%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT026+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 : Thu Sep 24 01:25:19 PM UTC 2026
% Result : Theorem 0.03s 0.30s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 11
% Syntax : Number of formulae : 106 ( 14 unt; 0 def)
% Number of atoms : 344 ( 64 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 395 ( 157 ~; 188 |; 37 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 128 ( 124 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E,S1,S2,T] :
( ( cardinality_at_time(S2,T) = zero
& greater(cardinality_at_time(S1,T),zero)
& subpopulation(S2,E,T)
& subpopulation(S1,E,T)
& environment(E) )
=> selection_favors(S1,S2,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> greater_or_equal(cardinality_at_time(first_movers,T),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [E] :
( environment(E)
=> greater_or_equal(critical_point(E),appear(efficient_producers,E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] :
( ( greater(Y,Z)
& greater(X,Y) )
=> greater(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [E,T] :
( ( greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) )
=> selection_favors(efficient_producers,first_movers,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [E,T] :
( ( greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) )
=> selection_favors(efficient_producers,first_movers,T) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,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(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ! [E] :
( ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( 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(thm)],[f14]) ).
fof(f16,plain,
! [E,S1,S2,T] :
( selection_favors(S1,S2,T)
| cardinality_at_time(S2,T) != zero
| ~ greater(cardinality_at_time(S1,T),zero)
| ~ subpopulation(S2,E,T)
| ~ subpopulation(S1,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [S1,S2,T] :
( selection_favors(S1,S2,T)
| cardinality_at_time(S2,T) != zero
| ~ greater(cardinality_at_time(S1,T),zero)
| ! [E] :
( ~ subpopulation(S2,E,T)
| ~ subpopulation(S1,E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( selection_favors(X1,X3,X2)
| cardinality_at_time(X3,X2) != zero
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X3,X0,X2)
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,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(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1] :
( 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(thm)],[f19]) ).
fof(f21,plain,
! [E,T] :
( greater_or_equal(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [T] :
( greater_or_equal(cardinality_at_time(first_movers,T),zero)
| ! [E] :
( ~ in_environment(E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [E,T] :
( ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f25,plain,
! [X0,X1] :
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f27,plain,
! [E] :
( greater_or_equal(critical_point(E),appear(efficient_producers,E))
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0] :
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X,Y,Z] :
( greater(X,Z)
| ~ greater(Y,Z)
| ~ greater(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X,Z] :
( greater(X,Z)
| ! [Y] :
( ~ greater(Y,Z)
| ~ greater(X,Y) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,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)],[f8]) ).
fof(f33,plain,
( ! [X,Y] :
( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ! [X,Y] :
( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f37,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(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
! [X0,X1,X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| X1 != critical_point(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,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(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f41,plain,
! [T] :
( greater(cardinality_at_time(efficient_producers,T),zero)
| ! [E] :
( ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ in_environment(E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( 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(thm)],[f41]) ).
fof(f43,plain,
? [E,T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f44,plain,
? [T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& ? [E] :
( greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
( ~ selection_favors(efficient_producers,first_movers,sK0_skl)
& greater(sK0_skl,critical_point(sK1_skl))
& in_environment(sK1_skl,sK0_skl)
& environment(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(T,sK0_skl),skolemize(E,sK1_skl)],[f44]) ).
fof(f46,plain,
environment(sK1_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
in_environment(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
greater(sK0_skl,critical_point(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,plain,
~ selection_favors(efficient_producers,first_movers,sK0_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f52,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,critical_point(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f39]) ).
fof(f54,plain,
( greater_or_equal(cardinality_at_time(first_movers,sK0_skl),zero)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f23,f47]) ).
fof(f55,plain,
greater_or_equal(cardinality_at_time(first_movers,sK0_skl),zero),
inference(forward_subsumption_resolution,[status(thm)],[f54,f46]) ).
fof(f56,plain,
greater_or_equal(sK0_skl,critical_point(sK1_skl)),
inference(resolution,[status(thm)],[f35,f48]) ).
fof(f57,plain,
( subpopulation(first_movers,sK1_skl,sK0_skl)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f25,f47]) ).
fof(f58,plain,
subpopulation(first_movers,sK1_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f57,f46]) ).
fof(f59,plain,
( subpopulation(efficient_producers,sK1_skl,sK0_skl)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f26,f47]) ).
fof(f60,plain,
subpopulation(efficient_producers,sK1_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f59,f46]) ).
fof(f61,plain,
greater_or_equal(critical_point(sK1_skl),appear(efficient_producers,sK1_skl)),
inference(resolution,[status(thm)],[f28,f46]) ).
fof(f64,plain,
( cardinality_at_time(first_movers,sK0_skl) = zero
| greater(cardinality_at_time(first_movers,sK0_skl),zero) ),
inference(resolution,[status(thm)],[f55,f34]) ).
fof(f65,plain,
( critical_point(sK1_skl) = appear(efficient_producers,sK1_skl)
| greater(critical_point(sK1_skl),appear(efficient_producers,sK1_skl)) ),
inference(resolution,[status(thm)],[f61,f34]) ).
fof(f66,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ greater(cardinality_at_time(efficient_producers,sK0_skl),zero)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0)
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(resolution,[status(thm)],[f64,f20]) ).
fof(f70,plain,
! [X0] :
( greater(X0,appear(efficient_producers,sK1_skl))
| ~ greater(X0,critical_point(sK1_skl))
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(resolution,[status(thm)],[f65,f31]) ).
fof(f74,plain,
( greater(sK0_skl,appear(efficient_producers,sK1_skl))
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(resolution,[status(thm)],[f70,f48]) ).
fof(f75,plain,
( greater_or_equal(sK0_skl,appear(efficient_producers,sK1_skl))
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(resolution,[status(thm)],[f74,f35]) ).
fof(f77,plain,
( greater(cardinality_at_time(efficient_producers,sK0_skl),zero)
| ~ in_environment(sK1_skl,sK0_skl)
| ~ environment(sK1_skl)
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(resolution,[status(thm)],[f75,f42]) ).
fof(f79,plain,
( greater(cardinality_at_time(efficient_producers,sK0_skl),zero)
| ~ in_environment(sK1_skl,sK0_skl)
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f46]) ).
fof(f80,plain,
( greater(cardinality_at_time(efficient_producers,sK0_skl),zero)
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f47]) ).
fof(f81,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0)
| cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(resolution,[status(thm)],[f80,f66]) ).
fof(f84,plain,
( subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl)
| ~ environment(sK1_skl)
| cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(resolution,[status(thm)],[f81,f47]) ).
fof(f85,plain,
( subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl)
| cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f46]) ).
fof(f87,plain,
( greater(growth_rate(efficient_producers,sK0_skl),growth_rate(first_movers,sK0_skl))
| ~ greater(sK0_skl,critical_point(sK1_skl))
| ~ environment(sK1_skl)
| cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(resolution,[status(thm)],[f85,f52]) ).
fof(f88,plain,
( greater(growth_rate(efficient_producers,sK0_skl),growth_rate(first_movers,sK0_skl))
| ~ greater(sK0_skl,critical_point(sK1_skl))
| cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f46]) ).
fof(f89,plain,
( greater(growth_rate(efficient_producers,sK0_skl),growth_rate(first_movers,sK0_skl))
| cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f48]) ).
fof(f90,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,sK0_skl)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0)
| cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(resolution,[status(thm)],[f89,f15]) ).
fof(f93,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0)
| cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f49]) ).
fof(f94,plain,
! [X0] :
( ~ in_environment(X0,sK0_skl)
| ~ environment(X0)
| cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f81,f93]) ).
fof(f98,plain,
( ~ environment(sK1_skl)
| cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(resolution,[status(thm)],[f94,f47]) ).
fof(f99,plain,
( cardinality_at_time(first_movers,sK0_skl) = zero
| critical_point(sK1_skl) = appear(efficient_producers,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f46]) ).
fof(f105,plain,
! [X0] :
( cardinality_at_time(first_movers,sK0_skl) = zero
| greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,critical_point(sK1_skl))
| ~ in_environment(sK1_skl,X0)
| ~ environment(sK1_skl) ),
inference(paramodulation,[status(thm)],[f99,f42]) ).
fof(f107,plain,
! [X0] :
( cardinality_at_time(first_movers,sK0_skl) = zero
| greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,critical_point(sK1_skl))
| ~ in_environment(sK1_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f46]) ).
fof(f108,plain,
( cardinality_at_time(first_movers,sK0_skl) = zero
| greater(cardinality_at_time(efficient_producers,sK0_skl),zero)
| ~ in_environment(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f107,f56]) ).
fof(f110,plain,
( cardinality_at_time(first_movers,sK0_skl) = zero
| greater(cardinality_at_time(efficient_producers,sK0_skl),zero) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f47]) ).
fof(f111,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0)
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(backward_subsumption_resolution,[status(thm)],[f66,f110]) ).
fof(f115,plain,
( subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl)
| ~ environment(sK1_skl)
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(resolution,[status(thm)],[f111,f47]) ).
fof(f116,plain,
( subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl)
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f46]) ).
fof(f117,plain,
( greater(growth_rate(efficient_producers,sK0_skl),growth_rate(first_movers,sK0_skl))
| ~ greater(sK0_skl,critical_point(sK1_skl))
| ~ environment(sK1_skl)
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(resolution,[status(thm)],[f116,f52]) ).
fof(f118,plain,
( greater(growth_rate(efficient_producers,sK0_skl),growth_rate(first_movers,sK0_skl))
| ~ greater(sK0_skl,critical_point(sK1_skl))
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f46]) ).
fof(f119,plain,
( greater(growth_rate(efficient_producers,sK0_skl),growth_rate(first_movers,sK0_skl))
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f48]) ).
fof(f120,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,sK0_skl)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0)
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(resolution,[status(thm)],[f119,f15]) ).
fof(f123,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0)
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f49]) ).
fof(f124,plain,
! [X0] :
( ~ in_environment(X0,sK0_skl)
| ~ environment(X0)
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(backward_subsumption_resolution,[status(thm)],[f111,f123]) ).
fof(f128,plain,
( ~ environment(sK1_skl)
| cardinality_at_time(first_movers,sK0_skl) = zero ),
inference(resolution,[status(thm)],[f124,f47]) ).
fof(f129,plain,
cardinality_at_time(first_movers,sK0_skl) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f128,f46]) ).
fof(f142,plain,
! [X0,X1] :
( selection_favors(X1,first_movers,sK0_skl)
| ~ greater(cardinality_at_time(X1,sK0_skl),zero)
| ~ subpopulation(first_movers,X0,sK0_skl)
| ~ subpopulation(X1,X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f129,f18]) ).
fof(f146,plain,
! [X0] :
( critical_point(sK1_skl) = appear(efficient_producers,sK1_skl)
| selection_favors(efficient_producers,first_movers,sK0_skl)
| ~ subpopulation(first_movers,X0,sK0_skl)
| ~ subpopulation(efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f142,f80]) ).
fof(f148,plain,
! [X0] :
( critical_point(sK1_skl) = appear(efficient_producers,sK1_skl)
| ~ subpopulation(first_movers,X0,sK0_skl)
| ~ subpopulation(efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f49]) ).
fof(f153,plain,
( critical_point(sK1_skl) = appear(efficient_producers,sK1_skl)
| ~ subpopulation(efficient_producers,sK1_skl,sK0_skl)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f148,f58]) ).
fof(f154,plain,
( critical_point(sK1_skl) = appear(efficient_producers,sK1_skl)
| ~ subpopulation(efficient_producers,sK1_skl,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f46]) ).
fof(f165,plain,
critical_point(sK1_skl) = appear(efficient_producers,sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f154,f60]) ).
fof(f167,plain,
! [X0] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,critical_point(sK1_skl))
| ~ in_environment(sK1_skl,X0)
| ~ environment(sK1_skl) ),
inference(paramodulation,[status(thm)],[f165,f42]) ).
fof(f169,plain,
! [X0] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,critical_point(sK1_skl))
| ~ in_environment(sK1_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f46]) ).
fof(f170,plain,
( greater(cardinality_at_time(efficient_producers,sK0_skl),zero)
| ~ in_environment(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f169,f56]) ).
fof(f172,plain,
greater(cardinality_at_time(efficient_producers,sK0_skl),zero),
inference(forward_subsumption_resolution,[status(thm)],[f170,f47]) ).
fof(f174,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,sK0_skl)
| ~ subpopulation(first_movers,X0,sK0_skl)
| ~ subpopulation(efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f172,f142]) ).
fof(f177,plain,
! [X0] :
( ~ subpopulation(first_movers,X0,sK0_skl)
| ~ subpopulation(efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f49]) ).
fof(f181,plain,
( ~ subpopulation(efficient_producers,sK1_skl,sK0_skl)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f177,f58]) ).
fof(f182,plain,
~ subpopulation(efficient_producers,sK1_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f181,f46]) ).
fof(f183,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f182,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT026+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 01:21:21 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.30 % Refutation found
% 0.03/0.30 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.32 % Elapsed time: 0.025853 seconds
% 0.03/0.32 % CPU time: 0.046989 seconds
% 0.03/0.32 % Total memory used: 18.059 MB
% 0.03/0.32 % Net memory used: 18.009 MB
%------------------------------------------------------------------------------