%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 12:02:34 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 87 ( 14 unt; 5 def)
% Number of atoms : 335 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 436 ( 188 ~; 190 |; 41 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 6 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 76 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( environment(X0)
& ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) )
=> ? [X1] :
( in_environment(X0,X1)
& ~ 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',mp_earliest_time_growth_rate_exceeds) ).
fof(f2,axiom,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(f3,conjecture,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ~ 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',prove_l12) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ~ 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)) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0] :
( ( environment(X0)
& ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) )
=> ? [X3] :
( in_environment(X0,X3)
& ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X0,X4)
& greater(X4,X3) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ) ) ),
inference(rectify,[],[f1]) ).
fof(f6,plain,
! [X0] :
( ? [X3] :
( in_environment(X0,X3)
& ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
& ! [X4] :
( greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4))
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| ~ greater(X4,X3) ) )
| ~ environment(X0)
| ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ? [X3] :
( in_environment(X0,X3)
& ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
& ! [X4] :
( greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4))
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| ~ greater(X4,X3) ) )
| ~ environment(X0)
| ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) ) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
? [X0] :
( ! [X1] :
( ~ in_environment(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)
& stable(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,plain,
? [X0] :
( ! [X1] :
( ~ in_environment(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)
& stable(X0) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1,X4] :
( ~ subpopulations(first_movers,efficient_producers,X0,X4)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(X4,sK0(X0))
| ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
| greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1,X4] :
( subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| ~ environment(X0)
| ~ greater(X4,sK0(X0))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0,X1,X4] :
( greater_or_equal(sK1(X0,X1),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(X4,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0,X1] :
( greater_or_equal(sK1(X0,X1),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| in_environment(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f16,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| in_environment(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f17,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
| in_environment(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f18,plain,
! [X0,X1] :
( greater_or_equal(sK1(X0,X1),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK0(X0)),growth_rate(first_movers,sK0(X0))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f19,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK0(X0)),growth_rate(first_movers,sK0(X0))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
| ~ greater(growth_rate(efficient_producers,sK0(X0)),growth_rate(first_movers,sK0(X0))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f21,plain,
! [X2,X0] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X2,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,sK2(X0)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f23,plain,
! [X1] :
( ~ in_environment(sK3,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(sK4(X1),X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f24,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK3,sK4(X1))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(sK3,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f25,plain,
! [X1] :
( ~ in_environment(sK3,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(growth_rate(efficient_producers,sK4(X1)),growth_rate(first_movers,sK4(X1))) ),
inference(cnf_transformation,[],[f11]) ).
fof(f26,plain,
stable(sK3),
inference(cnf_transformation,[],[f11]) ).
fof(f27,plain,
environment(sK3),
inference(cnf_transformation,[],[f11]) ).
fof(f28,plain,
( ~ environment(sK3)
| in_environment(sK3,sK2(sK3)) ),
inference(resolution,[],[f22,f26]) ).
fof(f29,plain,
in_environment(sK3,sK2(sK3)),
inference(forward_subsumption_resolution,[],[f28,f27]) ).
fof(f46,plain,
! [X0] :
( ~ environment(sK3)
| ~ greater_or_equal(X0,sK2(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[],[f21,f26]) ).
fof(f47,plain,
! [X0] :
( ~ greater_or_equal(X0,sK2(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(forward_subsumption_resolution,[],[f46,f27]) ).
fof(f48,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK3,sK1(X0,sK2(sK3)))
| greater(growth_rate(efficient_producers,sK1(X0,sK2(sK3))),growth_rate(first_movers,sK1(X0,sK2(sK3))))
| ~ in_environment(X0,sK2(sK3))
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK0(X0)),growth_rate(first_movers,sK0(X0))) ),
inference(resolution,[],[f47,f18]) ).
fof(f49,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK3,sK1(X0,sK2(sK3)))
| greater(growth_rate(efficient_producers,sK1(X0,sK2(sK3))),growth_rate(first_movers,sK1(X0,sK2(sK3))))
| ~ in_environment(X0,sK2(sK3))
| ~ environment(X0)
| in_environment(X0,sK0(X0)) ),
inference(resolution,[],[f47,f15]) ).
fof(f50,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK3,sK1(X0,sK2(sK3)))
| ~ in_environment(X0,sK2(sK3))
| ~ environment(X0)
| in_environment(X0,sK0(X0)) ),
inference(forward_subsumption_resolution,[],[f49,f17]) ).
fof(f51,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK3,sK1(X0,sK2(sK3)))
| ~ in_environment(X0,sK2(sK3))
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK0(X0)),growth_rate(first_movers,sK0(X0))) ),
inference(forward_subsumption_resolution,[],[f48,f20]) ).
fof(f54,definition,
( spl5_4
<=> in_environment(sK3,sK0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f55,plain,
( ~ in_environment(sK3,sK0(sK3))
| spl5_4 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f56,plain,
( in_environment(sK3,sK0(sK3))
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f62,plain,
( greater(growth_rate(efficient_producers,sK0(sK3)),growth_rate(first_movers,sK0(sK3)))
| greater(sK4(sK0(sK3)),sK0(sK3))
| ~ spl5_4 ),
inference(resolution,[],[f56,f23]) ).
fof(f64,definition,
( spl5_6
<=> greater(sK4(sK0(sK3)),sK0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f66,plain,
( greater(sK4(sK0(sK3)),sK0(sK3))
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl5_7
<=> greater(growth_rate(efficient_producers,sK0(sK3)),growth_rate(first_movers,sK0(sK3))) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f70,plain,
( greater(growth_rate(efficient_producers,sK0(sK3)),growth_rate(first_movers,sK0(sK3)))
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( spl5_6
| spl5_7
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f62,f54,f68,f64]) ).
fof(f79,plain,
! [X0,X1] :
( ~ in_environment(X0,sK2(sK3))
| ~ environment(X0)
| ~ greater(X1,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,sK3,sK1(X0,sK2(sK3)))
| greater(growth_rate(efficient_producers,sK1(X0,sK2(sK3))),growth_rate(first_movers,sK1(X0,sK2(sK3)))) ),
inference(resolution,[],[f14,f47]) ).
fof(f80,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK3,sK1(X0,sK2(sK3)))
| ~ greater(X1,sK0(X0))
| ~ in_environment(X0,sK2(sK3))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f79,f12]) ).
fof(f82,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ environment(sK3)
| ~ greater(sK4(X0),sK0(sK3))
| ~ in_environment(sK3,X1)
| greater(growth_rate(efficient_producers,sK4(X0)),growth_rate(first_movers,sK4(X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sK3,X0) ),
inference(resolution,[],[f13,f24]) ).
fof(f90,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ environment(sK3)
| ~ greater(sK4(X0),sK0(sK3))
| ~ in_environment(sK3,X1)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sK3,X0) ),
inference(forward_subsumption_resolution,[],[f82,f25]) ).
fof(f91,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ greater(sK4(X0),sK0(sK3))
| ~ in_environment(sK3,X1)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sK3,X0) ),
inference(forward_subsumption_resolution,[],[f90,f27]) ).
fof(f93,definition,
( spl5_9
<=> ! [X0] :
( ~ greater(sK4(X0),sK0(sK3))
| ~ in_environment(sK3,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
fof(f94,plain,
( ! [X0] :
( ~ in_environment(sK3,X0)
| ~ greater(sK4(X0),sK0(sK3))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl5_10
<=> ! [X1] :
( subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ in_environment(sK3,X1) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f97,plain,
( ! [X1] :
( subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ in_environment(sK3,X1) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f98,plain,
( spl5_9
| spl5_10 ),
inference(avatar_split_clause,[],[f91,f96,f93]) ).
fof(f109,plain,
( ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| in_environment(sK3,sK0(sK3))
| ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| in_environment(sK3,sK0(sK3)) ),
inference(resolution,[],[f50,f16]) ).
fof(f110,plain,
( ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| in_environment(sK3,sK0(sK3)) ),
inference(duplicate_literal_removal,[],[f109]) ).
fof(f113,plain,
( ~ environment(sK3)
| in_environment(sK3,sK0(sK3)) ),
inference(forward_subsumption_resolution,[],[f110,f29]) ).
fof(f116,plain,
in_environment(sK3,sK0(sK3)),
inference(forward_subsumption_resolution,[],[f113,f27]) ).
fof(f119,plain,
( $false
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f116,f55]) ).
fof(f120,plain,
spl5_4,
inference(avatar_contradiction_clause,[],[f119]) ).
fof(f124,plain,
( ~ greater(sK4(sK0(sK3)),sK0(sK3))
| greater(growth_rate(efficient_producers,sK0(sK3)),growth_rate(first_movers,sK0(sK3)))
| ~ spl5_4
| ~ spl5_9 ),
inference(resolution,[],[f56,f94]) ).
fof(f128,plain,
( greater(growth_rate(efficient_producers,sK0(sK3)),growth_rate(first_movers,sK0(sK3)))
| ~ spl5_4
| ~ spl5_6
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f124,f66]) ).
fof(f129,plain,
( spl5_7
| ~ spl5_4
| ~ spl5_6
| ~ spl5_9 ),
inference(avatar_split_clause,[],[f128,f93,f64,f54,f68]) ).
fof(f131,plain,
( ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| ~ greater(growth_rate(efficient_producers,sK0(sK3)),growth_rate(first_movers,sK0(sK3)))
| ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| ~ greater(growth_rate(efficient_producers,sK0(sK3)),growth_rate(first_movers,sK0(sK3))) ),
inference(resolution,[],[f51,f19]) ).
fof(f134,plain,
( ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| ~ greater(growth_rate(efficient_producers,sK0(sK3)),growth_rate(first_movers,sK0(sK3))) ),
inference(duplicate_literal_removal,[],[f131]) ).
fof(f136,plain,
( ~ environment(sK3)
| ~ greater(growth_rate(efficient_producers,sK0(sK3)),growth_rate(first_movers,sK0(sK3))) ),
inference(forward_subsumption_resolution,[],[f134,f29]) ).
fof(f138,plain,
~ greater(growth_rate(efficient_producers,sK0(sK3)),growth_rate(first_movers,sK0(sK3))),
inference(forward_subsumption_resolution,[],[f136,f27]) ).
fof(f140,plain,
( $false
| ~ spl5_7 ),
inference(forward_subsumption_resolution,[],[f138,f70]) ).
fof(f141,plain,
~ spl5_7,
inference(avatar_contradiction_clause,[],[f140]) ).
fof(f149,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,sK2(sK3)))
| ~ greater(sK4(X0),sK0(sK3))
| ~ in_environment(sK3,sK2(sK3))
| greater(growth_rate(efficient_producers,sK4(X0)),growth_rate(first_movers,sK4(X0)))
| ~ environment(sK3)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sK3,X0) ),
inference(resolution,[],[f80,f24]) ).
fof(f168,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,sK2(sK3)))
| ~ greater(sK4(X0),sK0(sK3))
| ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sK3,X0) ),
inference(forward_subsumption_resolution,[],[f149,f25]) ).
fof(f172,plain,
( ! [X0] :
( ~ greater(sK4(X0),sK0(sK3))
| ~ in_environment(sK3,sK2(sK3))
| ~ environment(sK3)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sK3,X0) )
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f168,f97]) ).
fof(f179,plain,
( ! [X0] :
( ~ greater(sK4(X0),sK0(sK3))
| ~ environment(sK3)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sK3,X0) )
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f172,f29]) ).
fof(f181,plain,
( ! [X0] :
( ~ greater(sK4(X0),sK0(sK3))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sK3,X0) )
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f179,f27]) ).
fof(f182,plain,
( spl5_9
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f181,f96,f93]) ).
cnf(s4,plain,
( ~ spl5_4
| spl5_6
| spl5_7 ),
inference(sat_conversion,[],[f71]) ).
cnf(s6,plain,
( spl5_9
| spl5_10 ),
inference(sat_conversion,[],[f98]) ).
cnf(s7,plain,
spl5_4,
inference(sat_conversion,[],[f120]) ).
cnf(s9,plain,
( ~ spl5_4
| ~ spl5_6
| spl5_7
| ~ spl5_9 ),
inference(sat_conversion,[],[f129]) ).
cnf(s10,plain,
~ spl5_7,
inference(sat_conversion,[],[f141]) ).
cnf(s14,plain,
( spl5_9
| ~ spl5_10 ),
inference(sat_conversion,[],[f182]) ).
cnf(s15,plain,
( ~ spl5_4
| ~ spl5_6
| ~ spl5_9 ),
inference(rat,[],[s9,s10]) ).
cnf(s17,plain,
spl5_6,
inference(rat,[],[s4,s10,s7]) ).
cnf(s18,plain,
~ spl5_9,
inference(rat,[],[s15,s7,s17]) ).
cnf(s19,plain,
~ spl5_10,
inference(rat,[],[s14,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s6,s19,s18]) ).
fof(f183,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n020.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 17:22:20 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.45 % (3628763)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (3628772)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=766240889:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.45 % (3628772) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3628763-3628772"...
% 0.12/0.45 % (3628769)% WARNING: option uhcvi not known.
% 0.12/0.45 % (3628772)...printing done.
% 0.12/0.45 % (3628772)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (3628772)------------------------------
% 0.12/0.45 % (3628772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (3628772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (3628772)CaDiCaL version: 2.1.3
% 0.12/0.45 % (3628772)Termination reason: Refutation
% 0.12/0.45 % (3628772)Time elapsed: 0.003 s
% 0.12/0.45 % (3628772)Peak memory usage: 12 MB
% 0.12/0.45 % (3628772)Instructions burned: 8 (million)
% 0.12/0.45 % (3628763)Success in time 0.028 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------