%------------------------------------------------------------------------------
% File : Vampire-SAT---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 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 : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 25
% Syntax : Number of formulae : 133 ( 17 unt; 9 def)
% Number of atoms : 463 ( 20 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 671 ( 341 ~; 321 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 10 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 99 !; 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(f24,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(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,f24]) ).
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(f105,plain,
( ~ greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
| spl0_8 ),
inference(avatar_component_clause,[],[f104]) ).
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,
( critical_point(sk1) = appear(efficient_producers,sk1)
| ~ in_environment(sk1,sk2)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(forward_subsumption_resolution,[],[f91,f18]) ).
fof(f117,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(forward_subsumption_resolution,[],[f112,f19]) ).
fof(f119,definition,
( spl0_11
<=> greater(cardinality_at_time(efficient_producers,sk2),zero) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f121,plain,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f117,f79,f119]) ).
fof(f124,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(f125,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,[],[f124]) ).
fof(f128,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(f130,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,[],[f128,f18]) ).
fof(f135,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,[],[f130,f4]) ).
fof(f136,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,[],[f130,f125]) ).
fof(f140,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,[],[f136,f19]) ).
fof(f141,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,[],[f140,f25]) ).
fof(f142,plain,
( ! [X0] :
( ~ subpopulation(efficient_producers,X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f141,f21]) ).
fof(f143,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f142,f7]) ).
fof(f144,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2) )
| ~ spl0_1
| ~ spl0_6 ),
inference(duplicate_literal_removal,[],[f143]) ).
fof(f145,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f144,f6]) ).
fof(f146,plain,
( ~ environment(sk1)
| ~ spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f145,f19]) ).
fof(f147,plain,
( $false
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f146,f18]) ).
fof(f148,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f147]) ).
fof(f152,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(f165,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f152,f21]) ).
fof(f168,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,[],[f135,f42]) ).
fof(f169,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,[],[f168,f25]) ).
fof(f170,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sk2) )
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f169,f19]) ).
fof(f171,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f170,f165]) ).
fof(f172,plain,
( ~ environment(sk1)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(resolution,[],[f171,f19]) ).
fof(f173,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f172,f18]) ).
fof(f174,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f173]) ).
fof(f176,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(f177,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,[],[f176]) ).
fof(f178,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sk2) )
| ~ spl0_11 ),
inference(resolution,[],[f121,f4]) ).
fof(f182,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ environment(X0) )
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f178,f165]) ).
fof(f185,definition,
( spl0_14
<=> ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f186,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f192,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| selection_favors(efficient_producers,first_movers,sk2) )
| ~ spl0_1
| ~ spl0_11 ),
inference(resolution,[],[f177,f121]) ).
fof(f203,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_1
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f192,f21]) ).
fof(f221,definition,
( spl0_18
<=> ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ subpopulation(efficient_producers,X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f222,plain,
( ! [X0] :
( ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ subpopulation(first_movers,X0,sk2) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f228,plain,
( spl0_18
| ~ spl0_1
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f203,f119,f36,f221]) ).
fof(f229,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulation(first_movers,X0,sk2)
| ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_18 ),
inference(resolution,[],[f222,f7]) ).
fof(f230,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulation(first_movers,X0,sk2)
| ~ in_environment(X0,sk2) )
| ~ spl0_18 ),
inference(duplicate_literal_removal,[],[f229]) ).
fof(f231,plain,
( ! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sk2) )
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f230,f6]) ).
fof(f232,plain,
( spl0_14
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f231,f221,f185]) ).
fof(f233,plain,
( ~ environment(sk1)
| ~ spl0_14 ),
inference(resolution,[],[f186,f19]) ).
fof(f234,plain,
( $false
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f233,f18]) ).
fof(f235,plain,
~ spl0_14,
inference(avatar_contradiction_clause,[],[f234]) ).
fof(f236,plain,
( ~ spl0_2
| spl0_14
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f182,f119,f104,f185,f40]) ).
fof(f238,definition,
( spl0_20
<=> ! [X0] :
( ~ in_environment(X0,sk2)
| subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f239,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( ~ spl0_2
| spl0_20
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f178,f119,f238,f40]) ).
fof(f244,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ environment(X0)
| ~ greater(sk2,critical_point(X0))
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) )
| ~ spl0_20 ),
inference(resolution,[],[f239,f24]) ).
fof(f245,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ greater(sk2,critical_point(X0))
| greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) )
| ~ spl0_20 ),
inference(duplicate_literal_removal,[],[f244]) ).
fof(f246,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ greater(sk2,critical_point(X0)) )
| spl0_8
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f245,f105]) ).
fof(f247,plain,
( spl0_9
| spl0_8
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f246,f238,f104,f108]) ).
fof(f249,plain,
( ~ environment(sk1)
| ~ in_environment(sk1,sk2)
| ~ spl0_9 ),
inference(resolution,[],[f109,f20]) ).
fof(f251,plain,
( ~ in_environment(sk1,sk2)
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f249,f18]) ).
fof(f252,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f251,f19]) ).
fof(f253,plain,
~ spl0_9,
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(s7,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f122]) ).
cnf(s8,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f148]) ).
cnf(s10,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f174]) ).
cnf(s16,plain,
( ~ spl0_1
| ~ spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f228]) ).
cnf(s17,plain,
( spl0_14
| ~ spl0_18 ),
inference(sat_conversion,[],[f232]) ).
cnf(s18,plain,
~ spl0_14,
inference(sat_conversion,[],[f235]) ).
cnf(s19,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f236]) ).
cnf(s20,plain,
( ~ spl0_2
| ~ spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f240]) ).
cnf(s21,plain,
( spl0_8
| spl0_9
| ~ spl0_20 ),
inference(sat_conversion,[],[f247]) ).
cnf(s22,plain,
~ spl0_9,
inference(sat_conversion,[],[f253]) ).
cnf(s23,plain,
( spl0_8
| ~ spl0_20 ),
inference(rat,[],[s21,s22]) ).
cnf(s24,plain,
~ spl0_18,
inference(rat,[],[s17,s18]) ).
cnf(s25,plain,
( ~ spl0_1
| ~ spl0_11 ),
inference(rat,[],[s16,s24]) ).
cnf(s28,plain,
( ~ spl0_2
| ~ spl0_6
| spl0_8 ),
inference(rat,[],[s5,s22]) ).
cnf(s29,plain,
( ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s28,s10]) ).
cnf(s30,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s23,s19,s20,s18]) ).
cnf(s31,plain,
~ spl0_2,
inference(rat,[],[s30,s7,s29]) ).
cnf(s32,plain,
spl0_1,
inference(rat,[],[s1,s31]) ).
cnf(s33,plain,
~ spl0_11,
inference(rat,[],[s25,s32]) ).
cnf(s34,plain,
~ spl0_6,
inference(rat,[],[s8,s32]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s7,s33,s34]) ).
fof(f254,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT026-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n015.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 17:22:16 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 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
% 0.17/0.47 % (1880203)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1880211)dis+10_1_sil=32000:sp=arity:random_seed=2717118874:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (1880209)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1880211) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1880203-1880211"...
% 0.17/0.47 % (1880211)...printing done.
% 0.17/0.47 % (1880209)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2929269989:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (1880211)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1880211)------------------------------
% 0.17/0.47 % (1880211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1880211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1880211)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1880211)Termination reason: Refutation
% 0.17/0.47 % (1880211)Time elapsed: 0.005 s
% 0.17/0.47 % (1880211)Peak memory usage: 12 MB
% 0.17/0.47 % (1880211)Instructions burned: 11 (million)
% 0.17/0.47 % (1880203)Success in time 0.036 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------