%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT030-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 02:11:33 PM UTC 2026
% Result : Unsatisfiable 5.48s 1.31s
% Output : Proof 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 16
% Syntax : Number of formulae : 126 ( 17 unt; 0 def)
% Number of atoms : 392 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 478 ( 212 ~; 266 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,hypothesis,
( greater(growth_rate(efficient_producers,B),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/sandbox2/benchmark/theBenchmark.p',l1_11) ).
fof(f10_nnf,plain,
! [A,B] :
( greater(growth_rate(efficient_producers,B),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)],[f10]) ).
fof(f10_sk,plain,
! [A,B] :
( greater(growth_rate(efficient_producers,B),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)],[f10_nnf]) ).
cnf(c10,plain,
( greater(growth_rate(efficient_producers,X1),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)],[f10_sk]) ).
cnf(f11,negated_conjecture,
environment(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l12_12) ).
fof(f11_nnf,plain,
environment(sk4),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
environment(sk4),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(p35,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c10,c11]) ).
cnf(f12,negated_conjecture,
stable(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l12_13) ).
fof(f12_nnf,plain,
stable(sk4),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
stable(sk4),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p36,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(resolution,[status(thm)],[p35,c12]) ).
cnf(f9,hypothesis,
( in_environment(A,sk3(A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_10) ).
fof(f9_nnf,plain,
! [A] :
( in_environment(A,sk3(A))
| ~ stable(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] :
( in_environment(A,sk3(A))
| ~ stable(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p17,plain,
( in_environment(sk4,sk3(sk4))
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c9,c11]) ).
cnf(p18,plain,
in_environment(sk4,sk3(sk4)),
inference(resolution,[status(thm)],[p17,c12]) ).
cnf(f0,axiom,
( in_environment(A,sk2(A))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_1) ).
fof(f0_nnf,plain,
! [A,B] :
( in_environment(A,sk2(A))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( in_environment(A,sk2(A))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( in_environment(X0,sk2(X0))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p16,plain,
( in_environment(sk4,sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c0,c11]) ).
cnf(p22,plain,
( in_environment(sk4,sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p18,p16]) ).
cnf(p38,plain,
( in_environment(sk4,sk2(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p36,p22]) ).
cnf(f1,axiom,
( in_environment(A,sk2(A))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_2) ).
fof(f1_nnf,plain,
! [A,B] :
( in_environment(A,sk2(A))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( in_environment(A,sk2(A))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( in_environment(X0,sk2(X0))
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p19,plain,
( in_environment(sk4,sk2(sk4))
| greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c1,c11]) ).
cnf(p24,plain,
( in_environment(sk4,sk2(sk4))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p19,p18]) ).
cnf(p40,plain,
( in_environment(sk4,sk2(sk4))
| in_environment(sk4,sk2(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolution,[status(thm)],[p38,p24]) ).
cnf(p42,plain,
( in_environment(sk4,sk2(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(factoring,[status(thm)],[p40]) ).
cnf(f6,axiom,
( in_environment(A,sk2(A))
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_7) ).
fof(f6_nnf,plain,
! [A,B] :
( in_environment(A,sk2(A))
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( in_environment(A,sk2(A))
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( in_environment(X0,sk2(X0))
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p33,plain,
( in_environment(sk4,sk2(sk4))
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c6,c11]) ).
cnf(p34,plain,
( in_environment(sk4,sk2(sk4))
| ~ greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolution,[status(thm)],[p33,p18]) ).
cnf(p43,plain,
( in_environment(sk4,sk2(sk4))
| in_environment(sk4,sk2(sk4)) ),
inference(resolution,[status(thm)],[p42,p34]) ).
cnf(p45,plain,
in_environment(sk4,sk2(sk4)),
inference(factoring,[status(thm)],[p43]) ).
cnf(f13,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sk4,sk5(A))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l12_14) ).
fof(f13_nnf,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(A))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(A))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p48,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(resolution,[status(thm)],[p45,c13]) ).
cnf(f2,axiom,
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_3) ).
fof(f2_nnf,plain,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p25,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c2,c11]) ).
cnf(p26,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p25,p18]) ).
cnf(p59,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(resolution,[status(thm)],[p48,p26]) ).
cnf(p61,plain,
( greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(resolution,[status(thm)],[p59,p36]) ).
cnf(f4,axiom,
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_5) ).
fof(f4_nnf,plain,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p29,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c4,c11]) ).
cnf(p31,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p29,p18]) ).
cnf(p60,plain,
( greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(resolution,[status(thm)],[p48,p31]) ).
cnf(p76,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(resolution,[status(thm)],[p61,p60]) ).
cnf(p77,plain,
( greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(factoring,[status(thm)],[p76]) ).
cnf(f7,axiom,
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_8) ).
fof(f7_nnf,plain,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p37,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(p39,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolution,[status(thm)],[p37,p18]) ).
cnf(p78,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(resolution,[status(thm)],[p77,p39]) ).
cnf(p80,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(resolution,[status(thm)],[p78,p48]) ).
cnf(p81,plain,
subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))),
inference(factoring,[status(thm)],[p80]) ).
cnf(f3,axiom,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_4) ).
fof(f3_nnf,plain,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p27,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(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)],[c3,c11]) ).
cnf(p28,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p27,p18]) ).
cnf(p82,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p81,p28]) ).
cnf(f14,negated_conjecture,
( greater(sk5(A),A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l12_15) ).
fof(f14_nnf,plain,
! [A] :
( greater(sk5(A),A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A] :
( greater(sk5(A),A)
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( greater(sk5(X0),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p46,plain,
( greater(sk5(sk2(sk4)),sk2(sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(resolution,[status(thm)],[p45,c14]) ).
cnf(p56,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| greater(sk5(sk2(sk4)),sk2(sk4)) ),
inference(resolution,[status(thm)],[p46,p26]) ).
cnf(p58,plain,
( greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
| greater(sk5(sk2(sk4)),sk2(sk4)) ),
inference(resolution,[status(thm)],[p56,p36]) ).
cnf(p57,plain,
( greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
| greater(sk5(sk2(sk4)),sk2(sk4)) ),
inference(resolution,[status(thm)],[p46,p31]) ).
cnf(p68,plain,
( greater(sk5(sk2(sk4)),sk2(sk4))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(sk5(sk2(sk4)),sk2(sk4)) ),
inference(resolution,[status(thm)],[p58,p57]) ).
cnf(p70,plain,
( greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| greater(sk5(sk2(sk4)),sk2(sk4)) ),
inference(factoring,[status(thm)],[p68]) ).
cnf(p71,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater(sk5(sk2(sk4)),sk2(sk4)) ),
inference(resolution,[status(thm)],[p70,p39]) ).
cnf(p73,plain,
( greater(sk5(sk2(sk4)),sk2(sk4))
| greater(sk5(sk2(sk4)),sk2(sk4)) ),
inference(resolution,[status(thm)],[p71,p46]) ).
cnf(p75,plain,
greater(sk5(sk2(sk4)),sk2(sk4)),
inference(factoring,[status(thm)],[p73]) ).
cnf(p88,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p82,p75]) ).
cnf(f15,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sk5(A)),growth_rate(first_movers,sk5(A)))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l12_16) ).
fof(f15_nnf,plain,
! [A] :
( ~ greater(growth_rate(efficient_producers,sk5(A)),growth_rate(first_movers,sk5(A)))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A] :
( ~ greater(growth_rate(efficient_producers,sk5(A)),growth_rate(first_movers,sk5(A)))
| greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ in_environment(sk4,A) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ greater(growth_rate(efficient_producers,sk5(X0)),growth_rate(first_movers,sk5(X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p47,plain,
( ~ greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(resolution,[status(thm)],[p45,c15]) ).
cnf(p96,plain,
( greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p88,p47]) ).
cnf(p97,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[p96,p26]) ).
cnf(p103,plain,
subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)),
inference(factoring,[status(thm)],[p97]) ).
cnf(p105,plain,
( greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p103,p36]) ).
cnf(f5,axiom,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_6) ).
fof(f5_nnf,plain,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p30,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(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)],[c5,c11]) ).
cnf(p32,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p30,p18]) ).
cnf(p83,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p81,p32]) ).
cnf(p87,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p83,p75]) ).
cnf(p89,plain,
( greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p87,p47]) ).
cnf(p91,plain,
( greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[p89,p31]) ).
cnf(p94,plain,
greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)),
inference(factoring,[status(thm)],[p91]) ).
cnf(p116,plain,
greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))),
inference(resolution,[status(thm)],[p105,p94]) ).
cnf(f8,axiom,
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_9) ).
fof(f8_nnf,plain,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] :
( greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C))
| ~ greater(C,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p41,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c8,c11]) ).
cnf(p54,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolution,[status(thm)],[p41,p18]) ).
cnf(p118,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(resolution,[status(thm)],[p116,p54]) ).
cnf(p119,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4)) ),
inference(resolution,[status(thm)],[p118,p81]) ).
cnf(p121,plain,
greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4)))),
inference(resolution,[status(thm)],[p119,p75]) ).
cnf(p122,plain,
greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))),
inference(resolution,[status(thm)],[p121,p47]) ).
cnf(p117,plain,
~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))),
inference(resolution,[status(thm)],[p116,p39]) ).
cnf(p123,plain,
$false,
inference(resolution,[status(thm)],[p122,p117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT030-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 01:03:22 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.48/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.48/1.31 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------