)\mbox{ and }\mbox{icext}(c_2,x) ) )\qquad\mbox{fof}(\mbox{owl\_eqdis\_disjointwith},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x},\mbox{uri\_owl\_ObjectProperty})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_011\_Entity\_Types\_as\_Classes},\mbox{axiom})$

\medskip\textbf{SWB091+1.p} Max-1-QCR Extensional

For an individual w, if there is at most one triple w p x with x 
 in class c, then w is an instance of the max-1-QCR on p to c.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_z})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_maxqcr\_inst\_subj\_one},\mbox{conjecture})$

$\exists x_1,x_3,x_2,x_0{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_maxQualifiedCardinality},\mbox{uri\_ex\_z},\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},x_3,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},\mbox{uri\_ex\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x}_2,x_3) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_maxqcr\_inst\_subj\_one},\mbox{axiom})$

\medskip\textbf{SWB005+1.p} Everything is a Resource






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_rdf\_Property})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_o},\mbox{uri\_rdfs\_Resource})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_o},\mbox{uri\_owl\_Thing})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_005\_Everything\_is\_a\_Resource},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{uri\_ex\_o})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_005\_Everything\_is\_a\_Resource},\mbox{axiom})$

\medskip\textbf{SWB020+4.p} Logical Complications






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_d},\mbox{uri\_ex\_c}_3)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_020\_Logical\_Complications},\mbox{conjecture})$

$\exists \mbox{bNODE\_xs},\mbox{bNODE\_xc},\mbox{bNODE\_lu}_1,\mbox{bNODE\_lu}_2,\mbox{bNODE\_lu}_3,\mbox{bNODE\_li}_1,\mbox{bNODE\_li}_2{:}\;( \mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c},\mbox{bNODE\_lu}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_1,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_1,\mbox{bNODE\_lu}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_2,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_2,\mbox{bNODE\_lu}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_lu}_3,\mbox{uri\_ex\_c}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_lu}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_ex\_d},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_d},\mbox{bNODE\_xs})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{bNODE\_xs},\mbox{bNODE\_li}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_li}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_li}_1,\mbox{bNODE\_li}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_li}_2,\mbox{bNODE\_xc})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_li}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{bNODE\_xc},\mbox{uri\_ex\_c}_2) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_020\_Logical\_Complications},\mbox{axiom})$

\medskip\textbf{SWB082+1.p} Universal Restriction Comparison By Property

A universal restriction on some property and some class is a sub 
 class of another universal restriction on the same class but on a 
 sub property.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_x}_1)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_allvalues\_cmp\_prop},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_allValuesFrom},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_allValuesFrom},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p}_2)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_allvalues\_cmp\_prop},\mbox{axiom})$

\medskip\textbf{SWB047+1.p} Functional Inverse Property As Inverse-Functional

The inverse of a functional property is an inverse functional 
 property.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p}_2,\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_char\_inversefunc\_term},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p}_1,\mbox{uri\_owl\_FunctionalProperty})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_char\_inversefunc\_term},\mbox{axiom})$

\medskip\textbf{SWB016+4.p} Reflective Tautologies II






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_owl\_equivalentClass},\mbox{uri\_rdfs\_subClassOf})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_016\_Reflective\_Tautologies\_II},\mbox{conjecture})$

\medskip\textbf{SWB006+4.p} Literal Values represented by URIs and Blank Nodes






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_u},\mbox{uri\_ex\_w})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_006\_Literal\_Values\_represented\_by\_URIs\_and\_Blank\_Nodes},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_u},\mbox{literal\_plain}(\mbox{dat\_str\_abc}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{bNODE\_x},\mbox{literal\_plain}(\mbox{dat\_str\_abc}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{bNODE\_x},\mbox{uri\_ex\_w}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_006\_Literal\_Values\_represented\_by\_URIs\_and\_Blank\_Nodes},\mbox{axiom})$

\medskip\textbf{SWB012+1.p} Template Class






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_name},\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_alice},\mbox{uri\_foaf\_Person})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_012\_Template\_Class},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3,\mbox{bNODE\_r}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_Person},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_intersectionOf},\mbox{uri\_ex\_PersonAttribute},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_owl\_DatatypeProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_3,\mbox{bNODE\_r})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_3,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_r},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_r},\mbox{uri\_rdfs\_domain})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_hasValue},\mbox{bNODE\_r},\mbox{uri\_foaf\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_name},\mbox{uri\_ex\_PersonAttribute})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_name},\mbox{uri\_ex\_alice},\mbox{literal\_plain}(\mbox{dat\_str\_alice})) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_012\_Template\_Class},\mbox{axiom})$

\medskip\textbf{SWB022+3.p} List Member Access






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_X})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_Y})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_member},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_ex\_Z})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_022\_List\_Member\_Access},\mbox{conjecture})$

$\exists \mbox{bNODE\_pL},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33}{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_memberList},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_skos\_member},\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_first})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{bNODE\_pL},\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{bNODE\_pL})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_rest})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_MyOrderedCollection},\mbox{uri\_skos\_OrderedCollection})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_memberList},\mbox{uri\_ex\_MyOrderedCollection},\mbox{bNODE\_l}_{31})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{31},\mbox{uri\_ex\_X})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{32},\mbox{uri\_ex\_Y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{33},\mbox{uri\_ex\_Z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{33},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_022\_List\_Member\_Access},\mbox{axiom})$

\medskip\textbf{SWB098+1.p} Existential Restriction Comparison By Class

An existential restriction on some property and some class is a 
 sub class of another existential restriction on the same property 
 but on a super class.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_somevalues\_cmp\_class},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_somevalues\_cmp\_class},\mbox{axiom})$

\medskip\textbf{SWB014+2.p} Harry belongs to some Species






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall z,s_1,c_1,s_2,c_2{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,c_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,s_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},s_2,c_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_2,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_unionOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\mbox{ic}(c_1)\mbox{ and }\mbox{ic}(c_2)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff ( \mbox{icext}(c_1,x)\mbox{ or }\mbox{icext}(c_2,x) ) ) ) ) )\qquad\mbox{fof}(\mbox{owl\_bool\_unionof\_class}_{002},\mbox{axiom})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_harry},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_ex\_Species}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_014\_Harry\_belongs\_to\_some\_Species},\mbox{conjecture})$

$\exists \mbox{bNODE\_u},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Eagle},\mbox{uri\_ex\_Species})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Falcon},\mbox{uri\_ex\_Species})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_harry},\mbox{bNODE\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{bNODE\_u},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_Eagle})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_Falcon})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_014\_Harry\_belongs\_to\_some\_Species},\mbox{axiom})$

\medskip\textbf{SWB030+1.p} Bad Class






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{uri\_ex\_c},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_x},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_hasSelf},\mbox{bNODE\_x},\mbox{literal\_typed}(\mbox{dat\_str\_true},\mbox{uri\_xsd\_boolean})) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_030\_Bad\_Class},\mbox{axiom})$

\medskip\textbf{SWB084+1.p} Exact-2-QCR Intensional

If an individual w is an instance of the exact-2-QCR on property 
 p to class c, then two distinct individuals x1 and x2 exist in c 
 with w p x1 and w p x2




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_1,x_0{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x_0,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},x_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},x_1) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_exactqcr\_inst\_obj\_two},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_qualifiedCardinality},\mbox{uri\_ex\_z},\mbox{literal\_typed}(\mbox{dat\_str}_2,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_z})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_exactqcr\_inst\_obj\_two},\mbox{axiom})$

\medskip\textbf{SWB032+4.p} Datatype Relationships






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_xsd\_decimal},\mbox{uri\_xsd\_string})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_xsd\_integer},\mbox{uri\_xsd\_decimal})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_032\_Datatype\_Relationships},\mbox{conjecture})$

\medskip\textbf{SWB002+1.p} Existential Blank Nodes






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists \mbox{bNODE\_x},\mbox{bNODE\_y}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{bNODE\_x},\mbox{bNODE\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_q},\mbox{bNODE\_y},\mbox{bNODE\_x}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_002\_Existential\_Blank\_Nodes},\mbox{conjecture})$

$\exists \mbox{bNODE\_o}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_o})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_q},\mbox{bNODE\_o},\mbox{uri\_ex\_s}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_002\_Existential\_Blank\_Nodes},\mbox{axiom})$

\medskip\textbf{SWB007+2.p} Equal Classes






$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},x,y)\iff x = y )\qquad\mbox{fof}(\mbox{owl\_eqdis\_sameas},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_007\_Equal\_Classes},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c}_1)\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_007\_Equal\_Classes},\mbox{axiom})$

\medskip\textbf{SWB094+1.p} Min-QCR Comparison By Class

A min-QCR for some cardinality on some property and to some class 
 is a subclass of another min-QCR for the same cardinality on the 
 same property and to some super class.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_minqcr\_cmp\_class},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_x}_2,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_x}_1,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_minqcr\_cmp\_class},\mbox{axiom})$

\medskip\textbf{SWB063+1.p} Class Equivalence Extensional

If the extensions of two classes are equal, then the classes are 
 themselves equivalent.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_eqdis\_eqclass\_ext},\mbox{conjecture})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_2,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_1,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_eqdis\_eqclass\_ext},\mbox{axiom})$

\medskip\textbf{SWB026+3.p} Inferred Property Characteristics I






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_026\_Inferred\_Property\_Characteristics\_I},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2,\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p},\mbox{bNODE\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_1,\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{bNODE\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_2,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_026\_Inferred\_Property\_Characteristics\_I},\mbox{axiom})$

\medskip\textbf{SWB011+3.p} Entity Types as Classes






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_owl\_Class},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x},\mbox{uri\_owl\_ObjectProperty})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_011\_Entity\_Types\_as\_Classes},\mbox{axiom})$

\medskip\textbf{SWB025+1.p} Cyclic Dependencies between Complex Properties






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_ex\_hasUncle},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_charly})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasCousin},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_alice})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_025\_Cyclic\_Dependencies\_between\_Complex\_Properties},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_3{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_ex\_hasUncle},\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{uri\_ex\_hasCousin})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_ex\_hasFather})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_ex\_hasCousin},\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{uri\_ex\_hasUncle})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_l}_3,\mbox{uri\_ex\_hasFather})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasFather},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_dave})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasCousin},\mbox{uri\_ex\_alice},\mbox{uri\_ex\_bob})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasFather},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_charly})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_hasUncle},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_dave}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_025\_Cyclic\_Dependencies\_between\_Complex\_Properties},\mbox{axiom})$

\medskip\textbf{SWB088+1.p} Max-QCR Comparison By Cardinality

A max-QCR for some cardinality on some property and to some class 
 is a subclass of another max-QCR on the same property to the same 
 class and for some larger cardinality.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_maxqcr\_cmp\_card},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_maxQualifiedCardinality},\mbox{uri\_ex\_x}_2,\mbox{literal\_typed}(\mbox{dat\_str}_2,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_maxQualifiedCardinality},\mbox{uri\_ex\_x}_1,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_maxqcr\_cmp\_card},\mbox{axiom})$

\medskip\textbf{SWB027+4.p} Inferred Property Characteristics II






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_027\_Inferred\_Property\_Characteristics\_II},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_v}{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_owl\_sameAs},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{bNODE\_v})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_v},\mbox{uri\_ex\_p}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_027\_Inferred\_Property\_Characteristics\_II},\mbox{axiom})$

\medskip\textbf{SWB026+2.p} Inferred Property Characteristics I






$\forall p{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},p,\mbox{uri\_rdf\_Property})\iff \mbox{ip}(p) )\qquad\mbox{fof}(\mbox{rdf\_type\_ip},\mbox{axiom})$

$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall p,c,x,y{:}\;( ( \mbox{iext}(\mbox{uri\_rdfs\_domain},p,c)\mbox{ and }\mbox{iext}(p,x,y) ) \ \Rightarrow \ \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_domain\_main},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_rdfs\_domain},\mbox{uri\_rdf\_Property})\qquad\mbox{fof}(\mbox{rdfs\_domain\_domain},\mbox{axiom})$

$\forall z,s_1,a_1{:}\;( ( \mbox{iext}(\mbox{uri\_rdf\_first},s_1,a_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},s_1,\mbox{uri\_rdf\_nil}) ) \ \Rightarrow \ ( \mbox{iext}(\mbox{uri\_owl\_oneOf},z,s_1)\iff ( \mbox{ic}(z)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff x = a_1 ) ) ) )\qquad\mbox{fof}(\mbox{owl\_enum\_class}_{001},\mbox{axiom})$

$\forall p{:}\;( \mbox{icext}(\mbox{uri\_owl\_InverseFunctionalProperty},p)\iff ( \mbox{ip}(p)\mbox{ and }\forall x_1,x_2,y{:}\;( ( \mbox{iext}(p,x_1,y)\mbox{ and }\mbox{iext}(p,x_2,y) ) \ \Rightarrow \ x_1 = x_2 ) ) )\qquad\mbox{fof}(\mbox{owl\_char\_inversefunctional},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_026\_Inferred\_Property\_Characteristics\_I},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}_1,\mbox{bNODE\_x}_2,\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p},\mbox{bNODE\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_1,\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_w})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{bNODE\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{bNODE\_x}_2,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_026\_Inferred\_Property\_Characteristics\_I},\mbox{axiom})$

\medskip\textbf{SWB095+1.p} Min-QCR Comparison By Property

A min-QCR for some cardinality on some property and to some class 
 is a subclass of another min-QCR for the same cardinality to the 
 same class and on a super property.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_minqcr\_cmp\_prop},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_x}_2,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_x}_1,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_p}_2)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_minqcr\_cmp\_prop},\mbox{axiom})$

\medskip\textbf{SWB106+1.p} Self-Restriction As Existential Restriction

Self restrictions are more specific than unconstrained 
 existential restrictions.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_z}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_term\_selfsome},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{uri\_ex\_z}_2,\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_hasSelf},\mbox{uri\_ex\_z}_1,\mbox{literal\_typed}(\mbox{dat\_str\_true},\mbox{uri\_xsd\_boolean}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_term\_selfsome},\mbox{axiom})$

\medskip\textbf{SWB017+1.p} Built-in Based Definitions






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_017\_Built\_in\_Based\_Definitions},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_ex\_notInstanceOf},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_notInstanceOf},\mbox{uri\_ex\_u},\mbox{uri\_ex\_c})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_017\_Built\_in\_Based\_Definitions},\mbox{axiom})$

\medskip\textbf{SWB006+2.p} Literal Values represented by URIs and Blank Nodes






$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},x,y)\iff x = y )\qquad\mbox{fof}(\mbox{owl\_eqdis\_sameas},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_u},\mbox{uri\_ex\_w})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_006\_Literal\_Values\_represented\_by\_URIs\_and\_Blank\_Nodes},\mbox{conjecture})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_u},\mbox{literal\_plain}(\mbox{dat\_str\_abc}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{bNODE\_x},\mbox{literal\_plain}(\mbox{dat\_str\_abc}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{bNODE\_x},\mbox{uri\_ex\_w}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_006\_Literal\_Values\_represented\_by\_URIs\_and\_Blank\_Nodes},\mbox{axiom})$

\medskip\textbf{SWB008+2.p} Inverse Functional Data Properties






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{iext}(\mbox{uri\_owl\_sameAs},x,y)\iff x = y )\qquad\mbox{fof}(\mbox{owl\_eqdis\_sameas},\mbox{axiom})$

$\forall p{:}\;( \mbox{icext}(\mbox{uri\_owl\_InverseFunctionalProperty},p)\iff ( \mbox{ip}(p)\mbox{ and }\forall x_1,x_2,y{:}\;( ( \mbox{iext}(p,x_1,y)\mbox{ and }\mbox{iext}(p,x_2,y) ) \ \Rightarrow \ x_1 = x_2 ) ) )\qquad\mbox{fof}(\mbox{owl\_char\_inversefunctional},\mbox{axiom})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_bob},\mbox{uri\_ex\_robert})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_008\_Inverse\_Functional\_Data\_Properties},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_owl\_DatatypeProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_owl\_InverseFunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_ex\_bob},\mbox{literal\_plain}(\mbox{dat\_str\_xyz}))\mbox{ and }\mbox{iext}(\mbox{uri\_foaf\_mbox\_sha1sum},\mbox{uri\_ex\_robert},\mbox{literal\_plain}(\mbox{dat\_str\_xyz}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_008\_Inverse\_Functional\_Data\_Properties},\mbox{axiom})$

\medskip\textbf{SWB021+3.p} Composite Enumerations






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_c}_3,\mbox{uri\_ex\_c}_4)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_021\_Composite\_Enumerations},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33},\mbox{bNODE\_l}_{41},\mbox{bNODE\_l}_{42}{:}\;( \mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_1,\mbox{bNODE\_l}_{11})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{11},\mbox{uri\_ex\_w}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{11},\mbox{bNODE\_l}_{12})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{12},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{12},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_2,\mbox{bNODE\_l}_{21})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{21},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{21},\mbox{bNODE\_l}_{22})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{22},\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{22},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},\mbox{uri\_ex\_c}_3,\mbox{bNODE\_l}_{31})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{31},\mbox{uri\_ex\_w}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{31},\mbox{bNODE\_l}_{32})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{32},\mbox{uri\_ex\_w}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{32},\mbox{bNODE\_l}_{33})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{33},\mbox{uri\_ex\_w}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{33},\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c}_4,\mbox{bNODE\_l}_{41})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{41},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{41},\mbox{bNODE\_l}_{42})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_{42},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_{42},\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_021\_Composite\_Enumerations},\mbox{axiom})$

\medskip\textbf{SWB060+1.p} Disjoint Class Union As Disjointness

The component classes on the right hand side of a disjoint-union 
 axiom are pairwise disjoint.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_eqdis\_disjointunion\_disjoint},\mbox{conjecture})$

$\exists x_1,x_0{:}\;( \mbox{iext}(\mbox{uri\_owl\_disjointUnionOf},\mbox{uri\_ex\_c}_3,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_eqdis\_disjointunion\_disjoint},\mbox{axiom})$

\medskip\textbf{SWB014+3.p} Harry belongs to some Species






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_harry},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_ex\_Species}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_014\_Harry\_belongs\_to\_some\_Species},\mbox{conjecture})$

$\exists \mbox{bNODE\_u},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Eagle},\mbox{uri\_ex\_Species})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Falcon},\mbox{uri\_ex\_Species})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_harry},\mbox{bNODE\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{bNODE\_u},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_Eagle})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_Falcon})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_014\_Harry\_belongs\_to\_some\_Species},\mbox{axiom})$

\medskip\textbf{SWB018+3.p} Modified Logical Vocabulary Semantics






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_u},\mbox{uri\_ex\_Person})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_018\_Modified\_Logical\_Vocabulary\_Semantics},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_Person})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_018\_Modified\_Logical\_Vocabulary\_Semantics},\mbox{axiom})$

\medskip\textbf{SWB085+1.p} Exact-2-QCR Extensional

For an individual w, if there are exactly two triples w p x1 and 
 w p x2 with x1 and x2 being instances of class c, then w is an 
 instance of the exact-2-QCR on p to c.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_z})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_exactqcr\_inst\_subj\_two},\mbox{conjecture})$

$\exists x_3,x_4,x_0,x_1,x_2{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},x_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_qualifiedCardinality},\mbox{uri\_ex\_z},\mbox{literal\_typed}(\mbox{dat\_str}_2,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x}_3,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_x}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_x}_1,\mbox{uri\_ex\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},\mbox{uri\_ex\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},\mbox{uri\_ex\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},\mbox{uri\_ex\_x}_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_4,\mbox{uri\_ex\_x}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_4,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_3,\mbox{uri\_ex\_x}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_3,x_4)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x}_2,\mbox{uri\_ex\_c}) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_exactqcr\_inst\_subj\_two},\mbox{axiom})$

\medskip\textbf{SWB065+1.p} Individual Equality Extensional

If two individuals are equal, then the owl:sameAs relation holds 
 between them.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_w},\mbox{uri\_ex\_u})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_eqdis\_sameas\_ext},\mbox{conjecture})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_1,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},x_1) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_eqdis\_sameas\_ext},\mbox{axiom})$

\medskip\textbf{SWB042+1.p} Property Chain Extensional

If the chain of extensions of two properties p1 and p2 is a 
 subset of the extension of a property p, then a sub property 
 chain axiom is entailed for p and the chain properties p1 and p2.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_ex\_p},x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_chain\_ext},\mbox{conjecture})$

$\exists x_2,x_1,x_4,x_5,x_0,x_3{:}\;( \mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p}_1,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p}_2,\mbox{uri\_ex\_z},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_2,\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p}_1,\mbox{uri\_ex\_x},\mbox{uri\_ex\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p}_2,x_3)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_4,\mbox{uri\_ex\_p}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_4,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_3,x_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_5,\mbox{uri\_ex\_p}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_5,x_4) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_chain\_ext},\mbox{axiom})$

\medskip\textbf{SWB078+1.p} Property Range Super-Class OWL

Every super class of a range for a given property is itself a 
 range for that property.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_rdfsext\_range\_superclass},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_rdfsext\_range\_superclass},\mbox{axiom})$

\medskip\textbf{SWB009+4.p} Existential Restriction Entailments






$\mbox{include}(\mbox{'Axioms/SWB003+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_ex\_c}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_009\_Existential\_Restriction\_Entailments},\mbox{conjecture})$

$\exists \mbox{bNODE\_z}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_ObjectProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_s},\mbox{bNODE\_z})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_z},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_someValuesFrom},\mbox{bNODE\_z},\mbox{uri\_ex\_c}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_009\_Existential\_Restriction\_Entailments},\mbox{axiom})$

\medskip\textbf{SWB046+1.p} Inverse-Functional Property Extensional

If the extension of a property is inverse functional, then the 
 property itself is.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_char\_inversefunc\_ext},\mbox{conjecture})$

$\exists x_1,x_0{:}\;( \mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_oneOf},x_1,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_x},\mbox{uri\_ex\_y})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_domain},\mbox{uri\_ex\_p},x_1) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_char\_inversefunc\_ext},\mbox{axiom})$

\medskip\textbf{SWB030+2.p} Bad Class






$\forall x,c{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x,c)\iff \mbox{icext}(c,x) )\qquad\mbox{fof}(\mbox{rdfs\_cext\_def},\mbox{axiom})$

$\forall z,p,v{:}\;( ( \mbox{iext}(\mbox{uri\_owl\_hasSelf},z,v)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},z,p) ) \ \Rightarrow \ \forall x{:}\;( \mbox{icext}(z,x)\iff \mbox{iext}(p,x,x) ) )\qquad\mbox{fof}(\mbox{owl\_restrict\_hasself},\mbox{axiom})$

$\forall z,c{:}\;( \mbox{iext}(\mbox{uri\_owl\_complementOf},z,c) \ \Rightarrow \ ( \mbox{ic}(z)\mbox{ and }\mbox{ic}(c)\mbox{ and }\forall x{:}\;( \mbox{icext}(z,x)\iff \neg\,\mbox{icext}(c,x) ) ) )\qquad\mbox{fof}(\mbox{owl\_bool\_complementof\_class},\mbox{axiom})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_c},\mbox{uri\_owl\_Class})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_complementOf},\mbox{uri\_ex\_c},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_owl\_Restriction})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{bNODE\_x},\mbox{uri\_rdf\_type})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_hasSelf},\mbox{bNODE\_x},\mbox{literal\_typed}(\mbox{dat\_str\_true},\mbox{uri\_xsd\_boolean})) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_030\_Bad\_Class},\mbox{axiom})$

\medskip\textbf{SWB101+1.p} Cardinality Restriction As QCR

A cardinality restriction can be written as a QCR to class 
 owl:Thing.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_owl\_equivalentClass},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_z}_2)\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_term\_cardqcr},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_qualifiedCardinality},\mbox{uri\_ex\_z}_2,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_2,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z}_2,\mbox{uri\_owl\_Thing})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_cardinality},\mbox{uri\_ex\_z}_1,\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z}_1,\mbox{uri\_ex\_p})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_term\_cardqcr},\mbox{axiom})$

\medskip\textbf{SWB059+1.p} Disjoint Class Union Composite

If a class expresses the union of two disjoint component classes, 
 then the class expresses a disjoint union class axiom for the 
 component classes.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_1,x_0{:}\;( \mbox{iext}(\mbox{uri\_owl\_disjointUnionOf},\mbox{uri\_ex\_c}_3,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_eqdis\_disjointunion\_composite},\mbox{conjecture})$

$\exists x_0,x_1{:}\;( \mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{uri\_ex\_c}_3,x_0)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_disjointWith},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_1,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},x_0,\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},x_0,x_1) )\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_eqdis\_disjointunion\_composite},\mbox{axiom})$

\medskip\textbf{SWB097+1.p} Min-1-QCR Extensional

For a triple w p x, with x being an instance of the class c, the 
 individual w is an instance of the min-1-QCR on p to c.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_z})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_minqcr\_inst\_subj\_one},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_z},\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_x},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},\mbox{uri\_ex\_x})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_minqcr\_inst\_subj\_one},\mbox{axiom})$

\medskip\textbf{SWB071+1.p} Negative Individual Property Assertion Extensional

If a triple 's p o' does not hold, then the negative property 
 assertion NPA(s p o) is entailed.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_0{:}\;( \mbox{iext}(\mbox{uri\_owl\_sourceIndividual},x_0,\mbox{uri\_ex\_s})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_assertionProperty},x_0,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_targetIndividual},x_0,\mbox{uri\_ex\_o}_2) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_npa\_ind\_bw},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_FunctionalProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_s},\mbox{uri\_ex\_o}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_differentFrom},\mbox{uri\_ex\_o}_2,\mbox{uri\_ex\_o}_1)\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_npa\_ind\_bw},\mbox{axiom})$

\medskip\textbf{SWB096+1.p} Min-1-QCR Intensional

If an individual w is an instance of the min-1-QCR on property p 
 to class c, then an individual x exists with w p x and x in c.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists x_0{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},x_0,\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_ex\_p},\mbox{uri\_ex\_w},x_0) )\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_restrict\_minqcr\_inst\_obj\_one},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_minQualifiedCardinality},\mbox{uri\_ex\_z},\mbox{literal\_typed}(\mbox{dat\_str}_1,\mbox{uri\_xsd\_nonNegativeInteger}))\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onProperty},\mbox{uri\_ex\_z},\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_onClass},\mbox{uri\_ex\_z},\mbox{uri\_ex\_c})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_z})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_restrict\_minqcr\_inst\_obj\_one},\mbox{axiom})$

\medskip\textbf{SWB052+1.p} Transitive Irreflexive Property As Asymmetric

A transitive and irreflexive property is an asymmetric property.




$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_AsymmetricProperty})\qquad\mbox{fof}(\mbox{conclusion\_rdfbased\_sem\_char\_transitive\_term},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_TransitiveProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_IrreflexiveProperty})\qquad\mbox{fof}(\mbox{premise\_rdfbased\_sem\_char\_transitive\_term},\mbox{axiom})$

\medskip\textbf{SWB014+1.p} Harry belongs to some Species






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\exists \mbox{bNODE\_x}{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_harry},\mbox{bNODE\_x})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{bNODE\_x},\mbox{uri\_ex\_Species}) )\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_014\_Harry\_belongs\_to\_some\_Species},\mbox{conjecture})$

$\exists \mbox{bNODE\_u},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2{:}\;( \mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Eagle},\mbox{uri\_ex\_Species})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_Falcon},\mbox{uri\_ex\_Species})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_harry},\mbox{bNODE\_u})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_unionOf},\mbox{bNODE\_u},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_Eagle})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{uri\_ex\_Falcon})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_014\_Harry\_belongs\_to\_some\_Species},\mbox{axiom})$

\medskip\textbf{SWB027+3.p} Inferred Property Characteristics II






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_p},\mbox{uri\_owl\_InverseFunctionalProperty})\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_027\_Inferred\_Property\_Characteristics\_II},\mbox{conjecture})$

$\exists \mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2,\mbox{bNODE\_v}{:}\;( \mbox{iext}(\mbox{uri\_owl\_propertyChainAxiom},\mbox{uri\_owl\_sameAs},\mbox{bNODE\_l}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_1,\mbox{uri\_ex\_p})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_1,\mbox{bNODE\_l}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_first},\mbox{bNODE\_l}_2,\mbox{bNODE\_v})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_rest},\mbox{bNODE\_l}_2,\mbox{uri\_rdf\_nil})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_inverseOf},\mbox{bNODE\_v},\mbox{uri\_ex\_p}) )\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_027\_Inferred\_Property\_Characteristics\_II},\mbox{axiom})$

\medskip\textbf{SWB019+3.p} Disjoint Annotation Properties






$\mbox{include}(\mbox{'Axioms/SWB002+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_skos\_prefLabel},\mbox{uri\_owl\_AnnotationProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_prefLabel},\mbox{uri\_rdfs\_label})\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_skos\_altLabel},\mbox{uri\_owl\_AnnotationProperty})\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subPropertyOf},\mbox{uri\_skos\_altLabel},\mbox{uri\_rdfs\_label})\mbox{ and }\mbox{iext}(\mbox{uri\_owl\_propertyDisjointWith},\mbox{uri\_skos\_prefLabel},\mbox{uri\_skos\_altLabel})\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_prefLabel},\mbox{uri\_ex\_foo},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\mbox{ and }\mbox{iext}(\mbox{uri\_skos\_altLabel},\mbox{uri\_ex\_foo},\mbox{literal\_plain}(\mbox{dat\_str\_foo}))\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_019\_Disjoint\_Annotation\_Properties},\mbox{axiom})$

\medskip\textbf{SWB007+1.p} Equal Classes






$\mbox{include}(\mbox{'Axioms/SWB001+0.ax'})$

$\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c}_2)\qquad\mbox{fof}(\mbox{testcase\_conclusion\_fullish\_007\_Equal\_Classes},\mbox{conjecture})$

$\mbox{iext}(\mbox{uri\_owl\_sameAs},\mbox{uri\_ex\_c}_1,\mbox{uri\_ex\_c}_2)\mbox{ and }\mbox{iext}(\mbox{uri\_rdf\_type},\mbox{uri\_ex\_w},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_subClassOf},\mbox{uri\_ex\_c},\mbox{uri\_ex\_c}_1)\mbox{ and }\mbox{iext}(\mbox{uri\_rdfs\_range},\mbox{uri\_ex\_p},\mbox{uri\_ex\_c}_1)\qquad\mbox{fof}(\mbox{testcase\_premise\_fullish\_007\_Equal\_Classes},\mbox{axiom})$

\medskip
\end{document}