%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT026-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:02:04 PM UTC 2026
% Result : Unsatisfiable 2.67s 1.27s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 22
% Syntax : Number of formulae : 124 ( 15 unt; 6 def)
% Number of atoms : 455 ( 19 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 653 ( 322 ~; 325 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 7 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 97 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates_28) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulation(X1,X0,X2)
| ~ subpopulation(X3,X0,X2)
| ~ greater(cardinality_at_time(X1,X2),zero)
| cardinality_at_time(X3,X2) != zero
| selection_favors(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members_29) ).
fof(f3,plain,
! [X2,X3,X0,X1] :
( zero != cardinality_at_time(X3,X2)
| ~ subpopulation(X1,X0,X2)
| ~ subpopulation(X3,X0,X2)
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ environment(X0)
| selection_favors(X1,X3,X2) ),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_30) ).
fof(f5,axiom,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist_31) ).
fof(f6,axiom,
! [X0,X1] :
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_32) ).
fof(f7,axiom,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_33) ).
fof(f8,axiom,
! [X0] :
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP_34) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ greater(X0,X1)
| greater(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity_35) ).
fof(f10,axiom,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_36) ).
fof(f11,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_37) ).
fof(f15,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| X1 != critical_point(X0)
| ~ 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_40) ).
fof(f16,plain,
! [X2,X0,X1] :
( ~ environment(X0)
| critical_point(X0) != X1
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,axiom,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_41) ).
fof(f18,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_42) ).
fof(f19,negated_conjecture,
in_environment(sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_43) ).
fof(f20,negated_conjecture,
greater(sk2,critical_point(sk1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_44) ).
fof(f21,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_45) ).
fof(f23,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ environment(X0)
| ~ greater(X2,critical_point(X0))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(equality_resolution,[],[f16]) ).
fof(f25,plain,
greater_or_equal(sk2,critical_point(sk1)),
inference(resolution,[],[f11,f20]) ).
fof(f29,plain,
! [X0] :
( greater(critical_point(X0),appear(efficient_producers,X0))
| critical_point(X0) = appear(efficient_producers,X0)
| ~ environment(X0) ),
inference(resolution,[],[f10,f8]) ).
fof(f32,plain,
( ~ environment(sk1)
| greater_or_equal(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolution,[],[f5,f19]) ).
fof(f33,plain,
greater_or_equal(cardinality_at_time(first_movers,sk2),zero),
inference(forward_subsumption_resolution,[],[f32,f18]) ).
fof(f34,plain,
( greater(cardinality_at_time(first_movers,sk2),zero)
| zero = cardinality_at_time(first_movers,sk2) ),
inference(resolution,[],[f33,f10]) ).
fof(f36,definition,
( spl0_1
<=> zero = cardinality_at_time(first_movers,sk2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f38,plain,
( zero = cardinality_at_time(first_movers,sk2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f40,definition,
( spl0_2
<=> greater(cardinality_at_time(first_movers,sk2),zero) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f42,plain,
( greater(cardinality_at_time(first_movers,sk2),zero)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f34,f40,f36]) ).
fof(f63,plain,
! [X0,X1] :
( greater(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ greater(X1,critical_point(X0))
| critical_point(X0) = appear(efficient_producers,X0) ),
inference(resolution,[],[f29,f9]) ).
fof(f67,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(X1,critical_point(X0))
| critical_point(X0) = appear(efficient_producers,X0)
| ~ environment(X0) ),
inference(resolution,[],[f63,f11]) ).
fof(f68,plain,
! [X0,X1] :
( ~ greater(X0,critical_point(X1))
| appear(efficient_producers,X1) = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ environment(X1)
| greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(resolution,[],[f67,f17]) ).
fof(f70,plain,
! [X0,X1] :
( ~ greater(X0,critical_point(X1))
| appear(efficient_producers,X1) = critical_point(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(duplicate_literal_removal,[],[f68]) ).
fof(f79,definition,
( spl0_6
<=> critical_point(sk1) = appear(efficient_producers,sk1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f80,plain,
( critical_point(sk1) != appear(efficient_producers,sk1)
| spl0_6 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f88,plain,
( ! [X0] :
( ~ greater_or_equal(X0,critical_point(sk1))
| ~ in_environment(sk1,X0)
| ~ environment(sk1)
| greater(cardinality_at_time(efficient_producers,X0),zero) )
| ~ spl0_6 ),
inference(superposition,[],[f17,f81]) ).
fof(f90,plain,
( ! [X0] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sk1,X0)
| ~ greater_or_equal(X0,critical_point(sk1)) )
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f88,f18]) ).
fof(f91,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| ~ environment(sk1)
| ~ in_environment(sk1,sk2)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolution,[],[f70,f20]) ).
fof(f93,plain,
( ! [X0,X1] :
( ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ greater_or_equal(X0,critical_point(sk1))
| ~ in_environment(X1,X0)
| ~ in_environment(sk1,X0)
| ~ environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X0) )
| ~ spl0_6 ),
inference(resolution,[],[f90,f4]) ).
fof(f98,plain,
( ! [X0] :
( ~ greater_or_equal(sk2,critical_point(sk1))
| ~ in_environment(X0,sk2)
| ~ in_environment(sk1,sk2)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sk2) )
| ~ spl0_2
| ~ spl0_6 ),
inference(resolution,[],[f93,f42]) ).
fof(f99,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ in_environment(sk1,sk2)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sk2) )
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f98,f25]) ).
fof(f100,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2) )
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f99,f19]) ).
fof(f101,plain,
( ! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ greater(sk2,critical_point(X0))
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) )
| ~ spl0_2
| ~ spl0_6 ),
inference(resolution,[],[f100,f23]) ).
fof(f102,plain,
( ! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ greater(sk2,critical_point(X0))
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) )
| ~ spl0_2
| ~ spl0_6 ),
inference(duplicate_literal_removal,[],[f101]) ).
fof(f104,definition,
( spl0_8
<=> greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f106,plain,
( greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f108,definition,
( spl0_9
<=> ! [X0] :
( ~ environment(X0)
| ~ greater(sk2,critical_point(X0))
| ~ in_environment(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f109,plain,
( ! [X0] :
( ~ greater(sk2,critical_point(X0))
| ~ environment(X0)
| ~ in_environment(X0,sk2) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f110,plain,
( spl0_8
| spl0_9
| ~ spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f102,f79,f40,f108,f104]) ).
fof(f112,plain,
( ~ environment(sk1)
| ~ in_environment(sk1,sk2)
| greater(cardinality_at_time(efficient_producers,sk2),zero)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f91,f80]) ).
fof(f114,plain,
( ~ in_environment(sk1,sk2)
| greater(cardinality_at_time(efficient_producers,sk2),zero)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f112,f18]) ).
fof(f115,plain,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f114,f19]) ).
fof(f116,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sk2) )
| spl0_6 ),
inference(resolution,[],[f115,f4]) ).
fof(f120,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2) )
| ~ spl0_2
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f116,f42]) ).
fof(f131,plain,
( ! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ greater(sk2,critical_point(X0))
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) )
| ~ spl0_2
| spl0_6 ),
inference(resolution,[],[f120,f23]) ).
fof(f132,plain,
( ! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ greater(sk2,critical_point(X0))
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) )
| ~ spl0_2
| spl0_6 ),
inference(duplicate_literal_removal,[],[f131]) ).
fof(f133,plain,
( spl0_8
| spl0_9
| ~ spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f132,f79,f40,f108,f104]) ).
fof(f137,plain,
( ! [X0,X1] :
( zero != zero
| ~ subpopulation(X0,X1,sk2)
| ~ subpopulation(first_movers,X1,sk2)
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ~ environment(X1)
| selection_favors(X0,first_movers,sk2) )
| ~ spl0_1 ),
inference(superposition,[],[f3,f38]) ).
fof(f138,plain,
( ! [X0,X1] :
( ~ greater(cardinality_at_time(X0,sk2),zero)
| ~ subpopulation(first_movers,X1,sk2)
| ~ subpopulation(X0,X1,sk2)
| ~ environment(X1)
| selection_favors(X0,first_movers,sk2) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f137]) ).
fof(f140,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| selection_favors(efficient_producers,first_movers,sk2) )
| ~ spl0_1
| spl0_6 ),
inference(resolution,[],[f138,f115]) ).
fof(f145,plain,
( ! [X0] :
( ~ subpopulation(efficient_producers,X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_1
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f140,f21]) ).
fof(f147,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_1
| spl0_6 ),
inference(resolution,[],[f145,f7]) ).
fof(f148,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2) )
| ~ spl0_1
| spl0_6 ),
inference(duplicate_literal_removal,[],[f147]) ).
fof(f149,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_1
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f148,f6]) ).
fof(f150,plain,
( ~ environment(sk1)
| ~ spl0_1
| spl0_6 ),
inference(resolution,[],[f149,f19]) ).
fof(f151,plain,
( $false
| ~ spl0_1
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f150,f18]) ).
fof(f152,plain,
( ~ spl0_1
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f151]) ).
fof(f153,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2) )
| ~ spl0_2
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f116,f42]) ).
fof(f157,plain,
( ~ environment(sk1)
| ~ in_environment(sk1,sk2)
| ~ spl0_9 ),
inference(resolution,[],[f109,f20]) ).
fof(f160,plain,
( ~ in_environment(sk1,sk2)
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f157,f18]) ).
fof(f162,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f160,f19]) ).
fof(f163,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f162]) ).
fof(f166,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| selection_favors(efficient_producers,first_movers,sk2) )
| ~ spl0_8 ),
inference(resolution,[],[f106,f1]) ).
fof(f179,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f166,f21]) ).
fof(f182,plain,
( ! [X0] :
( ~ environment(X0)
| ~ environment(X0)
| ~ in_environment(X0,sk2) )
| ~ spl0_2
| spl0_6
| ~ spl0_8 ),
inference(resolution,[],[f179,f153]) ).
fof(f183,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_2
| spl0_6
| ~ spl0_8 ),
inference(duplicate_literal_removal,[],[f182]) ).
fof(f184,plain,
( ~ environment(sk1)
| ~ spl0_2
| spl0_6
| ~ spl0_8 ),
inference(resolution,[],[f183,f19]) ).
fof(f185,plain,
( $false
| ~ spl0_2
| spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f184,f18]) ).
fof(f186,plain,
( ~ spl0_2
| spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f185]) ).
fof(f189,plain,
( ! [X0,X1] :
( zero != zero
| ~ subpopulation(X0,X1,sk2)
| ~ subpopulation(first_movers,X1,sk2)
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ~ environment(X1)
| selection_favors(X0,first_movers,sk2) )
| ~ spl0_1 ),
inference(superposition,[],[f3,f38]) ).
fof(f190,plain,
( ! [X0,X1] :
( ~ greater(cardinality_at_time(X0,sk2),zero)
| ~ subpopulation(first_movers,X1,sk2)
| ~ subpopulation(X0,X1,sk2)
| ~ environment(X1)
| selection_favors(X0,first_movers,sk2) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f189]) ).
fof(f194,plain,
( ! [X0] :
( ~ greater_or_equal(X0,critical_point(sk1))
| ~ in_environment(sk1,X0)
| ~ environment(sk1)
| greater(cardinality_at_time(efficient_producers,X0),zero) )
| ~ spl0_6 ),
inference(superposition,[],[f17,f81]) ).
fof(f196,plain,
( ! [X0] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sk1,X0)
| ~ greater_or_equal(X0,critical_point(sk1)) )
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f194,f18]) ).
fof(f211,plain,
( ! [X0,X1] :
( ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ greater_or_equal(X0,critical_point(sk1))
| ~ in_environment(X1,X0)
| ~ in_environment(sk1,X0)
| ~ environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X0) )
| ~ spl0_6 ),
inference(resolution,[],[f196,f4]) ).
fof(f212,plain,
( ! [X0] :
( ~ in_environment(sk1,sk2)
| ~ greater_or_equal(sk2,critical_point(sk1))
| ~ subpopulation(first_movers,X0,sk2)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| selection_favors(efficient_producers,first_movers,sk2) )
| ~ spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f196,f190]) ).
fof(f216,plain,
( ! [X0] :
( ~ greater_or_equal(sk2,critical_point(sk1))
| ~ subpopulation(first_movers,X0,sk2)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| selection_favors(efficient_producers,first_movers,sk2) )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f212,f19]) ).
fof(f217,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| selection_favors(efficient_producers,first_movers,sk2) )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f216,f25]) ).
fof(f218,plain,
( ! [X0] :
( ~ subpopulation(efficient_producers,X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f217,f21]) ).
fof(f219,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f218,f7]) ).
fof(f220,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2) )
| ~ spl0_1
| ~ spl0_6 ),
inference(duplicate_literal_removal,[],[f219]) ).
fof(f221,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f220,f6]) ).
fof(f227,plain,
( ~ environment(sk1)
| ~ spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f221,f19]) ).
fof(f228,plain,
( $false
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f227,f18]) ).
fof(f229,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f228]) ).
fof(f239,definition,
( spl0_15
<=> ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f240,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f246,plain,
( ! [X0] :
( ~ greater_or_equal(sk2,critical_point(sk1))
| ~ in_environment(X0,sk2)
| ~ in_environment(sk1,sk2)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sk2) )
| ~ spl0_2
| ~ spl0_6 ),
inference(resolution,[],[f211,f42]) ).
fof(f247,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ in_environment(sk1,sk2)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sk2) )
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f246,f25]) ).
fof(f248,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sk2) )
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f247,f19]) ).
fof(f249,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f248,f179]) ).
fof(f250,plain,
( spl0_15
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f249,f104,f79,f40,f239]) ).
fof(f251,plain,
( ~ environment(sk1)
| ~ spl0_15 ),
inference(resolution,[],[f240,f19]) ).
fof(f252,plain,
( $false
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f251,f18]) ).
fof(f253,plain,
~ spl0_15,
inference(avatar_contradiction_clause,[],[f252]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s5,plain,
( ~ spl0_2
| ~ spl0_6
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f110]) ).
cnf(s6,plain,
( ~ spl0_2
| spl0_6
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f133]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f152]) ).
cnf(s8,plain,
~ spl0_9,
inference(sat_conversion,[],[f163]) ).
cnf(s10,plain,
( ~ spl0_2
| spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f186]) ).
cnf(s12,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f229]) ).
cnf(s14,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f250]) ).
cnf(s15,plain,
~ spl0_15,
inference(sat_conversion,[],[f253]) ).
cnf(s16,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(rat,[],[s14,s15]) ).
cnf(s18,plain,
( ~ spl0_2
| spl0_6
| spl0_8 ),
inference(rat,[],[s6,s8]) ).
cnf(s19,plain,
( ~ spl0_2
| ~ spl0_6
| spl0_8 ),
inference(rat,[],[s5,s8]) ).
cnf(s20,plain,
( ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s19,s16]) ).
cnf(s21,plain,
( spl0_6
| ~ spl0_2 ),
inference(rat,[],[s10,s18]) ).
cnf(s22,plain,
~ spl0_2,
inference(rat,[],[s21,s20]) ).
cnf(s23,plain,
spl0_1,
inference(rat,[],[s1,s22]) ).
cnf(s24,plain,
~ spl0_6,
inference(rat,[],[s12,s23]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s7,s24,s23]) ).
fof(f254,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT026-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 17:22:31 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.67/1.27 % (1880612)Input is clausal, will run a generic CNF schedule.
% 2.67/1.27 % (1880621)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2429946064:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.67/1.27 % (1880621)Instruction limit reached!
% 2.67/1.27 % (1880621)------------------------------
% 2.67/1.27 % (1880621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.27 % (1880621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.27 % (1880621)CaDiCaL version: 2.1.3
% 2.67/1.27 % (1880621)Termination reason: Instruction limit
% 2.67/1.27 % (1880621)Termination phase: Saturation
% 2.67/1.27 % (1880621)Time elapsed: 0.039 s
% 2.67/1.27 % (1880621)Peak memory usage: 89 MB
% 2.67/1.27 % (1880621)Instructions burned: 117 (million)
% 2.67/1.27 % (1880622)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2546376325:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.67/1.27 % (1880623)dis-21_1_sil=8000:lcm=predicate:random_seed=2237980907:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.67/1.27 % (1880620)lrs+10_1_sil=8000:sp=occurrence:random_seed=325091096:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.67/1.27 % (1880618)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2924609515:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.67/1.27 % (1880617)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4246866377:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.67/1.27 % (1880619)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1298449671:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.67/1.27 % (1880620)First to succeed.
% 2.67/1.27 % (1880620)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1880612"
% 2.67/1.27 % (1880622)Also succeeded, but the first one will report.
% 2.67/1.27 % (1880623)Instruction limit reached!
% 2.67/1.27 % (1880623)------------------------------
% 2.67/1.27 % (1880623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.27 % (1880623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.27 % (1880623)CaDiCaL version: 2.1.3
% 2.67/1.27 % (1880623)Termination reason: Instruction limit
% 2.67/1.27 % (1880623)Termination phase: Saturation
% 2.67/1.27 % (1880623)Time elapsed: 0.044 s
% 2.67/1.27 % (1880623)Peak memory usage: 88 MB
% 2.67/1.27 % (1880623)Instructions burned: 119 (million)
% 2.67/1.27 % (1880631)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2255071196:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.67/1.27 % (1880631)Instruction limit reached!
% 2.67/1.27 % (1880631)------------------------------
% 2.67/1.27 % (1880631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.27 % (1880631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.27 % (1880631)CaDiCaL version: 2.1.3
% 2.67/1.27 % (1880631)Termination reason: Instruction limit
% 2.67/1.27 % (1880631)Termination phase: Saturation
% 2.67/1.27 % (1880631)Time elapsed: 0.030 s
% 2.67/1.27 % (1880631)Peak memory usage: 87 MB
% 2.67/1.27 % (1880631)Instructions burned: 149 (million)
% 2.67/1.27 % (1880632)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3150612485:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 2.67/1.27 % (1880632)Refutation not found, incomplete strategy
% 2.67/1.27 % (1880632)------------------------------
% 2.67/1.27 % (1880632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.27 % (1880632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.27 % (1880632)CaDiCaL version: 2.1.3
% 2.67/1.27 % (1880632)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.27 % (1880632)Time elapsed: 0.002 s
% 2.67/1.27 % (1880632)Peak memory usage: 88 MB
% 2.67/1.27 % (1880632)Instructions burned: 2 (million)
% 2.67/1.27 % (1880634)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1867335379:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 2.67/1.27 % (1880620)Refutation found. Thanks to Tanya!
% 2.67/1.27 % SZS status Unsatisfiable for theBenchmark
% 2.67/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.36 % (1880620)------------------------------
% 3.39/1.36 % (1880620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.36 % (1880620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.36 % (1880620)CaDiCaL version: 2.1.3
% 3.39/1.36 % (1880620)Termination reason: Refutation
% 3.39/1.36 % (1880620)Time elapsed: 0.009 s
% 3.39/1.36 % (1880620)Peak memory usage: 89 MB
% 3.39/1.36 % (1880620)Instructions burned: 10 (million)
% 3.39/1.36 % (1880620)------------------------------
% 3.39/1.36 % (1880620)------------------------------
% 3.39/1.36 % (1880612)Success in time 0.415 s
% 3.39/1.36 % Vampire exiting
%------------------------------------------------------------------------------