%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT028-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 4.24s 1.46s
% Output : Proof 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 92 ( 13 unt; 0 def)
% Number of atoms : 331 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 441 ( 202 ~; 239 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,hypothesis,
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk3(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11_9) ).
fof(f8_nnf,plain,
! [A,B] :
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk3(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk3(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f9,negated_conjecture,
environment(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_10) ).
fof(f9_nnf,plain,
environment(sk4),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
environment(sk4),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(p37,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c8,c9]) ).
cnf(f10,negated_conjecture,
stable(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_11) ).
fof(f10_nnf,plain,
stable(sk4),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
stable(sk4),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(p38,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(resolution,[status(thm)],[p37,c10]) ).
cnf(f6,hypothesis,
( in_environment(A,sk3(A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11_7) ).
fof(f6_nnf,plain,
! [A] :
( in_environment(A,sk3(A))
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] :
( in_environment(A,sk3(A))
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p16,plain,
( in_environment(sk4,sk3(sk4))
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c6,c9]) ).
cnf(p18,plain,
in_environment(sk4,sk3(sk4)),
inference(resolution,[status(thm)],[p16,c10]) ).
cnf(f0,axiom,
( greater(sk2(A),appear(efficient_producers,A))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_1) ).
fof(f0_nnf,plain,
! [A,B] :
( greater(sk2(A),appear(efficient_producers,A))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( greater(sk2(A),appear(efficient_producers,A))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( greater(sk2(X0),appear(efficient_producers,X0))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p14,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0)
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c0,c9]) ).
cnf(p15,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[p14,c10]) ).
cnf(p19,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p18,p15]) ).
cnf(p39,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p38,p19]) ).
cnf(f1,axiom,
( greater(sk2(A),appear(efficient_producers,A))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_2) ).
fof(f1_nnf,plain,
! [A,B] :
( greater(sk2(A),appear(efficient_producers,A))
| 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] :
( greater(sk2(A),appear(efficient_producers,A))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( greater(sk2(X0),appear(efficient_producers,X0))
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p17,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0)
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c1,c9]) ).
cnf(p20,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[p17,c10]) ).
cnf(p22,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p20,p18]) ).
cnf(p40,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| greater(sk2(sk4),appear(efficient_producers,sk4))
| greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolution,[status(thm)],[p39,p22]) ).
cnf(p42,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(factoring,[status(thm)],[p40]) ).
cnf(f4,axiom,
( greater(sk2(A),appear(efficient_producers,A))
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_5) ).
fof(f4_nnf,plain,
! [A,B] :
( greater(sk2(A),appear(efficient_producers,A))
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( greater(sk2(A),appear(efficient_producers,A))
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( greater(sk2(X0),appear(efficient_producers,X0))
| ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p28,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0)
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c4,c9]) ).
cnf(p29,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[p28,c10]) ).
cnf(p30,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolution,[status(thm)],[p29,p18]) ).
cnf(p43,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| greater(sk2(sk4),appear(efficient_producers,sk4)) ),
inference(resolution,[status(thm)],[p42,p30]) ).
cnf(p44,plain,
greater(sk2(sk4),appear(efficient_producers,sk4)),
inference(factoring,[status(thm)],[p43]) ).
cnf(f11,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sk4,sk5(A))
| ~ greater(A,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_12) ).
fof(f11_nnf,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(A))
| ~ greater(A,appear(efficient_producers,sk4)) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(A))
| ~ greater(A,appear(efficient_producers,sk4)) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| ~ greater(X0,appear(efficient_producers,sk4)) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p46,plain,
subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))),
inference(resolution,[status(thm)],[p44,c11]) ).
cnf(f2,axiom,
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_3) ).
fof(f2_nnf,plain,
! [A,B,C] :
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p21,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0)
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c2,c9]) ).
cnf(p23,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[p21,c10]) ).
cnf(p24,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p23,p18]) ).
cnf(p49,plain,
( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater_or_equal(sk5(sk2(sk4)),sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p46,p24]) ).
cnf(f12,negated_conjecture,
( greater_or_equal(sk5(A),A)
| ~ greater(A,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_13) ).
fof(f12_nnf,plain,
! [A] :
( greater_or_equal(sk5(A),A)
| ~ greater(A,appear(efficient_producers,sk4)) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] :
( greater_or_equal(sk5(A),A)
| ~ greater(A,appear(efficient_producers,sk4)) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( greater_or_equal(sk5(X0),X0)
| ~ greater(X0,appear(efficient_producers,sk4)) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p45,plain,
greater_or_equal(sk5(sk2(sk4)),sk2(sk4)),
inference(resolution,[status(thm)],[p44,c12]) ).
cnf(p54,plain,
( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p49,p45]) ).
cnf(p56,plain,
( greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
| greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))) ),
inference(resolution,[status(thm)],[p54,p38]) ).
cnf(f3,axiom,
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_4) ).
fof(f3_nnf,plain,
! [A,B,C] :
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p25,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0)
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c3,c9]) ).
cnf(p26,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[p25,c10]) ).
cnf(p27,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p26,p18]) ).
cnf(p50,plain,
( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater_or_equal(sk5(sk2(sk4)),sk2(sk4))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p46,p27]) ).
cnf(p53,plain,
( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p50,p45]) ).
cnf(p58,plain,
( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
| greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))) ),
inference(resolution,[status(thm)],[p56,p53]) ).
cnf(p60,plain,
( greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))) ),
inference(factoring,[status(thm)],[p58]) ).
cnf(f5,axiom,
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_6) ).
fof(f5_nnf,plain,
! [A,B,C] :
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( greater(zero,growth_rate(first_movers,C))
| ~ greater_or_equal(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p32,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0)
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c5,c9]) ).
cnf(p41,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[p32,c10]) ).
cnf(p48,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolution,[status(thm)],[p41,p18]) ).
cnf(p61,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))) ),
inference(resolution,[status(thm)],[p60,p48]) ).
cnf(p62,plain,
( ~ greater_or_equal(sk5(sk2(sk4)),sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))) ),
inference(factoring,[status(thm)],[p61]) ).
cnf(p64,plain,
( ~ greater_or_equal(sk5(sk2(sk4)),sk2(sk4))
| greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))) ),
inference(resolution,[status(thm)],[p62,p46]) ).
cnf(p65,plain,
greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))),
inference(resolution,[status(thm)],[p64,p45]) ).
cnf(f13,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk5(A)))
| ~ greater(A,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_14) ).
fof(f13_nnf,plain,
! [A] :
( ~ greater(zero,growth_rate(first_movers,sk5(A)))
| ~ greater(A,appear(efficient_producers,sk4)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A] :
( ~ greater(zero,growth_rate(first_movers,sk5(A)))
| ~ greater(A,appear(efficient_producers,sk4)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ greater(zero,growth_rate(first_movers,sk5(X0)))
| ~ greater(X0,appear(efficient_producers,sk4)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p47,plain,
~ greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))),
inference(resolution,[status(thm)],[p44,c13]) ).
cnf(p66,plain,
$false,
inference(resolution,[status(thm)],[p65,p47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT028-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 01:04:41 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.24/1.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.24/1.46 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------