%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT030-1 : 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 : n010.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 12:02:05 PM UTC 2026
% Result : Unsatisfiable 0.57s 1.03s
% Output : Refutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 25
% Syntax : Number of formulae : 109 ( 8 unt; 9 def)
% Number of atoms : 364 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 488 ( 233 ~; 246 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 10 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in_environment(X0,sk2(X0))
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_1) ).
fof(f2,axiom,
! [X0,X1] :
( in_environment(X0,sk2(X0))
| ~ in_environment(X0,X1)
| greater_or_equal(sk1(X1,X0),X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_2) ).
fof(f3,axiom,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_3) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ greater(X2,sk2(X0))
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_4) ).
fof(f5,axiom,
! [X0,X1] :
( greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_5) ).
fof(f6,axiom,
! [X2,X0,X1] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ in_environment(X0,X1)
| greater_or_equal(sk1(X1,X0),X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,sk2(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_6) ).
fof(f7,axiom,
! [X0,X1] :
( in_environment(X0,sk2(X0))
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_7) ).
fof(f8,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_8) ).
fof(f9,axiom,
! [X2,X0,X1] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,sk2(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_9) ).
fof(f10,axiom,
! [X0] :
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_10) ).
fof(f11,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,sk3(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_11) ).
fof(f12,negated_conjecture,
environment(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l12_12) ).
fof(f13,negated_conjecture,
stable(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l12_13) ).
fof(f14,negated_conjecture,
! [X0] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk5(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l12_14) ).
fof(f15,negated_conjecture,
! [X0] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0)
| greater(sk5(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l12_15) ).
fof(f16,negated_conjecture,
! [X0] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0)
| ~ greater(growth_rate(efficient_producers,sk5(X0)),growth_rate(first_movers,sk5(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l12_16) ).
fof(f17,plain,
! [X0] :
( ~ in_environment(sk4,X0)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(resolution,[],[f8,f12]) ).
fof(f19,definition,
( spl0_1
<=> greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f21,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f23,definition,
( spl0_2
<=> ! [X0] :
( ~ in_environment(sk4,X0)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4))) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f24,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4))) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f25,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f17,f23,f19]) ).
fof(f32,definition,
( spl0_3
<=> greater(sk5(sk2(sk4)),sk2(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f34,plain,
( greater(sk5(sk2(sk4)),sk2(sk4))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f36,definition,
( spl0_4
<=> in_environment(sk4,sk2(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f38,plain,
( ~ in_environment(sk4,sk2(sk4))
| spl0_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f41,definition,
( spl0_5
<=> subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f43,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f46,definition,
( spl0_6
<=> greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4)))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f48,plain,
( ~ greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| spl0_6 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f50,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ environment(sk4) )
| spl0_4 ),
inference(resolution,[],[f38,f7]) ).
fof(f55,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4))) )
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f50,f12]) ).
fof(f56,plain,
( spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f55,f36,f23]) ).
fof(f57,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ stable(sk4)
| ~ environment(sk4)
| ~ spl0_2 ),
inference(resolution,[],[f24,f10]) ).
fof(f63,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ environment(sk4)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f57,f13]) ).
fof(f65,definition,
( spl0_7
<=> ! [X0] :
( ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f66,plain,
( ! [X0] :
( greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f73,definition,
( spl0_9
<=> ! [X0] :
( ~ in_environment(sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4)) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f74,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,plain,
( ~ greater(growth_rate(efficient_producers,sk1(sk3(sk4),sk4)),growth_rate(first_movers,sk1(sk3(sk4),sk4)))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f63,f12]) ).
fof(f104,plain,
( ! [X0] :
( ~ greater_or_equal(sk1(sk3(sk4),sk4),sk3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sk1(sk3(sk4),sk4))
| ~ stable(X0)
| ~ environment(X0) )
| ~ spl0_2 ),
inference(resolution,[],[f76,f11]) ).
fof(f127,plain,
( ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ stable(sk4)
| ~ environment(sk4)
| ~ in_environment(sk4,sk3(sk4))
| ~ environment(sk4)
| ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ spl0_2 ),
inference(resolution,[],[f104,f5]) ).
fof(f128,plain,
( ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ stable(sk4)
| ~ environment(sk4)
| ~ in_environment(sk4,sk3(sk4))
| ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f127]) ).
fof(f129,plain,
( ~ stable(sk4)
| ~ environment(sk4)
| ~ in_environment(sk4,sk3(sk4))
| ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f128,f3]) ).
fof(f130,plain,
( ~ environment(sk4)
| ~ in_environment(sk4,sk3(sk4))
| ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f129,f13]) ).
fof(f131,plain,
( ~ in_environment(sk4,sk3(sk4))
| ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f130,f12]) ).
fof(f138,definition,
( spl0_18
<=> in_environment(sk4,sk3(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f140,plain,
( ~ in_environment(sk4,sk3(sk4))
| spl0_18 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f141,plain,
( ~ spl0_1
| ~ spl0_18
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f131,f23,f138,f19]) ).
fof(f145,plain,
( ~ in_environment(sk4,sk2(sk4))
| ~ greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| spl0_1 ),
inference(resolution,[],[f21,f16]) ).
fof(f146,plain,
( ~ in_environment(sk4,sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| spl0_1 ),
inference(resolution,[],[f21,f14]) ).
fof(f147,plain,
( ~ in_environment(sk4,sk2(sk4))
| greater(sk5(sk2(sk4)),sk2(sk4))
| spl0_1 ),
inference(resolution,[],[f21,f15]) ).
fof(f148,plain,
( spl0_3
| ~ spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f147,f19,f36,f32]) ).
fof(f149,plain,
( spl0_5
| ~ spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f146,f19,f36,f41]) ).
fof(f150,plain,
( ~ spl0_6
| ~ spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f145,f19,f36,f46]) ).
fof(f152,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ environment(sk4) )
| spl0_4 ),
inference(resolution,[],[f38,f1]) ).
fof(f153,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0)
| ~ environment(sk4) )
| spl0_4 ),
inference(resolution,[],[f38,f2]) ).
fof(f154,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0) )
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f153,f12]) ).
fof(f155,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4)) )
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f152,f12]) ).
fof(f156,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f154,f36,f65]) ).
fof(f157,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f155,f36,f73]) ).
fof(f158,plain,
( ~ in_environment(sk4,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ stable(sk4)
| ~ environment(sk4)
| ~ spl0_2
| ~ spl0_7 ),
inference(resolution,[],[f66,f104]) ).
fof(f159,plain,
( ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ stable(sk4)
| ~ environment(sk4)
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f158,f10]) ).
fof(f160,plain,
( ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ environment(sk4)
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f159,f13]) ).
fof(f161,plain,
( ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f160,f12]) ).
fof(f163,plain,
( ~ in_environment(sk4,sk3(sk4))
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(resolution,[],[f74,f161]) ).
fof(f164,plain,
( ~ spl0_18
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f163,f73,f65,f23,f138]) ).
fof(f165,plain,
( ~ stable(sk4)
| ~ environment(sk4)
| spl0_18 ),
inference(resolution,[],[f140,f10]) ).
fof(f166,plain,
( ~ environment(sk4)
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f165,f13]) ).
fof(f167,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f166,f12]) ).
fof(f168,plain,
spl0_18,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f171,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| ~ environment(sk4)
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4)))) )
| ~ spl0_3 ),
inference(resolution,[],[f34,f4]) ).
fof(f172,plain,
( ! [X0,X1] :
( ~ greater(sk5(sk2(sk4)),sk2(X0))
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(sk4)))
| ~ in_environment(X0,X1)
| ~ environment(X0) )
| spl0_6 ),
inference(resolution,[],[f48,f9]) ).
fof(f173,plain,
( ! [X0,X1] :
( ~ greater(sk5(sk2(sk4)),sk2(X0))
| greater_or_equal(sk1(X1,X0),X1)
| ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(sk4)))
| ~ in_environment(X0,X1)
| ~ environment(X0) )
| spl0_6 ),
inference(resolution,[],[f48,f6]) ).
fof(f197,plain,
( ! [X0] :
( greater_or_equal(sk1(X0,sk4),X0)
| ~ subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| ~ in_environment(sk4,X0)
| ~ environment(sk4) )
| ~ spl0_3
| spl0_6 ),
inference(resolution,[],[f173,f34]) ).
fof(f198,plain,
( ! [X0] :
( greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0)
| ~ environment(sk4) )
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f197,f43]) ).
fof(f199,plain,
( ! [X0] :
( greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0) )
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f198,f12]) ).
fof(f200,plain,
( spl0_7
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f199,f46,f41,f32,f65]) ).
fof(f201,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ environment(sk4)
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4)))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f171,f43]) ).
fof(f202,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4)))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f201,f12]) ).
fof(f203,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4)) )
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f202,f48]) ).
fof(f204,plain,
( spl0_9
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f203,f46,f41,f32,f73]) ).
fof(f205,plain,
( ! [X0] :
( ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| ~ in_environment(sk4,X0)
| ~ environment(sk4) )
| ~ spl0_3
| spl0_6 ),
inference(resolution,[],[f172,f34]) ).
fof(f206,plain,
( ! [X0] :
( ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0)
| ~ environment(sk4) )
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f205,f43]) ).
fof(f207,plain,
( ! [X0] :
( ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0) )
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f206,f12]) ).
fof(f208,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f207,f46,f41,f32,f23]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s5,plain,
( spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s15,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_18 ),
inference(sat_conversion,[],[f141]) ).
cnf(s16,plain,
( spl0_1
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f148]) ).
cnf(s17,plain,
( spl0_1
| ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f149]) ).
cnf(s18,plain,
( spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f150]) ).
cnf(s19,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f156]) ).
cnf(s20,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f157]) ).
cnf(s21,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_18 ),
inference(sat_conversion,[],[f164]) ).
cnf(s22,plain,
spl0_18,
inference(sat_conversion,[],[f168]) ).
cnf(s26,plain,
( ~ spl0_3
| ~ spl0_5
| spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f200]) ).
cnf(s27,plain,
( ~ spl0_3
| ~ spl0_5
| spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f204]) ).
cnf(s28,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f208]) ).
cnf(s29,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(rat,[],[s21,s22]) ).
cnf(s30,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(rat,[],[s15,s22]) ).
cnf(s31,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s28,s17,s18,s16,s5]) ).
cnf(s32,plain,
( ~ spl0_4
| ~ spl0_3
| spl0_1 ),
inference(rat,[],[s29,s26,s27,s17,s18,s31]) ).
cnf(s33,plain,
( spl0_4
| ~ spl0_2 ),
inference(rat,[],[s29,s19,s20]) ).
cnf(s34,plain,
( ~ spl0_4
| spl0_1 ),
inference(rat,[],[s32,s16]) ).
cnf(s35,plain,
spl0_1,
inference(rat,[],[s34,s33,s31]) ).
cnf(s36,plain,
~ spl0_2,
inference(rat,[],[s30,s35]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s1,s36,s35]) ).
fof(f209,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT030-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 17:21:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.57/1.03 % (1184976)Input is clausal, will run a generic CNF schedule.
% 0.57/1.03 % (1184981)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=4077803104:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.57/1.03 % (1184982)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2161751014:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.57/1.03 % (1184986)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3290447516:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.57/1.03 % (1184985)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2484782896:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.57/1.03 % (1184984)lrs+10_1_sil=8000:sp=occurrence:random_seed=871584131:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.57/1.03 % (1184987)dis-21_1_sil=8000:lcm=predicate:random_seed=557271756: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)
% 0.57/1.03 % (1184983)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2220507217:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.57/1.03 % (1184987)Also succeeded, but the first one will report.
% 0.57/1.03 % (1184986)First to succeed.
% 0.57/1.03 % (1184986)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1184976"
% 0.57/1.03 % (1184984)Also succeeded, but the first one will report.
% 0.57/1.03 % (1184985)Instruction limit reached!
% 0.57/1.03 % (1184985)------------------------------
% 0.57/1.03 % (1184985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.57/1.03 % (1184985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/1.03 % (1184985)CaDiCaL version: 2.1.3
% 0.57/1.03 % (1184985)Termination reason: Instruction limit
% 0.57/1.03 % (1184985)Termination phase: Saturation
% 0.57/1.03 % (1184985)Time elapsed: 0.063 s
% 0.57/1.03 % (1184985)Peak memory usage: 88 MB
% 0.57/1.03 % (1184985)Instructions burned: 114 (million)
% 0.57/1.03 % (1184995)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=955826769:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.57/1.03 % (1184986)Refutation found. Thanks to Tanya!
% 0.57/1.03 % SZS status Unsatisfiable for theBenchmark
% 0.57/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 3.17/1.12 % (1184986)------------------------------
% 3.17/1.12 % (1184986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.12 % (1184986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.12 % (1184986)CaDiCaL version: 2.1.3
% 3.17/1.12 % (1184986)Termination reason: Refutation
% 3.17/1.12 % (1184986)Time elapsed: 0.006 s
% 3.17/1.12 % (1184986)Peak memory usage: 89 MB
% 3.17/1.12 % (1184986)Instructions burned: 7 (million)
% 3.17/1.12 % (1184986)------------------------------
% 3.17/1.12 % (1184986)------------------------------
% 3.17/1.12 % (1184976)Success in time 0.417 s
% 3.17/1.12 % Vampire exiting
%------------------------------------------------------------------------------