%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 02:11:21 PM UTC 2026
% Result : Theorem 3.32s 11.54s
% Output : Proof 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 4
% Syntax : Number of formulae : 108 ( 8 unt; 0 def)
% Number of atoms : 385 ( 67 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 409 ( 132 ~; 235 |; 33 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 24 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5) ).
fof(f3_neg,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [E] :
( ~ in_environment(E,critical_point(E))
& stable(E)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ~ in_environment(sk4,critical_point(sk4))
& stable(sk4)
& environment(sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f3_nnf]) ).
cnf(c14,plain,
environment(sk4),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f2,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(f2_nnf,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,To) )
| ~ stable(E)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [E,T] :
( ( ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,sk3(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,sk3(E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f2_nnf]) ).
cnf(c12,plain,
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p29,plain,
( in_environment(sk4,sk3(sk4))
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c14,c12]) ).
cnf(c15,plain,
stable(sk4),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p31,plain,
in_environment(sk4,sk3(sk4)),
inference(resolution,[status(thm)],[p29,c15]) ).
fof(f0,axiom,
! [E] :
( ( ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) )
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).
fof(f0_nnf,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) )
| ! [To] :
( ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To) )
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,To,T] :
( ( ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,sk1(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,sk1(E)),growth_rate(first_movers,sk1(E)))
& in_environment(E,sk1(E)) )
| ( ~ greater(growth_rate(efficient_producers,sk0(E,To)),growth_rate(first_movers,sk0(E,To)))
& greater_or_equal(sk0(E,To),To)
& subpopulations(first_movers,efficient_producers,E,sk0(E,To)) )
| ~ in_environment(E,To)
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c0,plain,
( in_environment(X0,sk1(X0))
| subpopulations(first_movers,efficient_producers,X0,sk0(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p17,plain,
( in_environment(sk4,sk1(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,X0))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c14,c0]) ).
cnf(p33,plain,
( in_environment(sk4,sk1(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4))) ),
inference(resolution,[status(thm)],[p31,p17]) ).
cnf(c13,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p30,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)],[c14,c13]) ).
cnf(p32,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)],[p30,c15]) ).
cnf(p45,plain,
( greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4))))
| ~ greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| in_environment(sk4,sk1(sk4)) ),
inference(resolution,[status(thm)],[p33,p32]) ).
cnf(c3,plain,
( in_environment(X0,sk1(X0))
| greater_or_equal(sk0(X0,X1),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p20,plain,
( in_environment(sk4,sk1(sk4))
| greater_or_equal(sk0(sk4,X0),X0)
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c14,c3]) ).
cnf(p36,plain,
( in_environment(sk4,sk1(sk4))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4)) ),
inference(resolution,[status(thm)],[p31,p20]) ).
cnf(p46,plain,
( in_environment(sk4,sk1(sk4))
| greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4))))
| in_environment(sk4,sk1(sk4)) ),
inference(resolution,[status(thm)],[p45,p36]) ).
cnf(p47,plain,
( greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4))))
| in_environment(sk4,sk1(sk4)) ),
inference(factoring,[status(thm)],[p46]) ).
cnf(c6,plain,
( in_environment(X0,sk1(X0))
| ~ greater(growth_rate(efficient_producers,sk0(X0,X1)),growth_rate(first_movers,sk0(X0,X1)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p23,plain,
( in_environment(sk4,sk1(sk4))
| ~ greater(growth_rate(efficient_producers,sk0(sk4,X0)),growth_rate(first_movers,sk0(sk4,X0)))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c14,c6]) ).
cnf(p39,plain,
( in_environment(sk4,sk1(sk4))
| ~ greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4)))) ),
inference(resolution,[status(thm)],[p31,p23]) ).
cnf(p48,plain,
( in_environment(sk4,sk1(sk4))
| in_environment(sk4,sk1(sk4)) ),
inference(resolution,[status(thm)],[p47,p39]) ).
cnf(p51,plain,
in_environment(sk4,sk1(sk4)),
inference(factoring,[status(thm)],[p48]) ).
fof(f1,hypothesis,
! [E,To] :
( ( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& environment(E) )
=> To = critical_point(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f1_nnf,plain,
! [E,To] :
( To = critical_point(E)
| ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,To] :
( To = critical_point(E)
| ( ~ greater(growth_rate(efficient_producers,sk2(E,To)),growth_rate(first_movers,sk2(E,To)))
& greater(sk2(E,To),To)
& subpopulations(first_movers,efficient_producers,E,sk2(E,To)) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f1_nnf]) ).
cnf(c9,plain,
( X1 = critical_point(X0)
| subpopulations(first_movers,efficient_producers,X0,sk2(X0,X1))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p26,plain,
( X0 = critical_point(sk4)
| subpopulations(first_movers,efficient_producers,sk4,sk2(sk4,X0))
| ~ in_environment(sk4,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[status(thm)],[c14,c9]) ).
cnf(p58,plain,
( sk1(sk4) = critical_point(sk4)
| subpopulations(first_movers,efficient_producers,sk4,sk2(sk4,sk1(sk4)))
| greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4))) ),
inference(resolution,[status(thm)],[p51,p26]) ).
cnf(c4,plain,
( ~ greater(growth_rate(efficient_producers,sk1(X0)),growth_rate(first_movers,sk1(X0)))
| greater_or_equal(sk0(X0,X1),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p21,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| greater_or_equal(sk0(sk4,X0),X0)
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c14,c4]) ).
cnf(p37,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4)) ),
inference(resolution,[status(thm)],[p31,p21]) ).
cnf(p62,plain,
( greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4)
| subpopulations(first_movers,efficient_producers,sk4,sk2(sk4,sk1(sk4))) ),
inference(resolution,[status(thm)],[p58,p37]) ).
cnf(c5,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater_or_equal(sk0(X0,X1),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p22,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk1(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| greater_or_equal(sk0(sk4,X0),X0)
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c14,c5]) ).
cnf(p38,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk1(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4)) ),
inference(resolution,[status(thm)],[p31,p22]) ).
cnf(p75,plain,
( greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| ~ greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p62,p38]) ).
cnf(p86,plain,
( greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| ~ greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p75]) ).
cnf(c10,plain,
( X1 = critical_point(X0)
| greater(sk2(X0,X1),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p27,plain,
( X0 = critical_point(sk4)
| greater(sk2(sk4,X0),X0)
| ~ in_environment(sk4,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[status(thm)],[c14,c10]) ).
cnf(p59,plain,
( sk1(sk4) = critical_point(sk4)
| greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4))) ),
inference(resolution,[status(thm)],[p51,p27]) ).
cnf(p66,plain,
( greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4)
| greater(sk2(sk4,sk1(sk4)),sk1(sk4)) ),
inference(resolution,[status(thm)],[p59,p37]) ).
cnf(p91,plain,
( greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4)
| greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p86,p66]) ).
cnf(p98,plain,
( greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p91]) ).
cnf(p105,plain,
( greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p98]) ).
cnf(c11,plain,
( X1 = critical_point(X0)
| ~ greater(growth_rate(efficient_producers,sk2(X0,X1)),growth_rate(first_movers,sk2(X0,X1)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p28,plain,
( X0 = critical_point(sk4)
| ~ greater(growth_rate(efficient_producers,sk2(sk4,X0)),growth_rate(first_movers,sk2(sk4,X0)))
| ~ in_environment(sk4,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[status(thm)],[c14,c11]) ).
cnf(p60,plain,
( sk1(sk4) = critical_point(sk4)
| ~ greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4))) ),
inference(resolution,[status(thm)],[p51,p28]) ).
cnf(p110,plain,
( sk1(sk4) = critical_point(sk4)
| greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p105,p60]) ).
cnf(p120,plain,
( greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p110]) ).
cnf(p127,plain,
( greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p120,p37]) ).
cnf(p133,plain,
( greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p127]) ).
cnf(c1,plain,
( ~ greater(growth_rate(efficient_producers,sk1(X0)),growth_rate(first_movers,sk1(X0)))
| subpopulations(first_movers,efficient_producers,X0,sk0(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p18,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,X0))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c14,c1]) ).
cnf(p34,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4))) ),
inference(resolution,[status(thm)],[p31,p18]) ).
cnf(p65,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| sk1(sk4) = critical_point(sk4)
| greater(sk2(sk4,sk1(sk4)),sk1(sk4)) ),
inference(resolution,[status(thm)],[p59,p34]) ).
cnf(p83,plain,
( greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4))))
| ~ greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4)
| greater(sk2(sk4,sk1(sk4)),sk1(sk4)) ),
inference(resolution,[status(thm)],[p65,p32]) ).
cnf(p136,plain,
( greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4))))
| sk1(sk4) = critical_point(sk4)
| greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p133,p83]) ).
cnf(p137,plain,
( greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4))))
| greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p136]) ).
cnf(c7,plain,
( ~ greater(growth_rate(efficient_producers,sk1(X0)),growth_rate(first_movers,sk1(X0)))
| ~ greater(growth_rate(efficient_producers,sk0(X0,X1)),growth_rate(first_movers,sk0(X0,X1)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p24,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| ~ greater(growth_rate(efficient_producers,sk0(sk4,X0)),growth_rate(first_movers,sk0(sk4,X0)))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c14,c7]) ).
cnf(p40,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| ~ greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4)))) ),
inference(resolution,[status(thm)],[p31,p24]) ).
cnf(p138,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p137,p40]) ).
cnf(p141,plain,
( sk1(sk4) = critical_point(sk4)
| greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p138,p59]) ).
cnf(p143,plain,
( greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p141]) ).
cnf(p146,plain,
( greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p143]) ).
cnf(p61,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| sk1(sk4) = critical_point(sk4)
| subpopulations(first_movers,efficient_producers,sk4,sk2(sk4,sk1(sk4))) ),
inference(resolution,[status(thm)],[p58,p34]) ).
cnf(c2,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| subpopulations(first_movers,efficient_producers,X0,sk0(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p19,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk1(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,X0))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c14,c2]) ).
cnf(p35,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk1(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4))) ),
inference(resolution,[status(thm)],[p31,p19]) ).
cnf(p70,plain,
( greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| ~ greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p61,p35]) ).
cnf(p85,plain,
( greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| ~ greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p70]) ).
cnf(p147,plain,
( greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| sk1(sk4) = critical_point(sk4)
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p146,p85]) ).
cnf(p149,plain,
( greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p147]) ).
cnf(p151,plain,
( sk1(sk4) = critical_point(sk4)
| greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p149,p60]) ).
cnf(p153,plain,
( greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p151]) ).
cnf(p155,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p153,p34]) ).
cnf(p158,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk0(sk4,sk3(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p155]) ).
cnf(p160,plain,
( greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4))))
| ~ greater_or_equal(sk0(sk4,sk3(sk4)),sk3(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p158,p32]) ).
cnf(p162,plain,
( sk1(sk4) = critical_point(sk4)
| greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4))))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p160,p133]) ).
cnf(p163,plain,
( greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4))))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p162]) ).
cnf(p164,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p163,p40]) ).
cnf(p166,plain,
( sk1(sk4) = critical_point(sk4)
| subpopulations(first_movers,efficient_producers,sk4,sk2(sk4,sk1(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p164,p58]) ).
cnf(p168,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk2(sk4,sk1(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p166]) ).
cnf(c8,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(growth_rate(efficient_producers,sk0(X0,X1)),growth_rate(first_movers,sk0(X0,X1)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p25,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk1(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater(growth_rate(efficient_producers,sk0(sk4,X0)),growth_rate(first_movers,sk0(sk4,X0)))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c14,c8]) ).
cnf(p41,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk1(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater(growth_rate(efficient_producers,sk0(sk4,sk3(sk4))),growth_rate(first_movers,sk0(sk4,sk3(sk4)))) ),
inference(resolution,[status(thm)],[p31,p25]) ).
cnf(p165,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk1(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p163,p41]) ).
cnf(p171,plain,
( greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| ~ greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| sk1(sk4) = critical_point(sk4)
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p168,p165]) ).
cnf(p172,plain,
( greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| ~ greater(sk2(sk4,sk1(sk4)),sk1(sk4))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p171]) ).
cnf(p173,plain,
( sk1(sk4) = critical_point(sk4)
| greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p172,p146]) ).
cnf(p174,plain,
( greater(growth_rate(efficient_producers,sk2(sk4,sk1(sk4))),growth_rate(first_movers,sk2(sk4,sk1(sk4))))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p173]) ).
cnf(p175,plain,
( sk1(sk4) = critical_point(sk4)
| greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p174,p60]) ).
cnf(p176,plain,
( greater(growth_rate(efficient_producers,sk1(sk4)),growth_rate(first_movers,sk1(sk4)))
| sk1(sk4) = critical_point(sk4) ),
inference(factoring,[status(thm)],[p175]) ).
cnf(p177,plain,
( sk1(sk4) = critical_point(sk4)
| sk1(sk4) = critical_point(sk4) ),
inference(resolution,[status(thm)],[p176,p164]) ).
cnf(p178,plain,
sk1(sk4) = critical_point(sk4),
inference(factoring,[status(thm)],[p177]) ).
cnf(p191,plain,
in_environment(sk4,critical_point(sk4)),
inference(demodulation,[status(thm)],[p178,p51]) ).
cnf(c16,plain,
~ in_environment(sk4,critical_point(sk4)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p198,plain,
$false,
inference(resolution,[status(thm)],[p191,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.81 % Computer : n026.cluster.edu
% 0.11/10.81 % Model : x86_64 x86_64
% 0.11/10.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.81 % Memory : 8046.5625MB
% 0.11/10.81 % OS : Linux 6.8.0-71-generic
% 0.11/10.81 % CPULimit : 300
% 0.11/10.81 % WCLimit : 300
% 0.11/10.81 % DateTime : Thu Sep 24 01:06:06 UTC 2026
% 0.11/10.81 % CPUTime :
% 0.11/10.81 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.32/11.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.32/11.54 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------