%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT028+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 : n014.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 : Theorem 0.16s 10.82s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 65 ( 10 unt; 0 def)
% Number of atoms : 250 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 304 ( 119 ~; 142 |; 34 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 76 ( 0 sgn 21 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [E] :
( ( ? [T1] :
( ! [T] :
( ( greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& in_environment(E,T1) )
& stable(E)
& environment(E) )
=> ? [T2] :
( ! [T] :
( ( greater_or_equal(T,T2)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(T2,appear(efficient_producers,E)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).
fof(f0_nnf,plain,
! [E] :
( ? [T2] :
( ! [T] :
( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,T2)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& greater(T2,appear(efficient_producers,E)) )
| ! [T1] :
( ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,T1) )
| ~ stable(E)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,T1,T] :
( ( ( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,sk1(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& greater(sk1(E),appear(efficient_producers,E)) )
| ( ~ greater(zero,growth_rate(first_movers,sk0(E,T1)))
& greater_or_equal(sk0(E,T1),T1)
& subpopulations(first_movers,efficient_producers,E,sk0(E,T1)) )
| ~ in_environment(E,T1)
| ~ stable(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c5,plain,
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(zero,growth_rate(first_movers,sk0(X0,X1)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f2,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(To,appear(efficient_producers,E)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10) ).
fof(f2_neg,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(To,appear(efficient_producers,E)) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
? [E] :
( ! [To] :
( ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ greater(To,appear(efficient_producers,E)) )
& stable(E)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [To] :
( ( ( ~ greater(zero,growth_rate(first_movers,sk4(To)))
& greater_or_equal(sk4(To),To)
& subpopulations(first_movers,efficient_producers,sk3,sk4(To)) )
| ~ greater(To,appear(efficient_producers,sk3)) )
& stable(sk3)
& environment(sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f2_nnf]) ).
cnf(c9,plain,
environment(sk3),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p30,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X1)
| ~ greater(zero,growth_rate(first_movers,sk0(sk3,X0)))
| ~ in_environment(sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c5,c9]) ).
cnf(c10,plain,
stable(sk3),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p45,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X1)
| ~ greater(zero,growth_rate(first_movers,sk0(sk3,X0)))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[p30,c10]) ).
fof(f1,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) ) )
& in_environment(E,To) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11) ).
fof(f1_nnf,plain,
! [E] :
( ? [To] :
( ! [T] :
( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ~ 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(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ~ 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(c6,plain,
( in_environment(X0,sk2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p14,plain,
( in_environment(sk3,sk2(sk3))
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c6,c9]) ).
cnf(p15,plain,
in_environment(sk3,sk2(sk3)),
inference(resolution,[status(thm)],[p14,c10]) ).
cnf(p57,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| ~ greater(zero,growth_rate(first_movers,sk0(sk3,sk2(sk3)))) ),
inference(resolution,[status(thm)],[p45,p15]) ).
cnf(c3,plain,
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater_or_equal(sk0(X0,X1),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p21,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X1)
| greater_or_equal(sk0(sk3,X0),X0)
| ~ in_environment(sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c3,c9]) ).
cnf(p38,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(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)],[p21,c10]) ).
cnf(p53,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p38,p15]) ).
cnf(c8,plain,
( greater(zero,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(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c8,c9]) ).
cnf(p32,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(resolution,[status(thm)],[p31,c10]) ).
cnf(c0,plain,
( greater(sk1(X0),appear(efficient_producers,X0))
| subpopulations(first_movers,efficient_producers,X0,sk0(X0,X1))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p16,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,X0))
| ~ in_environment(sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c0,c9]) ).
cnf(p18,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,X0))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[p16,c10]) ).
cnf(p19,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p18,p15]) ).
cnf(p33,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| greater(zero,growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| ~ greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p32,p19]) ).
cnf(c2,plain,
( greater(sk1(X0),appear(efficient_producers,X0))
| greater_or_equal(sk0(X0,X1),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p20,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| greater_or_equal(sk0(sk3,X0),X0)
| ~ in_environment(sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c2,c9]) ).
cnf(p22,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| greater_or_equal(sk0(sk3,X0),X0)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[p20,c10]) ).
cnf(p23,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p22,p15]) ).
cnf(p37,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| greater(sk1(sk3),appear(efficient_producers,sk3))
| greater(zero,growth_rate(first_movers,sk0(sk3,sk2(sk3)))) ),
inference(resolution,[status(thm)],[p33,p23]) ).
cnf(p39,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| greater(zero,growth_rate(first_movers,sk0(sk3,sk2(sk3)))) ),
inference(factoring,[status(thm)],[p37]) ).
cnf(c4,plain,
( greater(sk1(X0),appear(efficient_producers,X0))
| ~ greater(zero,growth_rate(first_movers,sk0(X0,X1)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p25,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| ~ greater(zero,growth_rate(first_movers,sk0(sk3,X0)))
| ~ in_environment(sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c4,c9]) ).
cnf(p28,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| ~ greater(zero,growth_rate(first_movers,sk0(sk3,X0)))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[p25,c10]) ).
cnf(p29,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| ~ greater(zero,growth_rate(first_movers,sk0(sk3,sk2(sk3)))) ),
inference(resolution,[status(thm)],[p28,p15]) ).
cnf(p40,plain,
( greater(sk1(sk3),appear(efficient_producers,sk3))
| greater(sk1(sk3),appear(efficient_producers,sk3)) ),
inference(resolution,[status(thm)],[p39,p29]) ).
cnf(p41,plain,
greater(sk1(sk3),appear(efficient_producers,sk3)),
inference(factoring,[status(thm)],[p40]) ).
cnf(c11,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk4(X1))
| ~ greater(X1,appear(efficient_producers,sk3)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p43,plain,
subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3))),
inference(resolution,[status(thm)],[p41,c11]) ).
cnf(p54,plain,
( greater(zero,growth_rate(first_movers,sk4(sk1(sk3))))
| ~ greater_or_equal(sk4(sk1(sk3)),sk1(sk3))
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p53,p43]) ).
cnf(c12,plain,
( greater_or_equal(sk4(X1),X1)
| ~ greater(X1,appear(efficient_producers,sk3)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p42,plain,
greater_or_equal(sk4(sk1(sk3)),sk1(sk3)),
inference(resolution,[status(thm)],[p41,c12]) ).
cnf(p56,plain,
( greater(zero,growth_rate(first_movers,sk4(sk1(sk3))))
| greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)) ),
inference(resolution,[status(thm)],[p54,p42]) ).
cnf(c13,plain,
( ~ greater(zero,growth_rate(first_movers,sk4(X1)))
| ~ greater(X1,appear(efficient_producers,sk3)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p44,plain,
~ greater(zero,growth_rate(first_movers,sk4(sk1(sk3)))),
inference(resolution,[status(thm)],[p41,c13]) ).
cnf(p58,plain,
greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3)),
inference(resolution,[status(thm)],[p56,p44]) ).
cnf(c1,plain,
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| subpopulations(first_movers,efficient_producers,X0,sk0(X0,X1))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p17,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X1)
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,X0))
| ~ in_environment(sk3,X0)
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[c1,c9]) ).
cnf(p34,plain,
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(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)],[p17,c10]) ).
cnf(p48,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p34,p15]) ).
cnf(p49,plain,
( greater(zero,growth_rate(first_movers,sk4(sk1(sk3))))
| ~ greater_or_equal(sk4(sk1(sk3)),sk1(sk3))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p48,p43]) ).
cnf(p50,plain,
( greater(zero,growth_rate(first_movers,sk4(sk1(sk3))))
| subpopulations(first_movers,efficient_producers,sk3,sk0(sk3,sk2(sk3))) ),
inference(resolution,[status(thm)],[p49,p42]) ).
cnf(p52,plain,
( greater(zero,growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| ~ greater_or_equal(sk0(sk3,sk2(sk3)),sk2(sk3))
| greater(zero,growth_rate(first_movers,sk4(sk1(sk3)))) ),
inference(resolution,[status(thm)],[p50,p32]) ).
cnf(p60,plain,
( greater(zero,growth_rate(first_movers,sk0(sk3,sk2(sk3))))
| greater(zero,growth_rate(first_movers,sk4(sk1(sk3)))) ),
inference(resolution,[status(thm)],[p58,p52]) ).
cnf(p61,plain,
( greater(zero,growth_rate(first_movers,sk4(sk1(sk3))))
| greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(resolution,[status(thm)],[p57,p60]) ).
cnf(p62,plain,
( greater(zero,growth_rate(first_movers,sk4(sk1(sk3))))
| ~ greater_or_equal(sk4(sk1(sk3)),sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,sk4(sk1(sk3))) ),
inference(factoring,[status(thm)],[p61]) ).
cnf(p64,plain,
( greater(zero,growth_rate(first_movers,sk4(sk1(sk3))))
| ~ greater_or_equal(sk4(sk1(sk3)),sk1(sk3)) ),
inference(resolution,[status(thm)],[p62,p43]) ).
cnf(p65,plain,
greater(zero,growth_rate(first_movers,sk4(sk1(sk3)))),
inference(resolution,[status(thm)],[p64,p42]) ).
cnf(p66,plain,
$false,
inference(resolution,[status(thm)],[p65,p44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT028+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/10.40 % Computer : n014.cluster.edu
% 0.12/10.40 % Model : x86_64 x86_64
% 0.12/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.40 % Memory : 8046.5625MB
% 0.12/10.40 % OS : Linux 6.8.0-71-generic
% 0.15/10.40 % CPULimit : 300
% 0.15/10.40 % WCLimit : 300
% 0.15/10.40 % DateTime : Thu Sep 24 01:04:44 UTC 2026
% 0.15/10.40 % CPUTime :
% 0.15/10.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/10.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.82 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------