%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT027+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 02:11:22 PM UTC 2026
% Result : Theorem 17.34s 12.92s
% Output : Proof 17.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 9
% Syntax : Number of formulae : 112 ( 11 unt; 0 def)
% Number of atoms : 373 ( 21 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 404 ( 143 ~; 214 |; 35 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 56 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,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(To,appear(efficient_producers,E)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10) ).
fof(f7_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)],[f7]) ).
fof(f7_sk,plain,
! [E,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)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c11,plain,
( greater(sk1(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f8,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( contracts_from(To,first_movers)
& greater(To,appear(efficient_producers,E)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9) ).
fof(f8_neg,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( contracts_from(To,first_movers)
& greater(To,appear(efficient_producers,E)) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [E] :
( ! [To] :
( ~ contracts_from(To,first_movers)
| ~ greater(To,appear(efficient_producers,E)) )
& stable(E)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
! [To] :
( ( ~ contracts_from(To,first_movers)
| ~ greater(To,appear(efficient_producers,sk2)) )
& stable(sk2)
& environment(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f8_nnf]) ).
cnf(c13,plain,
environment(sk2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p44,plain,
( greater(sk1(sk2),appear(efficient_producers,sk2))
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[c11,c13]) ).
cnf(c14,plain,
stable(sk2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p45,plain,
greater(sk1(sk2),appear(efficient_producers,sk2)),
inference(resolution,[status(thm)],[p44,c14]) ).
fof(f2,axiom,
! [E,T1,T2] :
( ( greater(T2,T1)
& in_environment(E,T1)
& stable(E)
& environment(E) )
=> in_environment(E,T2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_long_stable_environments) ).
fof(f2_nnf,plain,
! [E,T1,T2] :
( in_environment(E,T2)
| ~ greater(T2,T1)
| ~ in_environment(E,T1)
| ~ stable(E)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [E,T1,T2] :
( in_environment(E,T2)
| ~ greater(T2,T1)
| ~ in_environment(E,T1)
| ~ stable(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c4,plain,
( in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p31,plain,
( in_environment(sk2,X1)
| ~ greater(X1,X0)
| ~ in_environment(sk2,X0)
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[c4,c13]) ).
cnf(p32,plain,
( in_environment(sk2,X1)
| ~ greater(X1,X0)
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[p31,c14]) ).
fof(f3,axiom,
! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,appear(efficient_producers,E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).
fof(f3_nnf,plain,
! [E] :
( in_environment(E,appear(efficient_producers,E))
| ~ stable(E)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [E] :
( in_environment(E,appear(efficient_producers,E))
| ~ stable(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p21,plain,
( in_environment(sk2,appear(efficient_producers,sk2))
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[c5,c13]) ).
cnf(p22,plain,
in_environment(sk2,appear(efficient_producers,sk2)),
inference(resolution,[status(thm)],[p21,c14]) ).
cnf(p33,plain,
( in_environment(sk2,X0)
| ~ greater(X0,appear(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p32,p22]) ).
cnf(p48,plain,
in_environment(sk2,sk1(sk2)),
inference(resolution,[status(thm)],[p45,p33]) ).
fof(f0,axiom,
! [E,To] :
( ( ! [T] :
( ( greater_or_equal(T,To)
& greater(cardinality_at_time(first_movers,T),zero) )
=> greater(zero,growth_rate(first_movers,T)) )
& in_environment(E,To)
& stable(E)
& environment(E) )
=> contracts_from(To,first_movers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from) ).
fof(f0_nnf,plain,
! [E,To] :
( contracts_from(To,first_movers)
| ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,To)
& greater(cardinality_at_time(first_movers,T),zero) )
| ~ in_environment(E,To)
| ~ stable(E)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,To] :
( contracts_from(To,first_movers)
| ( ~ greater(zero,growth_rate(first_movers,sk0(E,To)))
& greater_or_equal(sk0(E,To),To)
& greater(cardinality_at_time(first_movers,sk0(E,To)),zero) )
| ~ in_environment(E,To)
| ~ stable(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( contracts_from(X1,first_movers)
| greater_or_equal(sk0(X0,X1),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p19,plain,
( contracts_from(X0,first_movers)
| greater_or_equal(sk0(sk2,X0),X0)
| ~ in_environment(sk2,X0)
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[c1,c13]) ).
cnf(p20,plain,
( contracts_from(X0,first_movers)
| greater_or_equal(sk0(sk2,X0),X0)
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[p19,c14]) ).
cnf(p51,plain,
( contracts_from(sk1(sk2),first_movers)
| greater_or_equal(sk0(sk2,sk1(sk2)),sk1(sk2)) ),
inference(resolution,[status(thm)],[p48,p20]) ).
fof(f5,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f5_nnf,plain,
! [X,Y] :
( ( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( ( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p60,plain,
( sk0(sk2,sk1(sk2)) = sk1(sk2)
| greater(sk0(sk2,sk1(sk2)),sk1(sk2))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p51,c7]) ).
cnf(p54,plain,
( in_environment(sk2,X0)
| ~ greater(X0,sk1(sk2)) ),
inference(resolution,[status(thm)],[p48,p32]) ).
cnf(p68,plain,
( in_environment(sk2,sk0(sk2,sk1(sk2)))
| sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p60,p54]) ).
cnf(c0,plain,
( contracts_from(X1,first_movers)
| greater(cardinality_at_time(first_movers,sk0(X0,X1)),zero)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p16,plain,
( contracts_from(X0,first_movers)
| greater(cardinality_at_time(first_movers,sk0(sk2,X0)),zero)
| ~ in_environment(sk2,X0)
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[c0,c13]) ).
cnf(p17,plain,
( contracts_from(X0,first_movers)
| greater(cardinality_at_time(first_movers,sk0(sk2,X0)),zero)
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[p16,c14]) ).
cnf(p50,plain,
( contracts_from(sk1(sk2),first_movers)
| greater(cardinality_at_time(first_movers,sk0(sk2,sk1(sk2))),zero) ),
inference(resolution,[status(thm)],[p48,p17]) ).
cnf(p70,plain,
( contracts_from(sk1(sk2),first_movers)
| greater(cardinality_at_time(first_movers,sk1(sk2)),zero)
| in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(superposition,[status(thm)],[p68,p50]) ).
cnf(p76,plain,
( greater(cardinality_at_time(first_movers,sk1(sk2)),zero)
| in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p70]) ).
fof(f1,axiom,
! [E,T] :
( ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero)
& in_environment(E,T)
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f1_nnf,plain,
! [E,T] :
( subpopulations(first_movers,efficient_producers,E,T)
| ~ greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,T] :
( subpopulations(first_movers,efficient_producers,E,T)
| ~ greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p27,plain,
( subpopulations(first_movers,efficient_producers,sk2,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c3,c13]) ).
cnf(p53,plain,
( subpopulations(first_movers,efficient_producers,sk2,sk1(sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2)),zero)
| ~ greater(cardinality_at_time(first_movers,sk1(sk2)),zero) ),
inference(resolution,[status(thm)],[p48,p27]) ).
cnf(p80,plain,
( subpopulations(first_movers,efficient_producers,sk2,sk1(sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2)),zero)
| in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p76,p53]) ).
fof(f6,hypothesis,
! [E,T] :
( ( greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,T)
& environment(E) )
=> greater(cardinality_at_time(efficient_producers,T),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6) ).
fof(f6_nnf,plain,
! [E,T] :
( greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [E,T] :
( greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c10,plain,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p39,plain,
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,appear(efficient_producers,sk2))
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c10,c13]) ).
cnf(p55,plain,
( greater(cardinality_at_time(efficient_producers,sk1(sk2)),zero)
| ~ greater_or_equal(sk1(sk2),appear(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p48,p39]) ).
cnf(c8,plain,
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p47,plain,
greater_or_equal(sk1(sk2),appear(efficient_producers,sk2)),
inference(resolution,[status(thm)],[p45,c8]) ).
cnf(p63,plain,
greater(cardinality_at_time(efficient_producers,sk1(sk2)),zero),
inference(resolution,[status(thm)],[p55,p47]) ).
cnf(p88,plain,
( subpopulations(first_movers,efficient_producers,sk2,sk1(sk2))
| in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p80,p63]) ).
cnf(c12,plain,
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p56,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,sk2,X0)
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[c12,c13]) ).
cnf(p66,plain,
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,sk2,X0) ),
inference(resolution,[status(thm)],[p56,c14]) ).
cnf(p89,plain,
( greater(zero,growth_rate(first_movers,sk1(sk2)))
| ~ greater_or_equal(sk1(sk2),sk1(sk2))
| in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p88,p66]) ).
cnf(c9,plain,
( X0 != X1
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p18,plain,
greater_or_equal(X0,X0),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(p90,plain,
( greater(zero,growth_rate(first_movers,sk1(sk2)))
| in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p89,p18]) ).
cnf(c2,plain,
( contracts_from(X1,first_movers)
| ~ 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(p23,plain,
( contracts_from(X0,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk0(sk2,X0)))
| ~ in_environment(sk2,X0)
| ~ stable(sk2) ),
inference(resolution,[status(thm)],[c2,c13]) ).
cnf(p28,plain,
( contracts_from(X0,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk0(sk2,X0)))
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[p23,c14]) ).
cnf(p52,plain,
( contracts_from(sk1(sk2),first_movers)
| ~ greater(zero,growth_rate(first_movers,sk0(sk2,sk1(sk2)))) ),
inference(resolution,[status(thm)],[p48,p28]) ).
cnf(p71,plain,
( contracts_from(sk1(sk2),first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(sk2)))
| in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(superposition,[status(thm)],[p68,p52]) ).
cnf(p85,plain,
( ~ greater(zero,growth_rate(first_movers,sk1(sk2)))
| in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p71]) ).
cnf(p98,plain,
( in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers)
| in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p90,p85]) ).
cnf(p107,plain,
( contracts_from(sk1(sk2),first_movers)
| in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p98]) ).
cnf(p108,plain,
( in_environment(sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p107]) ).
cnf(p112,plain,
( subpopulations(first_movers,efficient_producers,sk2,sk0(sk2,sk1(sk2)))
| ~ greater(cardinality_at_time(efficient_producers,sk0(sk2,sk1(sk2))),zero)
| ~ greater(cardinality_at_time(first_movers,sk0(sk2,sk1(sk2))),zero)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p108,p27]) ).
cnf(p122,plain,
( contracts_from(sk1(sk2),first_movers)
| subpopulations(first_movers,efficient_producers,sk2,sk0(sk2,sk1(sk2)))
| ~ greater(cardinality_at_time(efficient_producers,sk0(sk2,sk1(sk2))),zero)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p112,p50]) ).
cnf(p123,plain,
( subpopulations(first_movers,efficient_producers,sk2,sk0(sk2,sk1(sk2)))
| ~ greater(cardinality_at_time(efficient_producers,sk0(sk2,sk1(sk2))),zero)
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p122]) ).
cnf(p114,plain,
( greater(cardinality_at_time(efficient_producers,sk0(sk2,sk1(sk2))),zero)
| ~ greater_or_equal(sk0(sk2,sk1(sk2)),appear(efficient_producers,sk2))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p108,p39]) ).
fof(f4,axiom,
! [X,Y,Z] :
( ( greater(Y,Z)
& greater(X,Y) )
=> greater(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( greater(X,Z)
| ~ greater(Y,Z)
| ~ greater(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( greater(X,Z)
| ~ greater(Y,Z)
| ~ greater(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c6,plain,
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p67,plain,
( greater(sk0(sk2,sk1(sk2)),X0)
| ~ greater(sk1(sk2),X0)
| sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p60,c6]) ).
cnf(p81,plain,
( greater(sk0(sk2,sk1(sk2)),appear(efficient_producers,sk2))
| sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p67,p45]) ).
cnf(p83,plain,
( greater_or_equal(sk0(sk2,sk1(sk2)),appear(efficient_producers,sk2))
| sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p81,c8]) ).
cnf(p117,plain,
( sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers)
| greater(cardinality_at_time(efficient_producers,sk0(sk2,sk1(sk2))),zero)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p114,p83]) ).
cnf(p119,plain,
( sk0(sk2,sk1(sk2)) = sk1(sk2)
| greater(cardinality_at_time(efficient_producers,sk0(sk2,sk1(sk2))),zero)
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p117]) ).
cnf(p124,plain,
( sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers)
| subpopulations(first_movers,efficient_producers,sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p123,p119]) ).
cnf(p125,plain,
( sk0(sk2,sk1(sk2)) = sk1(sk2)
| subpopulations(first_movers,efficient_producers,sk2,sk0(sk2,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p124]) ).
cnf(p128,plain,
( greater(zero,growth_rate(first_movers,sk0(sk2,sk1(sk2))))
| ~ greater_or_equal(sk0(sk2,sk1(sk2)),sk1(sk2))
| sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p125,p66]) ).
cnf(p129,plain,
( contracts_from(sk1(sk2),first_movers)
| greater(zero,growth_rate(first_movers,sk0(sk2,sk1(sk2))))
| sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p128,p51]) ).
cnf(p130,plain,
( greater(zero,growth_rate(first_movers,sk0(sk2,sk1(sk2))))
| sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p129]) ).
cnf(p135,plain,
( contracts_from(sk1(sk2),first_movers)
| sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p130,p52]) ).
cnf(p138,plain,
( sk0(sk2,sk1(sk2)) = sk1(sk2)
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p135]) ).
cnf(p139,plain,
( contracts_from(sk1(sk2),first_movers)
| greater(cardinality_at_time(first_movers,sk1(sk2)),zero)
| contracts_from(sk1(sk2),first_movers) ),
inference(superposition,[status(thm)],[p138,p50]) ).
cnf(p148,plain,
( greater(cardinality_at_time(first_movers,sk1(sk2)),zero)
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p139]) ).
cnf(p151,plain,
( subpopulations(first_movers,efficient_producers,sk2,sk1(sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2)),zero)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p148,p53]) ).
cnf(p155,plain,
( subpopulations(first_movers,efficient_producers,sk2,sk1(sk2))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p151,p63]) ).
cnf(p156,plain,
( greater(zero,growth_rate(first_movers,sk1(sk2)))
| ~ greater_or_equal(sk1(sk2),sk1(sk2))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p155,p66]) ).
cnf(p157,plain,
( greater(zero,growth_rate(first_movers,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p156,p18]) ).
cnf(p140,plain,
( contracts_from(sk1(sk2),first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(superposition,[status(thm)],[p138,p52]) ).
cnf(p153,plain,
( ~ greater(zero,growth_rate(first_movers,sk1(sk2)))
| contracts_from(sk1(sk2),first_movers) ),
inference(factoring,[status(thm)],[p140]) ).
cnf(p167,plain,
( contracts_from(sk1(sk2),first_movers)
| contracts_from(sk1(sk2),first_movers) ),
inference(resolution,[status(thm)],[p157,p153]) ).
cnf(p168,plain,
contracts_from(sk1(sk2),first_movers),
inference(factoring,[status(thm)],[p167]) ).
cnf(c15,plain,
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sk2)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p46,plain,
~ contracts_from(sk1(sk2),first_movers),
inference(resolution,[status(thm)],[p45,c15]) ).
cnf(p169,plain,
$false,
inference(resolution,[status(thm)],[p168,p46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT027+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.04/10.40 % Computer : n002.cluster.edu
% 0.04/10.40 % Model : x86_64 x86_64
% 0.04/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/10.40 % Memory : 8046.5625MB
% 0.04/10.40 % OS : Linux 6.8.0-71-generic
% 0.04/10.40 % CPULimit : 300
% 0.04/10.40 % WCLimit : 300
% 0.04/10.40 % DateTime : Thu Sep 24 01:07:18 UTC 2026
% 0.04/10.40 % CPUTime :
% 0.04/10.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.34/12.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.34/12.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------