%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT023-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:02:03 PM UTC 2026
% Result : Unsatisfiable 2.77s 1.27s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 25
% Syntax : Number of formulae : 109 ( 14 unt; 8 def)
% Number of atoms : 364 ( 17 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 475 ( 220 ~; 247 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 9 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 63 !; 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/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_19) ).
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/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_20) ).
fof(f3,axiom,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_21) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,sk2(X0))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_22) ).
fof(f5,axiom,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ~ in_environment(X0,X1)
| greater_or_equal(sk1(X1,X0),X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_23) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| greater_or_equal(sk1(X1,X0),X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,sk2(X0))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_24) ).
fof(f7,axiom,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| in_environment(X0,sk2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_25) ).
fof(f8,axiom,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,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/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_26) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,sk2(X0))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_27) ).
fof(f10,axiom,
! [X0,X1] :
( ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sk3(X1,X0))
| X1 = critical_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_28) ).
fof(f11,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sk3(X1,X0))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| greater(sk3(X1,X0),X1)
| X1 = critical_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_29) ).
fof(f13,plain,
! [X0,X1] :
( greater(sk3(X1,X0),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0,X1] :
( ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk3(X1,X0)),growth_rate(first_movers,sk3(X1,X0)))
| X1 = critical_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_30) ).
fof(f15,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk3(X1,X0)),growth_rate(first_movers,sk3(X1,X0)))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0] :
( in_environment(X0,sk4(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_31) ).
fof(f17,axiom,
! [X0,X1] :
( ~ greater_or_equal(X1,sk4(X0))
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_32) ).
fof(f18,negated_conjecture,
environment(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_33) ).
fof(f19,negated_conjecture,
stable(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_34) ).
fof(f20,negated_conjecture,
~ in_environment(sk5,critical_point(sk5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_35) ).
fof(f21,plain,
! [X0,X1] :
( ~ in_environment(sk5,X0)
| greater_or_equal(sk1(X0,sk5),X0)
| ~ subpopulations(first_movers,efficient_producers,sk5,X1)
| ~ greater(X1,sk2(sk5))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(resolution,[],[f6,f18]) ).
fof(f23,definition,
( spl0_1
<=> ! [X1] :
( ~ subpopulations(first_movers,efficient_producers,sk5,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk2(sk5)) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f24,plain,
( ! [X1] :
( ~ greater(X1,sk2(sk5))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,sk5,X1) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f26,definition,
( spl0_2
<=> ! [X0] :
( ~ in_environment(sk5,X0)
| greater_or_equal(sk1(X0,sk5),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f27,plain,
( ! [X0] :
( greater_or_equal(sk1(X0,sk5),X0)
| ~ in_environment(sk5,X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f28,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f21,f26,f23]) ).
fof(f29,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk1(sk4(X0),sk5))
| ~ stable(X0)
| ~ in_environment(sk5,sk4(X0))
| ~ environment(X0)
| greater(growth_rate(efficient_producers,sk1(sk4(X0),sk5)),growth_rate(first_movers,sk1(sk4(X0),sk5))) )
| ~ spl0_2 ),
inference(resolution,[],[f27,f17]) ).
fof(f30,plain,
! [X0,X1] :
( ~ in_environment(sk5,X0)
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X1)
| ~ greater(X1,sk2(sk5))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(resolution,[],[f4,f18]) ).
fof(f32,definition,
( spl0_3
<=> ! [X0] :
( ~ in_environment(sk5,X0)
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5)) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f33,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ in_environment(sk5,X0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f34,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f30,f32,f23]) ).
fof(f38,definition,
( spl0_4
<=> greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f40,plain,
( greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f42,definition,
( spl0_5
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0))
| critical_point(X0) = sk2(sk5)
| ~ environment(X0)
| ~ in_environment(X0,sk2(sk5)) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f43,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0))
| critical_point(X0) = sk2(sk5)
| ~ environment(X0)
| ~ in_environment(X0,sk2(sk5)) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f46,plain,
( ! [X0] :
( ~ in_environment(sk5,X0)
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ environment(sk5) )
| ~ spl0_4 ),
inference(resolution,[],[f40,f3]) ).
fof(f48,plain,
( ! [X0] :
( ~ in_environment(sk5,X0)
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5)) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f46,f18]) ).
fof(f50,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f48,f38,f32]) ).
fof(f51,plain,
( critical_point(sk5) = sk2(sk5)
| ~ environment(sk5)
| ~ in_environment(sk5,sk2(sk5))
| greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ in_environment(sk5,sk2(sk5))
| ~ environment(sk5)
| critical_point(sk5) = sk2(sk5)
| ~ spl0_5 ),
inference(resolution,[],[f43,f11]) ).
fof(f52,plain,
( critical_point(sk5) = sk2(sk5)
| ~ environment(sk5)
| ~ in_environment(sk5,sk2(sk5))
| greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ spl0_5 ),
inference(duplicate_literal_removal,[],[f51]) ).
fof(f53,plain,
( critical_point(sk5) = sk2(sk5)
| ~ in_environment(sk5,sk2(sk5))
| greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f52,f18]) ).
fof(f56,definition,
( spl0_6
<=> in_environment(sk5,sk2(sk5)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f57,plain,
( in_environment(sk5,sk2(sk5))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( ~ in_environment(sk5,sk2(sk5))
| spl0_6 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl0_7
<=> critical_point(sk5) = sk2(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f61,plain,
( critical_point(sk5) != sk2(sk5)
| spl0_7 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( critical_point(sk5) = sk2(sk5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f64,plain,
( ! [X0] :
( ~ in_environment(sk5,X0)
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ environment(sk5) )
| spl0_6 ),
inference(resolution,[],[f58,f1]) ).
fof(f66,plain,
( ! [X0] :
( ~ in_environment(sk5,X0)
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5)) )
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f64,f18]) ).
fof(f67,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f66,f56,f32]) ).
fof(f68,plain,
( ~ in_environment(sk5,sk4(sk5))
| ~ stable(sk5)
| ~ in_environment(sk5,sk4(sk5))
| ~ environment(sk5)
| greater(growth_rate(efficient_producers,sk1(sk4(sk5),sk5)),growth_rate(first_movers,sk1(sk4(sk5),sk5)))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f33,f29]) ).
fof(f69,plain,
( ~ in_environment(sk5,sk4(sk5))
| ~ stable(sk5)
| ~ environment(sk5)
| greater(growth_rate(efficient_producers,sk1(sk4(sk5),sk5)),growth_rate(first_movers,sk1(sk4(sk5),sk5)))
| ~ spl0_2
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f68]) ).
fof(f70,plain,
( ~ stable(sk5)
| ~ environment(sk5)
| greater(growth_rate(efficient_producers,sk1(sk4(sk5),sk5)),growth_rate(first_movers,sk1(sk4(sk5),sk5)))
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f69,f16]) ).
fof(f71,plain,
( ~ environment(sk5)
| greater(growth_rate(efficient_producers,sk1(sk4(sk5),sk5)),growth_rate(first_movers,sk1(sk4(sk5),sk5)))
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f70,f19]) ).
fof(f72,plain,
( greater(growth_rate(efficient_producers,sk1(sk4(sk5),sk5)),growth_rate(first_movers,sk1(sk4(sk5),sk5)))
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f71,f18]) ).
fof(f73,plain,
( ! [X0] :
( ~ in_environment(sk5,sk4(sk5))
| ~ environment(sk5)
| ~ subpopulations(first_movers,efficient_producers,sk5,X0)
| ~ greater(X0,sk2(sk5))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) )
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f72,f9]) ).
fof(f74,plain,
( ~ in_environment(sk5,sk4(sk5))
| ~ environment(sk5)
| in_environment(sk5,sk2(sk5))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f72,f7]) ).
fof(f75,plain,
( ~ in_environment(sk5,sk4(sk5))
| in_environment(sk5,sk2(sk5))
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f74,f18]) ).
fof(f82,definition,
( spl0_8
<=> in_environment(sk5,sk4(sk5)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f84,plain,
( ~ in_environment(sk5,sk4(sk5))
| spl0_8 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_6
| ~ spl0_8
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f75,f32,f26,f82,f56]) ).
fof(f86,plain,
( ~ in_environment(sk5,sk2(sk5))
| ~ spl0_7 ),
inference(superposition,[],[f20,f62]) ).
fof(f87,plain,
( $false
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f86,f57]) ).
fof(f88,plain,
( ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f87]) ).
fof(f91,plain,
( ! [X0] :
( ~ in_environment(sk5,X0)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk5)),growth_rate(first_movers,sk1(X0,sk5)))
| ~ environment(sk5) )
| ~ spl0_4 ),
inference(resolution,[],[f40,f8]) ).
fof(f94,plain,
( ! [X0] :
( ~ greater(growth_rate(efficient_producers,sk1(X0,sk5)),growth_rate(first_movers,sk1(X0,sk5)))
| ~ in_environment(sk5,X0) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f91,f18]) ).
fof(f95,plain,
( ~ in_environment(sk5,sk4(sk5))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(resolution,[],[f94,f72]) ).
fof(f96,plain,
( ~ spl0_8
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f95,f38,f32,f26,f82]) ).
fof(f97,plain,
( ~ stable(sk5)
| ~ environment(sk5)
| spl0_8 ),
inference(resolution,[],[f84,f16]) ).
fof(f98,plain,
( ~ environment(sk5)
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f97,f19]) ).
fof(f99,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f98,f18]) ).
fof(f100,plain,
spl0_8,
inference(avatar_contradiction_clause,[],[f99]) ).
fof(f101,plain,
( ! [X0] :
( ~ in_environment(sk5,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0)
| ~ greater(X0,sk2(sk5))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f73,f18]) ).
fof(f102,plain,
( spl0_1
| ~ spl0_8
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f101,f32,f26,f82,f23]) ).
fof(f103,plain,
( ! [X0] :
( greater(growth_rate(efficient_producers,sk3(sk2(sk5),X0)),growth_rate(first_movers,sk3(sk2(sk5),X0)))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0))
| greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ in_environment(X0,sk2(sk5))
| ~ environment(X0)
| critical_point(X0) = sk2(sk5) )
| ~ spl0_1 ),
inference(resolution,[],[f24,f13]) ).
fof(f104,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk5,sk3(sk2(sk5),X0))
| greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ in_environment(X0,sk2(sk5))
| ~ environment(X0)
| critical_point(X0) = sk2(sk5) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f103,f15]) ).
fof(f105,plain,
( spl0_4
| spl0_5
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f104,f23,f42,f38]) ).
fof(f108,plain,
( ! [X0] :
( ~ in_environment(sk5,X0)
| greater_or_equal(sk1(X0,sk5),X0)
| ~ environment(sk5) )
| ~ spl0_4 ),
inference(resolution,[],[f40,f5]) ).
fof(f109,plain,
( ! [X0] :
( ~ in_environment(sk5,X0)
| greater_or_equal(sk1(X0,sk5),X0) )
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f108,f18]) ).
fof(f111,plain,
( spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f109,f38,f26]) ).
fof(f113,plain,
( ~ in_environment(sk5,sk2(sk5))
| greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ spl0_5
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f53,f61]) ).
fof(f115,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_5
| spl0_7 ),
inference(avatar_split_clause,[],[f113,f60,f42,f56,f38]) ).
fof(f117,plain,
( ! [X0] :
( ~ in_environment(sk5,X0)
| greater_or_equal(sk1(X0,sk5),X0)
| ~ environment(sk5) )
| spl0_6 ),
inference(resolution,[],[f58,f2]) ).
fof(f118,plain,
( ! [X0] :
( ~ in_environment(sk5,X0)
| greater_or_equal(sk1(X0,sk5),X0) )
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f117,f18]) ).
fof(f119,plain,
( spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f118,f56,f26]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f50]) ).
cnf(s6,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f67]) ).
cnf(s8,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f85]) ).
cnf(s9,plain,
( ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f88]) ).
cnf(s11,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f96]) ).
cnf(s12,plain,
spl0_8,
inference(sat_conversion,[],[f100]) ).
cnf(s13,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(sat_conversion,[],[f102]) ).
cnf(s14,plain,
( ~ spl0_1
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f105]) ).
cnf(s15,plain,
( spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f111]) ).
cnf(s17,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f115]) ).
cnf(s18,plain,
( spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f119]) ).
cnf(s19,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(rat,[],[s11,s12]) ).
cnf(s20,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_6 ),
inference(rat,[],[s8,s12]) ).
cnf(s21,plain,
spl0_1,
inference(rat,[],[s13,s1,s2,s12]) ).
cnf(s22,plain,
spl0_2,
inference(rat,[],[s17,s14,s9,s15,s18,s21]) ).
cnf(s23,plain,
~ spl0_3,
inference(rat,[],[s17,s9,s14,s20,s19,s21,s22]) ).
cnf(s24,plain,
spl0_6,
inference(rat,[],[s6,s23]) ).
cnf(s25,plain,
~ spl0_4,
inference(rat,[],[s4,s23]) ).
cnf(s26,plain,
~ spl0_7,
inference(rat,[],[s9,s24]) ).
cnf(s27,plain,
spl0_5,
inference(rat,[],[s14,s21,s25]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s17,s25,s24,s26,s27]) ).
fof(f120,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 17:16:41 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.77/1.27 % (3191750)Input is clausal, will run a generic CNF schedule.
% 2.77/1.27 % (3191759)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2213643164:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.77/1.27 % (3191759)Instruction limit reached!
% 2.77/1.27 % (3191759)------------------------------
% 2.77/1.27 % (3191759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.27 % (3191759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.27 % (3191759)CaDiCaL version: 2.1.3
% 2.77/1.27 % (3191759)Termination reason: Instruction limit
% 2.77/1.27 % (3191759)Termination phase: Saturation
% 2.77/1.27 % (3191759)Time elapsed: 0.035 s
% 2.77/1.27 % (3191759)Peak memory usage: 88 MB
% 2.77/1.27 % (3191759)Instructions burned: 117 (million)
% 2.77/1.27 % (3191756)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1533557632:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.77/1.27 % (3191757)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2441886839:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.77/1.27 % (3191755)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=3947677824:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.77/1.27 % (3191758)lrs+10_1_sil=8000:sp=occurrence:random_seed=3711623760:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.77/1.27 % (3191760)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=533513173:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.77/1.27 % (3191761)dis-21_1_sil=8000:lcm=predicate:random_seed=2904723333: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)
% 2.77/1.27 % (3191761)Refutation not found, incomplete strategy
% 2.77/1.27 % (3191761)------------------------------
% 2.77/1.27 % (3191761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.27 % (3191761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.27 % (3191761)CaDiCaL version: 2.1.3
% 2.77/1.27 % (3191761)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.27 % (3191761)Time elapsed: 0.002 s
% 2.77/1.27 % (3191761)Peak memory usage: 88 MB
% 2.77/1.27 % (3191761)Instructions burned: 2 (million)
% 2.77/1.27 % (3191760)First to succeed.
% 2.77/1.27 % (3191760)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3191750"
% 2.77/1.27 % (3191758)Also succeeded, but the first one will report.
% 2.77/1.27 % (3191763)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=197514977:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.77/1.27 % (3191763)Instruction limit reached!
% 2.77/1.27 % (3191763)------------------------------
% 2.77/1.27 % (3191763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.27 % (3191763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.27 % (3191763)CaDiCaL version: 2.1.3
% 2.77/1.27 % (3191763)Termination reason: Instruction limit
% 2.77/1.27 % (3191763)Termination phase: Saturation
% 2.77/1.27 % (3191763)Time elapsed: 0.037 s
% 2.77/1.27 % (3191763)Peak memory usage: 88 MB
% 2.77/1.27 % (3191763)Instructions burned: 146 (million)
% 2.77/1.27 % (3191771)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1864731350:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.77/1.27 % (3191771)Refutation not found, incomplete strategy
% 2.77/1.27 % (3191771)------------------------------
% 2.77/1.27 % (3191771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.27 % (3191771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.27 % (3191771)CaDiCaL version: 2.1.3
% 2.77/1.27 % (3191771)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.27 % (3191771)Time elapsed: 0.001 s
% 2.77/1.27 % (3191771)Peak memory usage: 88 MB
% 2.77/1.27 % (3191771)Instructions burned: 2 (million)
% 2.77/1.27 % (3191761)------------------------------
% 2.77/1.27 % (3191761)------------------------------
% 2.77/1.27 % (3191760)Refutation found. Thanks to Tanya!
% 2.77/1.27 % SZS status Unsatisfiable for theBenchmark
% 2.77/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.47 % (3191760)------------------------------
% 3.52/1.47 % (3191760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.47 % (3191760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.47 % (3191760)CaDiCaL version: 2.1.3
% 3.52/1.47 % (3191760)Termination reason: Refutation
% 3.52/1.47 % (3191760)Time elapsed: 0.007 s
% 3.52/1.47 % (3191760)Peak memory usage: 89 MB
% 3.52/1.47 % (3191760)Instructions burned: 7 (million)
% 3.52/1.47 % (3191760)------------------------------
% 3.52/1.47 % (3191760)------------------------------
% 3.52/1.47 % (3191750)Success in time 0.416 s
% 3.52/1.47 % Vampire exiting
%------------------------------------------------------------------------------