%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 : Theorem 2.63s 1.09s
% Output : Proof 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 90 ( 13 unt; 0 def)
% Number of atoms : 287 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 317 ( 120 ~; 153 |; 35 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 76 ( 0 sgn 21 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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(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]) ).
fof(f2,conjecture,
! [E] :
( ( stable(E)
& 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/sandbox/benchmark/theBenchmark.p',prove_l12) ).
fof(f2_neg,negated_conjecture,
~ ! [E] :
( ( stable(E)
& 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) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_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) )
& stable(E)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [To] :
( ( ( ~ greater(growth_rate(efficient_producers,sk4(To)),growth_rate(first_movers,sk4(To)))
& greater(sk4(To),To)
& subpopulations(first_movers,efficient_producers,sk3,sk4(To)) )
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ in_environment(sk3,To) )
& stable(sk3)
& environment(sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f2_nnf]) ).
cnf(c11,plain,
environment(sk3),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p107,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X1)
| ~ greater(growth_rate(efficient_producers,sk0(sk3,X0)),growth_rate(first_movers,sk0(sk3,X0)))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c8,c11]) ).
fof(f1,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/sandbox/benchmark/theBenchmark.p',l1) ).
fof(f1_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)],[f1]) ).
fof(f1_sk,plain,
! [E,T] :
( ( ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,sk2(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,sk2(E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f1_nnf]) ).
cnf(c9,plain,
( in_environment(X0,sk2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p16,plain,
( in_environment(sk3,sk2(sk3))
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c9,c11]) ).
cnf(c12,plain,
stable(sk3),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p17,plain,
in_environment(sk3,sk2(sk3)),
inference(resolution,[status(thm)],[p16,c12]) ).
cnf(p108,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| ~ greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3)))) ),
inference(resolution,[status(thm)],[p107,p17]) ).
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(p89,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X1)
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,X0))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c2,c11]) ).
cnf(p90,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p89,p17]) ).
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(p60,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3)))
| ~ greater(growth_rate(efficient_producers,sk0(sk3,X0)),growth_rate(first_movers,sk0(sk3,X0)))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(p61,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3)))
| ~ greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3)))) ),
inference(resolution,[status(thm)],[p60,p17]) ).
cnf(c10,plain,
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p31,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c10,c11]) ).
cnf(p32,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(resolution,[status(thm)],[p31,c12]) ).
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(p23,plain,
( in_environment(sk3,sk1(sk3))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,X0))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c0,c11]) ).
cnf(p24,plain,
( in_environment(sk3,sk1(sk3))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p23,p17]) ).
cnf(p33,plain,
( in_environment(sk3,sk1(sk3))
| greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| ~ greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p32,p24]) ).
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(p21,plain,
( in_environment(sk3,sk1(sk3))
| greater_or_equal(sk0(sk3,X0),X0)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c3,c11]) ).
cnf(p22,plain,
( in_environment(sk3,sk1(sk3))
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p21,p17]) ).
cnf(p34,plain,
( in_environment(sk3,sk1(sk3))
| in_environment(sk3,sk1(sk3))
| greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3)))) ),
inference(resolution,[status(thm)],[p33,p22]) ).
cnf(p35,plain,
( in_environment(sk3,sk1(sk3))
| greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3)))) ),
inference(factoring,[status(thm)],[p34]) ).
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(p27,plain,
( in_environment(sk3,sk1(sk3))
| ~ greater(growth_rate(efficient_producers,sk0(sk3,X0)),growth_rate(first_movers,sk0(sk3,X0)))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c6,c11]) ).
cnf(p28,plain,
( in_environment(sk3,sk1(sk3))
| ~ greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3)))) ),
inference(resolution,[status(thm)],[p27,p17]) ).
cnf(p36,plain,
( in_environment(sk3,sk1(sk3))
| in_environment(sk3,sk1(sk3)) ),
inference(resolution,[status(thm)],[p35,p28]) ).
cnf(p37,plain,
in_environment(sk3,sk1(sk3)),
inference(factoring,[status(thm)],[p36]) ).
cnf(c13,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk4(X1))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(sk3,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p40,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3)))
| greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3))) ),
inference(resolution,[status(thm)],[p37,c13]) ).
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(p29,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,X0))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c1,c11]) ).
cnf(p30,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p29,p17]) ).
cnf(p47,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3))) ),
inference(resolution,[status(thm)],[p40,p30]) ).
cnf(p48,plain,
( greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| ~ greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3))
| subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3))) ),
inference(resolution,[status(thm)],[p47,p32]) ).
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(p25,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3)))
| greater_or_equal(sk0(sk3,X0),X0)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c4,c11]) ).
cnf(p26,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3)))
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p25,p17]) ).
cnf(p46,plain,
( greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3))
| subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3))) ),
inference(resolution,[status(thm)],[p40,p26]) ).
cnf(p58,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3)))
| greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3))) ),
inference(resolution,[status(thm)],[p48,p46]) ).
cnf(p59,plain,
( greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3))) ),
inference(factoring,[status(thm)],[p58]) ).
cnf(p64,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3)))
| ~ greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3))) ),
inference(resolution,[status(thm)],[p61,p59]) ).
cnf(p68,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3))) ),
inference(resolution,[status(thm)],[p64,p40]) ).
cnf(p69,plain,
subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3))),
inference(factoring,[status(thm)],[p68]) ).
cnf(p92,plain,
( greater(growth_rate(efficient_producers,sk4(sk1(sk3))),growth_rate(first_movers,sk4(sk1(sk3))))
| ~ greater(sk4(sk1(sk3)),sk1(sk3))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p90,p69]) ).
cnf(c14,plain,
( greater(sk4(X1),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(sk3,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p38,plain,
( greater(sk4(sk1(sk3)),sk1(sk3))
| greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3))) ),
inference(resolution,[status(thm)],[p37,c14]) ).
cnf(p44,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3)))
| greater(sk4(sk1(sk3)),sk1(sk3)) ),
inference(resolution,[status(thm)],[p38,p30]) ).
cnf(p45,plain,
( greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| ~ greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3))
| greater(sk4(sk1(sk3)),sk1(sk3)) ),
inference(resolution,[status(thm)],[p44,p32]) ).
cnf(p43,plain,
( greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3))
| greater(sk4(sk1(sk3)),sk1(sk3)) ),
inference(resolution,[status(thm)],[p38,p26]) ).
cnf(p55,plain,
( greater(sk4(sk1(sk3)),sk1(sk3))
| greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| greater(sk4(sk1(sk3)),sk1(sk3)) ),
inference(resolution,[status(thm)],[p45,p43]) ).
cnf(p57,plain,
( greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| greater(sk4(sk1(sk3)),sk1(sk3)) ),
inference(factoring,[status(thm)],[p55]) ).
cnf(p63,plain,
( greater(sk4(sk1(sk3)),sk1(sk3))
| ~ greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3))) ),
inference(resolution,[status(thm)],[p61,p57]) ).
cnf(p65,plain,
( greater(sk4(sk1(sk3)),sk1(sk3))
| greater(sk4(sk1(sk3)),sk1(sk3)) ),
inference(resolution,[status(thm)],[p63,p38]) ).
cnf(p67,plain,
greater(sk4(sk1(sk3)),sk1(sk3)),
inference(factoring,[status(thm)],[p65]) ).
cnf(p94,plain,
( greater(growth_rate(efficient_producers,sk4(sk1(sk3))),growth_rate(first_movers,sk4(sk1(sk3))))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p92,p67]) ).
cnf(c15,plain,
( ~ greater(growth_rate(efficient_producers,sk4(X1)),growth_rate(first_movers,sk4(X1)))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(sk3,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p39,plain,
( ~ greater(growth_rate(efficient_producers,sk4(sk1(sk3))),growth_rate(first_movers,sk4(sk1(sk3))))
| greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3))) ),
inference(resolution,[status(thm)],[p37,c15]) ).
cnf(p95,plain,
( greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p94,p39]) ).
cnf(p96,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p95,p30]) ).
cnf(p98,plain,
subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))),
inference(factoring,[status(thm)],[p96]) ).
cnf(p99,plain,
( greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| ~ greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p98,p32]) ).
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(p71,plain,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X1)
| greater_or_equal(sk0(sk3,X0),X0)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c5,c11]) ).
cnf(p72,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p71,p17]) ).
cnf(p74,plain,
( greater(growth_rate(efficient_producers,sk4(sk1(sk3))),growth_rate(first_movers,sk4(sk1(sk3))))
| ~ greater(sk4(sk1(sk3)),sk1(sk3))
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p72,p69]) ).
cnf(p76,plain,
( greater(growth_rate(efficient_producers,sk4(sk1(sk3))),growth_rate(first_movers,sk4(sk1(sk3))))
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p74,p67]) ).
cnf(p77,plain,
( greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3)))
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p76,p39]) ).
cnf(p78,plain,
( greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3))
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p77,p26]) ).
cnf(p82,plain,
greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)),
inference(factoring,[status(thm)],[p78]) ).
cnf(p101,plain,
greater(growth_rate(efficient_producers,sk0(sk3,sk2(sk3))),growth_rate(first_movers,sk0(sk3,sk2(sk3)))),
inference(resolution,[status(thm)],[p99,p82]) ).
cnf(p110,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(resolution,[status(thm)],[p108,p101]) ).
cnf(p111,plain,
( greater(growth_rate(efficient_producers,sk4(sk1(sk3))),growth_rate(first_movers,sk4(sk1(sk3))))
| ~ greater(sk4(sk1(sk3)),sk1(sk3)) ),
inference(resolution,[status(thm)],[p110,p69]) ).
cnf(p113,plain,
greater(growth_rate(efficient_producers,sk4(sk1(sk3))),growth_rate(first_movers,sk4(sk1(sk3)))),
inference(resolution,[status(thm)],[p111,p67]) ).
cnf(p114,plain,
greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3))),
inference(resolution,[status(thm)],[p113,p39]) ).
cnf(p102,plain,
~ greater(growth_rate(efficient_producers,sk1(sk3)),growth_rate(first_movers,sk1(sk3))),
inference(resolution,[status(thm)],[p101,p61]) ).
cnf(p115,plain,
$false,
inference(resolution,[status(thm)],[p114,p102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 01:07:48 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.63/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.63/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------