%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:11:34 PM UTC 2026
% Result : Theorem 12.14s 17.24s
% Output : Proof 12.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 18
% Syntax : Number of formulae : 129 ( 20 unt; 0 def)
% Number of atoms : 420 ( 13 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 506 ( 215 ~; 217 |; 53 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 185 ( 0 sgn 115 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,conjecture,
! [E,T] :
( ( greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) )
=> selection_favors(first_movers,efficient_producers,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3) ).
fof(f20_neg,negated_conjecture,
~ ! [E,T] :
( ( greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) )
=> selection_favors(first_movers,efficient_producers,T) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [E,T] :
( ~ selection_favors(first_movers,efficient_producers,T)
& greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
( ~ selection_favors(first_movers,efficient_producers,sk1)
& greater(critical_point(sk0),sk1)
& greater_or_equal(sk1,appear(efficient_producers,sk0))
& in_environment(sk0,critical_point(sk0))
& environment(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f20_nnf]) ).
cnf(c25,plain,
environment(sk0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f2,axiom,
! [E] :
( ( in_environment(E,critical_point(E))
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,critical_point(E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP) ).
fof(f2_nnf,plain,
! [E] :
( subpopulations(first_movers,efficient_producers,E,critical_point(E))
| ~ in_environment(E,critical_point(E))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [E] :
( subpopulations(first_movers,efficient_producers,E,critical_point(E))
| ~ in_environment(E,critical_point(E))
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p37,plain,
( subpopulations(first_movers,efficient_producers,sk0,critical_point(sk0))
| ~ in_environment(sk0,critical_point(sk0)) ),
inference(resolution,[status(thm)],[c25,c2]) ).
cnf(c26,plain,
in_environment(sk0,critical_point(sk0)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p58,plain,
subpopulations(first_movers,efficient_producers,sk0,critical_point(sk0)),
inference(resolution,[status(thm)],[p37,c26]) ).
fof(f14,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater_or_equal(T,appear(efficient_producers,E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared) ).
fof(f14_nnf,plain,
! [E,T] :
( greater_or_equal(T,appear(efficient_producers,E))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [E,T] :
( greater_or_equal(T,appear(efficient_producers,E))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c16,plain,
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p46,plain,
( greater_or_equal(X0,appear(efficient_producers,sk0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c25,c16]) ).
cnf(p70,plain,
greater_or_equal(critical_point(sk0),appear(efficient_producers,sk0)),
inference(resolution,[status(thm)],[p58,p46]) ).
fof(f15,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(f15_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)],[f15]) ).
fof(f15_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)],[f15_nnf]) ).
cnf(c17,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p82,plain,
( critical_point(sk0) = appear(efficient_producers,sk0)
| greater(critical_point(sk0),appear(efficient_producers,sk0)) ),
inference(resolution,[status(thm)],[p70,c17]) ).
fof(f11,axiom,
! [E,T] :
( ( greater(critical_point(E),T)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,critical_point(E))
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_time_points) ).
fof(f11_nnf,plain,
! [E,T] :
( in_environment(E,T)
| ~ greater(critical_point(E),T)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,critical_point(E))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [E,T] :
( in_environment(E,T)
| ~ greater(critical_point(E),T)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,critical_point(E))
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c13,plain,
( in_environment(X0,X1)
| ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p43,plain,
( in_environment(sk0,X0)
| ~ greater(critical_point(sk0),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk0))
| ~ in_environment(sk0,critical_point(sk0)) ),
inference(resolution,[status(thm)],[c25,c13]) ).
cnf(p64,plain,
( in_environment(sk0,X0)
| ~ greater(critical_point(sk0),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk0)) ),
inference(resolution,[status(thm)],[p43,c26]) ).
cnf(c19,plain,
( X0 != X1
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p31,plain,
greater_or_equal(X0,X0),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(p79,plain,
( in_environment(sk0,appear(efficient_producers,sk0))
| ~ greater(critical_point(sk0),appear(efficient_producers,sk0)) ),
inference(resolution,[status(thm)],[p64,p31]) ).
cnf(p90,plain,
( in_environment(sk0,appear(efficient_producers,sk0))
| critical_point(sk0) = appear(efficient_producers,sk0) ),
inference(resolution,[status(thm)],[p82,p79]) ).
fof(f8,axiom,
! [E,T1,T2,T] :
( ( greater_or_equal(T,T1)
& greater_or_equal(T2,T)
& in_environment(E,T2)
& in_environment(E,T1)
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_durations_are_time_intervals) ).
fof(f8_nnf,plain,
! [E,T1,T2,T] :
( in_environment(E,T)
| ~ greater_or_equal(T,T1)
| ~ greater_or_equal(T2,T)
| ~ in_environment(E,T2)
| ~ in_environment(E,T1)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [E,T1,T2,T] :
( in_environment(E,T)
| ~ greater_or_equal(T,T1)
| ~ greater_or_equal(T2,T)
| ~ in_environment(E,T2)
| ~ in_environment(E,T1)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( in_environment(X0,X3)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X2,X3)
| ~ in_environment(X0,X2)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p30,plain,
( in_environment(X0,X2)
| ~ greater_or_equal(X2,X1)
| ~ greater_or_equal(X1,X2)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(factoring,[status(thm)],[c10]) ).
cnf(p54,plain,
( in_environment(sk0,X1)
| ~ greater_or_equal(X1,X0)
| ~ greater_or_equal(X0,X1)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[p30,c25]) ).
cnf(p66,plain,
( in_environment(sk0,X0)
| ~ greater_or_equal(X0,critical_point(sk0))
| ~ greater_or_equal(critical_point(sk0),X0) ),
inference(resolution,[status(thm)],[p54,c26]) ).
cnf(p83,plain,
( in_environment(sk0,appear(efficient_producers,sk0))
| ~ greater_or_equal(appear(efficient_producers,sk0),critical_point(sk0)) ),
inference(resolution,[status(thm)],[p70,p66]) ).
cnf(p107,plain,
( in_environment(sk0,appear(efficient_producers,sk0))
| ~ greater_or_equal(critical_point(sk0),critical_point(sk0))
| in_environment(sk0,appear(efficient_producers,sk0)) ),
inference(superposition,[status(thm)],[p90,p83]) ).
cnf(p134,plain,
( ~ greater_or_equal(critical_point(sk0),critical_point(sk0))
| in_environment(sk0,appear(efficient_producers,sk0)) ),
inference(factoring,[status(thm)],[p107]) ).
cnf(p175,plain,
in_environment(sk0,appear(efficient_producers,sk0)),
inference(resolution,[status(thm)],[p134,p31]) ).
fof(f3,axiom,
! [E] :
( ( in_environment(E,appear(efficient_producers,E))
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,appear(efficient_producers,E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears) ).
fof(f3_nnf,plain,
! [E] :
( subpopulations(first_movers,efficient_producers,E,appear(efficient_producers,E))
| ~ in_environment(E,appear(efficient_producers,E))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [E] :
( subpopulations(first_movers,efficient_producers,E,appear(efficient_producers,E))
| ~ in_environment(E,appear(efficient_producers,E))
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p38,plain,
( subpopulations(first_movers,efficient_producers,sk0,appear(efficient_producers,sk0))
| ~ in_environment(sk0,appear(efficient_producers,sk0)) ),
inference(resolution,[status(thm)],[c25,c3]) ).
cnf(p194,plain,
subpopulations(first_movers,efficient_producers,sk0,appear(efficient_producers,sk0)),
inference(resolution,[status(thm)],[p175,p38]) ).
fof(f18,hypothesis,
! [E,T1,T2,T] :
( ( greater_or_equal(T2,T)
& greater_or_equal(T,T1)
& subpopulations(first_movers,efficient_producers,E,T2)
& subpopulations(first_movers,efficient_producers,E,T1)
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a10) ).
fof(f18_nnf,plain,
! [E,T1,T2,T] :
( subpopulations(first_movers,efficient_producers,E,T)
| ~ greater_or_equal(T2,T)
| ~ greater_or_equal(T,T1)
| ~ subpopulations(first_movers,efficient_producers,E,T2)
| ~ subpopulations(first_movers,efficient_producers,E,T1)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [E,T1,T2,T] :
( subpopulations(first_movers,efficient_producers,E,T)
| ~ greater_or_equal(T2,T)
| ~ greater_or_equal(T,T1)
| ~ subpopulations(first_movers,efficient_producers,E,T2)
| ~ subpopulations(first_movers,efficient_producers,E,T1)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c23,plain,
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p50,plain,
( subpopulations(first_movers,efficient_producers,sk0,X2)
| ~ greater_or_equal(X1,X2)
| ~ greater_or_equal(X2,X0)
| ~ subpopulations(first_movers,efficient_producers,sk0,X1)
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c25,c23]) ).
cnf(p220,plain,
( subpopulations(first_movers,efficient_producers,sk0,X1)
| ~ greater_or_equal(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sk0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[p194,p50]) ).
cnf(p248,plain,
( subpopulations(first_movers,efficient_producers,sk0,X0)
| ~ greater_or_equal(critical_point(sk0),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk0)) ),
inference(resolution,[status(thm)],[p220,p58]) ).
cnf(c27,plain,
greater_or_equal(sk1,appear(efficient_producers,sk0)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p293,plain,
( subpopulations(first_movers,efficient_producers,sk0,sk1)
| ~ greater_or_equal(critical_point(sk0),sk1) ),
inference(resolution,[status(thm)],[p248,c27]) ).
cnf(c28,plain,
greater(critical_point(sk0),sk1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(c18,plain,
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p53,plain,
greater_or_equal(critical_point(sk0),sk1),
inference(resolution,[status(thm)],[c28,c18]) ).
cnf(p326,plain,
subpopulations(first_movers,efficient_producers,sk0,sk1),
inference(resolution,[status(thm)],[p293,p53]) ).
fof(f19,hypothesis,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12) ).
fof(f19_nnf,plain,
! [E,T] :
( decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [E,T] :
( decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c24,plain,
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p51,plain,
( decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c25,c24]) ).
cnf(p370,plain,
decreases(difference(founding_rate(first_movers,sk1),founding_rate(efficient_producers,sk1))),
inference(resolution,[status(thm)],[p326,p51]) ).
fof(f4,axiom,
! [T] :
( ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) )
=> decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_difference_between_founding_rates) ).
fof(f4_nnf,plain,
! [T] :
( decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
| decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T] :
( decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
| decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p412,plain,
( decreases(difference(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1)))
| decreases(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))) ),
inference(resolution,[status(thm)],[p370,c4]) ).
fof(f1,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
fof(f1_nnf,plain,
! [E,T] :
( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,T] :
( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p36,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c25,c1]) ).
cnf(p366,plain,
~ decreases(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))),
inference(resolution,[status(thm)],[p326,p36]) ).
cnf(p459,plain,
decreases(difference(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1))),
inference(resolution,[status(thm)],[p412,p366]) ).
fof(f16,axiom,
! [E,T] :
( ( ~ greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater_or_equal(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_relationship_of_growth_rates) ).
fof(f16_nnf,plain,
! [E,T] :
( greater_or_equal(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
| greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [E,T] :
( greater_or_equal(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
| greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c20,plain,
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p47,plain,
( greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c25,c20]) ).
cnf(p71,plain,
( greater_or_equal(difference(growth_rate(first_movers,critical_point(sk0)),growth_rate(efficient_producers,critical_point(sk0))),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(sk0)),growth_rate(efficient_producers,critical_point(sk0)))) ),
inference(resolution,[status(thm)],[p58,p47]) ).
fof(f5,axiom,
! [E,T,To] :
( ( greater(To,T)
& greater_or_equal(T,appear(efficient_producers,E))
& greater_or_equal(difference(growth_rate(first_movers,To),growth_rate(efficient_producers,To)),zero)
& in_environment(E,To)
& environment(E) )
=> ( decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
=> greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_decreasing_function) ).
fof(f5_nnf,plain,
! [E,T,To] :
( greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
| ~ decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
| ~ greater(To,T)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ greater_or_equal(difference(growth_rate(first_movers,To),growth_rate(efficient_producers,To)),zero)
| ~ in_environment(E,To)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [E,To,T] :
( greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
| ~ decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
| ~ greater(To,T)
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ greater_or_equal(difference(growth_rate(first_movers,To),growth_rate(efficient_producers,To)),zero)
| ~ in_environment(E,To)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p39,plain,
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sk0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c25,c5]) ).
cnf(p59,plain,
( greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ greater(critical_point(sk0),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk0))
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(sk0)),growth_rate(efficient_producers,critical_point(sk0))),zero) ),
inference(resolution,[status(thm)],[p39,c26]) ).
cnf(p85,plain,
( greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ greater(critical_point(sk0),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk0))
| greater(zero,difference(growth_rate(first_movers,critical_point(sk0)),growth_rate(efficient_producers,critical_point(sk0)))) ),
inference(resolution,[status(thm)],[p71,p59]) ).
cnf(p92,plain,
( greater(difference(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1)),zero)
| ~ decreases(difference(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1)))
| ~ greater(critical_point(sk0),sk1)
| greater(zero,difference(growth_rate(first_movers,critical_point(sk0)),growth_rate(efficient_producers,critical_point(sk0)))) ),
inference(resolution,[status(thm)],[p85,c27]) ).
cnf(p112,plain,
( greater(difference(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1)),zero)
| ~ decreases(difference(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1)))
| greater(zero,difference(growth_rate(first_movers,critical_point(sk0)),growth_rate(efficient_producers,critical_point(sk0)))) ),
inference(resolution,[status(thm)],[p92,c28]) ).
cnf(p487,plain,
( greater(difference(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1)),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(sk0)),growth_rate(efficient_producers,critical_point(sk0)))) ),
inference(resolution,[status(thm)],[p459,p112]) ).
fof(f6,axiom,
! [T] :
( greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))
<=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_negative_growth_rate_difference) ).
fof(f6_nnf,plain,
! [T] :
( ( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) )
& ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [T] :
( ( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) )
& ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p518,plain,
( greater(growth_rate(efficient_producers,critical_point(sk0)),growth_rate(first_movers,critical_point(sk0)))
| greater(difference(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1)),zero) ),
inference(resolution,[status(thm)],[p487,c6]) ).
fof(f7,axiom,
! [T] :
( greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)
<=> greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_growth_rate_difference) ).
fof(f7_nnf,plain,
! [T] :
( ( ~ greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T))
| greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) )
& ( greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T))
| ~ greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [T] :
( ( ~ greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T))
| greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) )
& ( greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T))
| ~ greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c8,plain,
( greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))
| ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p613,plain,
( greater(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1))
| greater(growth_rate(efficient_producers,critical_point(sk0)),growth_rate(first_movers,critical_point(sk0))) ),
inference(resolution,[status(thm)],[p518,c8]) ).
fof(f17,hypothesis,
! [E,Tc] :
( ( Tc = critical_point(E)
& environment(E) )
=> ( ! [T] :
( ( greater(T,Tc)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f17_nnf,plain,
! [E,Tc] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) )
| Tc != critical_point(E)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [E,Tc,T] :
( ( ( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,Tc)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)) )
| Tc != critical_point(E)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c21,plain,
( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| X1 != critical_point(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p32,plain,
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ~ environment(X0) ),
inference(equality_resolution,[status(thm)],[c21]) ).
cnf(p55,plain,
~ greater(growth_rate(efficient_producers,critical_point(sk0)),growth_rate(first_movers,critical_point(sk0))),
inference(resolution,[status(thm)],[p32,c25]) ).
cnf(p641,plain,
greater(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1)),
inference(resolution,[status(thm)],[p613,p55]) ).
fof(f13,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> subpopulations(efficient_producers,first_movers,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f13_nnf,plain,
! [E,T] :
( subpopulations(efficient_producers,first_movers,E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [E,T] :
( subpopulations(efficient_producers,first_movers,E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c15,plain,
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p45,plain,
( subpopulations(efficient_producers,first_movers,sk0,X0)
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c25,c15]) ).
cnf(p367,plain,
subpopulations(efficient_producers,first_movers,sk0,sk1),
inference(resolution,[status(thm)],[p326,p45]) ).
fof(f0,axiom,
! [E,S1,S2,T] :
( ( greater(growth_rate(S2,T),growth_rate(S1,T))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> selection_favors(S2,S1,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f0_nnf,plain,
! [E,S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p35,plain,
( selection_favors(X1,X0,X2)
| ~ greater(growth_rate(X1,X2),growth_rate(X0,X2))
| ~ subpopulations(X0,X1,sk0,X2) ),
inference(resolution,[status(thm)],[c25,c0]) ).
cnf(p407,plain,
( selection_favors(first_movers,efficient_producers,sk1)
| ~ greater(growth_rate(first_movers,sk1),growth_rate(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p367,p35]) ).
cnf(p715,plain,
selection_favors(first_movers,efficient_producers,sk1),
inference(resolution,[status(thm)],[p641,p407]) ).
cnf(c29,plain,
~ selection_favors(first_movers,efficient_producers,sk1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p725,plain,
$false,
inference(resolution,[status(thm)],[p715,c29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/15.41 % CPULimit : 300
% 0.07/15.41 % WCLimit : 300
% 0.07/15.41 % DateTime : Thu Sep 24 01:07:35 UTC 2026
% 0.07/15.41 % CPUTime :
% 0.07/15.41 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.14/17.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.14/17.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------