%------------------------------------------------------------------------------
% File : Vampire---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 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 : Theorem 1.59s 1.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 120 ( 15 unt; 6 def)
% Number of atoms : 382 ( 23 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 484 ( 222 ~; 204 |; 39 &)
% ( 7 <=>; 12 =>; 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 : 131 ( 0 sgn 127 !; 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] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( zero != cardinality_at_time(X2,X3)
| ~ environment(X0)
| ~ subpopulation(X1,X0,X3)
| ~ subpopulation(X2,X0,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| selection_favors(X1,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] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X0,X1] :
( subpopulation(first_movers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0] :
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X2,X0,X1] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f45,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f46,plain,
! [X2,X0,X1] :
( 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(cnf_transformation,[],[f27]) ).
fof(f48,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(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(f55,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,critical_point(X0))
| ~ environment(X0) ),
inference(equality_resolution,[],[f46]) ).
fof(f71,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(f76,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,[],[f71,f50]) ).
fof(f78,definition,
( spl2_3
<=> greater(cardinality_at_time(efficient_producers,sK1),zero) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f79,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| spl2_3 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl2_4
<=> greater(cardinality_at_time(first_movers,sK1),zero) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f84,plain,
( ~ greater(cardinality_at_time(first_movers,sK1),zero)
| spl2_4 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f86,definition,
( spl2_5
<=> subpopulations(first_movers,efficient_producers,sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f88,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( ~ spl2_3
| ~ spl2_4
| spl2_5 ),
inference(avatar_split_clause,[],[f76,f86,f82,f78]) ).
fof(f90,plain,
( ! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sK1)
| ~ greater_or_equal(sK1,appear(efficient_producers,X0)) )
| spl2_3 ),
inference(resolution,[],[f80,f48]) ).
fof(f107,definition,
( spl2_8
<=> ! [X0] :
( ~ environment(X0)
| ~ greater_or_equal(sK1,appear(efficient_producers,X0))
| ~ in_environment(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f108,plain,
( ! [X0] :
( ~ greater_or_equal(sK1,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ in_environment(X0,sK1) )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f116,plain,
( spl2_8
| spl2_3 ),
inference(avatar_split_clause,[],[f90,f78,f107]) ).
fof(f121,definition,
( spl2_10
<=> greater_or_equal(cardinality_at_time(first_movers,sK1),zero) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f122,plain,
( greater_or_equal(cardinality_at_time(first_movers,sK1),zero)
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( ~ greater_or_equal(cardinality_at_time(first_movers,sK1),zero)
| spl2_10 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f125,definition,
( spl2_11
<=> zero = cardinality_at_time(first_movers,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f127,plain,
( zero = cardinality_at_time(first_movers,sK1)
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f129,plain,
( ! [X0] :
( ~ in_environment(X0,sK1)
| ~ environment(X0) )
| spl2_10 ),
inference(resolution,[],[f123,f38]) ).
fof(f131,plain,
( ~ environment(sK0)
| spl2_10 ),
inference(resolution,[],[f129,f50]) ).
fof(f132,plain,
( $false
| spl2_10 ),
inference(forward_subsumption_resolution,[],[f131,f51]) ).
fof(f133,plain,
spl2_10,
inference(avatar_contradiction_clause,[],[f132]) ).
fof(f134,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ greater(sK1,critical_point(sK0))
| ~ environment(sK0)
| ~ spl2_5 ),
inference(resolution,[],[f88,f55]) ).
fof(f135,plain,
( ~ environment(sK0)
| selection_favors(efficient_producers,first_movers,sK1)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ spl2_5 ),
inference(resolution,[],[f88,f35]) ).
fof(f136,plain,
( selection_favors(efficient_producers,first_movers,sK1)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f135,f51]) ).
fof(f137,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ environment(sK0)
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f134,f49]) ).
fof(f138,plain,
( ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f136,f52]) ).
fof(f139,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f137,f51]) ).
fof(f154,plain,
( $false
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f139,f138]) ).
fof(f155,plain,
~ spl2_5,
inference(avatar_contradiction_clause,[],[f154]) ).
fof(f171,plain,
( ! [X0] :
( ~ in_environment(X0,sK1)
| ~ environment(X0)
| ~ greater(sK1,appear(efficient_producers,X0)) )
| ~ spl2_8 ),
inference(resolution,[],[f108,f45]) ).
fof(f183,plain,
( ~ environment(sK0)
| ~ greater(sK1,appear(efficient_producers,sK0))
| ~ spl2_8 ),
inference(resolution,[],[f171,f50]) ).
fof(f184,plain,
( ~ greater(sK1,appear(efficient_producers,sK0))
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f183,f51]) ).
fof(f188,plain,
( ! [X0] :
( ~ greater(X0,appear(efficient_producers,sK0))
| ~ greater(sK1,X0) )
| ~ spl2_8 ),
inference(resolution,[],[f184,f42]) ).
fof(f206,plain,
( ! [X0] :
( ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| appear(efficient_producers,sK0) = X0
| ~ greater(sK1,X0) )
| ~ spl2_8 ),
inference(resolution,[],[f188,f43]) ).
fof(f253,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| ~ greater(sK1,critical_point(sK0))
| ~ environment(sK0)
| ~ spl2_8 ),
inference(resolution,[],[f206,f41]) ).
fof(f254,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| ~ environment(sK0)
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f253,f49]) ).
fof(f255,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f254,f51]) ).
fof(f267,plain,
( ~ greater(sK1,critical_point(sK0))
| ~ spl2_8 ),
inference(superposition,[],[f184,f255]) ).
fof(f271,plain,
( $false
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f267,f49]) ).
fof(f272,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f274,plain,
( zero = cardinality_at_time(first_movers,sK1)
| ~ greater_or_equal(cardinality_at_time(first_movers,sK1),zero)
| spl2_4 ),
inference(resolution,[],[f84,f43]) ).
fof(f276,plain,
( zero = cardinality_at_time(first_movers,sK1)
| spl2_4
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f274,f122]) ).
fof(f277,plain,
( spl2_11
| spl2_4
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f276,f121,f82,f125]) ).
fof(f281,plain,
( ! [X0,X1] :
( zero != zero
| ~ environment(X0)
| ~ subpopulation(X1,X0,sK1)
| ~ subpopulation(first_movers,X0,sK1)
| ~ greater(cardinality_at_time(X1,sK1),zero)
| selection_favors(X1,first_movers,sK1) )
| ~ spl2_11 ),
inference(superposition,[],[f36,f127]) ).
fof(f282,plain,
( ! [X0,X1] :
( ~ subpopulation(first_movers,X0,sK1)
| ~ subpopulation(X1,X0,sK1)
| ~ environment(X0)
| ~ greater(cardinality_at_time(X1,sK1),zero)
| selection_favors(X1,first_movers,sK1) )
| ~ spl2_11 ),
inference(trivial_inequality_removal,[],[f281]) ).
fof(f286,plain,
( ! [X0,X1] :
( ~ subpopulation(X0,X1,sK1)
| ~ environment(X1)
| ~ greater(cardinality_at_time(X0,sK1),zero)
| selection_favors(X0,first_movers,sK1)
| ~ environment(X1)
| ~ in_environment(X1,sK1) )
| ~ spl2_11 ),
inference(resolution,[],[f282,f40]) ).
fof(f288,plain,
( ! [X0,X1] :
( ~ in_environment(X1,sK1)
| ~ environment(X1)
| ~ greater(cardinality_at_time(X0,sK1),zero)
| selection_favors(X0,first_movers,sK1)
| ~ subpopulation(X0,X1,sK1) )
| ~ spl2_11 ),
inference(duplicate_literal_removal,[],[f286]) ).
fof(f291,plain,
( ! [X0] :
( ~ environment(sK0)
| ~ greater(cardinality_at_time(X0,sK1),zero)
| selection_favors(X0,first_movers,sK1)
| ~ subpopulation(X0,sK0,sK1) )
| ~ spl2_11 ),
inference(resolution,[],[f288,f50]) ).
fof(f292,plain,
( ! [X0] :
( selection_favors(X0,first_movers,sK1)
| ~ greater(cardinality_at_time(X0,sK1),zero)
| ~ subpopulation(X0,sK0,sK1) )
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f291,f51]) ).
fof(f297,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ subpopulation(efficient_producers,sK0,sK1)
| ~ spl2_11 ),
inference(resolution,[],[f292,f52]) ).
fof(f298,plain,
( ~ subpopulation(efficient_producers,sK0,sK1)
| ~ spl2_3
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f297,f79]) ).
fof(f299,plain,
( ~ environment(sK0)
| ~ in_environment(sK0,sK1)
| ~ spl2_3
| ~ spl2_11 ),
inference(resolution,[],[f298,f39]) ).
fof(f300,plain,
( ~ in_environment(sK0,sK1)
| ~ spl2_3
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f299,f51]) ).
fof(f301,plain,
( $false
| ~ spl2_3
| ~ spl2_11 ),
inference(forward_subsumption_resolution,[],[f300,f50]) ).
fof(f302,plain,
( ~ spl2_3
| ~ spl2_11 ),
inference(avatar_contradiction_clause,[],[f301]) ).
cnf(s2,plain,
( ~ spl2_3
| ~ spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f89]) ).
cnf(s5,plain,
( spl2_3
| spl2_8 ),
inference(sat_conversion,[],[f116]) ).
cnf(s8,plain,
spl2_10,
inference(sat_conversion,[],[f133]) ).
cnf(s10,plain,
~ spl2_5,
inference(sat_conversion,[],[f155]) ).
cnf(s15,plain,
~ spl2_8,
inference(sat_conversion,[],[f272]) ).
cnf(s16,plain,
( spl2_4
| ~ spl2_10
| spl2_11 ),
inference(sat_conversion,[],[f277]) ).
cnf(s17,plain,
( ~ spl2_3
| ~ spl2_11 ),
inference(sat_conversion,[],[f302]) ).
cnf(s19,plain,
spl2_3,
inference(rat,[],[s5,s15]) ).
cnf(s20,plain,
~ spl2_11,
inference(rat,[],[s17,s19]) ).
cnf(s22,plain,
spl2_4,
inference(rat,[],[s16,s8,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s2,s10,s22,s19]) ).
fof(f303,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT026+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n015.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 17:23:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 1.59/1.31 % (1881445)Detected formulas, will run a generic FOF schedule.
% 1.59/1.31 % (1881454)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=738600611:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.59/1.31 % (1881454)Instruction limit reached!
% 1.59/1.31 % (1881454)------------------------------
% 1.59/1.31 % (1881454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.59/1.31 % (1881454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/1.31 % (1881454)CaDiCaL version: 2.1.3
% 1.59/1.31 % (1881454)Termination reason: Instruction limit
% 1.59/1.31 % (1881454)Termination phase: Saturation
% 1.59/1.31 % (1881454)Time elapsed: 0.038 s
% 1.59/1.31 % (1881454)Peak memory usage: 88 MB
% 1.59/1.31 % (1881454)Instructions burned: 121 (million)
% 1.59/1.31 % (1881450)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=2745920912:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.59/1.31 % (1881456)dis-21_1_sil=8000:lcm=predicate:random_seed=1053448438:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.59/1.31 % (1881451)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4146146744:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.59/1.31 % (1881452)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3702804473:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.59/1.31 % (1881453)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2704987057:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.59/1.31 % (1881455)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2829590231:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.59/1.31 % (1881455)First to succeed.
% 1.59/1.31 % (1881455)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1881445"
% 1.59/1.31 % (1881453)Instruction limit reached!
% 1.59/1.31 % (1881453)------------------------------
% 1.59/1.31 % (1881453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.59/1.31 % (1881453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/1.31 % (1881453)CaDiCaL version: 2.1.3
% 1.59/1.31 % (1881453)Termination reason: Instruction limit
% 1.59/1.31 % (1881453)Termination phase: Saturation
% 1.59/1.31 % (1881453)Time elapsed: 0.044 s
% 1.59/1.31 % (1881453)Peak memory usage: 88 MB
% 1.59/1.31 % (1881453)Instructions burned: 109 (million)
% 1.59/1.31 % (1881456)Instruction limit reached!
% 1.59/1.31 % (1881456)------------------------------
% 1.59/1.31 % (1881456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.59/1.31 % (1881456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/1.31 % (1881456)CaDiCaL version: 2.1.3
% 1.59/1.31 % (1881456)Termination reason: Instruction limit
% 1.59/1.31 % (1881456)Termination phase: Saturation
% 1.59/1.31 % (1881456)Time elapsed: 0.050 s
% 1.59/1.31 % (1881456)Peak memory usage: 88 MB
% 1.59/1.31 % (1881456)Instructions burned: 135 (million)
% 1.59/1.31 % (1881458)lrs+10_1_sil=8000:sp=occurrence:random_seed=4054352018:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 1.59/1.31 % (1881458)Also succeeded, but the first one will report.
% 1.59/1.31 % (1881465)lrs+10_1_sil=32000:urr=on:br=off:random_seed=533331802:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 1.59/1.31 % (1881466)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1418965185:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 1.59/1.31 % (1881465)Refutation not found, incomplete strategy
% 1.59/1.31 % (1881465)------------------------------
% 1.59/1.31 % (1881465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.59/1.31 % (1881465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.59/1.31 % (1881465)CaDiCaL version: 2.1.3
% 1.59/1.31 % (1881465)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.31 % (1881465)Time elapsed: 0.002 s
% 1.59/1.31 % (1881465)Peak memory usage: 88 MB
% 1.59/1.31 % (1881465)Instructions burned: 2 (million)
% 1.59/1.31 % (1881466)Also succeeded, but the first one will report.
% 1.59/1.31 % (1881455)Refutation found. Thanks to Tanya!
% 1.59/1.31 % SZS status Theorem for theBenchmark
% 1.59/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.51 % (1881455)------------------------------
% 0.19/1.51 % (1881455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (1881455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (1881455)CaDiCaL version: 2.1.3
% 0.19/1.51 % (1881455)Termination reason: Refutation
% 0.19/1.51 % (1881455)Time elapsed: 0.012 s
% 0.19/1.51 % (1881455)Peak memory usage: 90 MB
% 0.19/1.51 % (1881455)Instructions burned: 13 (million)
% 0.19/1.51 % (1881455)------------------------------
% 0.19/1.51 % (1881455)------------------------------
% 0.19/1.51 % (1881445)Success in time 0.445 s
% 0.19/1.51 % Vampire exiting
%------------------------------------------------------------------------------