%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT026+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 : Tue Sep 29 12:02:33 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 18
% Syntax : Number of formulae : 138 ( 18 unt; 7 def)
% Number of atoms : 393 ( 29 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 459 ( 204 ~; 196 |; 39 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 8 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 125 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3)
& greater(growth_rate(X2,X3),growth_rate(X1,X3)) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulation(X1,X0,X3)
& subpopulation(X2,X0,X3)
& greater(cardinality_at_time(X1,X3),zero)
& cardinality_at_time(X2,X3) = zero )
=> selection_favors(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members) ).
fof(f3,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1)
& greater(cardinality_at_time(first_movers,X1),zero)
& greater(cardinality_at_time(efficient_producers,X1),zero) )
=> subpopulations(first_movers,efficient_producers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f4,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1) )
=> greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist) ).
fof(f5,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1) )
=> ( subpopulation(first_movers,X0,X1)
& subpopulation(efficient_producers,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(f6,axiom,
! [X0] :
( environment(X0)
=> greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( greater(X0,X1)
& greater(X1,X2) )
=> greater(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f8,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( greater(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f9,axiom,
! [X0,X1] :
( ( environment(X0)
& X1 = critical_point(X0) )
=> ( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f10,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1)
& greater_or_equal(X1,appear(efficient_producers,X0)) )
=> greater(cardinality_at_time(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(f11,conjecture,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1)
& greater(X1,critical_point(X0)) )
=> selection_favors(efficient_producers,first_movers,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1)
& greater(X1,critical_point(X0)) )
=> selection_favors(efficient_producers,first_movers,X1) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(ennf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( selection_favors(X1,X2,X3)
| ~ environment(X0)
| ~ subpopulation(X1,X0,X3)
| ~ subpopulation(X2,X0,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| zero != cardinality_at_time(X2,X3) ),
inference(ennf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( selection_favors(X1,X2,X3)
| ~ environment(X0)
| ~ subpopulation(X1,X0,X3)
| ~ subpopulation(X2,X0,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| zero != cardinality_at_time(X2,X3) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(ennf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( subpopulation(first_movers,X0,X1)
& subpopulation(efficient_producers,X0,X1) )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1] :
( ( subpopulation(first_movers,X0,X1)
& subpopulation(efficient_producers,X0,X1) )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0] :
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f24,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f25,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1) ) )
| ~ environment(X0)
| critical_point(X0) != X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] :
( ( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1) ) )
| ~ environment(X0)
| critical_point(X0) != X1 ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f29,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
? [X0,X1] :
( ~ selection_favors(efficient_producers,first_movers,X1)
& environment(X0)
& in_environment(X0,X1)
& greater(X1,critical_point(X0)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f31,plain,
? [X0,X1] :
( ~ selection_favors(efficient_producers,first_movers,X1)
& environment(X0)
& in_environment(X0,X1)
& greater(X1,critical_point(X0)) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) )
& ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) )
& ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ~ selection_favors(efficient_producers,first_movers,sK1)
& environment(sK0)
& in_environment(sK0,sK1)
& greater(sK1,critical_point(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f31]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| selection_favors(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| selection_favors(X1,X2,X3)
| ~ subpopulation(X1,X0,X3)
| ~ subpopulation(X2,X0,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| zero != cardinality_at_time(X2,X3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X0,X1] :
( ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0,X1] :
( ~ environment(X0)
| greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1] :
( ~ environment(X0)
| subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X0,X1] :
( ~ environment(X0)
| subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0] :
( ~ environment(X0)
| greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ greater(X0,X1)
| greater(X0,X2)
| ~ greater(X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f45,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| critical_point(X0) != X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1] :
( ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
greater(sK1,critical_point(sK0)),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
in_environment(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
environment(sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
~ selection_favors(efficient_producers,first_movers,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
greater_or_equal(sK1,critical_point(sK0)),
inference(resolution,[],[f45,f49]) ).
fof(f55,plain,
greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0)),
inference(resolution,[],[f41,f51]) ).
fof(f56,plain,
! [X0] :
( ~ in_environment(sK0,X0)
| subpopulation(efficient_producers,sK0,X0) ),
inference(resolution,[],[f39,f51]) ).
fof(f57,plain,
subpopulation(efficient_producers,sK0,sK1),
inference(resolution,[],[f56,f50]) ).
fof(f58,plain,
! [X0] :
( ~ in_environment(sK0,X0)
| subpopulation(first_movers,sK0,X0) ),
inference(resolution,[],[f40,f51]) ).
fof(f59,plain,
! [X0] :
( ~ greater(critical_point(sK0),X0)
| greater(sK1,X0) ),
inference(resolution,[],[f42,f49]) ).
fof(f60,plain,
subpopulation(first_movers,sK0,sK1),
inference(resolution,[],[f58,f50]) ).
fof(f62,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| greater(critical_point(sK0),appear(efficient_producers,sK0)) ),
inference(resolution,[],[f43,f55]) ).
fof(f64,definition,
( spl2_1
<=> greater(critical_point(sK0),appear(efficient_producers,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f66,plain,
( greater(critical_point(sK0),appear(efficient_producers,sK0))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl2_2
<=> critical_point(sK0) = appear(efficient_producers,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f70,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f62,f68,f64]) ).
fof(f72,plain,
! [X0] :
( ~ in_environment(sK0,X0)
| greater_or_equal(cardinality_at_time(first_movers,X0),zero) ),
inference(resolution,[],[f38,f51]) ).
fof(f74,plain,
( greater_or_equal(sK1,appear(efficient_producers,sK0))
| ~ spl2_2 ),
inference(superposition,[],[f54,f70]) ).
fof(f75,plain,
( greater(sK1,appear(efficient_producers,sK0))
| ~ spl2_2 ),
inference(superposition,[],[f49,f70]) ).
fof(f79,plain,
! [X0] :
( ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ in_environment(sK0,X0)
| greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(resolution,[],[f48,f51]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ greater(growth_rate(X0,X2),growth_rate(X1,X2))
| ~ subpopulations(X1,X0,sK0,X2)
| selection_favors(X0,X1,X2) ),
inference(resolution,[],[f35,f51]) ).
fof(f84,plain,
! [X0] :
( ~ in_environment(sK0,X0)
| subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(resolution,[],[f37,f51]) ).
fof(f85,plain,
greater_or_equal(cardinality_at_time(first_movers,sK1),zero),
inference(resolution,[],[f72,f50]) ).
fof(f86,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| critical_point(sK0) != X1 ),
inference(resolution,[],[f46,f51]) ).
fof(f87,plain,
( ! [X0,X1] :
( ~ greater(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| appear(efficient_producers,sK0) != X1
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f86,f70]) ).
fof(f88,plain,
( zero = cardinality_at_time(first_movers,sK1)
| greater(cardinality_at_time(first_movers,sK1),zero) ),
inference(resolution,[],[f85,f43]) ).
fof(f90,definition,
( spl2_3
<=> greater(cardinality_at_time(first_movers,sK1),zero) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f92,plain,
( greater(cardinality_at_time(first_movers,sK1),zero)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl2_4
<=> zero = cardinality_at_time(first_movers,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f96,plain,
( zero = cardinality_at_time(first_movers,sK1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f88,f94,f90]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ greater(cardinality_at_time(X0,X2),zero)
| ~ subpopulation(X0,sK0,X2)
| ~ subpopulation(X1,sK0,X2)
| selection_favors(X0,X1,X2)
| zero != cardinality_at_time(X1,X2) ),
inference(resolution,[],[f36,f51]) ).
fof(f101,plain,
( ~ in_environment(sK0,sK1)
| greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ spl2_2 ),
inference(resolution,[],[f79,f74]) ).
fof(f104,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f101,f50]) ).
fof(f117,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ greater(cardinality_at_time(first_movers,sK1),zero)
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero) ),
inference(resolution,[],[f84,f50]) ).
fof(f118,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f117,f92]) ).
fof(f119,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f118,f104]) ).
fof(f121,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| appear(efficient_producers,sK0) != appear(efficient_producers,sK0)
| greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ spl2_2 ),
inference(resolution,[],[f87,f75]) ).
fof(f124,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f121]) ).
fof(f147,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f124,f119]) ).
fof(f157,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| selection_favors(efficient_producers,first_movers,sK1)
| ~ spl2_2
| ~ spl2_3 ),
inference(resolution,[],[f147,f82]) ).
fof(f174,plain,
( selection_favors(efficient_producers,first_movers,sK1)
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f157,f119]) ).
fof(f175,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f174,f52]) ).
fof(f176,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f175]) ).
fof(f187,definition,
( spl2_17
<=> greater(cardinality_at_time(efficient_producers,sK1),zero) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f188,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f189,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| spl2_17 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f191,definition,
( spl2_18
<=> subpopulations(first_movers,efficient_producers,sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
fof(f193,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
( ~ spl2_17
| spl2_18
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f118,f90,f191,f187]) ).
fof(f195,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| critical_point(sK0) != critical_point(sK0) ),
inference(resolution,[],[f86,f49]) ).
fof(f197,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1)) ),
inference(trivial_inequality_removal,[],[f195]) ).
fof(f204,definition,
( spl2_20
<=> greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_20])],[avatar_definition]) ).
fof(f206,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,plain,
( spl2_20
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f197,f191,f204]) ).
fof(f208,plain,
( greater(sK1,appear(efficient_producers,sK0))
| ~ spl2_1 ),
inference(resolution,[],[f66,f59]) ).
fof(f214,plain,
( greater_or_equal(sK1,appear(efficient_producers,sK0))
| ~ spl2_1 ),
inference(resolution,[],[f208,f45]) ).
fof(f215,plain,
( ~ in_environment(sK0,sK1)
| greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ spl2_1 ),
inference(resolution,[],[f214,f79]) ).
fof(f217,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f215,f50]) ).
fof(f218,plain,
( $false
| ~ spl2_1
| spl2_17 ),
inference(forward_subsumption_resolution,[],[f217,f189]) ).
fof(f219,plain,
( ~ spl2_1
| spl2_17 ),
inference(avatar_contradiction_clause,[],[f218]) ).
fof(f220,plain,
( $false
| ~ spl2_2
| spl2_17 ),
inference(forward_subsumption_resolution,[],[f104,f189]) ).
fof(f221,plain,
( ~ spl2_2
| spl2_17 ),
inference(avatar_contradiction_clause,[],[f220]) ).
fof(f222,plain,
( ! [X0] :
( ~ subpopulation(efficient_producers,sK0,sK1)
| ~ subpopulation(X0,sK0,sK1)
| selection_favors(efficient_producers,X0,sK1)
| zero != cardinality_at_time(X0,sK1) )
| ~ spl2_17 ),
inference(resolution,[],[f188,f98]) ).
fof(f227,plain,
( ! [X0] :
( ~ subpopulation(X0,sK0,sK1)
| selection_favors(efficient_producers,X0,sK1)
| zero != cardinality_at_time(X0,sK1) )
| ~ spl2_17 ),
inference(forward_subsumption_resolution,[],[f222,f57]) ).
fof(f246,plain,
( selection_favors(efficient_producers,first_movers,sK1)
| zero != cardinality_at_time(first_movers,sK1)
| ~ spl2_17 ),
inference(resolution,[],[f227,f60]) ).
fof(f247,plain,
( zero != cardinality_at_time(first_movers,sK1)
| ~ spl2_17 ),
inference(forward_subsumption_resolution,[],[f246,f52]) ).
fof(f257,plain,
( $false
| ~ spl2_4
| ~ spl2_17 ),
inference(forward_subsumption_resolution,[],[f247,f96]) ).
fof(f258,plain,
( ~ spl2_4
| ~ spl2_17 ),
inference(avatar_contradiction_clause,[],[f257]) ).
fof(f270,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| selection_favors(efficient_producers,first_movers,sK1)
| ~ spl2_20 ),
inference(resolution,[],[f206,f82]) ).
fof(f279,plain,
( selection_favors(efficient_producers,first_movers,sK1)
| ~ spl2_18
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f270,f193]) ).
fof(f280,plain,
( $false
| ~ spl2_18
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f279,f52]) ).
fof(f281,plain,
( ~ spl2_18
| ~ spl2_20 ),
inference(avatar_contradiction_clause,[],[f280]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f71]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f97]) ).
cnf(s7,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f176]) ).
cnf(s9,plain,
( ~ spl2_3
| ~ spl2_17
| spl2_18 ),
inference(sat_conversion,[],[f194]) ).
cnf(s11,plain,
( ~ spl2_18
| spl2_20 ),
inference(sat_conversion,[],[f207]) ).
cnf(s12,plain,
( ~ spl2_1
| spl2_17 ),
inference(sat_conversion,[],[f219]) ).
cnf(s13,plain,
( ~ spl2_2
| spl2_17 ),
inference(sat_conversion,[],[f221]) ).
cnf(s15,plain,
( ~ spl2_4
| ~ spl2_17 ),
inference(sat_conversion,[],[f258]) ).
cnf(s18,plain,
( ~ spl2_18
| ~ spl2_20 ),
inference(sat_conversion,[],[f281]) ).
cnf(s19,plain,
~ spl2_2,
inference(rat,[],[s2,s15,s7,s13]) ).
cnf(s20,plain,
spl2_1,
inference(rat,[],[s1,s19]) ).
cnf(s21,plain,
spl2_17,
inference(rat,[],[s12,s20]) ).
cnf(s22,plain,
~ spl2_4,
inference(rat,[],[s15,s21]) ).
cnf(s23,plain,
spl2_3,
inference(rat,[],[s2,s22]) ).
cnf(s24,plain,
spl2_18,
inference(rat,[],[s9,s21,s23]) ).
cnf(s25,plain,
~ spl2_20,
inference(rat,[],[s18,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s11,s25,s24]) ).
fof(f282,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT026+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 17:22:46 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.45 % (1881031)Will run a generic schedule for satisfiability detection.
% 0.15/0.45 % (1881038)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1858977721:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.45 % (1881036)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2219451444_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.45 % (1881042)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2923588848:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.45 % (1881039)dis+10_1_sil=32000:sp=arity:random_seed=1431079981:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.45 % (1881040)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2359588584:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.45 % (1881041)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1775303948:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.45 % TRYING [1]
% 0.15/0.45 % (1881037)% WARNING: option uhcvi not known.
% 0.15/0.45 % TRYING [2]
% 0.15/0.45 % TRYING [3]
% 0.15/0.45 % (1881041) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1881031-1881041"...
% 0.15/0.45 % (1881037)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4118318008:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.45 % (1881039) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1881031-1881039"...
% 0.15/0.45 % (1881041)...printing done.
% 0.15/0.45 % (1881041)Refutation found. Thanks to Tanya!
% 0.15/0.45 % SZS status Theorem for theBenchmark
% 0.15/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.45 % (1881041)------------------------------
% 0.15/0.45 % (1881041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.45 % (1881041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.45 % (1881041)CaDiCaL version: 2.1.3
% 0.15/0.45 % (1881041)Termination reason: Refutation
% 0.15/0.45 % (1881041)Time elapsed: 0.008 s
% 0.15/0.45 % (1881041)Peak memory usage: 12 MB
% 0.15/0.45 % (1881041)Instructions burned: 9 (million)
% 0.15/0.45 % (1881031)Success in time 0.042 s
% 0.15/0.45 % Vampire exiting
%------------------------------------------------------------------------------