%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT027-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 10.26s 1.99s
% Output : Proof 10.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 16
% Syntax : Number of formulae : 130 ( 15 unt; 0 def)
% Number of atoms : 403 ( 22 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 467 ( 194 ~; 273 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f11,hypothesis,
( greater(sk2(A),appear(efficient_producers,A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10_35) ).
fof(f11_nnf,plain,
! [A] :
( greater(sk2(A),appear(efficient_producers,A))
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] :
( greater(sk2(A),appear(efficient_producers,A))
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(f13,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_37) ).
fof(f13_nnf,plain,
environment(sk3),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
environment(sk3),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(p44,plain,
( greater(sk2(sk3),appear(efficient_producers,sk3))
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c11,c13]) ).
cnf(f14,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_38) ).
fof(f14_nnf,plain,
stable(sk3),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
stable(sk3),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(p45,plain,
greater(sk2(sk3),appear(efficient_producers,sk3)),
inference(resolution,[status(thm)],[p44,c14]) ).
cnf(f4,axiom,
( in_environment(A,C)
| ~ greater(C,B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_long_stable_environments_28) ).
fof(f4_nnf,plain,
! [A,B,C] :
( in_environment(A,C)
| ~ greater(C,B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( in_environment(A,C)
| ~ greater(C,B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p31,plain,
( in_environment(sk3,X1)
| ~ greater(X1,X0)
| ~ in_environment(sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c4,c13]) ).
cnf(p32,plain,
( in_environment(sk3,X1)
| ~ greater(X1,X0)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[p31,c14]) ).
cnf(f5,axiom,
( in_environment(A,appear(efficient_producers,A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_EP_in_stable_environments_29) ).
fof(f5_nnf,plain,
! [A] :
( in_environment(A,appear(efficient_producers,A))
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( in_environment(A,appear(efficient_producers,A))
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p21,plain,
( in_environment(sk3,appear(efficient_producers,sk3))
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c5,c13]) ).
cnf(p22,plain,
in_environment(sk3,appear(efficient_producers,sk3)),
inference(resolution,[status(thm)],[p21,c14]) ).
cnf(p33,plain,
( in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(resolution,[status(thm)],[p32,p22]) ).
cnf(p48,plain,
in_environment(sk3,sk2(sk3)),
inference(resolution,[status(thm)],[p45,p33]) ).
cnf(f1,axiom,
( contracts_from(B,first_movers)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_25) ).
fof(f1_nnf,plain,
! [A,B] :
( contracts_from(B,first_movers)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( contracts_from(B,first_movers)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( contracts_from(X1,first_movers)
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p19,plain,
( contracts_from(X0,first_movers)
| greater_or_equal(sk1(X0,sk3),X0)
| ~ in_environment(sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c1,c13]) ).
cnf(p20,plain,
( contracts_from(X0,first_movers)
| greater_or_equal(sk1(X0,sk3),X0)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[p19,c14]) ).
cnf(p51,plain,
( contracts_from(sk2(sk3),first_movers)
| greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolution,[status(thm)],[p48,p20]) ).
cnf(f7,axiom,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_31) ).
fof(f7_nnf,plain,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p60,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p51,c7]) ).
cnf(p54,plain,
( in_environment(sk3,X0)
| ~ greater(X0,sk2(sk3)) ),
inference(resolution,[status(thm)],[p48,p32]) ).
cnf(p68,plain,
( in_environment(sk3,sk1(sk2(sk3),sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p60,p54]) ).
cnf(f0,axiom,
( contracts_from(B,first_movers)
| greater(cardinality_at_time(first_movers,sk1(B,A)),zero)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_24) ).
fof(f0_nnf,plain,
! [A,B] :
( contracts_from(B,first_movers)
| greater(cardinality_at_time(first_movers,sk1(B,A)),zero)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( contracts_from(B,first_movers)
| greater(cardinality_at_time(first_movers,sk1(B,A)),zero)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( contracts_from(X1,first_movers)
| greater(cardinality_at_time(first_movers,sk1(X1,X0)),zero)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p16,plain,
( contracts_from(X0,first_movers)
| greater(cardinality_at_time(first_movers,sk1(X0,sk3)),zero)
| ~ in_environment(sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c0,c13]) ).
cnf(p17,plain,
( contracts_from(X0,first_movers)
| greater(cardinality_at_time(first_movers,sk1(X0,sk3)),zero)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[p16,c14]) ).
cnf(p50,plain,
( contracts_from(sk2(sk3),first_movers)
| greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) ),
inference(resolution,[status(thm)],[p48,p17]) ).
cnf(p70,plain,
( contracts_from(sk2(sk3),first_movers)
| greater(cardinality_at_time(first_movers,sk2(sk3)),zero)
| in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(superposition,[status(thm)],[p68,p50]) ).
cnf(p76,plain,
( greater(cardinality_at_time(first_movers,sk2(sk3)),zero)
| in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p70]) ).
cnf(f3,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/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_27) ).
fof(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,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)],[f3_sk]) ).
cnf(p27,plain,
( subpopulations(first_movers,efficient_producers,sk3,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c3,c13]) ).
cnf(p53,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| ~ greater(cardinality_at_time(first_movers,sk2(sk3)),zero) ),
inference(resolution,[status(thm)],[p48,p27]) ).
cnf(p80,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p76,p53]) ).
cnf(f10,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/sandbox2/benchmark/theBenchmark.p',t6_34) ).
fof(f10_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)],[f10]) ).
fof(f10_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)],[f10_nnf]) ).
cnf(c10,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)],[f10_sk]) ).
cnf(p39,plain,
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,appear(efficient_producers,sk3))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c10,c13]) ).
cnf(p55,plain,
( greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| ~ greater_or_equal(sk2(sk3),appear(efficient_producers,sk3)) ),
inference(resolution,[status(thm)],[p48,p39]) ).
cnf(f8,axiom,
( greater_or_equal(A,B)
| ~ greater(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_32) ).
fof(f8_nnf,plain,
! [A,B] :
( greater_or_equal(A,B)
| ~ greater(A,B) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( greater_or_equal(A,B)
| ~ greater(A,B) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p47,plain,
greater_or_equal(sk2(sk3),appear(efficient_producers,sk3)),
inference(resolution,[status(thm)],[p45,c8]) ).
cnf(p63,plain,
greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero),
inference(resolution,[status(thm)],[p55,p47]) ).
cnf(p88,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
| in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p80,p63]) ).
cnf(f12,hypothesis,
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10_36) ).
fof(f12_nnf,plain,
! [A,B] :
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B] :
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p56,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c12,c13]) ).
cnf(p66,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(resolution,[status(thm)],[p56,c14]) ).
cnf(p89,plain,
( greater(zero,growth_rate(first_movers,sk2(sk3)))
| ~ greater_or_equal(sk2(sk3),sk2(sk3))
| in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p88,p66]) ).
cnf(f9,axiom,
( greater_or_equal(A,B)
| A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_33) ).
fof(f9_nnf,plain,
! [A,B] :
( greater_or_equal(A,B)
| A != B ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] :
( greater_or_equal(A,B)
| A != B ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( greater_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p18,plain,
greater_or_equal(X0,X0),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(p90,plain,
( greater(zero,growth_rate(first_movers,sk2(sk3)))
| in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p89,p18]) ).
cnf(f2,axiom,
( contracts_from(B,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_26) ).
fof(f2_nnf,plain,
! [A,B] :
( contracts_from(B,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( contracts_from(B,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( contracts_from(X1,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p23,plain,
( contracts_from(X0,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk3)))
| ~ in_environment(sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c2,c13]) ).
cnf(p28,plain,
( contracts_from(X0,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk3)))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[p23,c14]) ).
cnf(p52,plain,
( contracts_from(sk2(sk3),first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolution,[status(thm)],[p48,p28]) ).
cnf(p71,plain,
( contracts_from(sk2(sk3),first_movers)
| ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(superposition,[status(thm)],[p68,p52]) ).
cnf(p85,plain,
( ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p71]) ).
cnf(p98,plain,
( in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers)
| in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p90,p85]) ).
cnf(p107,plain,
( contracts_from(sk2(sk3),first_movers)
| in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p98]) ).
cnf(p108,plain,
( in_environment(sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p107]) ).
cnf(p112,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p108,p27]) ).
cnf(p122,plain,
( contracts_from(sk2(sk3),first_movers)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p112,p50]) ).
cnf(p123,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p122]) ).
cnf(p114,plain,
( greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ greater_or_equal(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p108,p39]) ).
cnf(f6,axiom,
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity_30) ).
fof(f6_nnf,plain,
! [A,B,C] :
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p67,plain,
( greater(sk1(sk2(sk3),sk3),X0)
| ~ greater(sk2(sk3),X0)
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p60,c6]) ).
cnf(p81,plain,
( greater(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p67,p45]) ).
cnf(p83,plain,
( greater_or_equal(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p81,c8]) ).
cnf(p117,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers)
| greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p114,p83]) ).
cnf(p119,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p117]) ).
cnf(p124,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p123,p119]) ).
cnf(p125,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p124]) ).
cnf(p128,plain,
( greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p125,p66]) ).
cnf(p129,plain,
( contracts_from(sk2(sk3),first_movers)
| greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p128,p51]) ).
cnf(p130,plain,
( greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p129]) ).
cnf(p135,plain,
( contracts_from(sk2(sk3),first_movers)
| sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p130,p52]) ).
cnf(p138,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p135]) ).
cnf(p139,plain,
( contracts_from(sk2(sk3),first_movers)
| greater(cardinality_at_time(first_movers,sk2(sk3)),zero)
| contracts_from(sk2(sk3),first_movers) ),
inference(superposition,[status(thm)],[p138,p50]) ).
cnf(p148,plain,
( greater(cardinality_at_time(first_movers,sk2(sk3)),zero)
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p139]) ).
cnf(p151,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p148,p53]) ).
cnf(p155,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p151,p63]) ).
cnf(p156,plain,
( greater(zero,growth_rate(first_movers,sk2(sk3)))
| ~ greater_or_equal(sk2(sk3),sk2(sk3))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p155,p66]) ).
cnf(p157,plain,
( greater(zero,growth_rate(first_movers,sk2(sk3)))
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p156,p18]) ).
cnf(p140,plain,
( contracts_from(sk2(sk3),first_movers)
| ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| contracts_from(sk2(sk3),first_movers) ),
inference(superposition,[status(thm)],[p138,p52]) ).
cnf(p153,plain,
( ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| contracts_from(sk2(sk3),first_movers) ),
inference(factoring,[status(thm)],[p140]) ).
cnf(p167,plain,
( contracts_from(sk2(sk3),first_movers)
| contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[p157,p153]) ).
cnf(p168,plain,
contracts_from(sk2(sk3),first_movers),
inference(factoring,[status(thm)],[p167]) ).
cnf(f15,negated_conjecture,
( ~ contracts_from(A,first_movers)
| ~ greater(A,appear(efficient_producers,sk3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_39) ).
fof(f15_nnf,plain,
! [A] :
( ~ contracts_from(A,first_movers)
| ~ greater(A,appear(efficient_producers,sk3)) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A] :
( ~ contracts_from(A,first_movers)
| ~ greater(A,appear(efficient_producers,sk3)) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ contracts_from(X0,first_movers)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p46,plain,
~ contracts_from(sk2(sk3),first_movers),
inference(resolution,[status(thm)],[p45,c15]) ).
cnf(p169,plain,
$false,
inference(resolution,[status(thm)],[p168,p46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT027-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n013.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 01:03:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.26/1.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.26/1.99 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------