%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT026+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:11:22 PM UTC 2026
% Result : Theorem 11.60s 2.14s
% Output : Proof 11.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 11
% Syntax : Number of formulae : 96 ( 11 unt; 0 def)
% Number of atoms : 302 ( 38 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 336 ( 130 ~; 157 |; 36 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 79 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f7_nnf,plain,
! [X,Y] :
( ( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c8,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f5,axiom,
! [E] :
( environment(E)
=> greater_or_equal(critical_point(E),appear(efficient_producers,E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
fof(f5_nnf,plain,
! [E] :
( greater_or_equal(critical_point(E),appear(efficient_producers,E))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [E] :
( greater_or_equal(critical_point(E),appear(efficient_producers,E))
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c6,plain,
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f10,conjecture,
! [E,T] :
( ( greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) )
=> selection_favors(efficient_producers,first_movers,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8) ).
fof(f10_neg,negated_conjecture,
~ ! [E,T] :
( ( greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) )
=> selection_favors(efficient_producers,first_movers,T) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [E,T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ~ selection_favors(efficient_producers,first_movers,sk1)
& greater(sk1,critical_point(sk0))
& in_environment(sk0,sk1)
& environment(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f10_nnf]) ).
cnf(c14,plain,
environment(sk0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p24,plain,
greater_or_equal(critical_point(sk0),appear(efficient_producers,sk0)),
inference(resolution,[status(thm)],[c6,c14]) ).
cnf(p40,plain,
( critical_point(sk0) = appear(efficient_producers,sk0)
| greater(critical_point(sk0),appear(efficient_producers,sk0)) ),
inference(resolution,[status(thm)],[c8,p24]) ).
fof(f6,axiom,
! [X,Y,Z] :
( ( greater(Y,Z)
& greater(X,Y) )
=> greater(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f6_nnf,plain,
! [X,Y,Z] :
( greater(X,Z)
| ~ greater(Y,Z)
| ~ greater(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,Z] :
( greater(X,Z)
| ~ greater(Y,Z)
| ~ greater(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c7,plain,
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(c16,plain,
greater(sk1,critical_point(sk0)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p37,plain,
( greater(sk1,X0)
| ~ greater(critical_point(sk0),X0) ),
inference(resolution,[status(thm)],[c7,c16]) ).
cnf(p46,plain,
( greater(sk1,appear(efficient_producers,sk0))
| critical_point(sk0) = appear(efficient_producers,sk0) ),
inference(resolution,[status(thm)],[p40,p37]) ).
fof(f9,hypothesis,
! [E,T] :
( ( greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,T)
& environment(E) )
=> greater(cardinality_at_time(efficient_producers,T),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(f9_nnf,plain,
! [E,T] :
( greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [E,T] :
( greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c13,plain,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p53,plain,
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,appear(efficient_producers,sk0))
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c13,c14]) ).
cnf(c15,plain,
in_environment(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p54,plain,
( greater(cardinality_at_time(efficient_producers,sk1),zero)
| ~ greater_or_equal(sk1,appear(efficient_producers,sk0)) ),
inference(resolution,[status(thm)],[p53,c15]) ).
cnf(p55,plain,
( greater(cardinality_at_time(efficient_producers,sk1),zero)
| ~ greater_or_equal(sk1,critical_point(sk0))
| greater(sk1,appear(efficient_producers,sk0)) ),
inference(superposition,[status(thm)],[p46,p54]) ).
cnf(c9,plain,
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p19,plain,
greater_or_equal(sk1,critical_point(sk0)),
inference(resolution,[status(thm)],[c9,c16]) ).
cnf(p56,plain,
( greater(cardinality_at_time(efficient_producers,sk1),zero)
| greater(sk1,appear(efficient_producers,sk0)) ),
inference(resolution,[status(thm)],[p55,p19]) ).
fof(f3,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> greater_or_equal(cardinality_at_time(first_movers,T),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist) ).
fof(f3_nnf,plain,
! [E,T] :
( greater_or_equal(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [E,T] :
( greater_or_equal(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p28,plain,
( greater_or_equal(cardinality_at_time(first_movers,X0),zero)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c3,c14]) ).
cnf(p32,plain,
greater_or_equal(cardinality_at_time(first_movers,sk1),zero),
inference(resolution,[status(thm)],[p28,c15]) ).
cnf(p41,plain,
( cardinality_at_time(first_movers,sk1) = zero
| greater(cardinality_at_time(first_movers,sk1),zero) ),
inference(resolution,[status(thm)],[c8,p32]) ).
fof(f2,axiom,
! [E,T] :
( ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero)
& in_environment(E,T)
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f2_nnf,plain,
! [E,T] :
( subpopulations(first_movers,efficient_producers,E,T)
| ~ greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [E,T] :
( subpopulations(first_movers,efficient_producers,E,T)
| ~ greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p25,plain,
( subpopulations(first_movers,efficient_producers,sk0,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c2,c14]) ).
cnf(p26,plain,
( subpopulations(first_movers,efficient_producers,sk0,sk1)
| ~ greater(cardinality_at_time(efficient_producers,sk1),zero)
| ~ greater(cardinality_at_time(first_movers,sk1),zero) ),
inference(resolution,[status(thm)],[p25,c15]) ).
cnf(p42,plain,
( subpopulations(first_movers,efficient_producers,sk0,sk1)
| ~ greater(cardinality_at_time(efficient_producers,sk1),zero)
| cardinality_at_time(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p41,p26]) ).
cnf(p61,plain,
( subpopulations(first_movers,efficient_producers,sk0,sk1)
| cardinality_at_time(first_movers,sk1) = zero
| greater(sk1,appear(efficient_producers,sk0)) ),
inference(resolution,[status(thm)],[p56,p42]) ).
cnf(p62,plain,
( greater_or_equal(sk1,appear(efficient_producers,sk0))
| subpopulations(first_movers,efficient_producers,sk0,sk1)
| cardinality_at_time(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p61,c9]) ).
cnf(p64,plain,
( greater(cardinality_at_time(efficient_producers,sk1),zero)
| subpopulations(first_movers,efficient_producers,sk0,sk1)
| cardinality_at_time(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p62,p54]) ).
cnf(p68,plain,
( subpopulations(first_movers,efficient_producers,sk0,sk1)
| cardinality_at_time(first_movers,sk1) = zero
| subpopulations(first_movers,efficient_producers,sk0,sk1)
| cardinality_at_time(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p64,p42]) ).
cnf(p69,plain,
( subpopulations(first_movers,efficient_producers,sk0,sk1)
| subpopulations(first_movers,efficient_producers,sk0,sk1)
| cardinality_at_time(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p68]) ).
cnf(p71,plain,
( subpopulations(first_movers,efficient_producers,sk0,sk1)
| cardinality_at_time(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p69]) ).
fof(f8,hypothesis,
! [E,Tc] :
( ( Tc = critical_point(E)
& environment(E) )
=> ( ! [T] :
( ( greater(T,Tc)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f8_nnf,plain,
! [E,Tc] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) )
| Tc != critical_point(E)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [E,Tc,T] :
( ( ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) )
| Tc != critical_point(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c12,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| X1 != critical_point(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p51,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk0,X1)
| X0 != critical_point(sk0) ),
inference(resolution,[status(thm)],[c12,c14]) ).
cnf(p52,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,critical_point(sk0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(equality_resolution,[status(thm)],[p51]) ).
cnf(p73,plain,
( greater(growth_rate(efficient_producers,sk1),growth_rate(first_movers,sk1))
| ~ greater(sk1,critical_point(sk0))
| cardinality_at_time(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p71,p52]) ).
cnf(p74,plain,
( greater(growth_rate(efficient_producers,sk1),growth_rate(first_movers,sk1))
| cardinality_at_time(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p73,c16]) ).
fof(f0,axiom,
! [E,S1,S2,T] :
( ( greater(growth_rate(S2,T),growth_rate(S1,T))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> selection_favors(S2,S1,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f0_nnf,plain,
! [E,S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p18,plain,
( selection_favors(X1,X0,X2)
| ~ greater(growth_rate(X1,X2),growth_rate(X0,X2))
| ~ subpopulations(X0,X1,sk0,X2) ),
inference(resolution,[status(thm)],[c0,c14]) ).
cnf(p72,plain,
( selection_favors(efficient_producers,first_movers,sk1)
| ~ greater(growth_rate(efficient_producers,sk1),growth_rate(first_movers,sk1))
| cardinality_at_time(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p71,p18]) ).
cnf(p77,plain,
( selection_favors(efficient_producers,first_movers,sk1)
| cardinality_at_time(first_movers,sk1) = zero
| cardinality_at_time(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p74,p72]) ).
cnf(p78,plain,
( selection_favors(efficient_producers,first_movers,sk1)
| cardinality_at_time(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p77]) ).
fof(f4,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(f4_nnf,plain,
! [E,T] :
( ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [E,T] :
( ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p33,plain,
( subpopulation(efficient_producers,sk0,X0)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c5,c14]) ).
cnf(p34,plain,
subpopulation(efficient_producers,sk0,sk1),
inference(resolution,[status(thm)],[p33,c15]) ).
fof(f1,axiom,
! [E,S1,S2,T] :
( ( cardinality_at_time(S2,T) = zero
& greater(cardinality_at_time(S1,T),zero)
& subpopulation(S2,E,T)
& subpopulation(S1,E,T)
& environment(E) )
=> selection_favors(S1,S2,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members) ).
fof(f1_nnf,plain,
! [E,S1,S2,T] :
( selection_favors(S1,S2,T)
| cardinality_at_time(S2,T) != zero
| ~ greater(cardinality_at_time(S1,T),zero)
| ~ subpopulation(S2,E,T)
| ~ subpopulation(S1,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,S1,T,S2] :
( selection_favors(S1,S2,T)
| cardinality_at_time(S2,T) != zero
| ~ greater(cardinality_at_time(S1,T),zero)
| ~ subpopulation(S2,E,T)
| ~ subpopulation(S1,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( selection_favors(X1,X2,X3)
| cardinality_at_time(X2,X3) != zero
| ~ greater(cardinality_at_time(X1,X3),zero)
| ~ subpopulation(X2,X0,X3)
| ~ subpopulation(X1,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p22,plain,
( selection_favors(X0,X2,X1)
| cardinality_at_time(X2,X1) != zero
| ~ greater(cardinality_at_time(X0,X1),zero)
| ~ subpopulation(X2,sk0,X1)
| ~ subpopulation(X0,sk0,X1) ),
inference(resolution,[status(thm)],[c1,c14]) ).
cnf(p35,plain,
( selection_favors(efficient_producers,X0,sk1)
| cardinality_at_time(X0,sk1) != zero
| ~ greater(cardinality_at_time(efficient_producers,sk1),zero)
| ~ subpopulation(X0,sk0,sk1) ),
inference(resolution,[status(thm)],[p34,p22]) ).
cnf(c4,plain,
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p27,plain,
( subpopulation(first_movers,sk0,X0)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c4,c14]) ).
cnf(p29,plain,
subpopulation(first_movers,sk0,sk1),
inference(resolution,[status(thm)],[p27,c15]) ).
cnf(p39,plain,
( selection_favors(efficient_producers,first_movers,sk1)
| cardinality_at_time(first_movers,sk1) != zero
| ~ greater(cardinality_at_time(efficient_producers,sk1),zero) ),
inference(resolution,[status(thm)],[p35,p29]) ).
cnf(p60,plain,
( selection_favors(efficient_producers,first_movers,sk1)
| cardinality_at_time(first_movers,sk1) != zero
| greater(sk1,appear(efficient_producers,sk0)) ),
inference(resolution,[status(thm)],[p56,p39]) ).
cnf(p82,plain,
( selection_favors(efficient_producers,first_movers,sk1)
| greater(sk1,appear(efficient_producers,sk0))
| selection_favors(efficient_producers,first_movers,sk1) ),
inference(resolution,[status(thm)],[p78,p60]) ).
cnf(p83,plain,
( greater(sk1,appear(efficient_producers,sk0))
| selection_favors(efficient_producers,first_movers,sk1) ),
inference(factoring,[status(thm)],[p82]) ).
cnf(p84,plain,
( greater_or_equal(sk1,appear(efficient_producers,sk0))
| selection_favors(efficient_producers,first_movers,sk1) ),
inference(resolution,[status(thm)],[p83,c9]) ).
cnf(p86,plain,
( greater(cardinality_at_time(efficient_producers,sk1),zero)
| selection_favors(efficient_producers,first_movers,sk1) ),
inference(resolution,[status(thm)],[p84,p54]) ).
cnf(p90,plain,
( selection_favors(efficient_producers,first_movers,sk1)
| cardinality_at_time(first_movers,sk1) != zero
| selection_favors(efficient_producers,first_movers,sk1) ),
inference(resolution,[status(thm)],[p86,p39]) ).
cnf(p91,plain,
( cardinality_at_time(first_movers,sk1) != zero
| selection_favors(efficient_producers,first_movers,sk1) ),
inference(factoring,[status(thm)],[p90]) ).
cnf(p92,plain,
( selection_favors(efficient_producers,first_movers,sk1)
| selection_favors(efficient_producers,first_movers,sk1) ),
inference(resolution,[status(thm)],[p91,p78]) ).
cnf(p93,plain,
selection_favors(efficient_producers,first_movers,sk1),
inference(factoring,[status(thm)],[p92]) ).
cnf(c17,plain,
~ selection_favors(efficient_producers,first_movers,sk1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p94,plain,
$false,
inference(resolution,[status(thm)],[p93,c17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT026+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.37 % Computer : n019.cluster.edu
% 0.03/0.37 % Model : x86_64 x86_64
% 0.03/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.37 % Memory : 8046.5625MB
% 0.03/0.37 % OS : Linux 6.8.0-71-generic
% 0.03/0.37 % CPULimit : 300
% 0.03/0.37 % WCLimit : 300
% 0.03/0.37 % DateTime : Thu Sep 24 01:03:49 UTC 2026
% 0.03/0.38 % CPUTime :
% 0.03/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.60/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.60/2.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------