%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT028-1 : 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 : n007.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 1.11s 1.14s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 92 ( 10 unt; 6 def)
% Number of atoms : 415 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 614 ( 291 ~; 317 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 7 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_1) ).
fof(f2,axiom,
! [X0,X1] :
( greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| greater_or_equal(sk1(X1,X0),X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_2) ).
fof(f3,axiom,
! [X2,X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sk2(X0))
| greater(zero,growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_3) ).
fof(f4,axiom,
! [X2,X0,X1] :
( greater_or_equal(sk1(X1,X0),X1)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sk2(X0))
| greater(zero,growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_4) ).
fof(f5,axiom,
! [X0,X1] :
( ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_5) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sk2(X0))
| greater(zero,growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_6) ).
fof(f7,axiom,
! [X0] :
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11_7) ).
fof(f9,axiom,
! [X0,X1] :
( greater(zero,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/sandbox/benchmark/theBenchmark.p',l11_9) ).
fof(f10,negated_conjecture,
environment(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_10) ).
fof(f11,negated_conjecture,
stable(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_11) ).
fof(f12,negated_conjecture,
! [X0] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| ~ greater(X0,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_12) ).
fof(f13,negated_conjecture,
! [X0] :
( ~ greater(X0,appear(efficient_producers,sk4))
| greater_or_equal(sk5(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_13) ).
fof(f14,negated_conjecture,
! [X0] :
( ~ greater(zero,growth_rate(first_movers,sk5(X0)))
| ~ greater(X0,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_14) ).
fof(f20,plain,
! [X0] :
( ~ stable(sk4)
| ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0)
| ~ environment(sk4)
| greater_or_equal(sk5(sk2(sk4)),sk2(sk4)) ),
inference(resolution,[],[f2,f13]) ).
fof(f21,plain,
! [X0] :
( ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0)
| ~ environment(sk4)
| greater_or_equal(sk5(sk2(sk4)),sk2(sk4)) ),
inference(forward_subsumption_resolution,[],[f20,f11]) ).
fof(f22,plain,
! [X0] :
( ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0)
| greater_or_equal(sk5(sk2(sk4)),sk2(sk4)) ),
inference(forward_subsumption_resolution,[],[f21,f10]) ).
fof(f24,definition,
( spl0_1
<=> greater_or_equal(sk5(sk2(sk4)),sk2(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f25,plain,
( greater_or_equal(sk5(sk2(sk4)),sk2(sk4))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f27,definition,
( spl0_2
<=> ! [X0] :
( ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f28,plain,
( ! [X0] :
( greater_or_equal(sk1(X0,sk4),X0)
| ~ in_environment(sk4,X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f29,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f22,f27,f24]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X2,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X2)
| ~ stable(X0)
| ~ greater_or_equal(sk1(X1,X0),sk3(X2))
| ~ environment(X2) ),
inference(resolution,[],[f5,f9]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X3,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sk2(X0))
| greater(zero,growth_rate(first_movers,X2))
| ~ stable(X3)
| ~ stable(X0)
| ~ greater_or_equal(sk1(X1,X0),sk3(X3))
| ~ environment(X3) ),
inference(resolution,[],[f6,f9]) ).
fof(f33,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ stable(X0)
| ~ greater_or_equal(sk1(X1,X0),sk3(X0))
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0)) ),
inference(resolution,[],[f30,f1]) ).
fof(f34,plain,
! [X0,X1] :
( ~ greater_or_equal(sk1(X1,X0),sk3(X0))
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ in_environment(X0,X1) ),
inference(duplicate_literal_removal,[],[f33]) ).
fof(f36,plain,
( ~ environment(sk4)
| greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ stable(sk4)
| ~ in_environment(sk4,sk3(sk4))
| ~ in_environment(sk4,sk3(sk4))
| ~ spl0_2 ),
inference(resolution,[],[f34,f28]) ).
fof(f39,plain,
( ~ environment(sk4)
| greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ stable(sk4)
| ~ in_environment(sk4,sk3(sk4))
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f36]) ).
fof(f41,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ stable(sk4)
| ~ in_environment(sk4,sk3(sk4))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f39,f10]) ).
fof(f42,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ in_environment(sk4,sk3(sk4))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f41,f11]) ).
fof(f44,definition,
( spl0_3
<=> in_environment(sk4,sk3(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f45,plain,
( ~ in_environment(sk4,sk3(sk4))
| spl0_3 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,definition,
( spl0_4
<=> greater(sk2(sk4),appear(efficient_producers,sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f48,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f42,f27,f47,f44]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sk2(X0))
| greater(zero,growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ stable(X0)
| ~ greater_or_equal(sk1(X1,X0),sk3(X0))
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,sk2(X0))
| greater(zero,growth_rate(first_movers,X3)) ),
inference(resolution,[],[f31,f3]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ greater_or_equal(sk1(X1,X0),sk3(X0))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sk2(X0))
| greater(zero,growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,sk2(X0))
| greater(zero,growth_rate(first_movers,X3)) ),
inference(duplicate_literal_removal,[],[f50]) ).
fof(f56,plain,
( ~ stable(sk4)
| ~ environment(sk4)
| spl0_3 ),
inference(resolution,[],[f45,f7]) ).
fof(f57,plain,
( ~ environment(sk4)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f56,f11]) ).
fof(f58,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f57,f10]) ).
fof(f59,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f58]) ).
fof(f60,plain,
( greater_or_equal(sk5(sk2(sk4)),sk2(sk4))
| ~ spl0_4 ),
inference(resolution,[],[f48,f13]) ).
fof(f61,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f60,f47,f24]) ).
fof(f63,plain,
( ! [X0,X1] :
( ~ environment(sk4)
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(X0,sk2(sk4))
| greater(zero,growth_rate(first_movers,X0))
| ~ stable(sk4)
| ~ in_environment(sk4,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater_or_equal(X1,sk2(sk4))
| greater(zero,growth_rate(first_movers,X1))
| ~ in_environment(sk4,sk3(sk4)) )
| ~ spl0_2 ),
inference(resolution,[],[f55,f28]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,sk2(X0))
| greater(zero,growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ in_environment(X0,sk3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sk2(X0))
| greater(zero,growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ in_environment(X0,sk3(X0))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,sk2(X0))
| greater(zero,growth_rate(first_movers,X3)) ),
inference(resolution,[],[f55,f4]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,sk2(X0))
| greater(zero,growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ in_environment(X0,sk3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sk2(X0))
| greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,sk2(X0))
| greater(zero,growth_rate(first_movers,X3)) ),
inference(duplicate_literal_removal,[],[f64]) ).
fof(f66,plain,
( ! [X0,X1] :
( ~ environment(sk4)
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(X0,sk2(sk4))
| greater(zero,growth_rate(first_movers,X0))
| ~ stable(sk4)
| ~ in_environment(sk4,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater_or_equal(X1,sk2(sk4))
| greater(zero,growth_rate(first_movers,X1)) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f63]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( greater(zero,growth_rate(first_movers,X3))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,sk2(X0))
| greater(zero,growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sk2(X0))
| greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,sk2(X0))
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f65,f7]) ).
fof(f68,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(X0,sk2(sk4))
| greater(zero,growth_rate(first_movers,X0))
| ~ stable(sk4)
| ~ in_environment(sk4,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater_or_equal(X1,sk2(sk4))
| greater(zero,growth_rate(first_movers,X1)) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f66,f10]) ).
fof(f69,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(X0,sk2(sk4))
| greater(zero,growth_rate(first_movers,X0))
| ~ in_environment(sk4,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater_or_equal(X1,sk2(sk4))
| greater(zero,growth_rate(first_movers,X1)) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f68,f11]) ).
fof(f71,definition,
( spl0_5
<=> ! [X1] :
( ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk2(sk4)) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f72,plain,
( ! [X1] :
( greater(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater_or_equal(X1,sk2(sk4)) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( spl0_5
| ~ spl0_3
| spl0_5
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f69,f27,f71,f44,f71]) ).
fof(f74,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| ~ greater_or_equal(sk5(X0),sk2(sk4))
| ~ greater(X0,appear(efficient_producers,sk4)) )
| ~ spl0_5 ),
inference(resolution,[],[f72,f14]) ).
fof(f77,plain,
( ! [X0] :
( ~ greater_or_equal(sk5(X0),sk2(sk4))
| ~ greater(X0,appear(efficient_producers,sk4)) )
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f74,f12]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk5(X3))
| ~ greater_or_equal(X1,sk2(X0))
| greater(zero,growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sk2(X0))
| greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(sk5(X3),sk2(X0))
| ~ environment(X0)
| ~ greater(X3,appear(efficient_producers,sk4)) ),
inference(resolution,[],[f67,f14]) ).
fof(f81,plain,
( ~ greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f77,f25]) ).
fof(f82,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f81,f48]) ).
fof(f83,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f82]) ).
fof(f95,plain,
( ! [X0] :
( ~ stable(sk4)
| ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0)
| ~ environment(sk4) )
| ~ spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f81,f2]) ).
fof(f96,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0)
| ~ environment(sk4) )
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f95,f11]) ).
fof(f97,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0) )
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f96,f10]) ).
fof(f98,plain,
( spl0_2
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f97,f71,f24,f27]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ greater_or_equal(X0,sk2(sk4))
| greater(zero,growth_rate(first_movers,X0))
| ~ stable(sk4)
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater_or_equal(X1,sk2(sk4))
| greater(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(sk5(X2),sk2(sk4))
| ~ environment(sk4)
| ~ greater(X2,appear(efficient_producers,sk4))
| ~ greater(X2,appear(efficient_producers,sk4)) ),
inference(resolution,[],[f78,f12]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ greater_or_equal(X0,sk2(sk4))
| greater(zero,growth_rate(first_movers,X0))
| ~ stable(sk4)
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater_or_equal(X1,sk2(sk4))
| greater(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(sk5(X2),sk2(sk4))
| ~ environment(sk4)
| ~ greater(X2,appear(efficient_producers,sk4)) ),
inference(duplicate_literal_removal,[],[f99]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ greater_or_equal(X0,sk2(sk4))
| greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater_or_equal(X1,sk2(sk4))
| greater(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(sk5(X2),sk2(sk4))
| ~ environment(sk4)
| ~ greater(X2,appear(efficient_producers,sk4)) ),
inference(forward_subsumption_resolution,[],[f104,f11]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ greater_or_equal(X0,sk2(sk4))
| greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater_or_equal(X1,sk2(sk4))
| greater(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(sk5(X2),sk2(sk4))
| ~ greater(X2,appear(efficient_producers,sk4)) ),
inference(forward_subsumption_resolution,[],[f107,f10]) ).
fof(f110,definition,
( spl0_7
<=> ! [X2] :
( ~ greater_or_equal(sk5(X2),sk2(sk4))
| ~ greater(X2,appear(efficient_producers,sk4)) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f111,plain,
( ! [X2] :
( ~ greater_or_equal(sk5(X2),sk2(sk4))
| ~ greater(X2,appear(efficient_producers,sk4)) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f112,plain,
( spl0_7
| spl0_5
| spl0_5 ),
inference(avatar_split_clause,[],[f108,f71,f71,f110]) ).
fof(f143,plain,
( ~ greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ spl0_1
| ~ spl0_7 ),
inference(resolution,[],[f111,f25]) ).
fof(f150,plain,
( ! [X0] :
( ~ stable(sk4)
| ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0)
| ~ environment(sk4) )
| ~ spl0_1
| ~ spl0_7 ),
inference(resolution,[],[f143,f2]) ).
fof(f151,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0)
| ~ environment(sk4) )
| ~ spl0_1
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f150,f11]) ).
fof(f153,plain,
( ! [X0] :
( ~ in_environment(sk4,X0)
| greater_or_equal(sk1(X0,sk4),X0) )
| ~ spl0_1
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f151,f10]) ).
fof(f155,plain,
( spl0_2
| ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f153,f110,f24,f27]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f59]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f61]) ).
cnf(s5,plain,
( spl0_5
| ~ spl0_3
| ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_5 ),
inference(rat,[],[s5]) ).
cnf(s7,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f83]) ).
cnf(s9,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f98]) ).
cnf(s10,plain,
( spl0_5
| spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f112]) ).
cnf(s11,plain,
( spl0_5
| spl0_7 ),
inference(rat,[],[s10]) ).
cnf(s13,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_7 ),
inference(sat_conversion,[],[f155]) ).
cnf(s15,plain,
( ~ spl0_2
| spl0_4 ),
inference(rat,[],[s2,s3]) ).
cnf(s16,plain,
spl0_1,
inference(rat,[],[s15,s1,s4]) ).
cnf(s17,plain,
spl0_2,
inference(rat,[],[s11,s9,s13,s16]) ).
cnf(s18,plain,
spl0_5,
inference(rat,[],[s6,s3,s17]) ).
cnf(s19,plain,
spl0_4,
inference(rat,[],[s15,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s7,s16,s18,s19]) ).
fof(f157,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT028-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 17:19:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 1.11/1.14 % (1676538)Input is clausal, will run a generic CNF schedule.
% 1.11/1.14 % (1676547)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1152320409:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.11/1.14 % (1676547)First to succeed.
% 1.11/1.14 % (1676547)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1676538"
% 1.11/1.14 % (1676548)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1009959340:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.11/1.14 % (1676543)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=1262245546:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.11/1.14 % (1676549)dis-21_1_sil=8000:lcm=predicate:random_seed=928715459: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)
% 1.11/1.14 % (1676546)lrs+10_1_sil=8000:sp=occurrence:random_seed=3115345226:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.11/1.14 % (1676544)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=924295045:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.11/1.14 % (1676545)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=222564045:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.11/1.14 % (1676546)Also succeeded, but the first one will report.
% 1.11/1.14 % (1676549)Also succeeded, but the first one will report.
% 1.11/1.14 % (1676548)Also succeeded, but the first one will report.
% 1.11/1.14 % (1676547)Refutation found. Thanks to Tanya!
% 1.11/1.14 % SZS status Unsatisfiable for theBenchmark
% 1.11/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.36 % (1676547)------------------------------
% 2.60/1.36 % (1676547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.36 % (1676547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.36 % (1676547)CaDiCaL version: 2.1.3
% 2.60/1.36 % (1676547)Termination reason: Refutation
% 2.60/1.36 % (1676547)Time elapsed: 0.004 s
% 2.60/1.36 % (1676547)Peak memory usage: 89 MB
% 2.60/1.36 % (1676547)Instructions burned: 9 (million)
% 2.60/1.36 % (1676547)------------------------------
% 2.60/1.36 % (1676547)------------------------------
% 2.60/1.36 % (1676538)Success in time 0.288 s
% 2.60/1.36 % Vampire exiting
%------------------------------------------------------------------------------