%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT026-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 : Unsatisfiable 16.91s 2.77s
% Output : Proof 16.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 107 ( 20 unt; 0 def)
% Number of atoms : 298 ( 36 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 350 ( 159 ~; 191 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 132 ( 0 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,axiom,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_36) ).
fof(f8_nnf,plain,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f6,axiom,
( greater_or_equal(critical_point(A),appear(efficient_producers,A))
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_after_EP_34) ).
fof(f6_nnf,plain,
! [A] :
( greater_or_equal(critical_point(A),appear(efficient_producers,A))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] :
( greater_or_equal(critical_point(A),appear(efficient_producers,A))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f14,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_42) ).
fof(f14_nnf,plain,
environment(sk1),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
environment(sk1),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(p24,plain,
greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)),
inference(resolution,[status(thm)],[c6,c14]) ).
cnf(p40,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[c8,p24]) ).
cnf(f7,axiom,
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity_35) ).
fof(f7_nnf,plain,
! [A,B,C] :
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] :
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f16,negated_conjecture,
greater(sk2,critical_point(sk1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_44) ).
fof(f16_nnf,plain,
greater(sk2,critical_point(sk1)),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
greater(sk2,critical_point(sk1)),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(p37,plain,
( greater(sk2,X0)
| ~ greater(critical_point(sk1),X0) ),
inference(resolution,[status(thm)],[c7,c16]) ).
cnf(p46,plain,
( greater(sk2,appear(efficient_producers,sk1))
| critical_point(sk1) = appear(efficient_producers,sk1) ),
inference(resolution,[status(thm)],[p40,p37]) ).
cnf(f13,hypothesis,
( greater(cardinality_at_time(efficient_producers,B),zero)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_41) ).
fof(f13_nnf,plain,
! [A,B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f13_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)],[f13_sk]) ).
cnf(p53,plain,
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c13,c14]) ).
cnf(f15,negated_conjecture,
in_environment(sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_43) ).
fof(f15_nnf,plain,
in_environment(sk1,sk2),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
in_environment(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(p54,plain,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ greater_or_equal(sk2,appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p53,c15]) ).
cnf(p55,plain,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ greater_or_equal(sk2,critical_point(sk1))
| greater(sk2,appear(efficient_producers,sk1)) ),
inference(superposition,[status(thm)],[p46,p54]) ).
cnf(f9,axiom,
( greater_or_equal(A,B)
| ~ greater(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_37) ).
fof(f9_nnf,plain,
! [A,B] :
( greater_or_equal(A,B)
| ~ greater(A,B) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] :
( greater_or_equal(A,B)
| ~ greater(A,B) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p19,plain,
greater_or_equal(sk2,critical_point(sk1)),
inference(resolution,[status(thm)],[c9,c16]) ).
cnf(p56,plain,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| greater(sk2,appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p55,p19]) ).
cnf(f3,axiom,
( greater_or_equal(cardinality_at_time(first_movers,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_exist_31) ).
fof(f3_nnf,plain,
! [A,B] :
( greater_or_equal(cardinality_at_time(first_movers,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( greater_or_equal(cardinality_at_time(first_movers,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
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(sk1,X0) ),
inference(resolution,[status(thm)],[c3,c14]) ).
cnf(p32,plain,
greater_or_equal(cardinality_at_time(first_movers,sk2),zero),
inference(resolution,[status(thm)],[p28,c15]) ).
cnf(p41,plain,
( cardinality_at_time(first_movers,sk2) = zero
| greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolution,[status(thm)],[c8,p32]) ).
cnf(f2,axiom,
( subpopulations(first_movers,efficient_producers,A,B)
| ~ greater(cardinality_at_time(efficient_producers,B),zero)
| ~ greater(cardinality_at_time(first_movers,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_30) ).
fof(f2_nnf,plain,
! [A,B] :
( subpopulations(first_movers,efficient_producers,A,B)
| ~ greater(cardinality_at_time(efficient_producers,B),zero)
| ~ greater(cardinality_at_time(first_movers,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( subpopulations(first_movers,efficient_producers,A,B)
| ~ greater(cardinality_at_time(efficient_producers,B),zero)
| ~ greater(cardinality_at_time(first_movers,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
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,sk1,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c2,c14]) ).
cnf(p26,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolution,[status(thm)],[p25,c15]) ).
cnf(p42,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolution,[status(thm)],[p41,p26]) ).
cnf(p61,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| greater(sk2,appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p56,p42]) ).
cnf(p62,plain,
( greater_or_equal(sk2,appear(efficient_producers,sk1))
| subpopulations(first_movers,efficient_producers,sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolution,[status(thm)],[p61,c9]) ).
cnf(p64,plain,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| subpopulations(first_movers,efficient_producers,sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolution,[status(thm)],[p62,p54]) ).
cnf(p68,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| subpopulations(first_movers,efficient_producers,sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolution,[status(thm)],[p64,p42]) ).
cnf(p69,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| subpopulations(first_movers,efficient_producers,sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero ),
inference(factoring,[status(thm)],[p68]) ).
cnf(p71,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| cardinality_at_time(first_movers,sk2) = zero ),
inference(factoring,[status(thm)],[p69]) ).
cnf(f12,hypothesis,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| B != critical_point(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_40) ).
fof(f12_nnf,plain,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| B != critical_point(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| B != critical_point(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f12_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)],[f12_sk]) ).
cnf(p51,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| X0 != critical_point(sk1) ),
inference(resolution,[status(thm)],[c12,c14]) ).
cnf(p52,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,critical_point(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(equality_resolution,[status(thm)],[p51]) ).
cnf(p73,plain,
( greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
| ~ greater(sk2,critical_point(sk1))
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolution,[status(thm)],[p71,p52]) ).
cnf(p74,plain,
( greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolution,[status(thm)],[p73,c16]) ).
cnf(f0,axiom,
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates_28) ).
fof(f0_nnf,plain,
! [A,B,C,D] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C,D] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
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,sk1,X2) ),
inference(resolution,[status(thm)],[c0,c14]) ).
cnf(p72,plain,
( selection_favors(efficient_producers,first_movers,sk2)
| ~ greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolution,[status(thm)],[p71,p18]) ).
cnf(p77,plain,
( selection_favors(efficient_producers,first_movers,sk2)
| cardinality_at_time(first_movers,sk2) = zero
| cardinality_at_time(first_movers,sk2) = zero ),
inference(resolution,[status(thm)],[p74,p72]) ).
cnf(p78,plain,
( selection_favors(efficient_producers,first_movers,sk2)
| cardinality_at_time(first_movers,sk2) = zero ),
inference(factoring,[status(thm)],[p77]) ).
cnf(f5,axiom,
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_33) ).
fof(f5_nnf,plain,
! [A,B] :
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p33,plain,
( subpopulation(efficient_producers,sk1,X0)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c5,c14]) ).
cnf(p34,plain,
subpopulation(efficient_producers,sk1,sk2),
inference(resolution,[status(thm)],[p33,c15]) ).
cnf(f1,axiom,
( selection_favors(B,D,C)
| cardinality_at_time(D,C) != zero
| ~ greater(cardinality_at_time(B,C),zero)
| ~ subpopulation(D,A,C)
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp2_favour_members_29) ).
fof(f1_nnf,plain,
! [A,B,C,D] :
( selection_favors(B,D,C)
| cardinality_at_time(D,C) != zero
| ~ greater(cardinality_at_time(B,C),zero)
| ~ subpopulation(D,A,C)
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C,D] :
( selection_favors(B,D,C)
| cardinality_at_time(D,C) != zero
| ~ greater(cardinality_at_time(B,C),zero)
| ~ subpopulation(D,A,C)
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( selection_favors(X1,X3,X2)
| cardinality_at_time(X3,X2) != zero
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X3,X0,X2)
| ~ subpopulation(X1,X0,X2)
| ~ 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,sk1,X1)
| ~ subpopulation(X0,sk1,X1) ),
inference(resolution,[status(thm)],[c1,c14]) ).
cnf(p35,plain,
( selection_favors(efficient_producers,X0,sk2)
| cardinality_at_time(X0,sk2) != zero
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ subpopulation(X0,sk1,sk2) ),
inference(resolution,[status(thm)],[p34,p22]) ).
cnf(f4,axiom,
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_32) ).
fof(f4_nnf,plain,
! [A,B] :
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
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,sk1,X0)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c4,c14]) ).
cnf(p29,plain,
subpopulation(first_movers,sk1,sk2),
inference(resolution,[status(thm)],[p27,c15]) ).
cnf(p39,plain,
( selection_favors(efficient_producers,first_movers,sk2)
| cardinality_at_time(first_movers,sk2) != zero
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolution,[status(thm)],[p35,p29]) ).
cnf(p60,plain,
( selection_favors(efficient_producers,first_movers,sk2)
| cardinality_at_time(first_movers,sk2) != zero
| greater(sk2,appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p56,p39]) ).
cnf(p82,plain,
( selection_favors(efficient_producers,first_movers,sk2)
| greater(sk2,appear(efficient_producers,sk1))
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolution,[status(thm)],[p78,p60]) ).
cnf(p83,plain,
( greater(sk2,appear(efficient_producers,sk1))
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(factoring,[status(thm)],[p82]) ).
cnf(p84,plain,
( greater_or_equal(sk2,appear(efficient_producers,sk1))
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolution,[status(thm)],[p83,c9]) ).
cnf(p86,plain,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolution,[status(thm)],[p84,p54]) ).
cnf(p90,plain,
( selection_favors(efficient_producers,first_movers,sk2)
| cardinality_at_time(first_movers,sk2) != zero
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolution,[status(thm)],[p86,p39]) ).
cnf(p91,plain,
( cardinality_at_time(first_movers,sk2) != zero
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(factoring,[status(thm)],[p90]) ).
cnf(p92,plain,
( selection_favors(efficient_producers,first_movers,sk2)
| selection_favors(efficient_producers,first_movers,sk2) ),
inference(resolution,[status(thm)],[p91,p78]) ).
cnf(p93,plain,
selection_favors(efficient_producers,first_movers,sk2),
inference(factoring,[status(thm)],[p92]) ).
cnf(f17,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_45) ).
fof(f17_nnf,plain,
~ selection_favors(efficient_producers,first_movers,sk2),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
~ selection_favors(efficient_producers,first_movers,sk2),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
~ selection_favors(efficient_producers,first_movers,sk2),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p94,plain,
$false,
inference(resolution,[status(thm)],[p93,c17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT026-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 01:04:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.91/2.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.91/2.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------