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    \textbf{MGT001-0.ax} Inequalities.






$\mbox{smaller\_or\_equal}(a,b) \ \Rightarrow \ ( \mbox{smaller}(a,b)\mbox{ or }a = b )\qquad\mbox{cnf}(\mbox{definition\_smaller\_or\_equal}_1,\mbox{axiom})$

$\mbox{smaller}(a,b) \ \Rightarrow \ \mbox{smaller\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{definition\_smaller\_or\_equal}_2,\mbox{axiom})$

$a = b \ \Rightarrow \ \mbox{smaller\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{definition\_smaller\_or\_equal}_3,\mbox{axiom})$

$\mbox{greater\_or\_equal}(a,b) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b )\qquad\mbox{cnf}(\mbox{definition\_greater\_or\_equal}_4,\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \mbox{greater\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{definition\_greater\_or\_equal}_5,\mbox{axiom})$

$a = b \ \Rightarrow \ \mbox{greater\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{definition\_greater\_or\_equal}_6,\mbox{axiom})$

$\mbox{smaller}(a,b) \ \Rightarrow \ \mbox{greater}(b,a)\qquad\mbox{cnf}(\mbox{definition\_smaller}_7,\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \mbox{smaller}(b,a)\qquad\mbox{cnf}(\mbox{definition\_smaller}_8,\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \neg\,\mbox{greater}(b,a)\qquad\mbox{cnf}(\mbox{meaning\_postulate\_greater\_strict}_9,\mbox{axiom})$

$( \mbox{greater}(a,b)\mbox{ and }\mbox{greater}(b,c) ) \ \Rightarrow \ \mbox{greater}(a,c)\qquad\mbox{cnf}(\mbox{meaning\_postulate\_greater\_transitive}_{10},\mbox{axiom})$

$\mbox{smaller}(a,b)\mbox{ or }a = b\mbox{ or }\mbox{greater}(a,b)\qquad\mbox{cnf}(\mbox{meaning\_postulate\_greater\_comparable}_{11},\mbox{axiom})$

\medskip\textbf{MGT001+0.ax} Inequalities.






$\forall x,y{:}\;( \mbox{smaller\_or\_equal}(x,y)\iff ( \mbox{smaller}(x,y)\mbox{ or }x = y ) )\qquad\mbox{fof}(\mbox{definition\_smaller\_or\_equal},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{greater\_or\_equal}(x,y)\iff ( \mbox{greater}(x,y)\mbox{ or }x = y ) )\qquad\mbox{fof}(\mbox{definition\_greater\_or\_equal},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{smaller}(x,y)\iff \mbox{greater}(y,x) )\qquad\mbox{fof}(\mbox{definition\_smaller},\mbox{axiom})$

$\forall x,y{:}\;\neg\,\mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,x)\qquad\mbox{fof}(\mbox{meaning\_postulate\_greater\_strict},\mbox{axiom})$

$\forall x,y,z{:}\;( ( \mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,z) ) \ \Rightarrow \ \mbox{greater}(x,z) )\qquad\mbox{fof}(\mbox{meaning\_postulate\_greater\_transitive},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{smaller}(x,y)\mbox{ or }x = y\mbox{ or }\mbox{greater}(x,y) )\qquad\mbox{fof}(\mbox{meaning\_postulate\_greater\_comparable},\mbox{axiom})$

\medskip\textbf{MGT032+2.p} Selection favours EPs above FMs

In stable environments, selection favors efficient producers
 above first movers past a certain point in time.




$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t)\mbox{ and }\mbox{greater}(\mbox{growth\_rate}(s_2,t),\mbox{growth\_rate}(s_1,t)) ) \ \Rightarrow \ \mbox{selection\_favors}(s_2,s_1,t) )\qquad\mbox{fof}(\mbox{mp1\_high\_growth\_rates},\mbox{axiom})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(l_1,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},t) ) ) )\qquad\mbox{fof}(\mbox{prove\_t}_1,\mbox{conjecture})$

\medskip\textbf{MGT036-1.p} First movers never outcompete efficient producers.






$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b) ) \ \Rightarrow \ \mbox{subpopulations}(\mbox{efficient\_producers},\mbox{first\_movers},a,b)\qquad\mbox{cnf}(\mbox{mp\_symmetry\_of\_FM\_and\_EP}_1,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b) ) \ \Rightarrow \ \mbox{in\_environment}(a,b)\qquad\mbox{cnf}(\mbox{mp\_time\_point\_occur}_2,\mbox{axiom})$

$\mbox{greater}(0,\mbox{growth\_rate}(b,c)) \ \Rightarrow \ \mbox{environment}(a)\qquad\mbox{cnf}(\mbox{mp\_growth\_rate\_relationships}_3,\mbox{axiom})$

$\mbox{greater}(0,\mbox{growth\_rate}(a,d)) \ \Rightarrow \ \mbox{subpopulations}(a,b,c,d)\qquad\mbox{cnf}(\mbox{mp\_growth\_rate\_relationships}_4,\mbox{axiom})$

$\mbox{greater\_or\_equal}(\mbox{growth\_rate}(a,b),0) \ \Rightarrow \ \neg\,\mbox{greater}(0,\mbox{growth\_rate}(a,b))\qquad\mbox{cnf}(\mbox{mp\_growth\_rate\_relationships}_5,\mbox{axiom})$

$( \mbox{environment}(c)\mbox{ and }\mbox{subpopulations}(a,d,c,b) ) \ \Rightarrow \ ( \mbox{greater}(0,\mbox{growth\_rate}(a,b))\mbox{ or }\mbox{greater\_or\_equal}(\mbox{growth\_rate}(a,b),0) )\qquad\mbox{cnf}(\mbox{mp\_growth\_rate\_relationships}_6,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{greater\_or\_equal}(\mbox{growth\_rate}(c,d),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(b,d)) ) \ \Rightarrow \ \mbox{outcompetes}(c,b,d)\qquad\mbox{cnf}(\mbox{d2}_7,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{outcompetes}(c,b,d) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{growth\_rate}(c,d),0)\qquad\mbox{cnf}(\mbox{d2}_8,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{outcompetes}(c,b,d) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(b,d))\qquad\mbox{cnf}(\mbox{d2}_9,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{resilience}(d),\mbox{resilience}(c))\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(d,b)) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(c,b))\qquad\mbox{cnf}(\mbox{a12}_{10},\mbox{hypothesis})$

$\mbox{greater}(\mbox{resilience}(\mbox{efficient\_producers}),\mbox{resilience}(\mbox{first\_movers}))\qquad\mbox{cnf}(\mbox{a2}_{11},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{prove\_t5}_{12},\mbox{negated\_conjecture})$

$\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t5}_{13},\mbox{negated\_conjecture})$

$\mbox{outcompetes}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t5}_{14},\mbox{negated\_conjecture})$

\medskip\textbf{MGT049+1.p} Structural position does not vary with its age

An organization's structural position does not vary with its age.




$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x,t_0,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ ( ( \mbox{greater}(\mbox{external\_ties}(x,t),\mbox{external\_ties}(x,t_0)) \ \Rightarrow \ \mbox{greater}(\mbox{position}(x,t),\mbox{position}(x,t_0)) )\mbox{ and }( \mbox{external\_ties}(x,t) = \mbox{external\_ties}(x,t_0) \ \Rightarrow \ \mbox{position}(x,t) = \mbox{position}(x,t_0) ) ) )\qquad\mbox{fof}(\mbox{assumption}_6,\mbox{axiom})$

$\forall x,t_0,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ \mbox{external\_ties}(x,t) = \mbox{external\_ties}(x,t_0) )\qquad\mbox{fof}(\mbox{assumption}_{11},\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{greater}(\mbox{age}(x,t),\mbox{age}(x,t_0)) ) \ \Rightarrow \ \mbox{position}(x,t) = \mbox{position}(x,t_0) )\qquad\mbox{fof}(\mbox{lemma}_6,\mbox{conjecture})$

\medskip\textbf{MGT040-2.p} Selection favours FMs above EPs if change is not extreme

Selection favors first movers above efficient producers if
 environmental change is rapid but not extreme during the
 observational period.




$( \mbox{observational\_period}(a)\mbox{ and }\mbox{propagation\_strategy}(\mbox{first\_movers})\mbox{ and }\mbox{propagation\_strategy}(\mbox{efficient\_producers}) ) \ \Rightarrow \ ( \mbox{environment}(\mbox{sk}_1(a))\mbox{ or }\mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},a) )\qquad\mbox{cnf}(\mbox{mp3\_favoured\_trategy}_{23},\mbox{axiom})$

$( \mbox{observational\_period}(a)\mbox{ and }\mbox{propagation\_strategy}(\mbox{first\_movers})\mbox{ and }\mbox{propagation\_strategy}(\mbox{efficient\_producers}) ) \ \Rightarrow \ ( \mbox{in\_environment}(a,\mbox{sk}_1(a))\mbox{ or }\mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},a) )\qquad\mbox{cnf}(\mbox{mp3\_favoured\_trategy}_{24},\mbox{axiom})$

$( \mbox{observational\_period}(a)\mbox{ and }\mbox{propagation\_strategy}(\mbox{first\_movers})\mbox{ and }\mbox{propagation\_strategy}(\mbox{efficient\_producers})\mbox{ and }\mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},\mbox{end\_time}(\mbox{sk}_1(a))) ) \ \Rightarrow \ \mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},a)\qquad\mbox{cnf}(\mbox{mp3\_favoured\_trategy}_{25},\mbox{axiom})$

$( \mbox{observational\_period}(a)\mbox{ and }\mbox{rapid\_change}(a)\mbox{ and }\mbox{environment}(b)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ \neg\,\mbox{in\_environment}(b,\mbox{critical\_point}(b))\qquad\mbox{cnf}(\mbox{mp5\_rapid\_change\_is\_non\_critical}_{26},\mbox{axiom})$

$( \mbox{observational\_period}(a)\mbox{ and }\mbox{environment}(b)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{empty}(b) ) \ \Rightarrow \ \mbox{extreme}(a)\qquad\mbox{cnf}(\mbox{mp6\_not\_extreme\_change\_means\_not\_empty}_{27},\mbox{axiom})$

$\mbox{propagation\_strategy}(\mbox{first\_movers})\qquad\mbox{cnf}(\mbox{mp\_organizational\_sets1}_{28},\mbox{axiom})$

$\mbox{propagation\_strategy}(\mbox{efficient\_producers})\qquad\mbox{cnf}(\mbox{mp\_organizational\_sets2}_{29},\mbox{axiom})$

$\mbox{environment}(a) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{end\_time}(a))\qquad\mbox{cnf}(\mbox{mp\_endpoint\_in\_environment}_{30},\mbox{axiom})$

$\mbox{environment}(a) \ \Rightarrow \ ( \mbox{in\_environment}(a,\mbox{critical\_point}(a))\mbox{ or }\mbox{greater}(\mbox{critical\_point}(a),\mbox{end\_time}(a)) )\qquad\mbox{cnf}(\mbox{mp\_critical\_point\_not\_before\_opening}_{31},\mbox{axiom})$

$\mbox{environment}(a) \ \Rightarrow \ ( \mbox{empty}(a)\mbox{ or }\mbox{greater\_or\_equal}(\mbox{end\_time}(a),\mbox{appear}(\mbox{an\_organisation},a)) )\qquad\mbox{cnf}(\mbox{mp\_non\_empty\_means\_organisations}_{32},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{appear}(\mbox{efficient\_producers},a))\mbox{ and }\mbox{greater}(\mbox{critical\_point}(a),b) ) \ \Rightarrow \ ( \mbox{in\_environment}(a,\mbox{critical\_point}(a))\mbox{ or }\mbox{selection\_favors}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{end\_time}(a)) )\qquad\mbox{cnf}(\mbox{mp\_selection\_favours\_in\_time}_{33},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{appear}(\mbox{efficient\_producers},a))\mbox{ and }\mbox{greater}(\mbox{critical\_point}(a),b)\mbox{ and }\mbox{selection\_favors}(\mbox{first\_movers},\mbox{efficient\_producers},b) ) \ \Rightarrow \ ( \mbox{in\_environment}(a,\mbox{critical\_point}(a))\mbox{ or }\mbox{selection\_favors}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{end\_time}(a)) )\qquad\mbox{cnf}(\mbox{mp\_selection\_favours\_in\_time}_{34},\mbox{axiom})$

$\mbox{greater\_or\_equal}(a,b) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b )\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{35},\mbox{axiom})$

$\mbox{in\_environment}(a,b) \ \Rightarrow \ ( \mbox{greater}(\mbox{appear}(\mbox{efficient\_producers},a),b)\mbox{ or }\mbox{greater\_or\_equal}(b,\mbox{appear}(\mbox{efficient\_producers},a)) )\qquad\mbox{cnf}(\mbox{mp\_appearance\_of\_EP}_{36},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{appear}(\mbox{first\_movers},a))\mbox{ and }\mbox{greater}(\mbox{appear}(\mbox{efficient\_producers},a),b) ) \ \Rightarrow \ \mbox{selection\_favors}(\mbox{first\_movers},\mbox{efficient\_producers},b)\qquad\mbox{cnf}(\mbox{t2}_{37},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,\mbox{critical\_point}(a))\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{appear}(\mbox{efficient\_producers},a))\mbox{ and }\mbox{greater}(\mbox{critical\_point}(a),b) ) \ \Rightarrow \ \mbox{selection\_favors}(\mbox{first\_movers},\mbox{efficient\_producers},b)\qquad\mbox{cnf}(\mbox{t3}_{38},\mbox{hypothesis})$

$\mbox{observational\_period}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t9}_{39},\mbox{negated\_conjecture})$

$\mbox{rapid\_change}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t9}_{40},\mbox{negated\_conjecture})$

$\neg\,\mbox{extreme}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t9}_{41},\mbox{negated\_conjecture})$

$\neg\,\mbox{selection\_favors}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t9}_{42},\mbox{negated\_conjecture})$

\medskip\textbf{MGT013+1.p} If organization complexity increases, its size cannot decrease

If the complexity of an organization gets bigger, its size
 cannot get smaller (in lack of reorganization).




$\forall x,y{:}\;\neg\,\mbox{greater}(x,y)\mbox{ and }x = y\qquad\mbox{fof}(\mbox{mp6}_1,\mbox{axiom})$

$\forall x,y{:}\;\neg\,\mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,x)\qquad\mbox{fof}(\mbox{mp6}_2,\mbox{axiom})$

$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \mbox{time}(t) )\qquad\mbox{fof}(\mbox{mp}_{15},\mbox{axiom})$

$\forall t_1,t_2{:}\;( ( \mbox{time}(t_1)\mbox{ and }\mbox{time}(t_2) ) \ \Rightarrow \ ( \mbox{greater}(t_1,t_2)\mbox{ or }t_1 = t_2\mbox{ or }\mbox{greater}(t_2,t_1) ) )\qquad\mbox{fof}(\mbox{mp}_{16},\mbox{axiom})$

$\forall x,t_1,t_2{:}\;( \mbox{reorganization\_free}(x,t_1,t_2) \ \Rightarrow \ \mbox{reorganization\_free}(x,t_2,t_1) )\qquad\mbox{fof}(\mbox{mp}_{17},\mbox{axiom})$

$\forall x,c_1,c_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{complexity}(x,c_1,t_1)\mbox{ and }\mbox{complexity}(x,c_2,t_2)\mbox{ and }t_1 = t_2 ) \ \Rightarrow \ c_1 = c_2 )\qquad\mbox{fof}(\mbox{mp}_{18},\mbox{axiom})$

$\forall x,s_1,s_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(x,s_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \neg\,\mbox{greater}(s_1,s_2) )\qquad\mbox{fof}(\mbox{t11\_FOL},\mbox{hypothesis})$

$\forall x,c_1,c_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{complexity}(x,c_1,t_1)\mbox{ and }\mbox{complexity}(x,c_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \neg\,\mbox{greater}(c_1,c_2) )\qquad\mbox{fof}(\mbox{t12\_FOL},\mbox{hypothesis})$

$\forall x,c_1,c_2,s_1,s_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{complexity}(x,c_1,t_1)\mbox{ and }\mbox{complexity}(x,c_2,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(x,s_2,t_2)\mbox{ and }\mbox{greater}(c_2,c_1) ) \ \Rightarrow \ \neg\,\mbox{greater}(s_1,s_2) )\qquad\mbox{fof}(\mbox{t13\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT003-1.p} Organizational death rates decrease with age.






$\mbox{reorganization\_free}(a,b,c) \ \Rightarrow \ \mbox{reorganization\_free}(a,b,b)\qquad\mbox{cnf}(\mbox{mp4}_1,\mbox{axiom})$

$\mbox{reorganization\_free}(a,b,c) \ \Rightarrow \ \mbox{reorganization\_free}(a,c,c)\qquad\mbox{cnf}(\mbox{mp4}_2,\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{inertia}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp5}_3,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reorganization\_free}(a,b,b)\mbox{ and }\mbox{reorganization\_free}(c,d,d)\mbox{ and }\mbox{inertia}(a,e,b)\mbox{ and }\mbox{inertia}(c,f,d)\mbox{ and }\mbox{survival\_chance}(a,g,b)\mbox{ and }\mbox{survival\_chance}(c,h,d)\mbox{ and }\mbox{greater}(f,e) ) \ \Rightarrow \ \mbox{greater}(h,g)\qquad\mbox{cnf}(\mbox{t1\_FOL}_4,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{inertia}(a,d,b)\mbox{ and }\mbox{inertia}(a,e,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \mbox{greater}(e,d)\qquad\mbox{cnf}(\mbox{t2\_FOL}_5,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t3\_FOL}_6,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t3\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t3\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_2,\mbox{sk}_3,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t3\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t3\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_6,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t3\_FOL}_{11},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_4,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{t3\_FOL}_{12},\mbox{negated\_conjecture})$

\medskip\textbf{MGT048-1.p} Capability decreases monotonically with its age

An organization's capability decreases monotonically with its age.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{capability}(a,b),\mbox{capability}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_5}_{32},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\mbox{ and }\mbox{greater}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{capability}(a,b),\mbox{capability}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_5}_{33},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{stock\_of\_knowledge}(a,b) = \mbox{stock\_of\_knowledge}(a,c)\mbox{ and }\mbox{internal\_friction}(a,b) = \mbox{internal\_friction}(a,c) ) \ \Rightarrow \ \mbox{capability}(a,b) = \mbox{capability}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_5}_{34},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ \mbox{stock\_of\_knowledge}(a,b) = \mbox{stock\_of\_knowledge}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_10}_{35},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{age}(a,b),\mbox{age}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_12}_{36},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{lemma\_5}_{37},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{age}(\mbox{sk}_1,\mbox{sk}_3),\mbox{age}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{lemma\_5}_{38},\mbox{negated\_conjecture})$

$\neg\,\mbox{smaller}(\mbox{capability}(\mbox{sk}_1,\mbox{sk}_3),\mbox{capability}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{lemma\_5}_{39},\mbox{negated\_conjecture})$

\medskip\textbf{MGT052-1.p} The environment at any time is similar with itself






$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$\mbox{dissimilar}(a,b,c) \ \Rightarrow \ \mbox{organization}(a)\qquad\mbox{cnf}(\mbox{definition\_2}_{29},\mbox{axiom})$

$\mbox{dissimilar}(a,b,c) \ \Rightarrow \ ( \mbox{is\_aligned}(a,b)\mbox{ or }\mbox{is\_aligned}(a,c) )\qquad\mbox{cnf}(\mbox{definition\_2}_{30},\mbox{axiom})$

$( \mbox{dissimilar}(a,b,c)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ \neg\,\mbox{is\_aligned}(a,c)\qquad\mbox{cnf}(\mbox{definition\_2}_{31},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,b)\mbox{ or }\mbox{dissimilar}(a,b,c) )\qquad\mbox{cnf}(\mbox{definition\_2}_{32},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,c)\mbox{ or }\mbox{dissimilar}(a,b,c) )\qquad\mbox{cnf}(\mbox{definition\_2}_{33},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,c)\mbox{ or }\mbox{dissimilar}(a,c,b) )\qquad\mbox{cnf}(\mbox{definition\_2}_{34},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,b)\mbox{ or }\mbox{dissimilar}(a,c,b) )\qquad\mbox{cnf}(\mbox{definition\_2}_{35},\mbox{axiom})$

$\mbox{dissimilar}(\mbox{sk}_1,\mbox{sk}_2,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{background\_assumption\_1}_{36},\mbox{negated\_conjecture})$

\medskip\textbf{MGT008-1.p} Organizational death rates decrease with size.






$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{inertia}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp5}_1,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,d)\mbox{ and }\mbox{size}(a,f,b)\mbox{ and }\mbox{size}(c,g,d)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,d)\mbox{ and }\mbox{greater}(g,f) ) \ \Rightarrow \ \mbox{greater}(i,h)\qquad\mbox{cnf}(\mbox{a5\_FOL}_2,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reorganization\_free}(a,b,b)\mbox{ and }\mbox{reorganization\_free}(c,d,d)\mbox{ and }\mbox{inertia}(a,e,b)\mbox{ and }\mbox{inertia}(c,f,d)\mbox{ and }\mbox{survival\_chance}(a,g,b)\mbox{ and }\mbox{survival\_chance}(c,h,d)\mbox{ and }\mbox{greater}(f,e) ) \ \Rightarrow \ \mbox{greater}(h,g)\qquad\mbox{cnf}(\mbox{t1\_FOL}_3,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t8\_FOL}_4,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t8\_FOL}_5,\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_2,\mbox{sk}_9,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t8\_FOL}_6,\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_3,\mbox{sk}_{10},\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t8\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t8\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t8\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t8\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_3,\mbox{sk}_6,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t8\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_2,\mbox{sk}_7,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t8\_FOL}_{12},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_3,\mbox{sk}_8,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t8\_FOL}_{13},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_8,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t8\_FOL}_{14},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_6,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t8\_FOL}_{15},\mbox{negated\_conjecture})$

\medskip\textbf{MGT059+1.p} Hazard of mortality is constant during periods of immunity

An organization's hazard of mortality is constant during periods
 in which it has immunity.




$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ ( ( \mbox{has\_immunity}(x,t) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{very\_low} )\mbox{ and }( \neg\,\mbox{has\_immunity}(x,t) \ \Rightarrow \ ( ( ( \mbox{is\_aligned}(x,t)\mbox{ and }\mbox{positional\_advantage}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{low} )\mbox{ and }( ( \neg\,\mbox{is\_aligned}(x,t)\mbox{ and }\mbox{positional\_advantage}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{mod}_1 )\mbox{ and }( ( \mbox{is\_aligned}(x,t)\mbox{ and }\neg\,\mbox{positional\_advantage}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{mod}_2 )\mbox{ and }( ( \neg\,\mbox{is\_aligned}(x,t)\mbox{ and }\neg\,\mbox{positional\_advantage}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{high} ) ) ) ) )\qquad\mbox{fof}(\mbox{assumption}_{17},\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{has\_immunity}(x,t_0)\mbox{ and }\mbox{has\_immunity}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t_0) = \mbox{hazard\_of\_mortality}(x,t) )\qquad\mbox{fof}(\mbox{assumption}_2,\mbox{conjecture})$

\medskip\textbf{MGT015-1.p} Complexity increases the expected duration of reorganisation.






$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{inertia}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp5}_1,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,d)\mbox{ and }\mbox{complexity}(a,f,b)\mbox{ and }\mbox{complexity}(c,g,d)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,d)\mbox{ and }\mbox{greater}(g,f) ) \ \Rightarrow \ \mbox{greater}(i,h)\qquad\mbox{cnf}(\mbox{a12\_FOL}_2,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,b)\mbox{ and }\mbox{reorganization}(a,b,f)\mbox{ and }\mbox{reorganization}(c,b,d)\mbox{ and }\mbox{reorganization\_type}(a,g,b)\mbox{ and }\mbox{reorganization\_type}(c,g,b)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,b)\mbox{ and }\mbox{greater}(i,h) ) \ \Rightarrow \ \mbox{greater}(d,f)\qquad\mbox{cnf}(\mbox{a13\_FOL}_3,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t15\_FOL}_4,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t15\_FOL}_5,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t15\_FOL}_6,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t15\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_3,\mbox{sk}_5,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t15\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_2,\mbox{sk}_8,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t15\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_3,\mbox{sk}_8,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t15\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{reorganization\_type}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t15\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{reorganization\_type}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t15\_FOL}_{12},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_2,\mbox{sk}_6,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t15\_FOL}_{13},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_3,\mbox{sk}_7,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t15\_FOL}_{14},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_7,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t15\_FOL}_{15},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_{10},\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t15\_FOL}_{16},\mbox{negated\_conjecture})$

\medskip\textbf{MGT014-1.p} If orgainzation size increases, its complexity cannot decrease

If the size of an organization gets bigger, its complexity
 cannot get smaller (in lack of reorganization).




$\mbox{greater}(a,b) \ \Rightarrow \ a\ne b\qquad\mbox{cnf}(\mbox{mp6\_1}_{18},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \neg\,\mbox{greater}(b,a)\qquad\mbox{cnf}(\mbox{mp6\_2}_{19},\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{time}(b)\qquad\mbox{cnf}(\mbox{mp15}_{20},\mbox{axiom})$

$( \mbox{time}(a)\mbox{ and }\mbox{time}(b) ) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b\mbox{ or }\mbox{greater}(b,a) )\qquad\mbox{cnf}(\mbox{mp16}_{21},\mbox{axiom})$

$\mbox{reorganization\_free}(a,b,c) \ \Rightarrow \ \mbox{reorganization\_free}(a,c,b)\qquad\mbox{cnf}(\mbox{mp17}_{22},\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{size}(a,d,b)\mbox{ and }\mbox{size}(a,e,c)\mbox{ and }b = c ) \ \Rightarrow \ d = e\qquad\mbox{cnf}(\mbox{mp19}_{23},\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{size}(a,d,b)\mbox{ and }\mbox{size}(a,e,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \neg\,\mbox{greater}(d,e)\qquad\mbox{cnf}(\mbox{t11\_FOL}_{24},\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{complexity}(a,d,b)\mbox{ and }\mbox{complexity}(a,e,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \neg\,\mbox{greater}(d,e)\qquad\mbox{cnf}(\mbox{t12\_FOL}_{25},\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_1,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t14\_FOL}_{26},\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_1,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t14\_FOL}_{27},\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_1,\mbox{sk}_6,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t14\_FOL}_{28},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_1,\mbox{sk}_2,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t14\_FOL}_{29},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_1,\mbox{sk}_3,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t14\_FOL}_{30},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_1,\mbox{sk}_4,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t14\_FOL}_{31},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_1,\mbox{sk}_5,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t14\_FOL}_{32},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_5,\mbox{sk}_4)\qquad\mbox{cnf}(\mbox{t14\_FOL}_{33},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_2,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{t14\_FOL}_{34},\mbox{negated\_conjecture})$

\medskip\textbf{MGT030+1.p} Earliest time point when FM growth rate exceeds EP growth rate

There is an earliest time point, past which FM's growth
 rate exceeds EP's growth rate.




$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\neg\,\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{to}),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{to}))\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds},\mbox{axiom})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(l_1,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\neg\,\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{to}),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{to}))\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(\mbox{prove\_l}_{12},\mbox{conjecture})$

\medskip\textbf{MGT012+1.p} Complexity of an organization cannot get smaller by age

Complexity of an organization cannot get smaller by age in
 lack of reorganization.




$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists i{:}\;\mbox{inertia}(x,i,t) )\qquad\mbox{fof}(\mbox{mp}_5,\mbox{axiom})$

$\forall x,y{:}\;\neg\,\mbox{greater}(x,y)\mbox{ and }x = y\qquad\mbox{fof}(\mbox{mp6}_1,\mbox{axiom})$

$\forall x,y{:}\;\neg\,\mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,x)\qquad\mbox{fof}(\mbox{mp6}_2,\mbox{axiom})$

$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists c{:}\;\mbox{class}(x,c,t) )\qquad\mbox{fof}(\mbox{mp}_9,\mbox{axiom})$

$\forall x,t_1,t_2,c_1,c_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{class}(x,c_1,t_1)\mbox{ and }\mbox{class}(x,c_2,t_2) ) \ \Rightarrow \ c_1 = c_2 )\qquad\mbox{fof}(\mbox{mp}_{10},\mbox{axiom})$

$\forall x,y,c,c_1,c_2,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{complexity}(x,c_1,t_1)\mbox{ and }\mbox{complexity}(y,c_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{greater}(c_2,c_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{a12\_FOL},\mbox{hypothesis})$

$\forall x,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(x,i_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{t2\_FOL},\mbox{hypothesis})$

$\forall x,c_1,c_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{complexity}(x,c_1,t_1)\mbox{ and }\mbox{complexity}(x,c_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \neg\,\mbox{greater}(c_1,c_2) )\qquad\mbox{fof}(\mbox{t12\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT054-1.p} Hazard of mortality increases in a drifting environment

An unendowed organization's hazard of mortality increases with
 age in a drifting environment.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,b) ) \ \Rightarrow \ \mbox{has\_endowment}(a)\qquad\mbox{cnf}(\mbox{assumption\_1}_{38},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,c)\mbox{ or }\mbox{greater}(\mbox{hazard\_of\_mortality}(a,c),\mbox{hazard\_of\_mortality}(a,b)) )\qquad\mbox{cnf}(\mbox{assumption\_3}_{39},\mbox{axiom})$

$\mbox{dissimilar}(a,b,c) \ \Rightarrow \ \mbox{organization}(a)\qquad\mbox{cnf}(\mbox{definition\_2}_{40},\mbox{axiom})$

$\mbox{dissimilar}(a,b,c) \ \Rightarrow \ ( \mbox{is\_aligned}(a,b)\mbox{ or }\mbox{is\_aligned}(a,c) )\qquad\mbox{cnf}(\mbox{definition\_2}_{41},\mbox{axiom})$

$( \mbox{dissimilar}(a,b,c)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ \neg\,\mbox{is\_aligned}(a,c)\qquad\mbox{cnf}(\mbox{definition\_2}_{42},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,b)\mbox{ or }\mbox{dissimilar}(a,b,c) )\qquad\mbox{cnf}(\mbox{definition\_2}_{43},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,c)\mbox{ or }\mbox{dissimilar}(a,b,c) )\qquad\mbox{cnf}(\mbox{definition\_2}_{44},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,c)\mbox{ or }\mbox{dissimilar}(a,c,b) )\qquad\mbox{cnf}(\mbox{definition\_2}_{45},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,b)\mbox{ or }\mbox{dissimilar}(a,c,b) )\qquad\mbox{cnf}(\mbox{definition\_2}_{46},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{age}(a,b) = 0 ) \ \Rightarrow \ \mbox{is\_aligned}(a,b)\qquad\mbox{cnf}(\mbox{assumption\_13}_{47},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,c)\mbox{ or }\mbox{greater}(\mbox{capability}(a,b),\mbox{capability}(a,c)) )\qquad\mbox{cnf}(\mbox{assumption\_14}_{48},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{age}(a,b) = 0\mbox{ and }\mbox{greater}(\mbox{age}(a,c),\mbox{sigma}) ) \ \Rightarrow \ \mbox{dissimilar}(a,b,c)\qquad\mbox{cnf}(\mbox{assumption\_15}_{49},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{age}(a,b) = 0\mbox{ and }\mbox{dissimilar}(a,b,c) ) \ \Rightarrow \ \mbox{greater}(\mbox{age}(a,c),\mbox{sigma})\qquad\mbox{cnf}(\mbox{assumption\_15}_{50},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{capability}(a,c),\mbox{capability}(a,b)) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{has\_immunity}(a,c)\mbox{ or }\mbox{greater}(\mbox{hazard\_of\_mortality}(a,b),\mbox{hazard\_of\_mortality}(a,c)) )\qquad\mbox{cnf}(\mbox{assumption\_16}_{51},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{theorem\_5}_{52},\mbox{negated\_conjecture})$

$\neg\,\mbox{has\_endowment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{theorem\_5}_{53},\mbox{negated\_conjecture})$

$\mbox{age}(\mbox{sk}_1,\mbox{sk}_2) = 0\qquad\mbox{cnf}(\mbox{theorem\_5}_{54},\mbox{negated\_conjecture})$

$\mbox{smaller\_or\_equal}(\mbox{age}(\mbox{sk}_1,\mbox{sk}_3),\mbox{sigma})\qquad\mbox{cnf}(\mbox{theorem\_5}_{55},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{age}(\mbox{sk}_1,\mbox{sk}_4),\mbox{sigma})\qquad\mbox{cnf}(\mbox{theorem\_5}_{56},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sigma},0)\qquad\mbox{cnf}(\mbox{theorem\_5}_{57},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_4),\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_3))\qquad\mbox{cnf}(\mbox{theorem\_5}_{58},\mbox{negated\_conjecture})$

\medskip\textbf{MGT015+1.p} Complexity increases the expected duration of reorganisation.






$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists i{:}\;\mbox{inertia}(x,i,t) )\qquad\mbox{fof}(\mbox{mp}_5,\mbox{axiom})$

$\forall x,y,c,c_1,c_2,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{complexity}(x,c_1,t_1)\mbox{ and }\mbox{complexity}(y,c_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{greater}(c_2,c_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{a12\_FOL},\mbox{hypothesis})$

$\forall x,y,\mbox{rt},c,i_1,i_2,\mbox{ta},\mbox{tb},\mbox{tc}{:}\;( ( \mbox{organization}(x,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{tc})\mbox{ and }\mbox{class}(x,c,\mbox{ta})\mbox{ and }\mbox{class}(y,c,\mbox{ta})\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reorganization}(y,\mbox{ta},\mbox{tc})\mbox{ and }\mbox{reorganization\_type}(x,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{reorganization\_type}(y,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{inertia}(x,i_1,\mbox{ta})\mbox{ and }\mbox{inertia}(y,i_2,\mbox{ta})\mbox{ and }\mbox{greater}(i_2,i_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{tc},\mbox{tb}) )\qquad\mbox{fof}(\mbox{a13\_FOL},\mbox{hypothesis})$

$\forall x,y,\mbox{re},c,c_1,c_2,\mbox{ta},\mbox{tb},\mbox{tc}{:}\;( ( \mbox{organization}(x,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{tc})\mbox{ and }\mbox{class}(x,c,\mbox{ta})\mbox{ and }\mbox{class}(y,c,\mbox{ta})\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reorganization}(y,\mbox{ta},\mbox{tc})\mbox{ and }\mbox{reorganization\_type}(x,\mbox{re},\mbox{ta})\mbox{ and }\mbox{reorganization\_type}(y,\mbox{re},\mbox{ta})\mbox{ and }\mbox{complexity}(x,c_1,\mbox{ta})\mbox{ and }\mbox{complexity}(y,c_2,\mbox{ta})\mbox{ and }\mbox{greater}(c_2,c_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{tc},\mbox{tb}) )\qquad\mbox{fof}(\mbox{t15\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT010-1.p} Large organization have higher reliability and accountability

Large organization have higher reliability and accountability
 than small organizations (of the same class).




$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{reproducibility}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp3}_1,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(j,i) ) \ \Rightarrow \ \mbox{greater}(f,e)\qquad\mbox{cnf}(\mbox{a2\_FOL}_2,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(j,i) ) \ \Rightarrow \ \mbox{greater}(h,g)\qquad\mbox{cnf}(\mbox{a2\_FOL}_3,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(f,e)\mbox{ and }\mbox{greater}(h,g) ) \ \Rightarrow \ \mbox{greater}(j,i)\qquad\mbox{cnf}(\mbox{a2\_FOL}_4,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reorganization\_free}(a,b,b)\mbox{ and }\mbox{reorganization\_free}(c,d,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,d)\mbox{ and }\mbox{reproducibility}(a,f,b)\mbox{ and }\mbox{reproducibility}(c,g,d)\mbox{ and }\mbox{size}(a,h,b)\mbox{ and }\mbox{size}(c,i,d)\mbox{ and }\mbox{greater}(i,h) ) \ \Rightarrow \ \mbox{greater}(g,f)\qquad\mbox{cnf}(\mbox{t9\_FOL}_5,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t10\_FOL}_6,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_{12})\qquad\mbox{cnf}(\mbox{t10\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_2,\mbox{sk}_{11},\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t10\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_3,\mbox{sk}_{12},\mbox{sk}_{12})\qquad\mbox{cnf}(\mbox{t10\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t10\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_{12})\qquad\mbox{cnf}(\mbox{t10\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{reliability}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t10\_FOL}_{12},\mbox{negated\_conjecture})$

$\mbox{reliability}(\mbox{sk}_3,\mbox{sk}_6,\mbox{sk}_{12})\qquad\mbox{cnf}(\mbox{t10\_FOL}_{13},\mbox{negated\_conjecture})$

$\mbox{accountability}(\mbox{sk}_2,\mbox{sk}_7,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t10\_FOL}_{14},\mbox{negated\_conjecture})$

$\mbox{accountability}(\mbox{sk}_3,\mbox{sk}_8,\mbox{sk}_{12})\qquad\mbox{cnf}(\mbox{t10\_FOL}_{15},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_2,\mbox{sk}_9,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t10\_FOL}_{16},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_3,\mbox{sk}_{10},\mbox{sk}_{12})\qquad\mbox{cnf}(\mbox{t10\_FOL}_{17},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_{10},\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t10\_FOL}_{18},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_6,\mbox{sk}_5) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{sk}_8,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t10\_FOL}_{19},\mbox{negated\_conjecture})$

\medskip\textbf{MGT027-1.p} The FM set contracts in stable environments

The first mover set begins to contract past a certain time
 in stable environments.




$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{first\_movers},\mbox{sk}_1(b,a)),0)\mbox{ or }\mbox{contracts\_from}(b,\mbox{first\_movers}) )\qquad\mbox{cnf}(\mbox{mp\_contracts\_from}_{24},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ ( \mbox{greater\_or\_equal}(\mbox{sk}_1(b,a),b)\mbox{ or }\mbox{contracts\_from}(b,\mbox{first\_movers}) )\qquad\mbox{cnf}(\mbox{mp\_contracts\_from}_{25},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_1(b,a))) ) \ \Rightarrow \ \mbox{contracts\_from}(b,\mbox{first\_movers})\qquad\mbox{cnf}(\mbox{mp\_contracts\_from}_{26},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{first\_movers},b),0)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{efficient\_producers},b),0) ) \ \Rightarrow \ \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\qquad\mbox{cnf}(\mbox{mp\_non\_empty\_fm\_and\_ep}_{27},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \mbox{in\_environment}(a,c)\qquad\mbox{cnf}(\mbox{mp\_long\_stable\_environments}_{28},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{appear}(\mbox{efficient\_producers},a))\qquad\mbox{cnf}(\mbox{mp\_EP\_in\_stable\_environments}_{29},\mbox{axiom})$

$( \mbox{greater}(a,b)\mbox{ and }\mbox{greater}(b,c) ) \ \Rightarrow \ \mbox{greater}(a,c)\qquad\mbox{cnf}(\mbox{mp\_greater\_transitivity}_{30},\mbox{axiom})$

$\mbox{greater\_or\_equal}(a,b) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b )\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{31},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \mbox{greater\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{32},\mbox{axiom})$

$a = b \ \Rightarrow \ \mbox{greater\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{33},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{appear}(\mbox{efficient\_producers},a)) ) \ \Rightarrow \ \mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{efficient\_producers},b),0)\qquad\mbox{cnf}(\mbox{t6}_{34},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \mbox{greater}(\mbox{sk}_2(a),\mbox{appear}(\mbox{efficient\_producers},a))\qquad\mbox{cnf}(\mbox{l10}_{35},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{sk}_2(a)) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},b))\qquad\mbox{cnf}(\mbox{l10}_{36},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_l9}_{37},\mbox{negated\_conjecture})$

$\mbox{stable}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_l9}_{38},\mbox{negated\_conjecture})$

$\mbox{greater}(a,\mbox{appear}(\mbox{efficient\_producers},\mbox{sk}_3)) \ \Rightarrow \ \neg\,\mbox{contracts\_from}(a,\mbox{first\_movers})\qquad\mbox{cnf}(\mbox{prove\_l9}_{39},\mbox{negated\_conjecture})$

\medskip\textbf{MGT052+1.p} The environment at any time is similar with itself






$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x,t_0,t{:}\;( \mbox{dissimilar}(x,t_0,t)\iff ( \mbox{organization}(x)\mbox{ and }\neg\,\mbox{is\_aligned}(x,t_0)\iff \mbox{is\_aligned}(x,t) ) )\qquad\mbox{fof}(\mbox{definition}_2,\mbox{axiom})$

$\forall x,t{:}\;\neg\,\mbox{dissimilar}(x,t,t)\qquad\mbox{fof}(\mbox{background\_assumption}_1,\mbox{conjecture})$

\medskip\textbf{MGT019+2.p} Growth rate of EPs exceeds that of FMs in stable environments

The growth rate of efficent producers exceeds the growth rate
 of first movers past a certain time in stable environments.




$\neg\,\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \mbox{greater}(\mbox{disbanding\_rate}(\mbox{first\_movers},t),\mbox{disbanding\_rate}(\mbox{efficient\_producers},t)) )\qquad\mbox{fof}(l_2,\mbox{axiom})$

$\forall t{:}\;( ( \mbox{greater}(\mbox{disbanding\_rate}(\mbox{first\_movers},t),\mbox{disbanding\_rate}(\mbox{efficient\_producers},t))\mbox{ and }\mbox{greater\_or\_equal}(\mbox{founding\_rate}(\mbox{efficient\_producers},t),\mbox{founding\_rate}(\mbox{first\_movers},t)) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) )\qquad\mbox{fof}(\mbox{mp\_EP\_lower\_disbanding\_rate},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{greater\_or\_equal}(x,y) \ \Rightarrow \ ( \mbox{greater}(x,y)\mbox{ or }x = y ) )\qquad\mbox{fof}(\mbox{mp\_greater\_or\_equal},\mbox{axiom})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{founding\_rate}(\mbox{efficient\_producers},t),\mbox{founding\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(a_8,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(\mbox{prove\_l}_1,\mbox{conjecture})$

\medskip\textbf{MGT006-1.p} Reliability and accountability increase with time.






$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{reproducibility}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp3}_1,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(j,i) ) \ \Rightarrow \ \mbox{greater}(f,e)\qquad\mbox{cnf}(\mbox{a2\_FOL}_2,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(j,i) ) \ \Rightarrow \ \mbox{greater}(h,g)\qquad\mbox{cnf}(\mbox{a2\_FOL}_3,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(f,e)\mbox{ and }\mbox{greater}(h,g) ) \ \Rightarrow \ \mbox{greater}(j,i)\qquad\mbox{cnf}(\mbox{a2\_FOL}_4,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{reproducibility}(a,d,b)\mbox{ and }\mbox{reproducibility}(a,e,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \mbox{greater}(e,d)\qquad\mbox{cnf}(\mbox{a4\_FOL}_5,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t6\_FOL}_6,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t6\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_2,\mbox{sk}_7,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t6\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{reliability}(\mbox{sk}_2,\mbox{sk}_3,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t6\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{reliability}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t6\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{accountability}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t6\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{accountability}(\mbox{sk}_2,\mbox{sk}_6,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t6\_FOL}_{12},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_8,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t6\_FOL}_{13},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_4,\mbox{sk}_3) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{sk}_6,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t6\_FOL}_{14},\mbox{negated\_conjecture})$

\medskip\textbf{MGT028+1.p} FMs have a negative growth rate in stable environments

First movers have negative growth rate past a certain point
 of time (also after the appearence of efficient producers)
 in stable environments.




$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e)\mbox{ and }\exists t_1{:}\;( \mbox{in\_environment}(e,t_1)\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,t_1) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) ) \ \Rightarrow \ \exists t_2{:}\;( \mbox{greater}(t_2,\mbox{appear}(\mbox{efficient\_producers},e))\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,t_2) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(\mbox{mp\_first\_movers\_negative\_growth},\mbox{axiom})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) ) )\qquad\mbox{fof}(l_{11},\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{greater}(\mbox{to},\mbox{appear}(\mbox{efficient\_producers},e))\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(\mbox{prove\_l}_{10},\mbox{conjecture})$

\medskip\textbf{MGT066-1.p} Inequalities.






$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

\medskip\textbf{MGT044+1.p} Capability increases monotonically with age

An organization's capability increases monotonically with its age.




$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x,t_0,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ ( ( ( \mbox{greater}(\mbox{stock\_of\_knowledge}(x,t),\mbox{stock\_of\_knowledge}(x,t_0))\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{internal\_friction}(x,t),\mbox{internal\_friction}(x,t_0)) ) \ \Rightarrow \ \mbox{greater}(\mbox{capability}(x,t),\mbox{capability}(x,t_0)) )\mbox{ and }( ( \mbox{smaller\_or\_equal}(\mbox{stock\_of\_knowledge}(x,t),\mbox{stock\_of\_knowledge}(x,t_0))\mbox{ and }\mbox{greater}(\mbox{internal\_friction}(x,t),\mbox{internal\_friction}(x,t_0)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{capability}(x,t),\mbox{capability}(x,t_0)) )\mbox{ and }( ( \mbox{stock\_of\_knowledge}(x,t) = \mbox{stock\_of\_knowledge}(x,t_0)\mbox{ and }\mbox{internal\_friction}(x,t) = \mbox{internal\_friction}(x,t_0) ) \ \Rightarrow \ \mbox{capability}(x,t) = \mbox{capability}(x,t_0) ) ) )\qquad\mbox{fof}(\mbox{assumption}_5,\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{greater}(\mbox{age}(x,t),\mbox{age}(x,t_0)) ) \ \Rightarrow \ \mbox{greater}(\mbox{stock\_of\_knowledge}(x,t),\mbox{stock\_of\_knowledge}(x,t_0)) )\qquad\mbox{fof}(\mbox{assumption}_7,\mbox{axiom})$

$\forall x,t_0,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ \mbox{internal\_friction}(x,t) = \mbox{internal\_friction}(x,t_0) )\qquad\mbox{fof}(\mbox{assumption}_9,\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{greater}(\mbox{age}(x,t),\mbox{age}(x,t_0)) ) \ \Rightarrow \ \mbox{greater}(\mbox{capability}(x,t),\mbox{capability}(x,t_0)) )\qquad\mbox{fof}(\mbox{lemma}_3,\mbox{conjecture})$

\medskip\textbf{MGT029+1.p} EPs have positive and FMs have negative growth rates

Efficient producers have positive, while first movers have
 negative growth rate past a certain point of time in stable
 environments.




$\forall x,y,z{:}\;( ( \mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,z) ) \ \Rightarrow \ \mbox{greater}(x,z) )\qquad\mbox{fof}(\mbox{mp\_greater\_transitivity},\mbox{axiom})$

$\forall e,t_1,t_2{:}\;( ( \mbox{in\_environment}(e,t_1)\mbox{ and }\mbox{in\_environment}(e,t_2) ) \ \Rightarrow \ ( \mbox{greater}(t_2,t_1)\mbox{ or }t_2 = t_1\mbox{ or }\mbox{greater}(t_1,t_2) ) )\qquad\mbox{fof}(\mbox{mp\_times\_in\_environment},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{greater\_or\_equal}(x,y)\iff ( \mbox{greater}(x,y)\mbox{ or }x = y ) )\qquad\mbox{fof}(\mbox{mp\_greater\_or\_equal},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{equilibrium}(e)) ) \ \Rightarrow \ ( ( \mbox{growth\_rate}(\mbox{first\_movers},t) = 0\mbox{ and }\mbox{growth\_rate}(\mbox{efficient\_producers},t) = 0 )\mbox{ or }( \mbox{greater}(\mbox{growth\_rate}(\mbox{first\_movers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{efficient\_producers},t)) )\mbox{ or }( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(l_6,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(l_1,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists t{:}\;( \mbox{in\_environment}(e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{equilibrium}(e)) ) )\qquad\mbox{fof}(a_4,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) ) )\qquad\mbox{fof}(\mbox{prove\_l}_{11},\mbox{conjecture})$

\medskip\textbf{MGT045+1.p} Structural position increases monotonically with age

An organization's structural position increases monotonically
 with its age.




$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x,t_0,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ ( ( \mbox{greater}(\mbox{external\_ties}(x,t),\mbox{external\_ties}(x,t_0)) \ \Rightarrow \ \mbox{greater}(\mbox{position}(x,t),\mbox{position}(x,t_0)) )\mbox{ and }( \mbox{external\_ties}(x,t) = \mbox{external\_ties}(x,t_0) \ \Rightarrow \ \mbox{position}(x,t) = \mbox{position}(x,t_0) ) ) )\qquad\mbox{fof}(\mbox{assumption}_6,\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{greater}(\mbox{age}(x,t),\mbox{age}(x,t_0)) ) \ \Rightarrow \ \mbox{greater}(\mbox{external\_ties}(x,t),\mbox{external\_ties}(x,t_0)) )\qquad\mbox{fof}(\mbox{assumption}_8,\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{greater}(\mbox{age}(x,t),\mbox{age}(x,t_0)) ) \ \Rightarrow \ \mbox{greater}(\mbox{position}(x,t),\mbox{position}(x,t_0)) )\qquad\mbox{fof}(\mbox{lemma}_4,\mbox{conjecture})$

\medskip\textbf{MGT033-1.p} Selection favors FMs above EPs until EPs appear

Selection favors first movers above efficient producers
 until the appearance of efficient producers.




$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulation}(b,a,c)\mbox{ and }\mbox{subpopulation}(d,a,c)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(b,c),0)\mbox{ and }\mbox{cardinality\_at\_time}(d,c) = 0 ) \ \Rightarrow \ \mbox{selection\_favors}(b,d,c)\qquad\mbox{cnf}(\mbox{mp2\_favour\_members}_{24},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{appear}(c,a),b) ) \ \Rightarrow \ \mbox{cardinality\_at\_time}(c,b) = 0\qquad\mbox{cnf}(\mbox{mp\_not\_present\_before\_appearance}_{25},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater}(\mbox{number\_of\_organizations}(a,b),0) ) \ \Rightarrow \ \mbox{subpopulation}(\mbox{sk}_1(b,a),a,b)\qquad\mbox{cnf}(\mbox{mp\_positive\_sum\_means\_members}_{26},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater}(\mbox{number\_of\_organizations}(a,b),0) ) \ \Rightarrow \ \mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{sk}_1(b,a),b),0)\qquad\mbox{cnf}(\mbox{mp\_positive\_sum\_means\_members}_{27},\mbox{axiom})$

$\mbox{cardinality\_at\_time}(a,t) = 0 \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{cardinality\_at\_time}(a,b),0)\qquad\mbox{cnf}(\mbox{mp\_zero\_is\_not\_positive}_{28},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater}(\mbox{number\_of\_organizations}(a,b),0) ) \ \Rightarrow \ \mbox{in\_environment}(a,b)\qquad\mbox{cnf}(\mbox{mp\_positive\_and\_sustains}_{29},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{in\_environment}(a,c)\mbox{ and }\mbox{greater\_or\_equal}(c,d)\mbox{ and }\mbox{greater\_or\_equal}(d,b) ) \ \Rightarrow \ \mbox{in\_environment}(a,d)\qquad\mbox{cnf}(\mbox{mp\_durations\_are\_time\_intervals}_{30},\mbox{axiom})$

$\mbox{environment}(a) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{start\_time}(a))\qquad\mbox{cnf}(\mbox{mp\_opening\_time\_in\_duration}_{31},\mbox{axiom})$

$\mbox{environment}(a) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{appear}(\mbox{first\_movers},a),\mbox{start\_time}(a))\qquad\mbox{cnf}(\mbox{mp\_no\_FM\_before\_opening}_{32},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ \mbox{subpopulation}(\mbox{first\_movers},a,b)\qquad\mbox{cnf}(\mbox{mp\_subpopulations}_{33},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ \mbox{subpopulation}(\mbox{efficient\_producers},a,b)\qquad\mbox{cnf}(\mbox{mp\_subpopulations}_{34},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,\mbox{appear}(\mbox{first\_movers},a)) ) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{appear}(\mbox{an\_organisation},a))\qquad\mbox{cnf}(\mbox{mp\_FM\_means\_organisations}_{35},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{appear}(\mbox{an\_organisation},a)) ) \ \Rightarrow \ \mbox{greater}(\mbox{number\_of\_organizations}(a,b),0)\qquad\mbox{cnf}(\mbox{a1}_{36},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulation}(b,a,c)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(b,c),0) ) \ \Rightarrow \ ( b = \mbox{efficient\_producers}\mbox{ or }b = \mbox{first\_movers} )\qquad\mbox{cnf}(\mbox{a9}_{37},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,\mbox{appear}(\mbox{an\_organisation},a)) ) \ \Rightarrow \ \mbox{appear}(\mbox{an\_organisation},a) = \mbox{appear}(\mbox{first\_movers},a)\qquad\mbox{cnf}(\mbox{l13}_{38},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t2}_{39},\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_2,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_t2}_{40},\mbox{negated\_conjecture})$

$\mbox{greater\_or\_equal}(\mbox{sk}_3,\mbox{appear}(\mbox{first\_movers},\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_t2}_{41},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{appear}(\mbox{efficient\_producers},\mbox{sk}_2),\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_t2}_{42},\mbox{negated\_conjecture})$

$\neg\,\mbox{selection\_favors}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_t2}_{43},\mbox{negated\_conjecture})$

\medskip\textbf{MGT008+1.p} Organizational death rates decrease with size.






$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists i{:}\;\mbox{inertia}(x,i,t) )\qquad\mbox{fof}(\mbox{mp}_5,\mbox{axiom})$

$\forall x,y,c,s_1,s_2,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(y,s_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{a5\_FOL},\mbox{hypothesis})$

$\forall x,y,t_1,t_2,i_1,i_2,p_1,p_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(y,t_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{survival\_chance}(x,p_1,t_1)\mbox{ and }\mbox{survival\_chance}(y,p_2,t_2)\mbox{ and }\mbox{greater}(i_2,i_1) ) \ \Rightarrow \ \mbox{greater}(p_2,p_1) )\qquad\mbox{fof}(\mbox{t1\_FOL},\mbox{hypothesis})$

$\forall x,y,c,p_1,p_2,s_1,s_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(y,t_2,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{survival\_chance}(x,p_1,t_1)\mbox{ and }\mbox{survival\_chance}(y,p_2,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(y,s_2,t_2)\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \mbox{greater}(p_2,p_1) )\qquad\mbox{fof}(\mbox{t8\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT020-1.p} First movers exceeds efficient producers disbanding rate






$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b) ) \ \Rightarrow \ \neg\,\mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},b)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},b))\qquad\mbox{cnf}(\mbox{l3}_{22},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,\mbox{initial\_FM\_EP}(a)) ) \ \Rightarrow \ \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,\mbox{initial\_FM\_EP}(a))\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_point}_{23},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(b,\mbox{initial\_FM\_EP}(a))\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_point}_{24},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater\_or\_equal}(b,c)\mbox{ and }\mbox{greater\_or\_equal}(d,b)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,d)\mbox{ and }\mbox{greater}(\mbox{disbanding\_rate}(\mbox{first\_movers},c),\mbox{disbanding\_rate}(\mbox{efficient\_producers},c)) ) \ \Rightarrow \ ( \mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},b)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},b))\mbox{ or }\mbox{greater}(\mbox{disbanding\_rate}(\mbox{first\_movers},d),\mbox{disbanding\_rate}(\mbox{efficient\_producers},d)) )\qquad\mbox{cnf}(\mbox{mp\_positive\_function\_difference}_{25},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b) ) \ \Rightarrow \ \mbox{in\_environment}(a,b)\qquad\mbox{cnf}(\mbox{mp\_time\_point\_occurs}_{26},\mbox{axiom})$

$\mbox{environment}(a) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{initial\_FM\_EP}(a),\mbox{start\_time}(a))\qquad\mbox{cnf}(\mbox{mp\_initial\_time}_{27},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{start\_time}(a))\mbox{ and }\mbox{greater}(c,b)\mbox{ and }\mbox{in\_environment}(a,c) ) \ \Rightarrow \ \mbox{in\_environment}(a,b)\qquad\mbox{cnf}(\mbox{mp\_times\_in\_order}_{28},\mbox{axiom})$

$( \mbox{greater}(a,b)\mbox{ and }\mbox{greater}(b,c) ) \ \Rightarrow \ \mbox{greater}(a,c)\qquad\mbox{cnf}(\mbox{mp\_greater\_transitivity}_{29},\mbox{axiom})$

$\mbox{greater\_or\_equal}(a,b) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b )\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{30},\mbox{axiom})$

$\mbox{environment}(a) \ \Rightarrow \ \mbox{greater}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{initial\_FM\_EP}(a)),\mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{initial\_FM\_EP}(a)))\qquad\mbox{cnf}(\mbox{a8}_{31},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,c)\mbox{ and }\mbox{greater\_or\_equal}(d,b)\mbox{ and }\mbox{greater\_or\_equal}(c,d) ) \ \Rightarrow \ \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,d)\qquad\mbox{cnf}(\mbox{a10}_{32},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{prove\_l2}_{33},\mbox{negated\_conjecture})$

$\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_l2}_{34},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2),\mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l2}_{35},\mbox{negated\_conjecture})$

\medskip\textbf{MGT022-2.p} Decreasing resource availability affects FMS more than EPs

Decreasing resource availability affects the disbanding rate
 of first movers more than the disbanding rate of efficient
 producers.




$\mbox{constant}(a) \ \Rightarrow \ \neg\,\mbox{decreases}(a)\qquad\mbox{cnf}(\mbox{mp\_constant\_not\_decrease}_1,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{greater}(\mbox{resilience}(c),\mbox{resilience}(b))\mbox{ and }\mbox{decreases}(\mbox{resources}(a,d)) ) \ \Rightarrow \ \mbox{increases}(\mbox{disbanding\_rate}(b,d)\setminus \mbox{disbanding\_rate}(c,d))\qquad\mbox{cnf}(\mbox{a6}_2,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{greater}(\mbox{resilience}(c),\mbox{resilience}(b))\mbox{ and }\mbox{constant}(\mbox{resources}(a,d)) ) \ \Rightarrow \ \mbox{constant}(\mbox{disbanding\_rate}(b,d)\setminus \mbox{disbanding\_rate}(c,d))\qquad\mbox{cnf}(\mbox{a6}_3,\mbox{hypothesis})$

$\mbox{greater}(\mbox{resilience}(\mbox{efficient\_producers}),\mbox{resilience}(\mbox{first\_movers}))\qquad\mbox{cnf}(\mbox{a2}_4,\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{prove\_l4}_5,\mbox{negated\_conjecture})$

$\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_l4}_6,\mbox{negated\_conjecture})$

$\mbox{decreases}(\mbox{resources}(\mbox{sk}_1,\mbox{sk}_2))\mbox{ or }\mbox{constant}(\mbox{resources}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l4}_7,\mbox{negated\_conjecture})$

$\mbox{decreases}(\mbox{resources}(\mbox{sk}_1,\mbox{sk}_2))\mbox{ or }\mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l4}_8,\mbox{negated\_conjecture})$

$\mbox{increases}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2)) \ \Rightarrow \ \mbox{constant}(\mbox{resources}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l4}_9,\mbox{negated\_conjecture})$

$\mbox{increases}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2)) \ \Rightarrow \ \mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l4}_{10},\mbox{negated\_conjecture})$

\medskip\textbf{MGT023+2.p} Stable environments have a critical point.






$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\neg\,\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{to}),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{to}))\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds},\mbox{axiom})$

$\forall e,\mbox{to}{:}\;( ( \mbox{environment}(e)\mbox{ and }\neg\,\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{to}),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{to}))\mbox{ and }\mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) \ \Rightarrow \ \mbox{to} = \mbox{critical\_point}(e) )\qquad\mbox{fof}(d_1,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(l_1,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \mbox{in\_environment}(e,\mbox{critical\_point}(e)) )\qquad\mbox{fof}(\mbox{prove\_l}_5,\mbox{conjecture})$

\medskip\textbf{MGT043-1.p} Conditions for a higher hazard of mortality

When an organization lacks immunity, the growth of internal
 friction elevates its hazard of mortality when its knowledge and
 the quality of its ties are constant.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{capability}(a,c),\mbox{capability}(a,b))\mbox{ and }\mbox{greater\_or\_equal}(\mbox{position}(a,c),\mbox{position}(a,b)) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{has\_immunity}(a,c)\mbox{ or }\mbox{smaller}(\mbox{hazard\_of\_mortality}(a,c),\mbox{hazard\_of\_mortality}(a,b)) )\qquad\mbox{cnf}(\mbox{assumption\_4}_{38},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater\_or\_equal}(\mbox{capability}(a,c),\mbox{capability}(a,b))\mbox{ and }\mbox{greater}(\mbox{position}(a,c),\mbox{position}(a,b)) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{has\_immunity}(a,c)\mbox{ or }\mbox{smaller}(\mbox{hazard\_of\_mortality}(a,c),\mbox{hazard\_of\_mortality}(a,b)) )\qquad\mbox{cnf}(\mbox{assumption\_4}_{39},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{capability}(a,c) = \mbox{capability}(a,b)\mbox{ and }\mbox{position}(a,c) = \mbox{position}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{has\_immunity}(a,c)\mbox{ or }\mbox{hazard\_of\_mortality}(a,c) = \mbox{hazard\_of\_mortality}(a,b) )\qquad\mbox{cnf}(\mbox{assumption\_4}_{40},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{capability}(a,b),\mbox{capability}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_5}_{41},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\mbox{ and }\mbox{greater}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{capability}(a,b),\mbox{capability}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_5}_{42},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{stock\_of\_knowledge}(a,b) = \mbox{stock\_of\_knowledge}(a,c)\mbox{ and }\mbox{internal\_friction}(a,b) = \mbox{internal\_friction}(a,c) ) \ \Rightarrow \ \mbox{capability}(a,b) = \mbox{capability}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_5}_{43},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{external\_ties}(a,b),\mbox{external\_ties}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{position}(a,b),\mbox{position}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_6}_{44},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{external\_ties}(a,b) = \mbox{external\_ties}(a,c) ) \ \Rightarrow \ \mbox{position}(a,b) = \mbox{position}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_6}_{45},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{lemma\_2}_{46},\mbox{negated\_conjecture})$

$\neg\,\mbox{has\_immunity}(\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{lemma\_2}_{47},\mbox{negated\_conjecture})$

$\neg\,\mbox{has\_immunity}(\mbox{sk}_1,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{lemma\_2}_{48},\mbox{negated\_conjecture})$

$\mbox{stock\_of\_knowledge}(\mbox{sk}_1,\mbox{sk}_3) = \mbox{stock\_of\_knowledge}(\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{lemma\_2}_{49},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{internal\_friction}(\mbox{sk}_1,\mbox{sk}_3),\mbox{internal\_friction}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{lemma\_2}_{50},\mbox{negated\_conjecture})$

$\mbox{external\_ties}(\mbox{sk}_1,\mbox{sk}_2) = \mbox{external\_ties}(\mbox{sk}_1,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{lemma\_2}_{51},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_3),\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{lemma\_2}_{52},\mbox{negated\_conjecture})$

\medskip\textbf{MGT053-1.p} The dissimilarity relation is symmetric






$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$\mbox{dissimilar}(a,b,c) \ \Rightarrow \ \mbox{organization}(a)\qquad\mbox{cnf}(\mbox{definition\_2}_{29},\mbox{axiom})$

$\mbox{dissimilar}(a,b,c) \ \Rightarrow \ ( \mbox{is\_aligned}(a,b)\mbox{ or }\mbox{is\_aligned}(a,c) )\qquad\mbox{cnf}(\mbox{definition\_2}_{30},\mbox{axiom})$

$( \mbox{dissimilar}(a,b,c)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ \neg\,\mbox{is\_aligned}(a,c)\qquad\mbox{cnf}(\mbox{definition\_2}_{31},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,b)\mbox{ or }\mbox{dissimilar}(a,b,c) )\qquad\mbox{cnf}(\mbox{definition\_2}_{32},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,c)\mbox{ or }\mbox{dissimilar}(a,b,c) )\qquad\mbox{cnf}(\mbox{definition\_2}_{33},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,c)\mbox{ or }\mbox{dissimilar}(a,c,b) )\qquad\mbox{cnf}(\mbox{definition\_2}_{34},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{is\_aligned}(a,b)\mbox{ or }\mbox{dissimilar}(a,c,b) )\qquad\mbox{cnf}(\mbox{definition\_2}_{35},\mbox{axiom})$

$\mbox{dissimilar}(\mbox{sk}_1,\mbox{sk}_2,\mbox{sk}_3)\mbox{ or }\mbox{dissimilar}(\mbox{sk}_1,\mbox{sk}_3,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{lemma\_7}_{36},\mbox{negated\_conjecture})$

$\mbox{dissimilar}(\mbox{sk}_1,\mbox{sk}_2,\mbox{sk}_3) \ \Rightarrow \ \mbox{dissimilar}(\mbox{sk}_1,\mbox{sk}_2,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{lemma\_7}_{37},\mbox{negated\_conjecture})$

$\mbox{dissimilar}(\mbox{sk}_1,\mbox{sk}_3,\mbox{sk}_2) \ \Rightarrow \ \mbox{dissimilar}(\mbox{sk}_1,\mbox{sk}_3,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{lemma\_7}_{38},\mbox{negated\_conjecture})$

$\mbox{dissimilar}(\mbox{sk}_1,\mbox{sk}_3,\mbox{sk}_2) \ \Rightarrow \ \neg\,\mbox{dissimilar}(\mbox{sk}_1,\mbox{sk}_2,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{lemma\_7}_{39},\mbox{negated\_conjecture})$

\medskip\textbf{MGT056+1.p} Conditions for a constant then jumping hazard of mortality 2

When (`eta' $>$= `sigma') in a drifting environment, an endowed
 organization's hazard of mortality remains constant until age
 `eta' and then jumps to a higher level in a drifting environment.




$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x{:}\;( \mbox{has\_endowment}(x)\iff \forall t{:}\;( \mbox{organization}(x)\mbox{ and }( \mbox{smaller\_or\_equal}(\mbox{age}(x,t),\mbox{eta}) \ \Rightarrow \ \mbox{has\_immunity}(x,t) )\mbox{ and }( \mbox{greater}(\mbox{age}(x,t),\mbox{eta}) \ \Rightarrow \ \neg\,\mbox{has\_immunity}(x,t) ) ) )\qquad\mbox{fof}(\mbox{definition}_1,\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{has\_immunity}(x,t_0)\mbox{ and }\mbox{has\_immunity}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t_0) = \mbox{hazard\_of\_mortality}(x,t) )\qquad\mbox{fof}(\mbox{assumption}_2,\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{has\_immunity}(x,t_0)\mbox{ and }\neg\,\mbox{has\_immunity}(x,t) ) \ \Rightarrow \ \mbox{greater}(\mbox{hazard\_of\_mortality}(x,t),\mbox{hazard\_of\_mortality}(x,t_0)) )\qquad\mbox{fof}(\mbox{assumption}_3,\mbox{axiom})$

$\forall x,t_0,t_1,t_2{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{has\_endowment}(x)\mbox{ and }\mbox{age}(x,t_0) = 0\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{age}(x,t_1),\mbox{eta})\mbox{ and }\mbox{greater}(\mbox{age}(x,t_2),\mbox{eta})\mbox{ and }\mbox{greater\_or\_equal}(\mbox{eta},\mbox{sigma})\mbox{ and }\mbox{greater}(\mbox{sigma},0) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{hazard\_of\_mortality}(x,t_2),\mbox{hazard\_of\_mortality}(x,t_1))\mbox{ and }\mbox{hazard\_of\_mortality}(x,t_1) = \mbox{hazard\_of\_mortality}(x,t_0) ) )\qquad\mbox{fof}(\mbox{lemma}_9,\mbox{conjecture})$

\medskip\textbf{MGT032-2.p} Selection favours EPs above FMs

In stable environments, selection favors efficient producers
 above first movers past a certain point in time.




$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{greater}(\mbox{growth\_rate}(c,d),\mbox{growth\_rate}(b,d)) ) \ \Rightarrow \ \mbox{selection\_favors}(c,b,d)\qquad\mbox{cnf}(\mbox{mp1\_high\_growth\_rates}_1,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{sk}_1(a))\qquad\mbox{cnf}(\mbox{l1}_2,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{sk}_1(a)) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},b),\mbox{growth\_rate}(\mbox{first\_movers},b))\qquad\mbox{cnf}(\mbox{l1}_3,\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t1}_4,\mbox{negated\_conjecture})$

$\mbox{stable}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t1}_5,\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_2,a) \ \Rightarrow \ \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_2,\mbox{sk}_3(a))\qquad\mbox{cnf}(\mbox{prove\_t1}_6,\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_2,a) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{sk}_3(a),a)\qquad\mbox{cnf}(\mbox{prove\_t1}_7,\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_2,a) \ \Rightarrow \ \neg\,\mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},\mbox{sk}_3(a))\qquad\mbox{cnf}(\mbox{prove\_t1}_8,\mbox{negated\_conjecture})$

\medskip\textbf{MGT066+1.p} Inequalities.






$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

\medskip\textbf{MGT002-1.p} Structural inertia increases monotonically with age.






$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{reproducibility}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp3}_1,\mbox{axiom})$

$\mbox{reorganization\_free}(a,b,c) \ \Rightarrow \ \mbox{reorganization\_free}(a,b,b)\qquad\mbox{cnf}(\mbox{mp4}_2,\mbox{axiom})$

$\mbox{reorganization\_free}(a,b,c) \ \Rightarrow \ \mbox{reorganization\_free}(a,c,c)\qquad\mbox{cnf}(\mbox{mp4}_3,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reorganization\_free}(a,b,b)\mbox{ and }\mbox{reorganization\_free}(c,d,d)\mbox{ and }\mbox{reproducibility}(a,e,b)\mbox{ and }\mbox{reproducibility}(c,f,d)\mbox{ and }\mbox{inertia}(a,g,b)\mbox{ and }\mbox{inertia}(c,h,d)\mbox{ and }\mbox{greater}(f,e) ) \ \Rightarrow \ \mbox{greater}(h,g)\qquad\mbox{cnf}(\mbox{a3\_FOL}_4,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reorganization\_free}(a,b,b)\mbox{ and }\mbox{reorganization\_free}(c,d,d)\mbox{ and }\mbox{reproducibility}(a,e,b)\mbox{ and }\mbox{reproducibility}(c,f,d)\mbox{ and }\mbox{inertia}(a,g,b)\mbox{ and }\mbox{inertia}(c,h,d)\mbox{ and }\mbox{greater}(h,g) ) \ \Rightarrow \ \mbox{greater}(f,e)\qquad\mbox{cnf}(\mbox{a3\_FOL}_5,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{reproducibility}(a,d,b)\mbox{ and }\mbox{reproducibility}(a,e,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \mbox{greater}(e,d)\qquad\mbox{cnf}(\mbox{a4\_FOL}_6,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t2\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t2\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t2\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{inertia}(\mbox{sk}_2,\mbox{sk}_3,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t2\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{inertia}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t2\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_6,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t2\_FOL}_{12},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_4,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{t2\_FOL}_{13},\mbox{negated\_conjecture})$

\medskip\textbf{MGT038-1.p} FMs become extinct in stable environments

First movers become extinct past a certain point in time
 in stable environments.




$\mbox{finite\_set}(\mbox{first\_movers})\qquad\mbox{cnf}(\mbox{mp7\_first\_movers\_exist}_{17},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{appear}(\mbox{first\_movers},a))\qquad\mbox{cnf}(\mbox{mp\_stable\_first\_movers}_{18},\mbox{axiom})$

$( \mbox{finite\_set}(a)\mbox{ and }\mbox{contracts\_from}(b,a) ) \ \Rightarrow \ \mbox{greater}(\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp\_contracting\_time}_{19},\mbox{axiom})$

$( \mbox{finite\_set}(a)\mbox{ and }\mbox{contracts\_from}(b,a) ) \ \Rightarrow \ \mbox{cardinality\_at\_time}(s,t_2) = 0\qquad\mbox{cnf}(\mbox{mp\_contracting\_time}_{20},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \mbox{in\_environment}(a,c)\qquad\mbox{cnf}(\mbox{mp\_long\_stable\_environments}_{21},\mbox{axiom})$

$( \mbox{greater}(a,b)\mbox{ and }\mbox{greater}(b,c) ) \ \Rightarrow \ \mbox{greater}(a,c)\qquad\mbox{cnf}(\mbox{mp\_greater\_transitivity}_{22},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \mbox{greater}(\mbox{sk}_2(a),\mbox{appear}(\mbox{efficient\_producers},a))\qquad\mbox{cnf}(\mbox{l9}_{23},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \mbox{contracts\_from}(\mbox{sk}_2(a),\mbox{first\_movers})\qquad\mbox{cnf}(\mbox{l9}_{24},\mbox{hypothesis})$

$\mbox{environment}(a) \ \Rightarrow \ \mbox{greater}(\mbox{appear}(\mbox{efficient\_producers},e),\mbox{appear}(\mbox{first\_movers},a))\qquad\mbox{cnf}(\mbox{a13}_{25},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_t7}_{26},\mbox{negated\_conjecture})$

$\mbox{stable}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_t7}_{27},\mbox{negated\_conjecture})$

$( \mbox{in\_environment}(\mbox{sk}_3,a)\mbox{ and }\mbox{greater}(a,\mbox{appear}(\mbox{first\_movers},\mbox{sk}_3)) ) \ \Rightarrow \ \mbox{cardinality\_at\_time}(\mbox{first\_movers},\mbox{to})\ne 0\qquad\mbox{cnf}(\mbox{prove\_t7}_{28},\mbox{negated\_conjecture})$

\medskip\textbf{MGT045-1.p} Structural position increases monotonically with age

An organization's structural position increases monotonically
 with its age.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{external\_ties}(a,b),\mbox{external\_ties}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{position}(a,b),\mbox{position}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_6}_{30},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{external\_ties}(a,b) = \mbox{external\_ties}(a,c) ) \ \Rightarrow \ \mbox{position}(a,b) = \mbox{position}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_6}_{31},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{age}(a,b),\mbox{age}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{external\_ties}(a,b),\mbox{external\_ties}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_8}_{32},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{lemma\_4}_{33},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{age}(\mbox{sk}_1,\mbox{sk}_3),\mbox{age}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{lemma\_4}_{34},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{position}(\mbox{sk}_1,\mbox{sk}_3),\mbox{position}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{lemma\_4}_{35},\mbox{negated\_conjecture})$

\medskip\textbf{MGT007-1.p} Reproducibility decreases during reorganization.






$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{reliability}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp1}_1,\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{accountability}(a,\mbox{sk}_2(b,a),b)\qquad\mbox{cnf}(\mbox{mp2}_2,\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{reproducibility}(a,\mbox{sk}_3(b,a),b)\qquad\mbox{cnf}(\mbox{mp\_not\_in\_TR}_3,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(j,i) ) \ \Rightarrow \ \mbox{greater}(f,e)\qquad\mbox{cnf}(\mbox{a2\_FOL}_4,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(j,i) ) \ \Rightarrow \ \mbox{greater}(h,g)\qquad\mbox{cnf}(\mbox{a2\_FOL}_5,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(f,e)\mbox{ and }\mbox{greater}(h,g) ) \ \Rightarrow \ \mbox{greater}(j,i)\qquad\mbox{cnf}(\mbox{a2\_FOL}_6,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization}(a,d,e)\mbox{ and }\mbox{reliability}(a,f,b)\mbox{ and }\mbox{reliability}(a,g,c)\mbox{ and }\mbox{accountability}(a,h,b)\mbox{ and }\mbox{accountability}(a,i,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ ( \mbox{greater}(d,b)\mbox{ or }\mbox{greater}(c,e)\mbox{ or }\mbox{greater}(f,g) )\qquad\mbox{cnf}(\mbox{a6\_FOL}_7,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization}(a,d,e)\mbox{ and }\mbox{reliability}(a,f,b)\mbox{ and }\mbox{reliability}(a,g,c)\mbox{ and }\mbox{accountability}(a,h,b)\mbox{ and }\mbox{accountability}(a,i,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ ( \mbox{greater}(d,b)\mbox{ or }\mbox{greater}(c,e)\mbox{ or }\mbox{greater}(h,i) )\qquad\mbox{cnf}(\mbox{a6\_FOL}_8,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_4,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t7\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_4,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t7\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_4,\mbox{sk}_9,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t7\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{reproducibility}(\mbox{sk}_4,\mbox{sk}_5,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t7\_FOL}_{12},\mbox{negated\_conjecture})$

$\mbox{reproducibility}(\mbox{sk}_4,\mbox{sk}_6,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t7\_FOL}_{13},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_9,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t7\_FOL}_{14},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_8,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t7\_FOL}_{15},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_8,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t7\_FOL}_{16},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_5,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t7\_FOL}_{17},\mbox{negated\_conjecture})$

\medskip\textbf{MGT058-1.p} An organization's position cannot be both fragile and robust






$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{fragile\_position}(a)\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{age}(a,b),\mbox{sigma}) ) \ \Rightarrow \ \mbox{positional\_advantage}(a,b)\qquad\mbox{cnf}(\mbox{definition\_3}_{30},\mbox{axiom})$

$( \mbox{fragile\_position}(a)\mbox{ and }\mbox{greater}(\mbox{age}(a,b),\mbox{sigma}) ) \ \Rightarrow \ \neg\,\mbox{positional\_advantage}(a,b)\qquad\mbox{cnf}(\mbox{definition\_3}_{31},\mbox{axiom})$

$\mbox{smaller\_or\_equal}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{sigma})\mbox{ or }\mbox{greater}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{sigma})\mbox{ or }\mbox{fragile\_position}(a)\qquad\mbox{cnf}(\mbox{definition\_3}_{32},\mbox{axiom})$

$\mbox{smaller\_or\_equal}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{sigma})\mbox{ or }\mbox{positional\_advantage}(a,\mbox{sk}_1(a))\mbox{ or }\mbox{fragile\_position}(a)\qquad\mbox{cnf}(\mbox{definition\_3}_{33},\mbox{axiom})$

$\mbox{positional\_advantage}(a,\mbox{sk}_1(a)) \ \Rightarrow \ ( \mbox{greater}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{sigma})\mbox{ or }\mbox{fragile\_position}(a) )\qquad\mbox{cnf}(\mbox{definition\_3}_{34},\mbox{axiom})$

$\mbox{positional\_advantage}(a,\mbox{sk}_1(a)) \ \Rightarrow \ ( \mbox{positional\_advantage}(a,\mbox{sk}_1(a))\mbox{ or }\mbox{fragile\_position}(a) )\qquad\mbox{cnf}(\mbox{definition\_3}_{35},\mbox{axiom})$

$( \mbox{robust\_position}(a)\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{age}(a,b),\mbox{tau}) ) \ \Rightarrow \ \neg\,\mbox{positional\_advantage}(a,b)\qquad\mbox{cnf}(\mbox{definition\_4}_{36},\mbox{axiom})$

$( \mbox{robust\_position}(a)\mbox{ and }\mbox{greater}(\mbox{age}(a,b),\mbox{tau}) ) \ \Rightarrow \ \mbox{positional\_advantage}(a,b)\qquad\mbox{cnf}(\mbox{definition\_4}_{37},\mbox{axiom})$

$\mbox{smaller\_or\_equal}(\mbox{age}(a,\mbox{sk}_2(a)),\mbox{tau})\mbox{ or }\mbox{greater}(\mbox{age}(a,\mbox{sk}_2(a)),\mbox{tau})\mbox{ or }\mbox{robust\_position}(a)\qquad\mbox{cnf}(\mbox{definition\_4}_{38},\mbox{axiom})$

$\mbox{positional\_advantage}(a,\mbox{sk}_2(a)) \ \Rightarrow \ ( \mbox{smaller\_or\_equal}(\mbox{age}(a,\mbox{sk}_2(a)),\mbox{tau})\mbox{ or }\mbox{robust\_position}(a) )\qquad\mbox{cnf}(\mbox{definition\_4}_{39},\mbox{axiom})$

$\mbox{positional\_advantage}(a,\mbox{sk}_2(a))\mbox{ or }\mbox{greater}(\mbox{age}(a,\mbox{sk}_2(a)),\mbox{tau})\mbox{ or }\mbox{robust\_position}(a)\qquad\mbox{cnf}(\mbox{definition\_4}_{40},\mbox{axiom})$

$\mbox{positional\_advantage}(a,\mbox{sk}_2(a)) \ \Rightarrow \ ( \mbox{positional\_advantage}(a,\mbox{sk}_2(a))\mbox{ or }\mbox{robust\_position}(a) )\qquad\mbox{cnf}(\mbox{definition\_4}_{41},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{lemma\_10}_{42},\mbox{negated\_conjecture})$

$\mbox{age}(\mbox{sk}_3,\mbox{sk}_4) = 0\qquad\mbox{cnf}(\mbox{lemma\_10}_{43},\mbox{negated\_conjecture})$

$\mbox{greater\_or\_equal}(\mbox{sigma},0)\qquad\mbox{cnf}(\mbox{lemma\_10}_{44},\mbox{negated\_conjecture})$

$\mbox{greater\_or\_equal}(\mbox{tau},0)\qquad\mbox{cnf}(\mbox{lemma\_10}_{45},\mbox{negated\_conjecture})$

$\mbox{fragile\_position}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{lemma\_10}_{46},\mbox{negated\_conjecture})$

$\mbox{robust\_position}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{lemma\_10}_{47},\mbox{negated\_conjecture})$

\medskip\textbf{MGT044-1.p} Capability increases monotonically with age

An organization's capability increases monotonically with its age.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{capability}(a,b),\mbox{capability}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_5}_{32},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\mbox{ and }\mbox{greater}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{capability}(a,b),\mbox{capability}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_5}_{33},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{stock\_of\_knowledge}(a,b) = \mbox{stock\_of\_knowledge}(a,c)\mbox{ and }\mbox{internal\_friction}(a,b) = \mbox{internal\_friction}(a,c) ) \ \Rightarrow \ \mbox{capability}(a,b) = \mbox{capability}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_5}_{34},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{age}(a,b),\mbox{age}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_7}_{35},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ \mbox{internal\_friction}(a,b) = \mbox{internal\_friction}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_9}_{36},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{lemma\_3}_{37},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{age}(\mbox{sk}_1,\mbox{sk}_3),\mbox{age}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{lemma\_3}_{38},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{capability}(\mbox{sk}_1,\mbox{sk}_3),\mbox{capability}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{lemma\_3}_{39},\mbox{negated\_conjecture})$

\medskip\textbf{MGT005-1.p} Complexity increases the risk of death due to reorganization.






$\mbox{greater}(a,b) \ \Rightarrow \ a\ne b\qquad\mbox{cnf}(\mbox{mp6\_1}_{26},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \neg\,\mbox{greater}(b,a)\qquad\mbox{cnf}(\mbox{mp6\_2}_{27},\mbox{axiom})$

$( \mbox{greater}(a,b)\mbox{ and }\mbox{greater}(b,c) ) \ \Rightarrow \ \mbox{greater}(a,c)\qquad\mbox{cnf}(\mbox{mp11}_{28},\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{survival\_chance}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp12}_{29},\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{greater}(d,b)\mbox{ and }\mbox{greater}(c,d) ) \ \Rightarrow \ \mbox{organization}(a,d)\qquad\mbox{cnf}(\mbox{mp13}_{30},\mbox{axiom})$

$\mbox{reorganization}(a,b,c) \ \Rightarrow \ \mbox{greater}(c,b)\qquad\mbox{cnf}(\mbox{mp7}_{31},\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{survival\_chance}(a,d,b)\mbox{ and }\mbox{survival\_chance}(a,e,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \mbox{greater}(e,d)\qquad\mbox{cnf}(\mbox{t3\_FOL}_{32},\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization}(a,d,e)\mbox{ and }\mbox{survival\_chance}(a,f,b)\mbox{ and }\mbox{survival\_chance}(a,g,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ ( \mbox{greater}(d,b)\mbox{ or }\mbox{greater}(c,e)\mbox{ or }\mbox{greater}(f,g) )\qquad\mbox{cnf}(\mbox{t4\_FOL}_{33},\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,b)\mbox{ and }\mbox{reorganization}(a,b,f)\mbox{ and }\mbox{reorganization}(c,b,d)\mbox{ and }\mbox{reorganization\_type}(a,g,b)\mbox{ and }\mbox{reorganization\_type}(c,g,b)\mbox{ and }\mbox{complexity}(a,h,b)\mbox{ and }\mbox{complexity}(c,i,b)\mbox{ and }\mbox{greater}(i,h) ) \ \Rightarrow \ \mbox{greater}(d,f)\qquad\mbox{cnf}(\mbox{a10\_FOL}_{34},\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,b)\mbox{ and }\mbox{organization}(a,d)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,b)\mbox{ and }\mbox{survival\_chance}(a,f,b)\mbox{ and }\mbox{survival\_chance}(c,f,b)\mbox{ and }\mbox{reorganization}(a,b,d)\mbox{ and }\mbox{reorganization}(c,b,g)\mbox{ and }\mbox{reorganization\_type}(a,h,b)\mbox{ and }\mbox{reorganization\_type}(c,h,b)\mbox{ and }\mbox{survival\_chance}(a,i,d)\mbox{ and }\mbox{survival\_chance}(c,j,d)\mbox{ and }\mbox{complexity}(a,k,b)\mbox{ and }\mbox{complexity}(c,l,b)\mbox{ and }\mbox{greater}(l,k) ) \ \Rightarrow \ ( \mbox{greater}(i,j)\mbox{ or }i = j )\qquad\mbox{cnf}(\mbox{a11\_FOL}_{35},\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{36},\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{37},\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_{13})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{38},\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_{13})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{39},\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{40},\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_3,\mbox{sk}_5,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{41},\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_2,\mbox{sk}_6,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{42},\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_3,\mbox{sk}_6,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{43},\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_2,\mbox{sk}_{11},\mbox{sk}_{12})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{44},\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_3,\mbox{sk}_{11},\mbox{sk}_{13})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{45},\mbox{negated\_conjecture})$

$\mbox{reorganization\_type}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{46},\mbox{negated\_conjecture})$

$\mbox{reorganization\_type}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{47},\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_2,\mbox{sk}_{12},\mbox{sk}_{13})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{48},\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_2,\mbox{sk}_7,\mbox{sk}_{13})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{49},\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_3,\mbox{sk}_8,\mbox{sk}_{13})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{50},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_2,\mbox{sk}_9,\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{51},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_3,\mbox{sk}_{10},\mbox{sk}_{11})\qquad\mbox{cnf}(\mbox{t5\_FOL}_{52},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_{10},\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t5\_FOL}_{53},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_7,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t5\_FOL}_{54},\mbox{negated\_conjecture})$

\medskip\textbf{MGT060+1.p} Hazard of mortality is lower during periods of immunity

An organization's hazard of mortality is lower during periods in
 which it has immunity than in periods in which it does not.




$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ ( ( \mbox{has\_immunity}(x,t) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{very\_low} )\mbox{ and }( \neg\,\mbox{has\_immunity}(x,t) \ \Rightarrow \ ( ( ( \mbox{is\_aligned}(x,t)\mbox{ and }\mbox{positional\_advantage}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{low} )\mbox{ and }( ( \neg\,\mbox{is\_aligned}(x,t)\mbox{ and }\mbox{positional\_advantage}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{mod}_1 )\mbox{ and }( ( \mbox{is\_aligned}(x,t)\mbox{ and }\neg\,\mbox{positional\_advantage}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{mod}_2 )\mbox{ and }( ( \neg\,\mbox{is\_aligned}(x,t)\mbox{ and }\neg\,\mbox{positional\_advantage}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{high} ) ) ) ) )\qquad\mbox{fof}(\mbox{assumption}_{17},\mbox{axiom})$

$\mbox{greater}(\mbox{high},\mbox{mod}_1)\qquad\mbox{fof}(\mbox{assumption\_18a},\mbox{axiom})$

$\mbox{greater}(\mbox{mod}_1,\mbox{low})\qquad\mbox{fof}(\mbox{assumption\_18b},\mbox{axiom})$

$\mbox{greater}(\mbox{low},\mbox{very\_low})\qquad\mbox{fof}(\mbox{assumption\_18c},\mbox{axiom})$

$\mbox{greater}(\mbox{high},\mbox{mod}_2)\qquad\mbox{fof}(\mbox{assumption\_18d},\mbox{axiom})$

$\mbox{greater}(\mbox{mod}_2,\mbox{low})\qquad\mbox{fof}(\mbox{assumption\_18e},\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{has\_immunity}(x,t_0)\mbox{ and }\neg\,\mbox{has\_immunity}(x,t) ) \ \Rightarrow \ \mbox{greater}(\mbox{hazard\_of\_mortality}(x,t),\mbox{hazard\_of\_mortality}(x,t_0)) )\qquad\mbox{fof}(\mbox{assumption}_3,\mbox{conjecture})$

\medskip\textbf{MGT036+2.p} First movers never outcompete efficient producers.






$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t) ) \ \Rightarrow \ \mbox{subpopulations}(s_2,s_1,e,t) )\qquad\mbox{fof}(\mbox{mp\_symmetry\_of\_subpopulations},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \mbox{in\_environment}(e,t) )\qquad\mbox{fof}(\mbox{mp\_time\_point\_occur},\mbox{axiom})$

$\forall e,s_1,s_2,t{:}\;( ( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{growth\_rate}(s_1,t),0) )\iff \neg\,\mbox{greater}(0,\mbox{growth\_rate}(s_1,t)) )\qquad\mbox{fof}(\mbox{mp\_growth\_rate\_relationships},\mbox{axiom})$

$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t) ) \ \Rightarrow \ ( ( \mbox{greater\_or\_equal}(\mbox{growth\_rate}(s_2,t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(s_1,t)) )\iff \mbox{outcompetes}(s_2,s_1,t) ) )\qquad\mbox{fof}(d_2,\mbox{hypothesis})$

$\mbox{greater}(\mbox{resilience}(\mbox{efficient\_producers}),\mbox{resilience}(\mbox{first\_movers}))\qquad\mbox{fof}(a_2,\mbox{hypothesis})$

$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{in\_environment}(e,t)\mbox{ and }\neg\,\mbox{greater}(0,\mbox{growth\_rate}(s_1,t))\mbox{ and }\mbox{greater}(\mbox{resilience}(s_2),\mbox{resilience}(s_1)) ) \ \Rightarrow \ \neg\,\mbox{greater}(0,\mbox{growth\_rate}(s_2,t)) )\qquad\mbox{fof}(a_{13},\mbox{hypothesis})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \neg\,\mbox{outcompetes}(\mbox{first\_movers},\mbox{efficient\_producers},t) )\qquad\mbox{fof}(\mbox{prove\_t}_5,\mbox{conjecture})$

\medskip\textbf{MGT004+1.p} Attempts at reorganization increase death rates.






$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists r{:}\;\mbox{reliability}(x,r,t) )\qquad\mbox{fof}(\mbox{mp}_1,\mbox{axiom})$

$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists a{:}\;\mbox{accountability}(x,a,t) )\qquad\mbox{fof}(\mbox{mp}_2,\mbox{axiom})$

$\forall x,y,r_1,r_2,a_1,a_2,p_1,p_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reliability}(x,r_1,t_1)\mbox{ and }\mbox{reliability}(y,r_2,t_2)\mbox{ and }\mbox{accountability}(x,a_1,t_1)\mbox{ and }\mbox{accountability}(y,a_2,t_2)\mbox{ and }\mbox{survival\_chance}(x,p_1,t_1)\mbox{ and }\mbox{survival\_chance}(y,p_2,t_2)\mbox{ and }\mbox{greater}(r_2,r_1)\mbox{ and }\mbox{greater}(a_2,a_1) ) \ \Rightarrow \ \mbox{greater}(p_2,p_1) )\qquad\mbox{fof}(\mbox{a1\_FOL},\mbox{hypothesis})$

$\forall x,r_1,r_2,a_1,a_2,t_1,t_2,\mbox{ta},\mbox{tb}{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reliability}(x,r_1,t_1)\mbox{ and }\mbox{reliability}(x,r_2,t_2)\mbox{ and }\mbox{accountability}(x,a_1,t_1)\mbox{ and }\mbox{accountability}(x,a_2,t_2)\mbox{ and }\neg\,\mbox{greater}(\mbox{ta},t_1)\mbox{ and }\mbox{greater}(t_2,t_1)\mbox{ and }\neg\,\mbox{greater}(t_2,\mbox{tb}) ) \ \Rightarrow \ ( \mbox{greater}(r_1,r_2)\mbox{ and }\mbox{greater}(a_1,a_2) ) )\qquad\mbox{fof}(\mbox{a6\_FOL},\mbox{hypothesis})$

$\forall x,p_1,p_2,t_1,t_2,\mbox{ta},\mbox{tb}{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{survival\_chance}(x,p_1,t_1)\mbox{ and }\mbox{survival\_chance}(x,p_2,t_2)\mbox{ and }\neg\,\mbox{greater}(\mbox{ta},t_1)\mbox{ and }\mbox{greater}(t_2,t_1)\mbox{ and }\neg\,\mbox{greater}(t_2,\mbox{tb}) ) \ \Rightarrow \ \mbox{greater}(p_1,p_2) )\qquad\mbox{fof}(\mbox{t4\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT038+1.p} FMs become extinct in stable environments

First movers become extinct past a certain point in time
 in stable environments.




$\mbox{finite\_set}(\mbox{first\_movers})\qquad\mbox{fof}(\mbox{mp7\_first\_movers\_exist},\mbox{axiom})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \mbox{in\_environment}(e,\mbox{appear}(\mbox{first\_movers},e)) )\qquad\mbox{fof}(\mbox{mp\_stable\_first\_movers},\mbox{axiom})$

$\forall s,\mbox{to}{:}\;( ( \mbox{finite\_set}(s)\mbox{ and }\mbox{contracts\_from}(\mbox{to},s) ) \ \Rightarrow \ \exists t_2{:}\;( \mbox{greater}(t_2,\mbox{to})\mbox{ and }\mbox{cardinality\_at\_time}(s,t_2) = 0 ) )\qquad\mbox{fof}(\mbox{mp\_contracting\_time},\mbox{axiom})$

$\forall e,t_1,t_2{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e)\mbox{ and }\mbox{in\_environment}(e,t_1)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \mbox{in\_environment}(e,t_2) )\qquad\mbox{fof}(\mbox{mp\_long\_stable\_environments},\mbox{axiom})$

$\forall x,y,z{:}\;( ( \mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,z) ) \ \Rightarrow \ \mbox{greater}(x,z) )\qquad\mbox{fof}(\mbox{mp\_greater\_transitivity},\mbox{axiom})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{greater}(\mbox{to},\mbox{appear}(\mbox{efficient\_producers},e))\mbox{ and }\mbox{contracts\_from}(\mbox{to},\mbox{first\_movers}) ) )\qquad\mbox{fof}(l_9,\mbox{hypothesis})$

$\forall e{:}\;( \mbox{environment}(e) \ \Rightarrow \ \mbox{greater}(\mbox{appear}(\mbox{efficient\_producers},e),\mbox{appear}(\mbox{first\_movers},e)) )\qquad\mbox{fof}(a_{13},\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\mbox{greater}(\mbox{to},\mbox{appear}(\mbox{first\_movers},e))\mbox{ and }\mbox{cardinality\_at\_time}(\mbox{first\_movers},\mbox{to}) = 0 ) )\qquad\mbox{fof}(\mbox{prove\_t}_7,\mbox{conjecture})$

\medskip\textbf{MGT012-1.p} Complexity of an organization cannot get smaller by age

Complexity of an organization cannot get smaller by age in
 lack of reorganization.




$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{inertia}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp5}_{20},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ a\ne b\qquad\mbox{cnf}(\mbox{mp6\_1}_{21},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \neg\,\mbox{greater}(b,a)\qquad\mbox{cnf}(\mbox{mp6\_2}_{22},\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{class}(a,\mbox{sk}_2(b,a),b)\qquad\mbox{cnf}(\mbox{mp9}_{23},\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{class}(a,d,b)\mbox{ and }\mbox{class}(a,e,c) ) \ \Rightarrow \ d = e\qquad\mbox{cnf}(\mbox{mp10}_{24},\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,d)\mbox{ and }\mbox{complexity}(a,f,b)\mbox{ and }\mbox{complexity}(c,g,d)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,d)\mbox{ and }\mbox{greater}(g,f) ) \ \Rightarrow \ \mbox{greater}(i,h)\qquad\mbox{cnf}(\mbox{a12\_FOL}_{25},\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{inertia}(a,d,b)\mbox{ and }\mbox{inertia}(a,e,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \mbox{greater}(e,d)\qquad\mbox{cnf}(\mbox{t2\_FOL}_{26},\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t12\_FOL}_{27},\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t12\_FOL}_{28},\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_3,\mbox{sk}_6,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t12\_FOL}_{29},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t12\_FOL}_{30},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_3,\mbox{sk}_5,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t12\_FOL}_{31},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_7,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t12\_FOL}_{32},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_4,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t12\_FOL}_{33},\mbox{negated\_conjecture})$

\medskip\textbf{MGT036-2.p} First movers never outcompete efficient producers.






$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d) ) \ \Rightarrow \ \mbox{subpopulations}(c,b,a,d)\qquad\mbox{cnf}(\mbox{mp\_symmetry\_of\_subpopulations}_1,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b) ) \ \Rightarrow \ \mbox{in\_environment}(a,b)\qquad\mbox{cnf}(\mbox{mp\_time\_point\_occur}_2,\mbox{axiom})$

$\mbox{greater}(0,\mbox{growth\_rate}(b,c)) \ \Rightarrow \ \mbox{environment}(a)\qquad\mbox{cnf}(\mbox{mp\_growth\_rate\_relationships}_3,\mbox{axiom})$

$\mbox{greater}(0,\mbox{growth\_rate}(a,d)) \ \Rightarrow \ \mbox{subpopulations}(a,b,c,d)\qquad\mbox{cnf}(\mbox{mp\_growth\_rate\_relationships}_4,\mbox{axiom})$

$\mbox{greater\_or\_equal}(\mbox{growth\_rate}(a,b),0) \ \Rightarrow \ \neg\,\mbox{greater}(0,\mbox{growth\_rate}(a,b))\qquad\mbox{cnf}(\mbox{mp\_growth\_rate\_relationships}_5,\mbox{axiom})$

$( \mbox{environment}(c)\mbox{ and }\mbox{subpopulations}(a,d,c,b) ) \ \Rightarrow \ ( \mbox{greater}(0,\mbox{growth\_rate}(a,b))\mbox{ or }\mbox{greater\_or\_equal}(\mbox{growth\_rate}(a,b),0) )\qquad\mbox{cnf}(\mbox{mp\_growth\_rate\_relationships}_6,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{greater\_or\_equal}(\mbox{growth\_rate}(c,d),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(b,d)) ) \ \Rightarrow \ \mbox{outcompetes}(c,b,d)\qquad\mbox{cnf}(\mbox{d2}_7,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{outcompetes}(c,b,d) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{growth\_rate}(c,d),0)\qquad\mbox{cnf}(\mbox{d2}_8,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{outcompetes}(c,b,d) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(b,d))\qquad\mbox{cnf}(\mbox{d2}_9,\mbox{hypothesis})$

$\mbox{greater}(\mbox{resilience}(\mbox{efficient\_producers}),\mbox{resilience}(\mbox{first\_movers}))\qquad\mbox{cnf}(\mbox{a2}_{10},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{resilience}(d),\mbox{resilience}(c))\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(d,b)) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(c,b))\qquad\mbox{cnf}(\mbox{a13}_{11},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{prove\_t5}_{12},\mbox{negated\_conjecture})$

$\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t5}_{13},\mbox{negated\_conjecture})$

$\mbox{outcompetes}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_t5}_{14},\mbox{negated\_conjecture})$

\medskip\textbf{MGT002+1.p} Structural inertia increases monotonically with age.






$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists \mbox{rp}{:}\;\mbox{reproducibility}(x,\mbox{rp},t) )\qquad\mbox{fof}(\mbox{mp}_3,\mbox{axiom})$

$\forall x,t_1,t_2{:}\;( \mbox{reorganization\_free}(x,t_1,t_2) \ \Rightarrow \ ( \mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(x,t_2,t_2) ) )\qquad\mbox{fof}(\mbox{mp}_4,\mbox{axiom})$

$\forall x,y,t_1,t_2,\mbox{rp}_1,\mbox{rp}_2,i_1,i_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(y,t_2,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(y,\mbox{rp}_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1)\iff \mbox{greater}(i_2,i_1) ) )\qquad\mbox{fof}(\mbox{a3\_FOL},\mbox{hypothesis})$

$\forall x,\mbox{rp}_1,\mbox{rp}_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1) )\qquad\mbox{fof}(\mbox{a4\_FOL},\mbox{hypothesis})$

$\forall x,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(x,i_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{t2\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT035+1.p} EPs outcompete FMs in stable environments

Efficient producers outcompete first movers past a certain
 time in stable environments.




$\forall x,y,z{:}\;( ( \mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,z) ) \ \Rightarrow \ \mbox{greater}(x,z) )\qquad\mbox{fof}(\mbox{mp\_greater\_transitivity},\mbox{axiom})$

$\forall e,t_1,t_2{:}\;( ( \mbox{in\_environment}(e,t_1)\mbox{ and }\mbox{in\_environment}(e,t_2) ) \ \Rightarrow \ ( \mbox{greater}(t_2,t_1)\mbox{ or }t_2 = t_1\mbox{ or }\mbox{greater}(t_1,t_2) ) )\qquad\mbox{fof}(\mbox{mp\_times\_in\_environment},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{greater\_or\_equal}(x,y)\iff ( \mbox{greater}(x,y)\mbox{ or }x = y ) )\qquad\mbox{fof}(\mbox{mp\_greater\_or\_equal},\mbox{axiom})$

$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t) ) \ \Rightarrow \ ( ( \mbox{greater\_or\_equal}(\mbox{growth\_rate}(s_2,t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(s_1,t)) )\iff \mbox{outcompetes}(s_2,s_1,t) ) )\qquad\mbox{fof}(d_2,\mbox{hypothesis})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{equilibrium}(e)) ) \ \Rightarrow \ ( ( \mbox{growth\_rate}(\mbox{first\_movers},t) = 0\mbox{ and }\mbox{growth\_rate}(\mbox{efficient\_producers},t) = 0 )\mbox{ or }( \mbox{greater}(\mbox{growth\_rate}(\mbox{first\_movers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{efficient\_producers},t)) )\mbox{ or }( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(l_6,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(l_1,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists t{:}\;( \mbox{in\_environment}(e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{equilibrium}(e)) ) )\qquad\mbox{fof}(a_4,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{outcompetes}(\mbox{efficient\_producers},\mbox{first\_movers},t) ) ) )\qquad\mbox{fof}(\mbox{prove\_t}_4,\mbox{conjecture})$

\medskip\textbf{MGT009-1.p} Large organization have higher reproducibility






$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{inertia}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp5}_1,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reorganization\_free}(a,b,b)\mbox{ and }\mbox{reorganization\_free}(c,d,d)\mbox{ and }\mbox{reproducibility}(a,e,b)\mbox{ and }\mbox{reproducibility}(c,f,d)\mbox{ and }\mbox{inertia}(a,g,b)\mbox{ and }\mbox{inertia}(c,h,d)\mbox{ and }\mbox{greater}(f,e) ) \ \Rightarrow \ \mbox{greater}(h,g)\qquad\mbox{cnf}(\mbox{a3\_FOL}_2,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reorganization\_free}(a,b,b)\mbox{ and }\mbox{reorganization\_free}(c,d,d)\mbox{ and }\mbox{reproducibility}(a,e,b)\mbox{ and }\mbox{reproducibility}(c,f,d)\mbox{ and }\mbox{inertia}(a,g,b)\mbox{ and }\mbox{inertia}(c,h,d)\mbox{ and }\mbox{greater}(h,g) ) \ \Rightarrow \ \mbox{greater}(f,e)\qquad\mbox{cnf}(\mbox{a3\_FOL}_3,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,d)\mbox{ and }\mbox{size}(a,f,b)\mbox{ and }\mbox{size}(c,g,d)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,d)\mbox{ and }\mbox{greater}(g,f) ) \ \Rightarrow \ \mbox{greater}(i,h)\qquad\mbox{cnf}(\mbox{a5\_FOL}_4,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t9\_FOL}_5,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t9\_FOL}_6,\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_2,\mbox{sk}_9,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t9\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_3,\mbox{sk}_{10},\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t9\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t9\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t9\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{reproducibility}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t9\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{reproducibility}(\mbox{sk}_3,\mbox{sk}_6,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t9\_FOL}_{12},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_2,\mbox{sk}_7,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t9\_FOL}_{13},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_3,\mbox{sk}_8,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t9\_FOL}_{14},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_8,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t9\_FOL}_{15},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_6,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t9\_FOL}_{16},\mbox{negated\_conjecture})$

\medskip\textbf{MGT027+1.p} The FM set contracts in stable environments

The first mover set begins to contract past a certain time
 in stable environments.




$\forall e,\mbox{to}{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e)\mbox{ and }\mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{first\_movers},t),0)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) \ \Rightarrow \ \mbox{contracts\_from}(\mbox{to},\mbox{first\_movers}) )\qquad\mbox{fof}(\mbox{mp\_contracts\_from},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{in\_environment}(e,t)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{first\_movers},t),0)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{efficient\_producers},t),0) ) \ \Rightarrow \ \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) )\qquad\mbox{fof}(\mbox{mp\_non\_empty\_fm\_and\_ep},\mbox{axiom})$

$\forall e,t_1,t_2{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e)\mbox{ and }\mbox{in\_environment}(e,t_1)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \mbox{in\_environment}(e,t_2) )\qquad\mbox{fof}(\mbox{mp\_long\_stable\_environments},\mbox{axiom})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \mbox{in\_environment}(e,\mbox{appear}(\mbox{efficient\_producers},e)) )\qquad\mbox{fof}(\mbox{mp\_EP\_in\_stable\_environments},\mbox{axiom})$

$\forall x,y,z{:}\;( ( \mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,z) ) \ \Rightarrow \ \mbox{greater}(x,z) )\qquad\mbox{fof}(\mbox{mp\_greater\_transitivity},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{greater\_or\_equal}(x,y)\iff ( \mbox{greater}(x,y)\mbox{ or }x = y ) )\qquad\mbox{fof}(\mbox{mp\_greater\_or\_equal},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{in\_environment}(e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{appear}(\mbox{efficient\_producers},e)) ) \ \Rightarrow \ \mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{efficient\_producers},t),0) )\qquad\mbox{fof}(t_6,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{greater}(\mbox{to},\mbox{appear}(\mbox{efficient\_producers},e))\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(l_{10},\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{greater}(\mbox{to},\mbox{appear}(\mbox{efficient\_producers},e))\mbox{ and }\mbox{contracts\_from}(\mbox{to},\mbox{first\_movers}) ) )\qquad\mbox{fof}(\mbox{prove\_l}_9,\mbox{conjecture})$

\medskip\textbf{MGT021-1.p} Difference between disbanding rates does not decrease

The difference between the disbanding rates of first movers
 and efficient producers does not decrease with time.




$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b) ) \ \Rightarrow \ \mbox{in\_environment}(a,b)\qquad\mbox{cnf}(\mbox{mp\_time\_point\_in\_environment}_{27},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b) ) \ \Rightarrow \ \mbox{greater}(\mbox{number\_of\_organizations}(a,b),0)\qquad\mbox{cnf}(\mbox{mp\_environment\_not\_empty}_{28},\mbox{axiom})$

$\mbox{increases}(a) \ \Rightarrow \ \neg\,\mbox{decreases}(a)\qquad\mbox{cnf}(\mbox{mp\_increase\_not\_decrease}_{29},\mbox{axiom})$

$\mbox{greater\_or\_equal}(a,b) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b )\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{30},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{number\_of\_organizations}(a,b),0)\mbox{ and }\mbox{greater}(\mbox{equilibrium}(a),b) ) \ \Rightarrow \ \mbox{decreases}(\mbox{resources}(a,b))\qquad\mbox{cnf}(\mbox{a3}_{31},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{number\_of\_organizations}(a,b),0) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{equilibrium}(a),b)\mbox{ or }\mbox{constant}(\mbox{resources}(a,b)) )\qquad\mbox{cnf}(\mbox{a3}_{32},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\mbox{ and }\mbox{decreases}(\mbox{resources}(a,b)) ) \ \Rightarrow \ \mbox{increases}(\mbox{disbanding\_rate}(\mbox{first\_movers},b)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},b))\qquad\mbox{cnf}(\mbox{l4}_{33},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\mbox{ and }\mbox{constant}(\mbox{resources}(a,b)) ) \ \Rightarrow \ \neg\,\mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},b)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},b))\qquad\mbox{cnf}(\mbox{l4}_{34},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{prove\_l3}_{35},\mbox{negated\_conjecture})$

$\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_l3}_{36},\mbox{negated\_conjecture})$

$\mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l3}_{37},\mbox{negated\_conjecture})$

\medskip\textbf{MGT050-1.p} Unendowed organization's hazard of mortality increases with age

An unendowed organization's hazard of mortality increases with
 its age.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,b) ) \ \Rightarrow \ \mbox{has\_endowment}(a)\qquad\mbox{cnf}(\mbox{assumption\_1}_{41},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{capability}(a,c),\mbox{capability}(a,b))\mbox{ and }\mbox{greater\_or\_equal}(\mbox{position}(a,c),\mbox{position}(a,b)) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{has\_immunity}(a,c)\mbox{ or }\mbox{smaller}(\mbox{hazard\_of\_mortality}(a,c),\mbox{hazard\_of\_mortality}(a,b)) )\qquad\mbox{cnf}(\mbox{assumption\_4}_{42},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater\_or\_equal}(\mbox{capability}(a,c),\mbox{capability}(a,b))\mbox{ and }\mbox{greater}(\mbox{position}(a,c),\mbox{position}(a,b)) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{has\_immunity}(a,c)\mbox{ or }\mbox{smaller}(\mbox{hazard\_of\_mortality}(a,c),\mbox{hazard\_of\_mortality}(a,b)) )\qquad\mbox{cnf}(\mbox{assumption\_4}_{43},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{capability}(a,c) = \mbox{capability}(a,b)\mbox{ and }\mbox{position}(a,c) = \mbox{position}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{has\_immunity}(a,c)\mbox{ or }\mbox{hazard\_of\_mortality}(a,c) = \mbox{hazard\_of\_mortality}(a,b) )\qquad\mbox{cnf}(\mbox{assumption\_4}_{44},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{capability}(a,b),\mbox{capability}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_5}_{45},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\mbox{ and }\mbox{greater}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{capability}(a,b),\mbox{capability}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_5}_{46},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{stock\_of\_knowledge}(a,b) = \mbox{stock\_of\_knowledge}(a,c)\mbox{ and }\mbox{internal\_friction}(a,b) = \mbox{internal\_friction}(a,c) ) \ \Rightarrow \ \mbox{capability}(a,b) = \mbox{capability}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_5}_{47},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{external\_ties}(a,b),\mbox{external\_ties}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{position}(a,b),\mbox{position}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_6}_{48},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{external\_ties}(a,b) = \mbox{external\_ties}(a,c) ) \ \Rightarrow \ \mbox{position}(a,b) = \mbox{position}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_6}_{49},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ \mbox{stock\_of\_knowledge}(a,b) = \mbox{stock\_of\_knowledge}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_10}_{50},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ \mbox{external\_ties}(a,b) = \mbox{external\_ties}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_11}_{51},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{age}(a,b),\mbox{age}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_12}_{52},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{theorem\_3}_{53},\mbox{negated\_conjecture})$

$\neg\,\mbox{has\_endowment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{theorem\_3}_{54},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{age}(\mbox{sk}_1,\mbox{sk}_3),\mbox{age}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{theorem\_3}_{55},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_3),\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{theorem\_3}_{56},\mbox{negated\_conjecture})$

\medskip\textbf{MGT058+1.p} An organization's position cannot be both fragile and robust






$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x{:}\;( \mbox{fragile\_position}(x)\iff \forall t{:}\;( ( \mbox{smaller\_or\_equal}(\mbox{age}(x,t),\mbox{sigma}) \ \Rightarrow \ \mbox{positional\_advantage}(x,t) )\mbox{ and }( \mbox{greater}(\mbox{age}(x,t),\mbox{sigma}) \ \Rightarrow \ \neg\,\mbox{positional\_advantage}(x,t) ) ) )\qquad\mbox{fof}(\mbox{definition}_3,\mbox{axiom})$

$\forall x{:}\;( \mbox{robust\_position}(x)\iff \forall t{:}\;( ( \mbox{smaller\_or\_equal}(\mbox{age}(x,t),\mbox{tau}) \ \Rightarrow \ \neg\,\mbox{positional\_advantage}(x,t) )\mbox{ and }( \mbox{greater}(\mbox{age}(x,t),\mbox{tau}) \ \Rightarrow \ \mbox{positional\_advantage}(x,t) ) ) )\qquad\mbox{fof}(\mbox{definition}_4,\mbox{axiom})$

$\forall x{:}\;( ( \mbox{organization}(x)\mbox{ and }\exists t_0{:}\;\mbox{age}(x,t_0) = 0\mbox{ and }\mbox{greater\_or\_equal}(\mbox{sigma},0)\mbox{ and }\mbox{greater\_or\_equal}(\mbox{tau},0) ) \ \Rightarrow \ \neg\,\mbox{fragile\_position}(x)\mbox{ and }\mbox{robust\_position}(x) )\qquad\mbox{fof}(\mbox{lemma}_{10},\mbox{conjecture})$

\medskip\textbf{MGT014+1.p} If orgainzation size increases, its complexity cannot decrease

If the size of an organization gets bigger, its complexity
 cannot get smaller (in lack of reorganization).




$\forall x,y{:}\;\neg\,\mbox{greater}(x,y)\mbox{ and }x = y\qquad\mbox{fof}(\mbox{mp6}_1,\mbox{axiom})$

$\forall x,y{:}\;\neg\,\mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,x)\qquad\mbox{fof}(\mbox{mp6}_2,\mbox{axiom})$

$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \mbox{time}(t) )\qquad\mbox{fof}(\mbox{mp}_{15},\mbox{axiom})$

$\forall t_1,t_2{:}\;( ( \mbox{time}(t_1)\mbox{ and }\mbox{time}(t_2) ) \ \Rightarrow \ ( \mbox{greater}(t_1,t_2)\mbox{ or }t_1 = t_2\mbox{ or }\mbox{greater}(t_2,t_1) ) )\qquad\mbox{fof}(\mbox{mp}_{16},\mbox{axiom})$

$\forall x,t_1,t_2{:}\;( \mbox{reorganization\_free}(x,t_1,t_2) \ \Rightarrow \ \mbox{reorganization\_free}(x,t_2,t_1) )\qquad\mbox{fof}(\mbox{mp}_{17},\mbox{axiom})$

$\forall x,s_1,s_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(x,s_2,t_2)\mbox{ and }t_1 = t_2 ) \ \Rightarrow \ s_1 = s_2 )\qquad\mbox{fof}(\mbox{mp}_{19},\mbox{axiom})$

$\forall x,s_1,s_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(x,s_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \neg\,\mbox{greater}(s_1,s_2) )\qquad\mbox{fof}(\mbox{t11\_FOL},\mbox{hypothesis})$

$\forall x,c_1,c_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{complexity}(x,c_1,t_1)\mbox{ and }\mbox{complexity}(x,c_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \neg\,\mbox{greater}(c_1,c_2) )\qquad\mbox{fof}(\mbox{t12\_FOL},\mbox{hypothesis})$

$\forall x,c_1,c_2,s_1,s_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{complexity}(x,c_1,t_1)\mbox{ and }\mbox{complexity}(x,c_2,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(x,s_2,t_2)\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \neg\,\mbox{greater}(c_1,c_2) )\qquad\mbox{fof}(\mbox{t14\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT049-1.p} Structural position does not vary with its age

An organization's structural position does not vary with its age.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{external\_ties}(a,b),\mbox{external\_ties}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{position}(a,b),\mbox{position}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_6}_{30},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{external\_ties}(a,b) = \mbox{external\_ties}(a,c) ) \ \Rightarrow \ \mbox{position}(a,b) = \mbox{position}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_6}_{31},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ \mbox{external\_ties}(a,b) = \mbox{external\_ties}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_11}_{32},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{lemma\_6}_{33},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{age}(\mbox{sk}_1,\mbox{sk}_3),\mbox{age}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{lemma\_6}_{34},\mbox{negated\_conjecture})$

$\mbox{position}(\mbox{sk}_1,\mbox{sk}_3)\ne \mbox{position}(\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{lemma\_6}_{35},\mbox{negated\_conjecture})$

\medskip\textbf{MGT021+1.p} Difference between disbanding rates does not decrease

The difference between the disbanding rates of first movers
 and efficient producers does not decrease with time.




$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \mbox{in\_environment}(e,t) )\qquad\mbox{fof}(\mbox{mp\_time\_point\_in\_environment},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \mbox{greater}(\mbox{number\_of\_organizations}(e,t),0) )\qquad\mbox{fof}(\mbox{mp\_environment\_not\_empty},\mbox{axiom})$

$\forall x{:}\;( \mbox{increases}(x) \ \Rightarrow \ \neg\,\mbox{decreases}(x) )\qquad\mbox{fof}(\mbox{mp\_increase\_not\_decrease},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{greater\_or\_equal}(x,y) \ \Rightarrow \ ( \mbox{greater}(x,y)\mbox{ or }x = y ) )\qquad\mbox{fof}(\mbox{mp\_greater\_or\_equal},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{in\_environment}(e,t)\mbox{ and }\mbox{greater}(\mbox{number\_of\_organizations}(e,t),0) ) \ \Rightarrow \ ( ( \mbox{greater}(\mbox{equilibrium}(e),t) \ \Rightarrow \ \mbox{decreases}(\mbox{resources}(e,t)) )\mbox{ and }( \neg\,\mbox{greater}(\mbox{equilibrium}(e),t) \ \Rightarrow \ \mbox{constant}(\mbox{resources}(e,t)) ) ) )\qquad\mbox{fof}(a_3,\mbox{hypothesis})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ ( ( \mbox{decreases}(\mbox{resources}(e,t)) \ \Rightarrow \ \mbox{increases}(\mbox{disbanding\_rate}(\mbox{first\_movers},t)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},t)) )\mbox{ and }( \mbox{constant}(\mbox{resources}(e,t)) \ \Rightarrow \ \neg\,\mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},t)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},t)) ) ) )\qquad\mbox{fof}(l_4,\mbox{hypothesis})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \neg\,\mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},t)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},t)) )\qquad\mbox{fof}(\mbox{prove\_l}_3,\mbox{conjecture})$

\medskip\textbf{MGT001-1.p} Selection favors organizations with high inertia

Selection within populations of organizations in modern
 societies favours organizations whose structure have high
 inertia.




$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{reliability}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp1}_1,\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{accountability}(a,\mbox{sk}_2(b,a),b)\qquad\mbox{cnf}(\mbox{mp2}_2,\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{reproducibility}(a,\mbox{sk}_3(b,a),b)\qquad\mbox{cnf}(\mbox{mp3}_3,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{survival\_chance}(a,i,b)\mbox{ and }\mbox{survival\_chance}(c,j,d)\mbox{ and }\mbox{greater}(f,e)\mbox{ and }\mbox{greater}(h,g) ) \ \Rightarrow \ \mbox{greater}(j,i)\qquad\mbox{cnf}(\mbox{a1\_FOL}_4,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(j,i) ) \ \Rightarrow \ \mbox{greater}(f,e)\qquad\mbox{cnf}(\mbox{a2\_FOL}_5,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(j,i) ) \ \Rightarrow \ \mbox{greater}(h,g)\qquad\mbox{cnf}(\mbox{a2\_FOL}_6,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{reproducibility}(a,i,b)\mbox{ and }\mbox{reproducibility}(c,j,d)\mbox{ and }\mbox{greater}(f,e)\mbox{ and }\mbox{greater}(h,g) ) \ \Rightarrow \ \mbox{greater}(j,i)\qquad\mbox{cnf}(\mbox{a2\_FOL}_7,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reorganization\_free}(a,b,b)\mbox{ and }\mbox{reorganization\_free}(c,d,d)\mbox{ and }\mbox{reproducibility}(a,e,b)\mbox{ and }\mbox{reproducibility}(c,f,d)\mbox{ and }\mbox{inertia}(a,g,b)\mbox{ and }\mbox{inertia}(c,h,d)\mbox{ and }\mbox{greater}(f,e) ) \ \Rightarrow \ \mbox{greater}(h,g)\qquad\mbox{cnf}(\mbox{a3\_FOL}_8,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reorganization\_free}(a,b,b)\mbox{ and }\mbox{reorganization\_free}(c,d,d)\mbox{ and }\mbox{reproducibility}(a,e,b)\mbox{ and }\mbox{reproducibility}(c,f,d)\mbox{ and }\mbox{inertia}(a,g,b)\mbox{ and }\mbox{inertia}(c,h,d)\mbox{ and }\mbox{greater}(h,g) ) \ \Rightarrow \ \mbox{greater}(f,e)\qquad\mbox{cnf}(\mbox{a3\_FOL}_9,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_4,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t1\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_5,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t1\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_4,\mbox{sk}_6,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t1\_FOL}_{12},\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_5,\mbox{sk}_7,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t1\_FOL}_{13},\mbox{negated\_conjecture})$

$\mbox{inertia}(\mbox{sk}_4,\mbox{sk}_8,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t1\_FOL}_{14},\mbox{negated\_conjecture})$

$\mbox{inertia}(\mbox{sk}_5,\mbox{sk}_9,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t1\_FOL}_{15},\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_4,\mbox{sk}_{10},\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t1\_FOL}_{16},\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_5,\mbox{sk}_{11},\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t1\_FOL}_{17},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_9,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t1\_FOL}_{18},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_{11},\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t1\_FOL}_{19},\mbox{negated\_conjecture})$

\medskip\textbf{MGT054+1.p} Hazard of mortality increases in a drifting environment

An unendowed organization's hazard of mortality increases with
 age in a drifting environment.




$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\neg\,\mbox{has\_endowment}(x) ) \ \Rightarrow \ \neg\,\mbox{has\_immunity}(x,t) )\qquad\mbox{fof}(\mbox{assumption}_1,\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{has\_immunity}(x,t_0)\mbox{ and }\neg\,\mbox{has\_immunity}(x,t) ) \ \Rightarrow \ \mbox{greater}(\mbox{hazard\_of\_mortality}(x,t),\mbox{hazard\_of\_mortality}(x,t_0)) )\qquad\mbox{fof}(\mbox{assumption}_3,\mbox{axiom})$

$\forall x,t_0,t{:}\;( \mbox{dissimilar}(x,t_0,t)\iff ( \mbox{organization}(x)\mbox{ and }\neg\,\mbox{is\_aligned}(x,t_0)\iff \mbox{is\_aligned}(x,t) ) )\qquad\mbox{fof}(\mbox{definition}_2,\mbox{axiom})$

$\forall x,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{age}(x,t) = 0 ) \ \Rightarrow \ \mbox{is\_aligned}(x,t) )\qquad\mbox{fof}(\mbox{assumption}_{13},\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{is\_aligned}(x,t_0)\mbox{ and }\neg\,\mbox{is\_aligned}(x,t) ) \ \Rightarrow \ \mbox{greater}(\mbox{capability}(x,t_0),\mbox{capability}(x,t)) )\qquad\mbox{fof}(\mbox{assumption}_{14},\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{age}(x,t_0) = 0 ) \ \Rightarrow \ ( \mbox{greater}(\mbox{age}(x,t),\mbox{sigma})\iff \mbox{dissimilar}(x,t_0,t) ) )\qquad\mbox{fof}(\mbox{assumption}_{15},\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\neg\,\mbox{has\_immunity}(x,t_0)\mbox{ and }\neg\,\mbox{has\_immunity}(x,t)\mbox{ and }\mbox{greater}(\mbox{capability}(x,t),\mbox{capability}(x,t_0)) ) \ \Rightarrow \ \mbox{greater}(\mbox{hazard\_of\_mortality}(x,t_0),\mbox{hazard\_of\_mortality}(x,t)) )\qquad\mbox{fof}(\mbox{assumption}_{16},\mbox{axiom})$

$\forall x,t_0,t_1,t_2{:}\;( ( \mbox{organization}(x)\mbox{ and }\neg\,\mbox{has\_endowment}(x)\mbox{ and }\mbox{age}(x,t_0) = 0\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{age}(x,t_1),\mbox{sigma})\mbox{ and }\mbox{greater}(\mbox{age}(x,t_2),\mbox{sigma})\mbox{ and }\mbox{greater}(\mbox{sigma},0) ) \ \Rightarrow \ \mbox{greater}(\mbox{hazard\_of\_mortality}(x,t_2),\mbox{hazard\_of\_mortality}(x,t_1)) )\qquad\mbox{fof}(\mbox{theorem}_5,\mbox{conjecture})$

\medskip\textbf{MGT024+1.p} Subpopulation growth rates are in equilibria

If a subpopulation has positive growth rate, then the other
 subpopulation must have negative growth rate in equilibrium.




$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \mbox{in\_environment}(e,t) )\qquad\mbox{fof}(\mbox{mp\_time\_point\_occur},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \mbox{greater}(\mbox{number\_of\_organizations}(e,t),0) )\qquad\mbox{fof}(\mbox{mp\_positive\_number\_of\_organizations},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{equilibrium}(e)) ) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{equilibrium}(e),t) )\qquad\mbox{fof}(\mbox{mp\_equilibrium},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{in\_environment}(e,t)\mbox{ and }\mbox{greater}(\mbox{number\_of\_organizations}(e,t),0) ) \ \Rightarrow \ ( ( \mbox{greater}(\mbox{equilibrium}(e),t) \ \Rightarrow \ \mbox{decreases}(\mbox{resources}(e,t)) )\mbox{ and }( \neg\,\mbox{greater}(\mbox{equilibrium}(e),t) \ \Rightarrow \ \mbox{constant}(\mbox{resources}(e,t)) ) ) )\qquad\mbox{fof}(a_3,\mbox{hypothesis})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{in\_environment}(e,t) ) \ \Rightarrow \ ( ( \mbox{decreases}(\mbox{resources}(e,t)) \ \Rightarrow \ \neg\,\mbox{decreases}(\mbox{number\_of\_organizations}(e,t)) )\mbox{ and }( \mbox{constant}(\mbox{resources}(e,t)) \ \Rightarrow \ \mbox{constant}(\mbox{number\_of\_organizations}(e,t)) ) ) )\qquad\mbox{fof}(a_6,\mbox{hypothesis})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{constant}(\mbox{number\_of\_organizations}(e,t)) ) \ \Rightarrow \ ( ( \mbox{growth\_rate}(\mbox{first\_movers},t) = 0\mbox{ and }\mbox{growth\_rate}(\mbox{efficient\_producers},t) = 0 )\mbox{ or }( \mbox{greater}(\mbox{growth\_rate}(\mbox{first\_movers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{efficient\_producers},t)) )\mbox{ or }( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(l_7,\mbox{hypothesis})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(t,\mbox{equilibrium}(e)) ) \ \Rightarrow \ ( ( \mbox{growth\_rate}(\mbox{first\_movers},t) = 0\mbox{ and }\mbox{growth\_rate}(\mbox{efficient\_producers},t) = 0 )\mbox{ or }( \mbox{greater}(\mbox{growth\_rate}(\mbox{first\_movers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{efficient\_producers},t)) )\mbox{ or }( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(\mbox{prove\_l}_6,\mbox{conjecture})$

\medskip\textbf{MGT003+1.p} Organizational death rates decrease with age.






$\forall x,t_1,t_2{:}\;( \mbox{reorganization\_free}(x,t_1,t_2) \ \Rightarrow \ ( \mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(x,t_2,t_2) ) )\qquad\mbox{fof}(\mbox{mp}_4,\mbox{axiom})$

$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists i{:}\;\mbox{inertia}(x,i,t) )\qquad\mbox{fof}(\mbox{mp}_5,\mbox{axiom})$

$\forall x,y,t_1,t_2,i_1,i_2,p_1,p_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(y,t_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{survival\_chance}(x,p_1,t_1)\mbox{ and }\mbox{survival\_chance}(y,p_2,t_2)\mbox{ and }\mbox{greater}(i_2,i_1) ) \ \Rightarrow \ \mbox{greater}(p_2,p_1) )\qquad\mbox{fof}(\mbox{t1\_FOL},\mbox{hypothesis})$

$\forall x,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(x,i_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{t2\_FOL},\mbox{hypothesis})$

$\forall x,p_1,p_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{survival\_chance}(x,p_1,t_1)\mbox{ and }\mbox{survival\_chance}(x,p_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \mbox{greater}(p_2,p_1) )\qquad\mbox{fof}(\mbox{t3\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT036+1.p} First movers never outcompete efficient producers.






$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \mbox{subpopulations}(\mbox{efficient\_producers},\mbox{first\_movers},e,t) )\qquad\mbox{fof}(\mbox{mp\_symmetry\_of\_FM\_and\_EP},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \mbox{in\_environment}(e,t) )\qquad\mbox{fof}(\mbox{mp\_time\_point\_occur},\mbox{axiom})$

$\forall e,s_1,s_2,t{:}\;( ( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{growth\_rate}(s_1,t),0) )\iff \neg\,\mbox{greater}(0,\mbox{growth\_rate}(s_1,t)) )\qquad\mbox{fof}(\mbox{mp\_growth\_rate\_relationships},\mbox{axiom})$

$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t) ) \ \Rightarrow \ ( ( \mbox{greater\_or\_equal}(\mbox{growth\_rate}(s_2,t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(s_1,t)) )\iff \mbox{outcompetes}(s_2,s_1,t) ) )\qquad\mbox{fof}(d_2,\mbox{hypothesis})$

$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{in\_environment}(e,t)\mbox{ and }\neg\,\mbox{greater}(0,\mbox{growth\_rate}(s_1,t))\mbox{ and }\mbox{greater}(\mbox{resilience}(s_2),\mbox{resilience}(s_1)) ) \ \Rightarrow \ \neg\,\mbox{greater}(0,\mbox{growth\_rate}(s_2,t)) )\qquad\mbox{fof}(a_{12},\mbox{hypothesis})$

$\mbox{greater}(\mbox{resilience}(\mbox{efficient\_producers}),\mbox{resilience}(\mbox{first\_movers}))\qquad\mbox{fof}(a_2,\mbox{hypothesis})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ \neg\,\mbox{outcompetes}(\mbox{first\_movers},\mbox{efficient\_producers},t) )\qquad\mbox{fof}(\mbox{prove\_t}_5,\mbox{conjecture})$

\medskip\textbf{MGT031+1.p} First movers appear first in an environment






$\forall e{:}\;( \mbox{environment}(e) \ \Rightarrow \ \mbox{greater}(\mbox{number\_of\_organizations}(e,\mbox{appear}(\mbox{an\_organisation},e)),0) )\qquad\mbox{fof}(\mbox{mp\_positive\_number\_when\_appear},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{greater}(\mbox{number\_of\_organizations}(e,t),0) ) \ \Rightarrow \ \exists s{:}\;( \mbox{subpopulation}(s,e,t)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(s,t),0) ) )\qquad\mbox{fof}(\mbox{mp\_number\_mean\_non\_empty},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{in\_environment}(e,t)\mbox{ and }\mbox{greater}(\mbox{appear}(\mbox{efficient\_producers},e),t) ) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{efficient\_producers},t),0) )\qquad\mbox{fof}(\mbox{mp\_no\_EP\_before\_appearance},\mbox{axiom})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{in\_environment}(e,t)\mbox{ and }\mbox{greater}(\mbox{appear}(\mbox{first\_movers},e),t) ) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{first\_movers},t),0) )\qquad\mbox{fof}(\mbox{mp\_no\_FM\_before\_appearance},\mbox{axiom})$

$\forall e{:}\;( \mbox{environment}(e) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{appear}(\mbox{first\_movers},e),\mbox{appear}(\mbox{an\_organisation},e)) )\qquad\mbox{fof}(\mbox{mp\_FM\_not\_precede\_first},\mbox{axiom})$

$\forall x,y,z{:}\;( ( \mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,z) ) \ \Rightarrow \ \mbox{greater}(x,z) )\qquad\mbox{fof}(\mbox{mp\_greater\_transitivity},\mbox{axiom})$

$\forall x,y{:}\;( \mbox{greater\_or\_equal}(x,y)\iff ( \mbox{greater}(x,y)\mbox{ or }x = y ) )\qquad\mbox{fof}(\mbox{mp\_greater\_or\_equal},\mbox{axiom})$

$\forall e,x,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulation}(x,e,t)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(x,t),0) ) \ \Rightarrow \ ( x = \mbox{efficient\_producers}\mbox{ or }x = \mbox{first\_movers} ) )\qquad\mbox{fof}(a_9,\mbox{hypothesis})$

$\forall e{:}\;( \mbox{environment}(e) \ \Rightarrow \ \mbox{greater}(\mbox{appear}(\mbox{efficient\_producers},e),\mbox{appear}(\mbox{first\_movers},e)) )\qquad\mbox{fof}(a_{13},\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{in\_environment}(e,\mbox{appear}(\mbox{an\_organisation},e)) ) \ \Rightarrow \ \mbox{appear}(\mbox{an\_organisation},e) = \mbox{appear}(\mbox{first\_movers},e) )\qquad\mbox{fof}(\mbox{prove\_l}_{13},\mbox{conjecture})$

\medskip\textbf{MGT016-1.p} More complex organizations have shorter reorganization

The more complex an organization is at the beginning of
 reorganization, the sooner disbanding due to reorganization
 (possibly) happens - i.e., the shorter is the reorganization.




$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{inertia}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp5}_1,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,d)\mbox{ and }\mbox{complexity}(a,f,b)\mbox{ and }\mbox{complexity}(c,g,d)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,d)\mbox{ and }\mbox{greater}(g,f) ) \ \Rightarrow \ \mbox{greater}(i,h)\qquad\mbox{cnf}(\mbox{a12\_FOL}_2,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,b)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,b)\mbox{ and }\mbox{reorganization}(a,b,f)\mbox{ and }\mbox{reorganization}(c,b,d)\mbox{ and }\mbox{reorganization\_type}(a,g,b)\mbox{ and }\mbox{reorganization\_type}(c,g,b)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,b)\mbox{ and }\mbox{greater}(i,h) ) \ \Rightarrow \ ( \mbox{organization}(c,d)\mbox{ or }\mbox{greater}(f,d) )\qquad\mbox{cnf}(\mbox{a14\_FOL}_3,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t16\_FOL}_4,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t16\_FOL}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{organization}(\mbox{sk}_3,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t16\_FOL}_6,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t16\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_3,\mbox{sk}_5,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t16\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_2,\mbox{sk}_8,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t16\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_3,\mbox{sk}_8,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t16\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{reorganization\_type}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t16\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{reorganization\_type}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t16\_FOL}_{12},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_2,\mbox{sk}_6,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t16\_FOL}_{13},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_3,\mbox{sk}_7,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t16\_FOL}_{14},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_7,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t16\_FOL}_{15},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_9,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t16\_FOL}_{16},\mbox{negated\_conjecture})$

\medskip\textbf{MGT028-1.p} FMs have a negative growth rate in stable environments

First movers have negative growth rate past a certain point
 of time (also after the appearence of efficient producers)
 in stable environments.




$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,\mbox{sk}_1(b,a))\mbox{ or }\mbox{greater}(\mbox{sk}_2(a),\mbox{appear}(\mbox{efficient\_producers},a)) )\qquad\mbox{cnf}(\mbox{mp\_first\_movers\_negative\_growth}_1,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ ( \mbox{greater\_or\_equal}(\mbox{sk}_1(b,a),b)\mbox{ or }\mbox{greater}(\mbox{sk}_2(a),\mbox{appear}(\mbox{efficient\_producers},a)) )\qquad\mbox{cnf}(\mbox{mp\_first\_movers\_negative\_growth}_2,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,c)\mbox{ and }\mbox{greater\_or\_equal}(c,\mbox{sk}_2(a)) ) \ \Rightarrow \ ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,\mbox{sk}_1(b,a))\mbox{ or }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},c)) )\qquad\mbox{cnf}(\mbox{mp\_first\_movers\_negative\_growth}_3,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,c)\mbox{ and }\mbox{greater\_or\_equal}(c,\mbox{sk}_2(a)) ) \ \Rightarrow \ ( \mbox{greater\_or\_equal}(\mbox{sk}_1(b,a),b)\mbox{ or }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},c)) )\qquad\mbox{cnf}(\mbox{mp\_first\_movers\_negative\_growth}_4,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_1(b,a))) ) \ \Rightarrow \ \mbox{greater}(\mbox{sk}_2(a),\mbox{appear}(\mbox{efficient\_producers},a))\qquad\mbox{cnf}(\mbox{mp\_first\_movers\_negative\_growth}_5,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_1(b,a)))\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,c)\mbox{ and }\mbox{greater\_or\_equal}(c,\mbox{sk}_2(a)) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},c))\qquad\mbox{cnf}(\mbox{mp\_first\_movers\_negative\_growth}_6,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{sk}_3(a))\qquad\mbox{cnf}(\mbox{l11}_7,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{sk}_3(a)) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},b),0)\qquad\mbox{cnf}(\mbox{l11}_8,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{sk}_3(a)) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},b))\qquad\mbox{cnf}(\mbox{l11}_9,\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_4)\qquad\mbox{cnf}(\mbox{prove\_l10}_{10},\mbox{negated\_conjecture})$

$\mbox{stable}(\mbox{sk}_4)\qquad\mbox{cnf}(\mbox{prove\_l10}_{11},\mbox{negated\_conjecture})$

$\mbox{greater}(a,\mbox{appear}(\mbox{efficient\_producers},\mbox{sk}_4)) \ \Rightarrow \ \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_4,\mbox{sk}_5(a))\qquad\mbox{cnf}(\mbox{prove\_l10}_{12},\mbox{negated\_conjecture})$

$\mbox{greater}(a,\mbox{appear}(\mbox{efficient\_producers},\mbox{sk}_4)) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{sk}_5(a),a)\qquad\mbox{cnf}(\mbox{prove\_l10}_{13},\mbox{negated\_conjecture})$

$\mbox{greater}(a,\mbox{appear}(\mbox{efficient\_producers},\mbox{sk}_4)) \ \Rightarrow \ \neg\,\mbox{greater}(0,\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_5(a)))\qquad\mbox{cnf}(\mbox{prove\_l10}_{14},\mbox{negated\_conjecture})$

\medskip\textbf{MGT039-1.p} Selection favours EPs above Fms if change is slow

Selection favors efficient producers above first movers if
 environmental change is slow.




$( \mbox{observational\_period}(a)\mbox{ and }\mbox{propagation\_strategy}(\mbox{first\_movers})\mbox{ and }\mbox{propagation\_strategy}(\mbox{efficient\_producers}) ) \ \Rightarrow \ ( \mbox{environment}(\mbox{sk}_1(a))\mbox{ or }\mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},a) )\qquad\mbox{cnf}(\mbox{mp3\_favoured\_trategy}_{20},\mbox{axiom})$

$( \mbox{observational\_period}(a)\mbox{ and }\mbox{propagation\_strategy}(\mbox{first\_movers})\mbox{ and }\mbox{propagation\_strategy}(\mbox{efficient\_producers}) ) \ \Rightarrow \ ( \mbox{in\_environment}(a,\mbox{sk}_1(a))\mbox{ or }\mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},a) )\qquad\mbox{cnf}(\mbox{mp3\_favoured\_trategy}_{21},\mbox{axiom})$

$( \mbox{observational\_period}(a)\mbox{ and }\mbox{propagation\_strategy}(\mbox{first\_movers})\mbox{ and }\mbox{propagation\_strategy}(\mbox{efficient\_producers})\mbox{ and }\mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},\mbox{end\_time}(\mbox{sk}_1(a))) ) \ \Rightarrow \ \mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},a)\qquad\mbox{cnf}(\mbox{mp3\_favoured\_trategy}_{22},\mbox{axiom})$

$( \mbox{observational\_period}(a)\mbox{ and }\mbox{slow\_change}(a)\mbox{ and }\mbox{environment}(b)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ \mbox{in\_environment}(b,\mbox{sk}_2(b,a))\qquad\mbox{cnf}(\mbox{mp4\_critical\_point}_{23},\mbox{axiom})$

$( \mbox{observational\_period}(a)\mbox{ and }\mbox{slow\_change}(a)\mbox{ and }\mbox{environment}(b)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ \mbox{greater}(\mbox{sk}_2(b,a),\mbox{critical\_point}(b))\qquad\mbox{cnf}(\mbox{mp4\_critical\_point}_{24},\mbox{axiom})$

$\mbox{propagation\_strategy}(\mbox{first\_movers})\qquad\mbox{cnf}(\mbox{mp\_organizational\_sets1}_{25},\mbox{axiom})$

$\mbox{propagation\_strategy}(\mbox{efficient\_producers})\qquad\mbox{cnf}(\mbox{mp\_organizational\_sets2}_{26},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{start\_time}(a))\mbox{ and }\mbox{greater\_or\_equal}(\mbox{end\_time}(a),b) ) \ \Rightarrow \ \mbox{in\_environment}(a,b)\qquad\mbox{cnf}(\mbox{mp\_time\_in\_environment}_{27},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{end\_time}(a),b)\qquad\mbox{cnf}(\mbox{mp\_environment\_end\_point}_{28},\mbox{axiom})$

$\mbox{environment}(a) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{critical\_point}(a),\mbox{start\_time}(a))\qquad\mbox{cnf}(\mbox{mp\_time\_of\_critical\_point}_{29},\mbox{axiom})$

$( \mbox{greater}(a,b)\mbox{ and }\mbox{greater}(b,c) ) \ \Rightarrow \ \mbox{greater}(a,c)\qquad\mbox{cnf}(\mbox{mp\_greater\_transitivity}_{30},\mbox{axiom})$

$\mbox{greater\_or\_equal}(a,b) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b )\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{31},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \mbox{greater\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{32},\mbox{axiom})$

$a = b \ \Rightarrow \ \mbox{greater\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{33},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater}(b,\mbox{start\_time}(a)) ) \ \Rightarrow \ ( \mbox{greater}(b,\mbox{end\_time}(a))\mbox{ or }\mbox{greater\_or\_equal}(\mbox{end\_time}(a),b) )\qquad\mbox{cnf}(\mbox{mp\_beginning\_and\_ending}_{34},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(b,\mbox{critical\_point}(a)) ) \ \Rightarrow \ \mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},b)\qquad\mbox{cnf}(\mbox{l8}_{35},\mbox{hypothesis})$

$\mbox{observational\_period}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_t8}_{36},\mbox{negated\_conjecture})$

$\mbox{slow\_change}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_t8}_{37},\mbox{negated\_conjecture})$

$\neg\,\mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_t8}_{38},\mbox{negated\_conjecture})$

\medskip\textbf{MGT006+1.p} Reliability and accountability increase with time.






$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists \mbox{rp}{:}\;\mbox{reproducibility}(x,\mbox{rp},t) )\qquad\mbox{fof}(\mbox{mp}_3,\mbox{axiom})$

$\forall x,y,t_1,t_2,r_1,r_2,a_1,a_2,\mbox{rp}_1,\mbox{rp}_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reliability}(x,r_1,t_1)\mbox{ and }\mbox{reliability}(y,r_2,t_2)\mbox{ and }\mbox{accountability}(x,a_1,t_1)\mbox{ and }\mbox{accountability}(y,a_2,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(y,\mbox{rp}_2,t_2) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1)\iff ( \mbox{greater}(r_2,r_1)\mbox{ and }\mbox{greater}(a_2,a_1) ) ) )\qquad\mbox{fof}(\mbox{a2\_FOL},\mbox{hypothesis})$

$\forall x,\mbox{rp}_1,\mbox{rp}_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1) )\qquad\mbox{fof}(\mbox{a4\_FOL},\mbox{hypothesis})$

$\forall x,r_1,r_2,a_1,a_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{reliability}(x,r_1,t_1)\mbox{ and }\mbox{reliability}(x,r_2,t_2)\mbox{ and }\mbox{accountability}(x,a_1,t_1)\mbox{ and }\mbox{accountability}(x,a_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ ( \mbox{greater}(r_2,r_1)\mbox{ and }\mbox{greater}(a_2,a_1) ) )\qquad\mbox{fof}(\mbox{t6\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT007+1.p} Reproducibility decreases during reorganization.






$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists r{:}\;\mbox{reliability}(x,r,t) )\qquad\mbox{fof}(\mbox{mp}_1,\mbox{axiom})$

$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists a{:}\;\mbox{accountability}(x,a,t) )\qquad\mbox{fof}(\mbox{mp}_2,\mbox{axiom})$

$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists a{:}\;\mbox{reproducibility}(x,a,t) )\qquad\mbox{fof}(\mbox{mp\_not\_in\_TR},\mbox{axiom})$

$\forall x,y,t_1,t_2,r_1,r_2,a_1,a_2,\mbox{rp}_1,\mbox{rp}_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reliability}(x,r_1,t_1)\mbox{ and }\mbox{reliability}(y,r_2,t_2)\mbox{ and }\mbox{accountability}(x,a_1,t_1)\mbox{ and }\mbox{accountability}(y,a_2,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(y,\mbox{rp}_2,t_2) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1)\iff ( \mbox{greater}(r_2,r_1)\mbox{ and }\mbox{greater}(a_2,a_1) ) ) )\qquad\mbox{fof}(\mbox{a2\_FOL},\mbox{hypothesis})$

$\forall x,r_1,r_2,a_1,a_2,t_1,t_2,\mbox{ta},\mbox{tb}{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reliability}(x,r_1,t_1)\mbox{ and }\mbox{reliability}(x,r_2,t_2)\mbox{ and }\mbox{accountability}(x,a_1,t_1)\mbox{ and }\mbox{accountability}(x,a_2,t_2)\mbox{ and }\neg\,\mbox{greater}(\mbox{ta},t_1)\mbox{ and }\mbox{greater}(t_2,t_1)\mbox{ and }\neg\,\mbox{greater}(t_2,\mbox{tb}) ) \ \Rightarrow \ ( \mbox{greater}(r_1,r_2)\mbox{ and }\mbox{greater}(a_1,a_2) ) )\qquad\mbox{fof}(\mbox{a6\_FOL},\mbox{hypothesis})$

$\forall x,\mbox{rp}_1,\mbox{rp}_2,t_1,t_2,\mbox{ta},\mbox{tb}{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_2,t_2)\mbox{ and }\neg\,\mbox{greater}(\mbox{ta},t_1)\mbox{ and }\mbox{greater}(t_2,t_1)\mbox{ and }\neg\,\mbox{greater}(t_2,\mbox{tb}) ) \ \Rightarrow \ \mbox{greater}(\mbox{rp}_1,\mbox{rp}_2) )\qquad\mbox{fof}(\mbox{t7\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT010+1.p} Large organization have higher reliability and accountability

Large organization have higher reliability and accountability
 than small organizations (of the same class).




$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists \mbox{rp}{:}\;\mbox{reproducibility}(x,\mbox{rp},t) )\qquad\mbox{fof}(\mbox{mp}_3,\mbox{axiom})$

$\forall x,y,t_1,t_2,r_1,r_2,a_1,a_2,\mbox{rp}_1,\mbox{rp}_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reliability}(x,r_1,t_1)\mbox{ and }\mbox{reliability}(y,r_2,t_2)\mbox{ and }\mbox{accountability}(x,a_1,t_1)\mbox{ and }\mbox{accountability}(y,a_2,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(y,\mbox{rp}_2,t_2) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1)\iff ( \mbox{greater}(r_2,r_1)\mbox{ and }\mbox{greater}(a_2,a_1) ) ) )\qquad\mbox{fof}(\mbox{a2\_FOL},\mbox{hypothesis})$

$\forall x,y,c,\mbox{rp}_1,\mbox{rp}_2,s_1,s_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(y,t_2,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(y,\mbox{rp}_2,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(y,s_2,t_2)\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1) )\qquad\mbox{fof}(\mbox{t9\_FOL},\mbox{hypothesis})$

$\forall x,y,c,r_1,r_2,a_1,a_2,s_1,s_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(y,t_2,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{reliability}(x,r_1,t_1)\mbox{ and }\mbox{reliability}(y,r_2,t_2)\mbox{ and }\mbox{accountability}(x,a_1,t_1)\mbox{ and }\mbox{accountability}(y,a_2,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(y,s_2,t_2)\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ ( \mbox{greater}(r_2,r_1)\mbox{ and }\mbox{greater}(a_2,a_1) ) )\qquad\mbox{fof}(\mbox{t10\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT009+1.p} Large organization have higher reproducibility






$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists i{:}\;\mbox{inertia}(x,i,t) )\qquad\mbox{fof}(\mbox{mp}_5,\mbox{axiom})$

$\forall x,y,t_1,t_2,\mbox{rp}_1,\mbox{rp}_2,i_1,i_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(y,t_2,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(y,\mbox{rp}_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1)\iff \mbox{greater}(i_2,i_1) ) )\qquad\mbox{fof}(\mbox{a3\_FOL},\mbox{hypothesis})$

$\forall x,y,c,s_1,s_2,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(y,s_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{a5\_FOL},\mbox{hypothesis})$

$\forall x,y,c,\mbox{rp}_1,\mbox{rp}_2,s_1,s_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(y,t_2,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(y,\mbox{rp}_2,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(y,s_2,t_2)\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1) )\qquad\mbox{fof}(\mbox{t9\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT011+1.p} Organizational size cannot decrease without reorganization






$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists i{:}\;\mbox{inertia}(x,i,t) )\qquad\mbox{fof}(\mbox{mp}_5,\mbox{axiom})$

$\forall x,y{:}\;\neg\,\mbox{greater}(x,y)\mbox{ and }x = y\qquad\mbox{fof}(\mbox{mp6}_1,\mbox{axiom})$

$\forall x,y{:}\;\neg\,\mbox{greater}(x,y)\mbox{ and }\mbox{greater}(y,x)\qquad\mbox{fof}(\mbox{mp6}_2,\mbox{axiom})$

$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists c{:}\;\mbox{class}(x,c,t) )\qquad\mbox{fof}(\mbox{mp}_9,\mbox{axiom})$

$\forall x,t_1,t_2,c_1,c_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{class}(x,c_1,t_1)\mbox{ and }\mbox{class}(x,c_2,t_2) ) \ \Rightarrow \ c_1 = c_2 )\qquad\mbox{fof}(\mbox{mp}_{10},\mbox{axiom})$

$\forall x,y,c,s_1,s_2,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(y,s_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{a5\_FOL},\mbox{hypothesis})$

$\forall x,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(x,i_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{t2\_FOL},\mbox{hypothesis})$

$\forall x,s_1,s_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(x,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(x,s_2,t_2)\mbox{ and }\mbox{greater}(t_2,t_1) ) \ \Rightarrow \ \neg\,\mbox{greater}(s_1,s_2) )\qquad\mbox{fof}(\mbox{t11\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT023-1.p} Stable environments have a critical point.






$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},b),\mbox{growth\_rate}(\mbox{first\_movers},b))\mbox{ or }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,\mbox{sk}_1(b,a))\mbox{ or }b = \mbox{critical\_point}(a) )\qquad\mbox{cnf}(\mbox{d1}_{17},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},b),\mbox{growth\_rate}(\mbox{first\_movers},b))\mbox{ or }\mbox{greater}(\mbox{sk}_1(b,a),b)\mbox{ or }b = \mbox{critical\_point}(a) )\qquad\mbox{cnf}(\mbox{d1}_{18},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_1(b,a)),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_1(b,a))) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},b),\mbox{growth\_rate}(\mbox{first\_movers},b))\mbox{ or }b = \mbox{critical\_point}(a) )\qquad\mbox{cnf}(\mbox{d1}_{19},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{sk}_2(a))\qquad\mbox{cnf}(\mbox{l12}_{20},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_2(a)),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_2(a)))\qquad\mbox{cnf}(\mbox{l12}_{21},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\mbox{ and }\mbox{greater}(b,\mbox{sk}_2(a)) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},b),\mbox{growth\_rate}(\mbox{first\_movers},b))\qquad\mbox{cnf}(\mbox{l12}_{22},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_l5}_{23},\mbox{negated\_conjecture})$

$\mbox{stable}(\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{prove\_l5}_{24},\mbox{negated\_conjecture})$

$\neg\,\mbox{in\_environment}(\mbox{sk}_3,\mbox{critical\_point}(\mbox{sk}_3))\qquad\mbox{cnf}(\mbox{prove\_l5}_{25},\mbox{negated\_conjecture})$

\medskip\textbf{MGT018+1.p} Larger organizations have shorter reorganization

The bigger an organization is at the beginning of
 reorganization, the sooner disbanding due to reorganization
 (possibly) happens - i.e., the shorter is the reorganization.




$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists i{:}\;\mbox{inertia}(x,i,t) )\qquad\mbox{fof}(\mbox{mp}_5,\mbox{axiom})$

$\forall x,y,c,s_1,s_2,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(y,s_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{a5\_FOL},\mbox{hypothesis})$

$\forall x,y,\mbox{rt},c,i_1,i_2,\mbox{ta},\mbox{tb},\mbox{tc}{:}\;( ( \mbox{organization}(x,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{ta})\mbox{ and }\neg\,\mbox{organization}(y,\mbox{tc})\mbox{ and }\mbox{class}(x,c,\mbox{ta})\mbox{ and }\mbox{class}(y,c,\mbox{ta})\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reorganization}(y,\mbox{ta},\mbox{tc})\mbox{ and }\mbox{reorganization\_type}(x,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{reorganization\_type}(y,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{inertia}(x,i_1,\mbox{ta})\mbox{ and }\mbox{inertia}(y,i_2,\mbox{ta})\mbox{ and }\mbox{greater}(i_2,i_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{tb},\mbox{tc}) )\qquad\mbox{fof}(\mbox{a14\_FOL},\mbox{hypothesis})$

$\forall x,y,\mbox{rt},c,s_1,s_2,\mbox{ta},\mbox{tb},\mbox{tc}{:}\;( ( \mbox{organization}(x,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{ta})\mbox{ and }\neg\,\mbox{organization}(y,\mbox{tc})\mbox{ and }\mbox{class}(x,c,\mbox{ta})\mbox{ and }\mbox{class}(y,c,\mbox{ta})\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reorganization}(y,\mbox{ta},\mbox{tc})\mbox{ and }\mbox{reorganization\_type}(x,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{reorganization\_type}(y,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{size}(x,s_1,\mbox{ta})\mbox{ and }\mbox{size}(y,s_2,\mbox{ta})\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{tb},\mbox{tc}) )\qquad\mbox{fof}(\mbox{t18\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT004-1.p} Attempts at reorganization increase death rates.






$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{reliability}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp1}_1,\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{accountability}(a,\mbox{sk}_2(b,a),b)\qquad\mbox{cnf}(\mbox{mp2}_2,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{reliability}(a,e,b)\mbox{ and }\mbox{reliability}(c,f,d)\mbox{ and }\mbox{accountability}(a,g,b)\mbox{ and }\mbox{accountability}(c,h,d)\mbox{ and }\mbox{survival\_chance}(a,i,b)\mbox{ and }\mbox{survival\_chance}(c,j,d)\mbox{ and }\mbox{greater}(f,e)\mbox{ and }\mbox{greater}(h,g) ) \ \Rightarrow \ \mbox{greater}(j,i)\qquad\mbox{cnf}(\mbox{a1\_FOL}_3,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization}(a,d,e)\mbox{ and }\mbox{reliability}(a,f,b)\mbox{ and }\mbox{reliability}(a,g,c)\mbox{ and }\mbox{accountability}(a,h,b)\mbox{ and }\mbox{accountability}(a,i,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ ( \mbox{greater}(d,b)\mbox{ or }\mbox{greater}(c,e)\mbox{ or }\mbox{greater}(f,g) )\qquad\mbox{cnf}(\mbox{a6\_FOL}_4,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization}(a,d,e)\mbox{ and }\mbox{reliability}(a,f,b)\mbox{ and }\mbox{reliability}(a,g,c)\mbox{ and }\mbox{accountability}(a,h,b)\mbox{ and }\mbox{accountability}(a,i,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ ( \mbox{greater}(d,b)\mbox{ or }\mbox{greater}(c,e)\mbox{ or }\mbox{greater}(h,i) )\qquad\mbox{cnf}(\mbox{a6\_FOL}_5,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t4\_FOL}_6,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t4\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_3,\mbox{sk}_8,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t4\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t4\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{survival\_chance}(\mbox{sk}_3,\mbox{sk}_5,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t4\_FOL}_{10},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_8,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t4\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_7,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t4\_FOL}_{12},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_7,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t4\_FOL}_{13},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_4,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t4\_FOL}_{14},\mbox{negated\_conjecture})$

\medskip\textbf{MGT036+3.p} First movers never outcompete efficient producers.






$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t) ) \ \Rightarrow \ \mbox{subpopulations}(s_2,s_1,e,t) )\qquad\mbox{fof}(\mbox{mp\_symmetry\_of\_subpopulations},\mbox{axiom})$

$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t) ) \ \Rightarrow \ ( ( \mbox{greater\_or\_equal}(\mbox{growth\_rate}(s_2,t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(s_1,t)) )\iff \mbox{outcompetes}(s_2,s_1,t) ) )\qquad\mbox{fof}(d_2,\mbox{hypothesis})$

$\exists e,t{:}\;( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater\_or\_equal}(\mbox{growth\_rate}(\mbox{first\_movers},t),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(\mbox{efficient\_producers},t)) )\qquad\mbox{fof}(\mbox{a13\_star},\mbox{hypothesis})$

$\exists e,t{:}\;( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{outcompetes}(\mbox{first\_movers},\mbox{efficient\_producers},t) )\qquad\mbox{fof}(\mbox{prove\_t5\_star},\mbox{conjecture})$

\medskip\textbf{MGT018-1.p} Larger organizations have shorter reorganization

The bigger an organization is at the beginning of
 reorganization, the sooner disbanding due to reorganization
 (possibly) happens - i.e., the shorter is the reorganization.




$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{inertia}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp5}_1,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,d)\mbox{ and }\mbox{size}(a,f,b)\mbox{ and }\mbox{size}(c,g,d)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,d)\mbox{ and }\mbox{greater}(g,f) ) \ \Rightarrow \ \mbox{greater}(i,h)\qquad\mbox{cnf}(\mbox{a5\_FOL}_2,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,b)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,b)\mbox{ and }\mbox{reorganization}(a,b,f)\mbox{ and }\mbox{reorganization}(c,b,d)\mbox{ and }\mbox{reorganization\_type}(a,g,b)\mbox{ and }\mbox{reorganization\_type}(c,g,b)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,b)\mbox{ and }\mbox{greater}(i,h) ) \ \Rightarrow \ ( \mbox{organization}(c,d)\mbox{ or }\mbox{greater}(f,d) )\qquad\mbox{cnf}(\mbox{a14\_FOL}_3,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t18\_FOL}_4,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t18\_FOL}_5,\mbox{negated\_conjecture})$

$\neg\,\mbox{organization}(\mbox{sk}_3,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t18\_FOL}_6,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t18\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_3,\mbox{sk}_5,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t18\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_2,\mbox{sk}_8,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t18\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_3,\mbox{sk}_8,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t18\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{reorganization\_type}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t18\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{reorganization\_type}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t18\_FOL}_{12},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_2,\mbox{sk}_6,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t18\_FOL}_{13},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_3,\mbox{sk}_7,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t18\_FOL}_{14},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_7,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t18\_FOL}_{15},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_9,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t18\_FOL}_{16},\mbox{negated\_conjecture})$

\medskip\textbf{MGT016+1.p} More complex organizations have shorter reorganization

The more complex an organization is at the beginning of
 reorganization, the sooner disbanding due to reorganization
 (possibly) happens - i.e., the shorter is the reorganization.




$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists i{:}\;\mbox{inertia}(x,i,t) )\qquad\mbox{fof}(\mbox{mp}_5,\mbox{axiom})$

$\forall x,y,c,c_1,c_2,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{complexity}(x,c_1,t_1)\mbox{ and }\mbox{complexity}(y,c_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{greater}(c_2,c_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{a12\_FOL},\mbox{hypothesis})$

$\forall x,y,\mbox{rt},c,i_1,i_2,\mbox{ta},\mbox{tb},\mbox{tc}{:}\;( ( \mbox{organization}(x,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{ta})\mbox{ and }\neg\,\mbox{organization}(y,\mbox{tc})\mbox{ and }\mbox{class}(x,c,\mbox{ta})\mbox{ and }\mbox{class}(y,c,\mbox{ta})\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reorganization}(y,\mbox{ta},\mbox{tc})\mbox{ and }\mbox{reorganization\_type}(x,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{reorganization\_type}(y,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{inertia}(x,i_1,\mbox{ta})\mbox{ and }\mbox{inertia}(y,i_2,\mbox{ta})\mbox{ and }\mbox{greater}(i_2,i_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{tb},\mbox{tc}) )\qquad\mbox{fof}(\mbox{a14\_FOL},\mbox{hypothesis})$

$\forall x,y,\mbox{rt},c,c_1,c_2,\mbox{ta},\mbox{tb},\mbox{tc}{:}\;( ( \mbox{organization}(x,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{ta})\mbox{ and }\neg\,\mbox{organization}(y,\mbox{tc})\mbox{ and }\mbox{class}(x,c,\mbox{ta})\mbox{ and }\mbox{class}(y,c,\mbox{ta})\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reorganization}(y,\mbox{ta},\mbox{tc})\mbox{ and }\mbox{reorganization\_type}(x,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{reorganization\_type}(y,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{complexity}(x,c_1,\mbox{ta})\mbox{ and }\mbox{complexity}(y,c_2,\mbox{ta})\mbox{ and }\mbox{greater}(c_2,c_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{tb},\mbox{tc}) )\qquad\mbox{fof}(\mbox{t16\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT023+1.p} Stable environments have a critical point.






$\forall e,\mbox{to}{:}\;( ( \mbox{environment}(e)\mbox{ and }\neg\,\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{to}),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{to}))\mbox{ and }\mbox{in\_environment}(e,\mbox{to})\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) \ \Rightarrow \ \mbox{to} = \mbox{critical\_point}(e) )\qquad\mbox{fof}(d_1,\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \exists \mbox{to}{:}\;( \mbox{in\_environment}(e,\mbox{to})\mbox{ and }\neg\,\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{to}),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{to}))\mbox{ and }\forall t{:}\;( ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t)\mbox{ and }\mbox{greater}(t,\mbox{to}) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},t),\mbox{growth\_rate}(\mbox{first\_movers},t)) ) ) )\qquad\mbox{fof}(l_{12},\mbox{hypothesis})$

$\forall e{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{stable}(e) ) \ \Rightarrow \ \mbox{in\_environment}(e,\mbox{critical\_point}(e)) )\qquad\mbox{fof}(\mbox{prove\_l}_5,\mbox{conjecture})$

\medskip\textbf{MGT041-2.p} There are non-FM and non-EP organisations

There are non-first mover and non-efficient producers
 organisations.




$\mbox{number\_of\_routines}(a,b,\mbox{low}) \ \Rightarrow \ \neg\,\mbox{number\_of\_routines}(a,b,\mbox{high})\qquad\mbox{cnf}(\mbox{mp\_not\_high\_and\_low}_1,\mbox{axiom})$

$( \mbox{organisation\_at\_time}(a,b)\mbox{ and }\mbox{efficient\_producer}(a)\mbox{ and }\mbox{founding\_time}(a,b) ) \ \Rightarrow \ \mbox{has\_elaborated\_routines}(a,b)\qquad\mbox{cnf}(\mbox{a14}_2,\mbox{hypothesis})$

$( \mbox{organisation\_at\_time}(a,b)\mbox{ and }\mbox{first\_mover}(a)\mbox{ and }\mbox{founding\_time}(a,b) ) \ \Rightarrow \ \mbox{number\_of\_routines}(a,b,\mbox{low})\qquad\mbox{cnf}(\mbox{a15}_3,\mbox{hypothesis})$

$\mbox{organisation\_at\_time}(\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{a16}_4,\mbox{hypothesis})$

$\mbox{founding\_time}(\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{a16}_5,\mbox{hypothesis})$

$\mbox{number\_of\_routines}(\mbox{sk}_1,\mbox{sk}_2,\mbox{high})\qquad\mbox{cnf}(\mbox{a16}_6,\mbox{hypothesis})$

$\neg\,\mbox{has\_elaborated\_routines}(\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{a16}_7,\mbox{hypothesis})$

$\mbox{organisation\_at\_time}(a,b) \ \Rightarrow \ ( \mbox{first\_mover}(a)\mbox{ or }\mbox{efficient\_producer}(a) )\qquad\mbox{cnf}(\mbox{prove\_t10}_8,\mbox{negated\_conjecture})$

\medskip\textbf{MGT059-1.p} Hazard of mortality is constant during periods of immunity

An organization's hazard of mortality is constant during periods
 in which it has immunity.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,b) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(a,b) = \mbox{very\_low}\qquad\mbox{cnf}(\mbox{assumption\_17}_{32},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b)\mbox{ and }\mbox{positional\_advantage}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{hazard\_of\_mortality}(a,b) = \mbox{low} )\qquad\mbox{cnf}(\mbox{assumption\_17}_{33},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{positional\_advantage}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{is\_aligned}(a,b)\mbox{ or }\mbox{hazard\_of\_mortality}(a,b) = \mbox{mod}_1 )\qquad\mbox{cnf}(\mbox{assumption\_17}_{34},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{positional\_advantage}(a,b)\mbox{ or }\mbox{hazard\_of\_mortality}(a,b) = \mbox{mod}_2 )\qquad\mbox{cnf}(\mbox{assumption\_17}_{35},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{is\_aligned}(a,b)\mbox{ or }\mbox{positional\_advantage}(a,b)\mbox{ or }\mbox{hazard\_of\_mortality}(a,b) = \mbox{high} )\qquad\mbox{cnf}(\mbox{assumption\_17}_{36},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{assumption\_2}_{37},\mbox{negated\_conjecture})$

$\mbox{has\_immunity}(\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{assumption\_2}_{38},\mbox{negated\_conjecture})$

$\mbox{has\_immunity}(\mbox{sk}_1,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{assumption\_2}_{39},\mbox{negated\_conjecture})$

$\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_2)\ne \mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{assumption\_2}_{40},\mbox{negated\_conjecture})$

\medskip\textbf{MGT026-1.p} Selection favors efficient producers past the critical point






$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{greater}(\mbox{growth\_rate}(c,d),\mbox{growth\_rate}(b,d)) ) \ \Rightarrow \ \mbox{selection\_favors}(c,b,d)\qquad\mbox{cnf}(\mbox{mp1\_high\_growth\_rates}_{28},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulation}(b,a,c)\mbox{ and }\mbox{subpopulation}(d,a,c)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(b,c),0)\mbox{ and }\mbox{cardinality\_at\_time}(d,c) = 0 ) \ \Rightarrow \ \mbox{selection\_favors}(b,d,c)\qquad\mbox{cnf}(\mbox{mp2\_favour\_members}_{29},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{first\_movers},b),0)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{efficient\_producers},b),0) ) \ \Rightarrow \ \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\qquad\mbox{cnf}(\mbox{mp\_non\_empty\_fm\_and\_ep}_{30},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{cardinality\_at\_time}(\mbox{first\_movers},b),0)\qquad\mbox{cnf}(\mbox{mp\_first\_movers\_exist}_{31},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ \mbox{subpopulation}(\mbox{first\_movers},a,b)\qquad\mbox{cnf}(\mbox{mp\_subpopulations}_{32},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ \mbox{subpopulation}(\mbox{efficient\_producers},a,b)\qquad\mbox{cnf}(\mbox{mp\_subpopulations}_{33},\mbox{axiom})$

$\mbox{environment}(a) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{critical\_point}(a),\mbox{appear}(\mbox{efficient\_producers},a))\qquad\mbox{cnf}(\mbox{mp\_critical\_point\_after\_EP}_{34},\mbox{axiom})$

$( \mbox{greater}(a,b)\mbox{ and }\mbox{greater}(b,c) ) \ \Rightarrow \ \mbox{greater}(a,c)\qquad\mbox{cnf}(\mbox{mp\_greater\_transitivity}_{35},\mbox{axiom})$

$\mbox{greater\_or\_equal}(a,b) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b )\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{36},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \mbox{greater\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{37},\mbox{axiom})$

$a = b \ \Rightarrow \ \mbox{greater\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{38},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }b = \mbox{critical\_point}(a) ) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},b),\mbox{growth\_rate}(\mbox{first\_movers},b))\qquad\mbox{cnf}(\mbox{d1}_{39},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }b = \mbox{critical\_point}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},c),\mbox{growth\_rate}(\mbox{first\_movers},c))\qquad\mbox{cnf}(\mbox{d1}_{40},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{appear}(\mbox{efficient\_producers},a)) ) \ \Rightarrow \ \mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{efficient\_producers},b),0)\qquad\mbox{cnf}(\mbox{t6}_{41},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{prove\_l8}_{42},\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_l8}_{43},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_2,\mbox{critical\_point}(\mbox{sk}_1))\qquad\mbox{cnf}(\mbox{prove\_l8}_{44},\mbox{negated\_conjecture})$

$\neg\,\mbox{selection\_favors}(\mbox{efficient\_producers},\mbox{first\_movers},\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_l8}_{45},\mbox{negated\_conjecture})$

\medskip\textbf{MGT043+1.p} Conditions for a higher hazard of mortality

When an organization lacks immunity, the growth of internal
 friction elevates its hazard of mortality when its knowledge and
 the quality of its ties are constant.




$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\neg\,\mbox{has\_immunity}(x,t_0)\mbox{ and }\neg\,\mbox{has\_immunity}(x,t) ) \ \Rightarrow \ ( ( ( \mbox{greater}(\mbox{capability}(x,t),\mbox{capability}(x,t_0))\mbox{ and }\mbox{greater\_or\_equal}(\mbox{position}(x,t),\mbox{position}(x,t_0)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{hazard\_of\_mortality}(x,t),\mbox{hazard\_of\_mortality}(x,t_0)) )\mbox{ and }( ( \mbox{greater\_or\_equal}(\mbox{capability}(x,t),\mbox{capability}(x,t_0))\mbox{ and }\mbox{greater}(\mbox{position}(x,t),\mbox{position}(x,t_0)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{hazard\_of\_mortality}(x,t),\mbox{hazard\_of\_mortality}(x,t_0)) )\mbox{ and }( ( \mbox{capability}(x,t) = \mbox{capability}(x,t_0)\mbox{ and }\mbox{position}(x,t) = \mbox{position}(x,t_0) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t) = \mbox{hazard\_of\_mortality}(x,t_0) ) ) )\qquad\mbox{fof}(\mbox{assumption}_4,\mbox{axiom})$

$\forall x,t_0,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ ( ( ( \mbox{greater}(\mbox{stock\_of\_knowledge}(x,t),\mbox{stock\_of\_knowledge}(x,t_0))\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{internal\_friction}(x,t),\mbox{internal\_friction}(x,t_0)) ) \ \Rightarrow \ \mbox{greater}(\mbox{capability}(x,t),\mbox{capability}(x,t_0)) )\mbox{ and }( ( \mbox{smaller\_or\_equal}(\mbox{stock\_of\_knowledge}(x,t),\mbox{stock\_of\_knowledge}(x,t_0))\mbox{ and }\mbox{greater}(\mbox{internal\_friction}(x,t),\mbox{internal\_friction}(x,t_0)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{capability}(x,t),\mbox{capability}(x,t_0)) )\mbox{ and }( ( \mbox{stock\_of\_knowledge}(x,t) = \mbox{stock\_of\_knowledge}(x,t_0)\mbox{ and }\mbox{internal\_friction}(x,t) = \mbox{internal\_friction}(x,t_0) ) \ \Rightarrow \ \mbox{capability}(x,t) = \mbox{capability}(x,t_0) ) ) )\qquad\mbox{fof}(\mbox{assumption}_5,\mbox{axiom})$

$\forall x,t_0,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ ( ( \mbox{greater}(\mbox{external\_ties}(x,t),\mbox{external\_ties}(x,t_0)) \ \Rightarrow \ \mbox{greater}(\mbox{position}(x,t),\mbox{position}(x,t_0)) )\mbox{ and }( \mbox{external\_ties}(x,t) = \mbox{external\_ties}(x,t_0) \ \Rightarrow \ \mbox{position}(x,t) = \mbox{position}(x,t_0) ) ) )\qquad\mbox{fof}(\mbox{assumption}_6,\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\neg\,\mbox{has\_immunity}(x,t_0)\mbox{ and }\neg\,\mbox{has\_immunity}(x,t)\mbox{ and }\mbox{stock\_of\_knowledge}(x,t) = \mbox{stock\_of\_knowledge}(x,t_0)\mbox{ and }\mbox{greater}(\mbox{internal\_friction}(x,t),\mbox{internal\_friction}(x,t_0))\mbox{ and }\mbox{external\_ties}(x,t_0) = \mbox{external\_ties}(x,t) ) \ \Rightarrow \ \mbox{greater}(\mbox{hazard\_of\_mortality}(x,t),\mbox{hazard\_of\_mortality}(x,t_0)) )\qquad\mbox{fof}(\mbox{lemma}_2,\mbox{conjecture})$

\medskip\textbf{MGT036-3.p} First movers never outcompete efficient producers.






$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d) ) \ \Rightarrow \ \mbox{subpopulations}(c,b,a,d)\qquad\mbox{cnf}(\mbox{mp\_symmetry\_of\_subpopulations}_1,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{greater\_or\_equal}(\mbox{growth\_rate}(c,d),0)\mbox{ and }\mbox{greater}(0,\mbox{growth\_rate}(b,d)) ) \ \Rightarrow \ \mbox{outcompetes}(c,b,d)\qquad\mbox{cnf}(\mbox{d2}_2,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{outcompetes}(c,b,d) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{growth\_rate}(c,d),0)\qquad\mbox{cnf}(\mbox{d2}_3,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{outcompetes}(c,b,d) ) \ \Rightarrow \ \mbox{greater}(0,\mbox{growth\_rate}(b,d))\qquad\mbox{cnf}(\mbox{d2}_4,\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{a13\_star}_5,\mbox{hypothesis})$

$\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{a13\_star}_6,\mbox{hypothesis})$

$\mbox{greater\_or\_equal}(\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_2),0)\qquad\mbox{cnf}(\mbox{a13\_star}_7,\mbox{hypothesis})$

$\mbox{greater}(0,\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{a13\_star}_8,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b) ) \ \Rightarrow \ \neg\,\mbox{outcompetes}(\mbox{first\_movers},\mbox{efficient\_producers},b)\qquad\mbox{cnf}(\mbox{prove\_t5\_star}_9,\mbox{negated\_conjecture})$

\medskip\textbf{MGT019-2.p} Growth rate of EPs exceeds that of FMs in stable environments

The growth rate of efficent producers exceeds the growth rate
 of first movers past a certain time in stable environments.




$\mbox{environment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{l2}_{22},\mbox{axiom})$

$\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{l2}_{23},\mbox{axiom})$

$\neg\,\mbox{greater}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2),\mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{l2}_{24},\mbox{axiom})$

$( \mbox{greater}(\mbox{disbanding\_rate}(\mbox{first\_movers},a),\mbox{disbanding\_rate}(\mbox{efficient\_producers},a))\mbox{ and }\mbox{greater\_or\_equal}(\mbox{founding\_rate}(\mbox{efficient\_producers},a),\mbox{founding\_rate}(\mbox{first\_movers},a)) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},a),\mbox{growth\_rate}(\mbox{first\_movers},a))\qquad\mbox{cnf}(\mbox{mp\_EP\_lower\_disbanding\_rate}_{25},\mbox{axiom})$

$\mbox{greater\_or\_equal}(a,b) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b )\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{26},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{sk}_3(a))\qquad\mbox{cnf}(\mbox{a8}_{27},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{sk}_3(a)) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{founding\_rate}(\mbox{efficient\_producers},b),\mbox{founding\_rate}(\mbox{first\_movers},b))\qquad\mbox{cnf}(\mbox{a8}_{28},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_4)\qquad\mbox{cnf}(\mbox{prove\_l1}_{29},\mbox{negated\_conjecture})$

$\mbox{stable}(\mbox{sk}_4)\qquad\mbox{cnf}(\mbox{prove\_l1}_{30},\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_4,a) \ \Rightarrow \ \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_4,\mbox{sk}_5(a))\qquad\mbox{cnf}(\mbox{prove\_l1}_{31},\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_4,a) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{sk}_5(a),a)\qquad\mbox{cnf}(\mbox{prove\_l1}_{32},\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_4,a) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_5(a)),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_5(a)))\qquad\mbox{cnf}(\mbox{prove\_l1}_{33},\mbox{negated\_conjecture})$

\medskip\textbf{MGT030-1.p} Earliest time point when FM growth rate exceeds EP growth rate

There is an earliest time point, past which FM's growth
 rate exceeds EP's growth rate.




$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,\mbox{sk}_1(b,a))\mbox{ or }\mbox{in\_environment}(a,\mbox{sk}_2(a)) )\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds}_1,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b) ) \ \Rightarrow \ ( \mbox{greater\_or\_equal}(\mbox{sk}_1(b,a),b)\mbox{ or }\mbox{in\_environment}(a,\mbox{sk}_2(a)) )\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds}_2,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_2(a)),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_2(a))) ) \ \Rightarrow \ \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,\mbox{sk}_1(b,a))\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds}_3,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,c)\mbox{ and }\mbox{greater}(c,\mbox{sk}_2(a)) ) \ \Rightarrow \ ( \mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,\mbox{sk}_1(b,a))\mbox{ or }\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},c),\mbox{growth\_rate}(\mbox{first\_movers},c)) )\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds}_4,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_2(a)),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_2(a))) ) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds}_5,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,c)\mbox{ and }\mbox{greater}(c,\mbox{sk}_2(a)) ) \ \Rightarrow \ ( \mbox{greater\_or\_equal}(\mbox{sk}_1(b,a),b)\mbox{ or }\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},c),\mbox{growth\_rate}(\mbox{first\_movers},c)) )\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds}_6,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_1(b,a)),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_1(b,a))) ) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{sk}_2(a))\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds}_7,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_1(b,a)),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_1(b,a))) ) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_2(a)),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_2(a)))\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds}_8,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_1(b,a)),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_1(b,a)))\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,c)\mbox{ and }\mbox{greater}(c,\mbox{sk}_2(a)) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},c),\mbox{growth\_rate}(\mbox{first\_movers},c))\qquad\mbox{cnf}(\mbox{mp\_earliest\_time\_growth\_rate\_exceeds}_9,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a) ) \ \Rightarrow \ \mbox{in\_environment}(a,\mbox{sk}_3(a))\qquad\mbox{cnf}(\mbox{l1}_{10},\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{stable}(a)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},a,b)\mbox{ and }\mbox{greater\_or\_equal}(b,\mbox{sk}_3(a)) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},b),\mbox{growth\_rate}(\mbox{first\_movers},b))\qquad\mbox{cnf}(\mbox{l1}_{11},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_4)\qquad\mbox{cnf}(\mbox{prove\_l12}_{12},\mbox{negated\_conjecture})$

$\mbox{stable}(\mbox{sk}_4)\qquad\mbox{cnf}(\mbox{prove\_l12}_{13},\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_4,a) \ \Rightarrow \ ( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},a),\mbox{growth\_rate}(\mbox{first\_movers},a))\mbox{ or }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_4,\mbox{sk}_5(a)) )\qquad\mbox{cnf}(\mbox{prove\_l12}_{14},\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_4,a) \ \Rightarrow \ ( \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},a),\mbox{growth\_rate}(\mbox{first\_movers},a))\mbox{ or }\mbox{greater}(\mbox{sk}_5(a),a) )\qquad\mbox{cnf}(\mbox{prove\_l12}_{15},\mbox{negated\_conjecture})$

$( \mbox{in\_environment}(\mbox{sk}_4,a)\mbox{ and }\mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},\mbox{sk}_5(a)),\mbox{growth\_rate}(\mbox{first\_movers},\mbox{sk}_5(a))) ) \ \Rightarrow \ \mbox{greater}(\mbox{growth\_rate}(\mbox{efficient\_producers},a),\mbox{growth\_rate}(\mbox{first\_movers},a))\qquad\mbox{cnf}(\mbox{prove\_l12}_{16},\mbox{negated\_conjecture})$

\medskip\textbf{MGT001+1.p} Selection favors organizations with high inertia

Selection within populations of organizations in modern
 societies favours organizations whose structure have high
 inertia.




$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists r{:}\;\mbox{reliability}(x,r,t) )\qquad\mbox{fof}(\mbox{mp}_1,\mbox{axiom})$

$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists a{:}\;\mbox{accountability}(x,a,t) )\qquad\mbox{fof}(\mbox{mp}_2,\mbox{axiom})$

$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists \mbox{rp}{:}\;\mbox{reproducibility}(x,\mbox{rp},t) )\qquad\mbox{fof}(\mbox{mp}_3,\mbox{axiom})$

$\forall x,y,r_1,r_2,a_1,a_2,p_1,p_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reliability}(x,r_1,t_1)\mbox{ and }\mbox{reliability}(y,r_2,t_2)\mbox{ and }\mbox{accountability}(x,a_1,t_1)\mbox{ and }\mbox{accountability}(y,a_2,t_2)\mbox{ and }\mbox{survival\_chance}(x,p_1,t_1)\mbox{ and }\mbox{survival\_chance}(y,p_2,t_2)\mbox{ and }\mbox{greater}(r_2,r_1)\mbox{ and }\mbox{greater}(a_2,a_1) ) \ \Rightarrow \ \mbox{greater}(p_2,p_1) )\qquad\mbox{fof}(\mbox{a1\_FOL},\mbox{hypothesis})$

$\forall x,y,t_1,t_2,r_1,r_2,a_1,a_2,\mbox{rp}_1,\mbox{rp}_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reliability}(x,r_1,t_1)\mbox{ and }\mbox{reliability}(y,r_2,t_2)\mbox{ and }\mbox{accountability}(x,a_1,t_1)\mbox{ and }\mbox{accountability}(y,a_2,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(y,\mbox{rp}_2,t_2) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1)\iff ( \mbox{greater}(r_2,r_1)\mbox{ and }\mbox{greater}(a_2,a_1) ) ) )\qquad\mbox{fof}(\mbox{a2\_FOL},\mbox{hypothesis})$

$\forall x,y,t_1,t_2,\mbox{rp}_1,\mbox{rp}_2,i_1,i_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(y,t_2,t_2)\mbox{ and }\mbox{reproducibility}(x,\mbox{rp}_1,t_1)\mbox{ and }\mbox{reproducibility}(y,\mbox{rp}_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{rp}_2,\mbox{rp}_1)\iff \mbox{greater}(i_2,i_1) ) )\qquad\mbox{fof}(\mbox{a3\_FOL},\mbox{hypothesis})$

$\forall x,y,t_1,t_2,i_1,i_2,p_1,p_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{reorganization\_free}(x,t_1,t_1)\mbox{ and }\mbox{reorganization\_free}(y,t_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{survival\_chance}(x,p_1,t_1)\mbox{ and }\mbox{survival\_chance}(y,p_2,t_2)\mbox{ and }\mbox{greater}(i_2,i_1) ) \ \Rightarrow \ \mbox{greater}(p_2,p_1) )\qquad\mbox{fof}(\mbox{t1\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT022+1.p} Decreasing resource availability affects FMS more than EPs

Decreasing resource availability affects the disbanding rate
 of first movers more than the disbanding rate of efficient
 producers.




$\forall x{:}\;( \mbox{constant}(x) \ \Rightarrow \ \neg\,\mbox{decreases}(x) )\qquad\mbox{fof}(\mbox{mp\_constant\_not\_decrease},\mbox{axiom})$

$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t)\mbox{ and }\mbox{greater}(\mbox{resilience}(s_2),\mbox{resilience}(s_1)) ) \ \Rightarrow \ ( ( \mbox{decreases}(\mbox{resources}(e,t)) \ \Rightarrow \ \mbox{increases}(\mbox{disbanding\_rate}(s_1,t)\setminus \mbox{disbanding\_rate}(s_2,t)) )\mbox{ and }( \mbox{constant}(\mbox{resources}(e,t)) \ \Rightarrow \ \mbox{constant}(\mbox{disbanding\_rate}(s_1,t)\setminus \mbox{disbanding\_rate}(s_2,t)) ) ) )\qquad\mbox{fof}(a_5,\mbox{hypothesis})$

$\mbox{greater}(\mbox{resilience}(\mbox{efficient\_producers}),\mbox{resilience}(\mbox{first\_movers}))\qquad\mbox{fof}(a_2,\mbox{hypothesis})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ ( ( \mbox{decreases}(\mbox{resources}(e,t)) \ \Rightarrow \ \mbox{increases}(\mbox{disbanding\_rate}(\mbox{first\_movers},t)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},t)) )\mbox{ and }( \mbox{constant}(\mbox{resources}(e,t)) \ \Rightarrow \ \neg\,\mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},t)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},t)) ) ) )\qquad\mbox{fof}(\mbox{prove\_l}_4,\mbox{conjecture})$

\medskip\textbf{MGT048+1.p} Capability decreases monotonically with its age

An organization's capability decreases monotonically with its age.




$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x,t_0,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ ( ( ( \mbox{greater}(\mbox{stock\_of\_knowledge}(x,t),\mbox{stock\_of\_knowledge}(x,t_0))\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{internal\_friction}(x,t),\mbox{internal\_friction}(x,t_0)) ) \ \Rightarrow \ \mbox{greater}(\mbox{capability}(x,t),\mbox{capability}(x,t_0)) )\mbox{ and }( ( \mbox{smaller\_or\_equal}(\mbox{stock\_of\_knowledge}(x,t),\mbox{stock\_of\_knowledge}(x,t_0))\mbox{ and }\mbox{greater}(\mbox{internal\_friction}(x,t),\mbox{internal\_friction}(x,t_0)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{capability}(x,t),\mbox{capability}(x,t_0)) )\mbox{ and }( ( \mbox{stock\_of\_knowledge}(x,t) = \mbox{stock\_of\_knowledge}(x,t_0)\mbox{ and }\mbox{internal\_friction}(x,t) = \mbox{internal\_friction}(x,t_0) ) \ \Rightarrow \ \mbox{capability}(x,t) = \mbox{capability}(x,t_0) ) ) )\qquad\mbox{fof}(\mbox{assumption}_5,\mbox{axiom})$

$\forall x,t_0,t{:}\;( \mbox{organization}(x) \ \Rightarrow \ \mbox{stock\_of\_knowledge}(x,t) = \mbox{stock\_of\_knowledge}(x,t_0) )\qquad\mbox{fof}(\mbox{assumption}_{10},\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{greater}(\mbox{age}(x,t),\mbox{age}(x,t_0)) ) \ \Rightarrow \ \mbox{greater}(\mbox{internal\_friction}(x,t),\mbox{internal\_friction}(x,t_0)) )\qquad\mbox{fof}(\mbox{assumption}_{12},\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{greater}(\mbox{age}(x,t),\mbox{age}(x,t_0)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{capability}(x,t),\mbox{capability}(x,t_0)) )\qquad\mbox{fof}(\mbox{lemma}_5,\mbox{conjecture})$

\medskip\textbf{MGT022-1.p} Decreasing resource availability affects FMS more than EPs

Decreasing resource availability affects the disbanding rate
 of first movers more than the disbanding rate of efficient
 producers.




$\mbox{constant}(a) \ \Rightarrow \ \neg\,\mbox{decreases}(a)\qquad\mbox{cnf}(\mbox{mp\_constant\_not\_decrease}_1,\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{greater}(\mbox{resilience}(c),\mbox{resilience}(b))\mbox{ and }\mbox{decreases}(\mbox{resources}(a,d)) ) \ \Rightarrow \ \mbox{increases}(\mbox{disbanding\_rate}(b,d)\setminus \mbox{disbanding\_rate}(c,d))\qquad\mbox{cnf}(\mbox{a5}_2,\mbox{hypothesis})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulations}(b,c,a,d)\mbox{ and }\mbox{greater}(\mbox{resilience}(c),\mbox{resilience}(b))\mbox{ and }\mbox{constant}(\mbox{resources}(a,d)) ) \ \Rightarrow \ \mbox{constant}(\mbox{disbanding\_rate}(b,d)\setminus \mbox{disbanding\_rate}(c,d))\qquad\mbox{cnf}(\mbox{a5}_3,\mbox{hypothesis})$

$\mbox{greater}(\mbox{resilience}(\mbox{efficient\_producers}),\mbox{resilience}(\mbox{first\_movers}))\qquad\mbox{cnf}(\mbox{a2}_4,\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{prove\_l4}_5,\mbox{negated\_conjecture})$

$\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_l4}_6,\mbox{negated\_conjecture})$

$\mbox{decreases}(\mbox{resources}(\mbox{sk}_1,\mbox{sk}_2))\mbox{ or }\mbox{constant}(\mbox{resources}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l4}_7,\mbox{negated\_conjecture})$

$\mbox{decreases}(\mbox{resources}(\mbox{sk}_1,\mbox{sk}_2))\mbox{ or }\mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l4}_8,\mbox{negated\_conjecture})$

$\mbox{increases}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2)) \ \Rightarrow \ \mbox{constant}(\mbox{resources}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l4}_9,\mbox{negated\_conjecture})$

$\mbox{increases}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2)) \ \Rightarrow \ \mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},\mbox{sk}_2)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l4}_{10},\mbox{negated\_conjecture})$

\medskip\textbf{MGT011-1.p} Organizational size cannot decrease without reorganization






$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{inertia}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp5}_{20},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ a\ne b\qquad\mbox{cnf}(\mbox{mp6\_1}_{21},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \neg\,\mbox{greater}(b,a)\qquad\mbox{cnf}(\mbox{mp6\_2}_{22},\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{class}(a,\mbox{sk}_2(b,a),b)\qquad\mbox{cnf}(\mbox{mp9}_{23},\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{class}(a,d,b)\mbox{ and }\mbox{class}(a,e,c) ) \ \Rightarrow \ d = e\qquad\mbox{cnf}(\mbox{mp10}_{24},\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,d)\mbox{ and }\mbox{size}(a,f,b)\mbox{ and }\mbox{size}(c,g,d)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,d)\mbox{ and }\mbox{greater}(g,f) ) \ \Rightarrow \ \mbox{greater}(i,h)\qquad\mbox{cnf}(\mbox{a5\_FOL}_{25},\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{inertia}(a,d,b)\mbox{ and }\mbox{inertia}(a,e,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \mbox{greater}(e,d)\qquad\mbox{cnf}(\mbox{t2\_FOL}_{26},\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t11\_FOL}_{27},\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t11\_FOL}_{28},\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_3,\mbox{sk}_6,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t11\_FOL}_{29},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t11\_FOL}_{30},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_3,\mbox{sk}_5,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t11\_FOL}_{31},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_7,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t11\_FOL}_{32},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_4,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t11\_FOL}_{33},\mbox{negated\_conjecture})$

\medskip\textbf{MGT056-1.p} Conditions for a constant then jumping hazard of mortality 2

When (`eta' $>$= `sigma') in a drifting environment, an endowed
 organization's hazard of mortality remains constant until age
 `eta' and then jumps to a higher level in a drifting environment.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$\mbox{has\_endowment}(a) \ \Rightarrow \ \mbox{organization}(a)\qquad\mbox{cnf}(\mbox{definition\_1}_{31},\mbox{axiom})$

$( \mbox{has\_endowment}(a)\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{age}(a,b),\mbox{eta}) ) \ \Rightarrow \ \mbox{has\_immunity}(a,b)\qquad\mbox{cnf}(\mbox{definition\_1}_{32},\mbox{axiom})$

$( \mbox{has\_endowment}(a)\mbox{ and }\mbox{greater}(\mbox{age}(a,b),\mbox{eta}) ) \ \Rightarrow \ \neg\,\mbox{has\_immunity}(a,b)\qquad\mbox{cnf}(\mbox{definition\_1}_{33},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ ( \mbox{smaller\_or\_equal}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{eta})\mbox{ or }\mbox{greater}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{eta})\mbox{ or }\mbox{has\_endowment}(a) )\qquad\mbox{cnf}(\mbox{definition\_1}_{34},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ ( \mbox{smaller\_or\_equal}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{eta})\mbox{ or }\mbox{has\_immunity}(a,\mbox{sk}_1(a))\mbox{ or }\mbox{has\_endowment}(a) )\qquad\mbox{cnf}(\mbox{definition\_1}_{35},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,\mbox{sk}_1(a)) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{eta})\mbox{ or }\mbox{has\_endowment}(a) )\qquad\mbox{cnf}(\mbox{definition\_1}_{36},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,\mbox{sk}_1(a)) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,\mbox{sk}_1(a))\mbox{ or }\mbox{has\_endowment}(a) )\qquad\mbox{cnf}(\mbox{definition\_1}_{37},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,b)\mbox{ and }\mbox{has\_immunity}(a,c) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(a,b) = \mbox{hazard\_of\_mortality}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_2}_{38},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,c)\mbox{ or }\mbox{greater}(\mbox{hazard\_of\_mortality}(a,c),\mbox{hazard\_of\_mortality}(a,b)) )\qquad\mbox{cnf}(\mbox{assumption\_3}_{39},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{lemma\_9}_{40},\mbox{negated\_conjecture})$

$\mbox{has\_endowment}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{lemma\_9}_{41},\mbox{negated\_conjecture})$

$\mbox{age}(\mbox{sk}_2,\mbox{sk}_3) = 0\qquad\mbox{cnf}(\mbox{lemma\_9}_{42},\mbox{negated\_conjecture})$

$\mbox{smaller\_or\_equal}(\mbox{age}(\mbox{sk}_2,\mbox{sk}_4),\mbox{eta})\qquad\mbox{cnf}(\mbox{lemma\_9}_{43},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{age}(\mbox{sk}_2,\mbox{sk}_5),\mbox{eta})\qquad\mbox{cnf}(\mbox{lemma\_9}_{44},\mbox{negated\_conjecture})$

$\mbox{greater\_or\_equal}(\mbox{eta},\mbox{sigma})\qquad\mbox{cnf}(\mbox{lemma\_9}_{45},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sigma},0)\qquad\mbox{cnf}(\mbox{lemma\_9}_{46},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{hazard\_of\_mortality}(\mbox{sk}_2,\mbox{sk}_5),\mbox{hazard\_of\_mortality}(\mbox{sk}_2,\mbox{sk}_4)) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(\mbox{sk}_2,\mbox{sk}_4)\ne \mbox{hazard\_of\_mortality}(\mbox{sk}_2,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{lemma\_9}_{47},\mbox{negated\_conjecture})$

\medskip\textbf{MGT022+2.p} Decreasing resource availability affects FMS more than EPs

Decreasing resource availability affects the disbanding rate
 of first movers more than the disbanding rate of efficient
 producers.




$\forall x{:}\;( \mbox{constant}(x) \ \Rightarrow \ \neg\,\mbox{decreases}(x) )\qquad\mbox{fof}(\mbox{mp\_constant\_not\_decrease},\mbox{axiom})$

$\forall e,s_1,s_2,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(s_1,s_2,e,t)\mbox{ and }\mbox{greater}(\mbox{resilience}(s_2),\mbox{resilience}(s_1)) ) \ \Rightarrow \ ( ( \mbox{decreases}(\mbox{resources}(e,t)) \ \Rightarrow \ \mbox{increases}(\mbox{disbanding\_rate}(s_1,t)\setminus \mbox{disbanding\_rate}(s_2,t)) )\mbox{ and }( \mbox{constant}(\mbox{resources}(e,t)) \ \Rightarrow \ \mbox{constant}(\mbox{disbanding\_rate}(s_1,t)\setminus \mbox{disbanding\_rate}(s_2,t)) ) ) )\qquad\mbox{fof}(a_6,\mbox{hypothesis})$

$\mbox{greater}(\mbox{resilience}(\mbox{efficient\_producers}),\mbox{resilience}(\mbox{first\_movers}))\qquad\mbox{fof}(a_2,\mbox{hypothesis})$

$\forall e,t{:}\;( ( \mbox{environment}(e)\mbox{ and }\mbox{subpopulations}(\mbox{first\_movers},\mbox{efficient\_producers},e,t) ) \ \Rightarrow \ ( ( \mbox{decreases}(\mbox{resources}(e,t)) \ \Rightarrow \ \mbox{increases}(\mbox{disbanding\_rate}(\mbox{first\_movers},t)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},t)) )\mbox{ and }( \mbox{constant}(\mbox{resources}(e,t)) \ \Rightarrow \ \neg\,\mbox{decreases}(\mbox{disbanding\_rate}(\mbox{first\_movers},t)\setminus \mbox{disbanding\_rate}(\mbox{efficient\_producers},t)) ) ) )\qquad\mbox{fof}(\mbox{prove\_l}_4,\mbox{conjecture})$

\medskip\textbf{MGT057+1.p} Conditions for a constant then increasing hazard of mortality

In a drifting environment, an endowed organization's hazard of
 mortality is constant during the period of immunity; beyond the
 period of immunity, the hazard rises with age.




$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x{:}\;( \mbox{has\_endowment}(x)\iff \forall t{:}\;( \mbox{organization}(x)\mbox{ and }( \mbox{smaller\_or\_equal}(\mbox{age}(x,t),\mbox{eta}) \ \Rightarrow \ \mbox{has\_immunity}(x,t) )\mbox{ and }( \mbox{greater}(\mbox{age}(x,t),\mbox{eta}) \ \Rightarrow \ \neg\,\mbox{has\_immunity}(x,t) ) ) )\qquad\mbox{fof}(\mbox{definition}_1,\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{has\_immunity}(x,t_0)\mbox{ and }\mbox{has\_immunity}(x,t) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(x,t_0) = \mbox{hazard\_of\_mortality}(x,t) )\qquad\mbox{fof}(\mbox{assumption}_2,\mbox{axiom})$

$\forall x,t_0,t{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{has\_immunity}(x,t_0)\mbox{ and }\neg\,\mbox{has\_immunity}(x,t) ) \ \Rightarrow \ \mbox{greater}(\mbox{hazard\_of\_mortality}(x,t),\mbox{hazard\_of\_mortality}(x,t_0)) )\qquad\mbox{fof}(\mbox{assumption}_3,\mbox{axiom})$

$\forall x,t_0,t_1,t_2{:}\;( ( \mbox{organization}(x)\mbox{ and }\mbox{has\_endowment}(x)\mbox{ and }\mbox{age}(x,t_0) = 0\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{age}(x,t_1),\mbox{eta})\mbox{ and }\mbox{greater}(\mbox{age}(x,t_2),\mbox{eta})\mbox{ and }\mbox{greater}(\mbox{eta},0) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{hazard\_of\_mortality}(x,t_2),\mbox{hazard\_of\_mortality}(x,t_1))\mbox{ and }\mbox{hazard\_of\_mortality}(x,t_1) = \mbox{hazard\_of\_mortality}(x,t_0) ) )\qquad\mbox{fof}(\mbox{theorem}_6,\mbox{conjecture})$

\medskip\textbf{MGT031-1.p} First movers appear first in an environment






$\mbox{environment}(a) \ \Rightarrow \ \mbox{greater}(\mbox{number\_of\_organizations}(e,\mbox{appear}(\mbox{an\_organisation},a)),0)\qquad\mbox{cnf}(\mbox{mp\_positive\_number\_when\_appear}_{20},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater}(\mbox{number\_of\_organizations}(a,b),0) ) \ \Rightarrow \ \mbox{subpopulation}(\mbox{sk}_1(b,a),a,b)\qquad\mbox{cnf}(\mbox{mp\_number\_mean\_non\_empty}_{21},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{greater}(\mbox{number\_of\_organizations}(a,b),0) ) \ \Rightarrow \ \mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{sk}_1(b,a),b),0)\qquad\mbox{cnf}(\mbox{mp\_number\_mean\_non\_empty}_{22},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{appear}(\mbox{efficient\_producers},a),b) ) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{efficient\_producers},b),0)\qquad\mbox{cnf}(\mbox{mp\_no\_EP\_before\_appearance}_{23},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{in\_environment}(a,b)\mbox{ and }\mbox{greater}(\mbox{appear}(\mbox{first\_movers},a),b) ) \ \Rightarrow \ \neg\,\mbox{greater}(\mbox{cardinality\_at\_time}(\mbox{first\_movers},b),0)\qquad\mbox{cnf}(\mbox{mp\_no\_FM\_before\_appearance}_{24},\mbox{axiom})$

$\mbox{environment}(a) \ \Rightarrow \ \mbox{greater\_or\_equal}(\mbox{appear}(\mbox{first\_movers},a),\mbox{appear}(\mbox{an\_organisation},a))\qquad\mbox{cnf}(\mbox{mp\_FM\_not\_precede\_first}_{25},\mbox{axiom})$

$( \mbox{greater}(a,b)\mbox{ and }\mbox{greater}(b,c) ) \ \Rightarrow \ \mbox{greater}(a,c)\qquad\mbox{cnf}(\mbox{mp\_greater\_transitivity}_{26},\mbox{axiom})$

$\mbox{greater\_or\_equal}(a,b) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b )\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{27},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \mbox{greater\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{28},\mbox{axiom})$

$a = b \ \Rightarrow \ \mbox{greater\_or\_equal}(a,b)\qquad\mbox{cnf}(\mbox{mp\_greater\_or\_equal}_{29},\mbox{axiom})$

$( \mbox{environment}(a)\mbox{ and }\mbox{subpopulation}(b,a,c)\mbox{ and }\mbox{greater}(\mbox{cardinality\_at\_time}(b,c),0) ) \ \Rightarrow \ ( b = \mbox{efficient\_producers}\mbox{ or }b = \mbox{first\_movers} )\qquad\mbox{cnf}(\mbox{a9}_{30},\mbox{hypothesis})$

$\mbox{environment}(a) \ \Rightarrow \ \mbox{greater}(\mbox{appear}(\mbox{efficient\_producers},e),\mbox{appear}(\mbox{first\_movers},a))\qquad\mbox{cnf}(\mbox{a13}_{31},\mbox{hypothesis})$

$\mbox{environment}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_l13}_{32},\mbox{negated\_conjecture})$

$\mbox{in\_environment}(\mbox{sk}_2,\mbox{appear}(\mbox{an\_organisation},\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{prove\_l13}_{33},\mbox{negated\_conjecture})$

$\mbox{appear}(\mbox{an\_organisation},\mbox{sk}_2)\ne \mbox{appear}(\mbox{first\_movers},\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{prove\_l13}_{34},\mbox{negated\_conjecture})$

\medskip\textbf{MGT060-1.p} Hazard of mortality is lower during periods of immunity

An organization's hazard of mortality is lower during periods in
 which it has immunity than in periods in which it does not.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,b) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(a,b) = \mbox{very\_low}\qquad\mbox{cnf}(\mbox{assumption\_17}_{32},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b)\mbox{ and }\mbox{positional\_advantage}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{hazard\_of\_mortality}(a,b) = \mbox{low} )\qquad\mbox{cnf}(\mbox{assumption\_17}_{33},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{positional\_advantage}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{is\_aligned}(a,b)\mbox{ or }\mbox{hazard\_of\_mortality}(a,b) = \mbox{mod}_1 )\qquad\mbox{cnf}(\mbox{assumption\_17}_{34},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{is\_aligned}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{positional\_advantage}(a,b)\mbox{ or }\mbox{hazard\_of\_mortality}(a,b) = \mbox{mod}_2 )\qquad\mbox{cnf}(\mbox{assumption\_17}_{35},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{is\_aligned}(a,b)\mbox{ or }\mbox{positional\_advantage}(a,b)\mbox{ or }\mbox{hazard\_of\_mortality}(a,b) = \mbox{high} )\qquad\mbox{cnf}(\mbox{assumption\_17}_{36},\mbox{axiom})$

$\mbox{greater}(\mbox{high},\mbox{mod}_1)\qquad\mbox{cnf}(\mbox{assumption\_18a}_{37},\mbox{axiom})$

$\mbox{greater}(\mbox{mod}_1,\mbox{low})\qquad\mbox{cnf}(\mbox{assumption\_18b}_{38},\mbox{axiom})$

$\mbox{greater}(\mbox{low},\mbox{very\_low})\qquad\mbox{cnf}(\mbox{assumption\_18c}_{39},\mbox{axiom})$

$\mbox{greater}(\mbox{high},\mbox{mod}_2)\qquad\mbox{cnf}(\mbox{assumption\_18d}_{40},\mbox{axiom})$

$\mbox{greater}(\mbox{mod}_2,\mbox{low})\qquad\mbox{cnf}(\mbox{assumption\_18e}_{41},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{assumption\_3}_{42},\mbox{negated\_conjecture})$

$\mbox{has\_immunity}(\mbox{sk}_1,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{assumption\_3}_{43},\mbox{negated\_conjecture})$

$\neg\,\mbox{has\_immunity}(\mbox{sk}_1,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{assumption\_3}_{44},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_3),\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{assumption\_3}_{45},\mbox{negated\_conjecture})$

\medskip\textbf{MGT046-1.p} Unendowed organization's hazard of mortality declines with age

An unendowed organization's hazard of mortality declines
 monotonically with its age.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,b) ) \ \Rightarrow \ \mbox{has\_endowment}(a)\qquad\mbox{cnf}(\mbox{assumption\_1}_{41},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{capability}(a,c),\mbox{capability}(a,b))\mbox{ and }\mbox{greater\_or\_equal}(\mbox{position}(a,c),\mbox{position}(a,b)) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{has\_immunity}(a,c)\mbox{ or }\mbox{smaller}(\mbox{hazard\_of\_mortality}(a,c),\mbox{hazard\_of\_mortality}(a,b)) )\qquad\mbox{cnf}(\mbox{assumption\_4}_{42},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater\_or\_equal}(\mbox{capability}(a,c),\mbox{capability}(a,b))\mbox{ and }\mbox{greater}(\mbox{position}(a,c),\mbox{position}(a,b)) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{has\_immunity}(a,c)\mbox{ or }\mbox{smaller}(\mbox{hazard\_of\_mortality}(a,c),\mbox{hazard\_of\_mortality}(a,b)) )\qquad\mbox{cnf}(\mbox{assumption\_4}_{43},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{capability}(a,c) = \mbox{capability}(a,b)\mbox{ and }\mbox{position}(a,c) = \mbox{position}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,b)\mbox{ or }\mbox{has\_immunity}(a,c)\mbox{ or }\mbox{hazard\_of\_mortality}(a,c) = \mbox{hazard\_of\_mortality}(a,b) )\qquad\mbox{cnf}(\mbox{assumption\_4}_{44},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{capability}(a,b),\mbox{capability}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_5}_{45},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\mbox{ and }\mbox{greater}(\mbox{internal\_friction}(a,b),\mbox{internal\_friction}(a,c)) ) \ \Rightarrow \ \mbox{smaller}(\mbox{capability}(a,b),\mbox{capability}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_5}_{46},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{stock\_of\_knowledge}(a,b) = \mbox{stock\_of\_knowledge}(a,c)\mbox{ and }\mbox{internal\_friction}(a,b) = \mbox{internal\_friction}(a,c) ) \ \Rightarrow \ \mbox{capability}(a,b) = \mbox{capability}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_5}_{47},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{external\_ties}(a,b),\mbox{external\_ties}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{position}(a,b),\mbox{position}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_6}_{48},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{external\_ties}(a,b) = \mbox{external\_ties}(a,c) ) \ \Rightarrow \ \mbox{position}(a,b) = \mbox{position}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_6}_{49},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{age}(a,b),\mbox{age}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{stock\_of\_knowledge}(a,b),\mbox{stock\_of\_knowledge}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_7}_{50},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{greater}(\mbox{age}(a,b),\mbox{age}(a,c)) ) \ \Rightarrow \ \mbox{greater}(\mbox{external\_ties}(a,b),\mbox{external\_ties}(a,c))\qquad\mbox{cnf}(\mbox{assumption\_8}_{51},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ \mbox{internal\_friction}(a,b) = \mbox{internal\_friction}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_9}_{52},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{theorem\_1}_{53},\mbox{negated\_conjecture})$

$\neg\,\mbox{has\_endowment}(\mbox{sk}_1)\qquad\mbox{cnf}(\mbox{theorem\_1}_{54},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{age}(\mbox{sk}_1,\mbox{sk}_3),\mbox{age}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{theorem\_1}_{55},\mbox{negated\_conjecture})$

$\neg\,\mbox{smaller}(\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_3),\mbox{hazard\_of\_mortality}(\mbox{sk}_1,\mbox{sk}_2))\qquad\mbox{cnf}(\mbox{theorem\_1}_{56},\mbox{negated\_conjecture})$

\medskip\textbf{MGT057-1.p} Conditions for a constant then increasing hazard of mortality

In a drifting environment, an endowed organization's hazard of
 mortality is constant during the period of immunity; beyond the
 period of immunity, the hazard rises with age.




$\mbox{include}(\mbox{'Axioms/MGT001-0.ax'})$

$\mbox{has\_endowment}(a) \ \Rightarrow \ \mbox{organization}(a)\qquad\mbox{cnf}(\mbox{definition\_1}_{31},\mbox{axiom})$

$( \mbox{has\_endowment}(a)\mbox{ and }\mbox{smaller\_or\_equal}(\mbox{age}(a,b),\mbox{eta}) ) \ \Rightarrow \ \mbox{has\_immunity}(a,b)\qquad\mbox{cnf}(\mbox{definition\_1}_{32},\mbox{axiom})$

$( \mbox{has\_endowment}(a)\mbox{ and }\mbox{greater}(\mbox{age}(a,b),\mbox{eta}) ) \ \Rightarrow \ \neg\,\mbox{has\_immunity}(a,b)\qquad\mbox{cnf}(\mbox{definition\_1}_{33},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ ( \mbox{smaller\_or\_equal}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{eta})\mbox{ or }\mbox{greater}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{eta})\mbox{ or }\mbox{has\_endowment}(a) )\qquad\mbox{cnf}(\mbox{definition\_1}_{34},\mbox{axiom})$

$\mbox{organization}(a) \ \Rightarrow \ ( \mbox{smaller\_or\_equal}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{eta})\mbox{ or }\mbox{has\_immunity}(a,\mbox{sk}_1(a))\mbox{ or }\mbox{has\_endowment}(a) )\qquad\mbox{cnf}(\mbox{definition\_1}_{35},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,\mbox{sk}_1(a)) ) \ \Rightarrow \ ( \mbox{greater}(\mbox{age}(a,\mbox{sk}_1(a)),\mbox{eta})\mbox{ or }\mbox{has\_endowment}(a) )\qquad\mbox{cnf}(\mbox{definition\_1}_{36},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,\mbox{sk}_1(a)) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,\mbox{sk}_1(a))\mbox{ or }\mbox{has\_endowment}(a) )\qquad\mbox{cnf}(\mbox{definition\_1}_{37},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,b)\mbox{ and }\mbox{has\_immunity}(a,c) ) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(a,b) = \mbox{hazard\_of\_mortality}(a,c)\qquad\mbox{cnf}(\mbox{assumption\_2}_{38},\mbox{axiom})$

$( \mbox{organization}(a)\mbox{ and }\mbox{has\_immunity}(a,b) ) \ \Rightarrow \ ( \mbox{has\_immunity}(a,c)\mbox{ or }\mbox{greater}(\mbox{hazard\_of\_mortality}(a,c),\mbox{hazard\_of\_mortality}(a,b)) )\qquad\mbox{cnf}(\mbox{assumption\_3}_{39},\mbox{axiom})$

$\mbox{organization}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{theorem\_6}_{40},\mbox{negated\_conjecture})$

$\mbox{has\_endowment}(\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{theorem\_6}_{41},\mbox{negated\_conjecture})$

$\mbox{age}(\mbox{sk}_2,\mbox{sk}_3) = 0\qquad\mbox{cnf}(\mbox{theorem\_6}_{42},\mbox{negated\_conjecture})$

$\mbox{smaller\_or\_equal}(\mbox{age}(\mbox{sk}_2,\mbox{sk}_4),\mbox{eta})\qquad\mbox{cnf}(\mbox{theorem\_6}_{43},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{age}(\mbox{sk}_2,\mbox{sk}_5),\mbox{eta})\qquad\mbox{cnf}(\mbox{theorem\_6}_{44},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{eta},0)\qquad\mbox{cnf}(\mbox{theorem\_6}_{45},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{hazard\_of\_mortality}(\mbox{sk}_2,\mbox{sk}_5),\mbox{hazard\_of\_mortality}(\mbox{sk}_2,\mbox{sk}_4)) \ \Rightarrow \ \mbox{hazard\_of\_mortality}(\mbox{sk}_2,\mbox{sk}_4)\ne \mbox{hazard\_of\_mortality}(\mbox{sk}_2,\mbox{sk}_3)\qquad\mbox{cnf}(\mbox{theorem\_6}_{46},\mbox{negated\_conjecture})$

\medskip\textbf{MGT041+2.p} There are non-FM and non-EP organisations

There are non-first mover and non-efficient producers
 organisations.




$\forall x,t{:}\;\neg\,\mbox{number\_of\_routines}(x,t,\mbox{low})\mbox{ and }\mbox{number\_of\_routines}(x,t,\mbox{high})\qquad\mbox{fof}(\mbox{mp\_not\_high\_and\_low},\mbox{axiom})$

$\forall x,t{:}\;( ( \mbox{organisation\_at\_time}(x,t)\mbox{ and }\mbox{efficient\_producer}(x)\mbox{ and }\mbox{founding\_time}(x,t) ) \ \Rightarrow \ \mbox{has\_elaborated\_routines}(x,t) )\qquad\mbox{fof}(a_{14},\mbox{hypothesis})$

$\forall x,t{:}\;( ( \mbox{organisation\_at\_time}(x,t)\mbox{ and }\mbox{first\_mover}(x)\mbox{ and }\mbox{founding\_time}(x,t) ) \ \Rightarrow \ \mbox{number\_of\_routines}(x,t,\mbox{low}) )\qquad\mbox{fof}(a_{15},\mbox{hypothesis})$

$\exists x,t{:}\;( \mbox{organisation\_at\_time}(x,t)\mbox{ and }\mbox{founding\_time}(x,t)\mbox{ and }\mbox{number\_of\_routines}(x,t,\mbox{high})\mbox{ and }\neg\,\mbox{has\_elaborated\_routines}(x,t) )\qquad\mbox{fof}(a_{16},\mbox{hypothesis})$

$\exists x,t{:}\;( \mbox{organisation\_at\_time}(x,t)\mbox{ and }\neg\,\mbox{first\_mover}(x)\mbox{ and }\neg\,\mbox{efficient\_producer}(x) )\qquad\mbox{fof}(\mbox{prove\_t}_{10},\mbox{conjecture})$

\medskip\textbf{MGT053+1.p} The dissimilarity relation is symmetric






$\mbox{include}(\mbox{'Axioms/MGT001+0.ax'})$

$\forall x,t_0,t{:}\;( \mbox{dissimilar}(x,t_0,t)\iff ( \mbox{organization}(x)\mbox{ and }\neg\,\mbox{is\_aligned}(x,t_0)\iff \mbox{is\_aligned}(x,t) ) )\qquad\mbox{fof}(\mbox{definition}_2,\mbox{axiom})$

$\forall x,t_1,t_2{:}\;( \mbox{dissimilar}(x,t_1,t_2)\iff \mbox{dissimilar}(x,t_2,t_1) )\qquad\mbox{fof}(\mbox{lemma}_7,\mbox{conjecture})$

\medskip\textbf{MGT013-1.p} If organization complexity increases, its size cannot decrease

If the complexity of an organization gets bigger, its size
 cannot get smaller (in lack of reorganization).




$\mbox{greater}(a,b) \ \Rightarrow \ a\ne b\qquad\mbox{cnf}(\mbox{mp6\_1}_{18},\mbox{axiom})$

$\mbox{greater}(a,b) \ \Rightarrow \ \neg\,\mbox{greater}(b,a)\qquad\mbox{cnf}(\mbox{mp6\_2}_{19},\mbox{axiom})$

$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{time}(b)\qquad\mbox{cnf}(\mbox{mp15}_{20},\mbox{axiom})$

$( \mbox{time}(a)\mbox{ and }\mbox{time}(b) ) \ \Rightarrow \ ( \mbox{greater}(a,b)\mbox{ or }a = b\mbox{ or }\mbox{greater}(b,a) )\qquad\mbox{cnf}(\mbox{mp16}_{21},\mbox{axiom})$

$\mbox{reorganization\_free}(a,b,c) \ \Rightarrow \ \mbox{reorganization\_free}(a,c,b)\qquad\mbox{cnf}(\mbox{mp17}_{22},\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{complexity}(a,d,b)\mbox{ and }\mbox{complexity}(a,e,c)\mbox{ and }b = c ) \ \Rightarrow \ d = e\qquad\mbox{cnf}(\mbox{mp18}_{23},\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{size}(a,d,b)\mbox{ and }\mbox{size}(a,e,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \neg\,\mbox{greater}(d,e)\qquad\mbox{cnf}(\mbox{t11\_FOL}_{24},\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(a,c)\mbox{ and }\mbox{reorganization\_free}(a,b,c)\mbox{ and }\mbox{complexity}(a,d,b)\mbox{ and }\mbox{complexity}(a,e,c)\mbox{ and }\mbox{greater}(c,b) ) \ \Rightarrow \ \neg\,\mbox{greater}(d,e)\qquad\mbox{cnf}(\mbox{t12\_FOL}_{25},\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_1,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t13\_FOL}_{26},\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_1,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t13\_FOL}_{27},\mbox{negated\_conjecture})$

$\mbox{reorganization\_free}(\mbox{sk}_1,\mbox{sk}_6,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t13\_FOL}_{28},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_1,\mbox{sk}_2,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t13\_FOL}_{29},\mbox{negated\_conjecture})$

$\mbox{complexity}(\mbox{sk}_1,\mbox{sk}_3,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t13\_FOL}_{30},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_1,\mbox{sk}_4,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t13\_FOL}_{31},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_1,\mbox{sk}_5,\mbox{sk}_7)\qquad\mbox{cnf}(\mbox{t13\_FOL}_{32},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_3,\mbox{sk}_2)\qquad\mbox{cnf}(\mbox{t13\_FOL}_{33},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_4,\mbox{sk}_5)\qquad\mbox{cnf}(\mbox{t13\_FOL}_{34},\mbox{negated\_conjecture})$

\medskip\textbf{MGT017+1.p} Length of reoganisation proportional to organization size

The length of reorganizational period grows by the size the
 organization begins reorganization (if the bigger organization
 survives it).




$\forall x,t{:}\;( \mbox{organization}(x,t) \ \Rightarrow \ \exists i{:}\;\mbox{inertia}(x,i,t) )\qquad\mbox{fof}(\mbox{mp}_5,\mbox{axiom})$

$\forall x,y,c,s_1,s_2,i_1,i_2,t_1,t_2{:}\;( ( \mbox{organization}(x,t_1)\mbox{ and }\mbox{organization}(y,t_2)\mbox{ and }\mbox{class}(x,c,t_1)\mbox{ and }\mbox{class}(y,c,t_2)\mbox{ and }\mbox{size}(x,s_1,t_1)\mbox{ and }\mbox{size}(y,s_2,t_2)\mbox{ and }\mbox{inertia}(x,i_1,t_1)\mbox{ and }\mbox{inertia}(y,i_2,t_2)\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \mbox{greater}(i_2,i_1) )\qquad\mbox{fof}(\mbox{a5\_FOL},\mbox{hypothesis})$

$\forall x,y,\mbox{rt},c,i_1,i_2,\mbox{ta},\mbox{tb},\mbox{tc}{:}\;( ( \mbox{organization}(x,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{tc})\mbox{ and }\mbox{class}(x,c,\mbox{ta})\mbox{ and }\mbox{class}(y,c,\mbox{ta})\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reorganization}(y,\mbox{ta},\mbox{tc})\mbox{ and }\mbox{reorganization\_type}(x,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{reorganization\_type}(y,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{inertia}(x,i_1,\mbox{ta})\mbox{ and }\mbox{inertia}(y,i_2,\mbox{ta})\mbox{ and }\mbox{greater}(i_2,i_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{tc},\mbox{tb}) )\qquad\mbox{fof}(\mbox{a13\_FOL},\mbox{hypothesis})$

$\forall x,y,\mbox{rt},c,s_1,s_2,\mbox{ta},\mbox{tb},\mbox{tc}{:}\;( ( \mbox{organization}(x,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{ta})\mbox{ and }\mbox{organization}(y,\mbox{tc})\mbox{ and }\mbox{class}(x,c,\mbox{ta})\mbox{ and }\mbox{class}(y,c,\mbox{ta})\mbox{ and }\mbox{reorganization}(x,\mbox{ta},\mbox{tb})\mbox{ and }\mbox{reorganization}(y,\mbox{ta},\mbox{tc})\mbox{ and }\mbox{reorganization\_type}(x,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{reorganization\_type}(y,\mbox{rt},\mbox{ta})\mbox{ and }\mbox{size}(x,s_1,\mbox{ta})\mbox{ and }\mbox{size}(y,s_2,\mbox{ta})\mbox{ and }\mbox{greater}(s_2,s_1) ) \ \Rightarrow \ \mbox{greater}(\mbox{tc},\mbox{tb}) )\qquad\mbox{fof}(\mbox{t17\_FOL},\mbox{conjecture})$

\medskip\textbf{MGT017-1.p} Length of reoganisation proportional to organization size

The length of reorganizational period grows by the size the
 organization begins reorganization (if the bigger organization
 survives it).




$\mbox{organization}(a,b) \ \Rightarrow \ \mbox{inertia}(a,\mbox{sk}_1(b,a),b)\qquad\mbox{cnf}(\mbox{mp5}_1,\mbox{axiom})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,d)\mbox{ and }\mbox{size}(a,f,b)\mbox{ and }\mbox{size}(c,g,d)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,d)\mbox{ and }\mbox{greater}(g,f) ) \ \Rightarrow \ \mbox{greater}(i,h)\qquad\mbox{cnf}(\mbox{a5\_FOL}_2,\mbox{hypothesis})$

$( \mbox{organization}(a,b)\mbox{ and }\mbox{organization}(c,b)\mbox{ and }\mbox{organization}(c,d)\mbox{ and }\mbox{class}(a,e,b)\mbox{ and }\mbox{class}(c,e,b)\mbox{ and }\mbox{reorganization}(a,b,f)\mbox{ and }\mbox{reorganization}(c,b,d)\mbox{ and }\mbox{reorganization\_type}(a,g,b)\mbox{ and }\mbox{reorganization\_type}(c,g,b)\mbox{ and }\mbox{inertia}(a,h,b)\mbox{ and }\mbox{inertia}(c,i,b)\mbox{ and }\mbox{greater}(i,h) ) \ \Rightarrow \ \mbox{greater}(d,f)\qquad\mbox{cnf}(\mbox{a13\_FOL}_3,\mbox{hypothesis})$

$\mbox{organization}(\mbox{sk}_2,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t17\_FOL}_4,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t17\_FOL}_5,\mbox{negated\_conjecture})$

$\mbox{organization}(\mbox{sk}_3,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t17\_FOL}_6,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_2,\mbox{sk}_5,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t17\_FOL}_7,\mbox{negated\_conjecture})$

$\mbox{class}(\mbox{sk}_3,\mbox{sk}_5,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t17\_FOL}_8,\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_2,\mbox{sk}_8,\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t17\_FOL}_9,\mbox{negated\_conjecture})$

$\mbox{reorganization}(\mbox{sk}_3,\mbox{sk}_8,\mbox{sk}_{10})\qquad\mbox{cnf}(\mbox{t17\_FOL}_{10},\mbox{negated\_conjecture})$

$\mbox{reorganization\_type}(\mbox{sk}_2,\mbox{sk}_4,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t17\_FOL}_{11},\mbox{negated\_conjecture})$

$\mbox{reorganization\_type}(\mbox{sk}_3,\mbox{sk}_4,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t17\_FOL}_{12},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_2,\mbox{sk}_6,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t17\_FOL}_{13},\mbox{negated\_conjecture})$

$\mbox{size}(\mbox{sk}_3,\mbox{sk}_7,\mbox{sk}_8)\qquad\mbox{cnf}(\mbox{t17\_FOL}_{14},\mbox{negated\_conjecture})$

$\mbox{greater}(\mbox{sk}_7,\mbox{sk}_6)\qquad\mbox{cnf}(\mbox{t17\_FOL}_{15},\mbox{negated\_conjecture})$

$\neg\,\mbox{greater}(\mbox{sk}_{10},\mbox{sk}_9)\qquad\mbox{cnf}(\mbox{t17\_FOL}_{16},\mbox{negated\_conjecture})$

\medskip
\end{document}