%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 12:02:32 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 100 ( 16 unt; 6 def)
% Number of atoms : 390 ( 17 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 503 ( 213 ~; 233 |; 39 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 83 !; 15 ?)
% 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/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).
fof(f2,axiom,
! [X0,X1] :
( ( environment(X0)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) )
=> X1 = critical_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f3,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/sandbox/benchmark/theBenchmark.p',l1) ).
fof(f4,conjecture,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> in_environment(X0,critical_point(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
fof(f5,negated_conjecture,
~ ! [X0] :
( ( environment(X0)
& stable(X0) )
=> in_environment(X0,critical_point(X0)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,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(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(ennf_transformation,[],[f6]) ).
fof(f8,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,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,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(X2,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f10,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,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(X2,X1) ) ),
inference(flattening,[],[f9]) ).
fof(f11,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,[],[f3]) ).
fof(f12,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,[],[f11]) ).
fof(f13,plain,
? [X0] :
( ~ in_environment(X0,critical_point(X0))
& environment(X0)
& stable(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f14,plain,
? [X0] :
( ~ in_environment(X0,critical_point(X0))
& environment(X0)
& stable(X0) ),
inference(flattening,[],[f13]) ).
fof(f15,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,[],[f8]) ).
fof(f16,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,[],[f8]) ).
fof(f17,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,[],[f8]) ).
fof(f18,plain,
! [X0,X1] :
( greater_or_equal(sK1(X0,X1),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| in_environment(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f19,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,[],[f8]) ).
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)))
| in_environment(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f21,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,[],[f8]) ).
fof(f22,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,[],[f8]) ).
fof(f23,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,[],[f8]) ).
fof(f24,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(sK2(X0,X1),X1)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sK2(X0,X1))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f26,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(growth_rate(efficient_producers,sK2(X0,X1)),growth_rate(first_movers,sK2(X0,X1)))
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f27,plain,
! [X2,X0] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X2,sK3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f28,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,sK3(X0)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f29,plain,
stable(sK4),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
environment(sK4),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
~ in_environment(sK4,critical_point(sK4)),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
( ~ environment(sK4)
| in_environment(sK4,sK3(sK4)) ),
inference(resolution,[],[f28,f29]) ).
fof(f33,plain,
in_environment(sK4,sK3(sK4)),
inference(forward_subsumption_resolution,[],[f32,f30]) ).
fof(f34,plain,
! [X0] :
( ~ environment(sK4)
| ~ greater_or_equal(X0,sK3(sK4))
| ~ subpopulations(first_movers,efficient_producers,sK4,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution,[],[f27,f29]) ).
fof(f35,plain,
! [X0] :
( ~ greater_or_equal(X0,sK3(sK4))
| ~ subpopulations(first_movers,efficient_producers,sK4,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(forward_subsumption_resolution,[],[f34,f30]) ).
fof(f38,definition,
( spl5_1
<=> in_environment(sK4,sK0(sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f40,plain,
( in_environment(sK4,sK0(sK4))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f46,plain,
! [X0] :
( ~ in_environment(sK4,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| greater(sK2(sK4,X0),X0)
| critical_point(sK4) = X0 ),
inference(resolution,[],[f24,f30]) ).
fof(f47,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK4,sK1(X0,sK3(sK4)))
| greater(growth_rate(efficient_producers,sK1(X0,sK3(sK4))),growth_rate(first_movers,sK1(X0,sK3(sK4))))
| ~ in_environment(X0,sK3(sK4))
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK0(X0)),growth_rate(first_movers,sK0(X0))) ),
inference(resolution,[],[f35,f21]) ).
fof(f48,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK4,sK1(X0,sK3(sK4)))
| greater(growth_rate(efficient_producers,sK1(X0,sK3(sK4))),growth_rate(first_movers,sK1(X0,sK3(sK4))))
| ~ in_environment(X0,sK3(sK4))
| ~ environment(X0)
| in_environment(X0,sK0(X0)) ),
inference(resolution,[],[f35,f18]) ).
fof(f49,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK4,sK1(X0,sK3(sK4)))
| ~ in_environment(X0,sK3(sK4))
| ~ environment(X0)
| in_environment(X0,sK0(X0)) ),
inference(forward_subsumption_resolution,[],[f48,f20]) ).
fof(f50,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK4,sK1(X0,sK3(sK4)))
| ~ in_environment(X0,sK3(sK4))
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK0(X0)),growth_rate(first_movers,sK0(X0))) ),
inference(forward_subsumption_resolution,[],[f47,f23]) ).
fof(f52,plain,
( ~ in_environment(sK4,sK3(sK4))
| ~ environment(sK4)
| in_environment(sK4,sK0(sK4))
| ~ in_environment(sK4,sK3(sK4))
| ~ environment(sK4)
| in_environment(sK4,sK0(sK4)) ),
inference(resolution,[],[f49,f19]) ).
fof(f53,plain,
( ~ in_environment(sK4,sK3(sK4))
| ~ environment(sK4)
| in_environment(sK4,sK0(sK4)) ),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f55,plain,
( ~ environment(sK4)
| in_environment(sK4,sK0(sK4)) ),
inference(forward_subsumption_resolution,[],[f53,f33]) ).
fof(f57,plain,
in_environment(sK4,sK0(sK4)),
inference(forward_subsumption_resolution,[],[f55,f30]) ).
fof(f59,plain,
spl5_1,
inference(avatar_split_clause,[],[f57,f38]) ).
fof(f61,definition,
( spl5_3
<=> greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4))) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f62,plain,
( greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4)))
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( ~ greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4)))
| spl5_3 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f67,plain,
! [X0,X1] :
( ~ in_environment(X0,sK3(sK4))
| ~ 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,sK4,sK1(X0,sK3(sK4)))
| greater(growth_rate(efficient_producers,sK1(X0,sK3(sK4))),growth_rate(first_movers,sK1(X0,sK3(sK4)))) ),
inference(resolution,[],[f17,f35]) ).
fof(f68,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK4,sK1(X0,sK3(sK4)))
| ~ greater(X1,sK0(X0))
| ~ in_environment(X0,sK3(sK4))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f67,f15]) ).
fof(f71,plain,
( greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4)))
| greater(sK2(sK4,sK0(sK4)),sK0(sK4))
| critical_point(sK4) = sK0(sK4)
| ~ spl5_1 ),
inference(resolution,[],[f46,f40]) ).
fof(f73,definition,
( spl5_4
<=> critical_point(sK4) = sK0(sK4) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f74,plain,
( critical_point(sK4) != sK0(sK4)
| spl5_4 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( critical_point(sK4) = sK0(sK4)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl5_5
<=> greater(sK2(sK4,sK0(sK4)),sK0(sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f79,plain,
( greater(sK2(sK4,sK0(sK4)),sK0(sK4))
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( spl5_4
| spl5_5
| spl5_3
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f71,f38,f61,f77,f73]) ).
fof(f108,plain,
( ~ in_environment(sK4,sK0(sK4))
| ~ spl5_4 ),
inference(superposition,[],[f31,f75]) ).
fof(f109,plain,
( $false
| ~ spl5_1
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f108,f40]) ).
fof(f110,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f109]) ).
fof(f143,plain,
( ~ in_environment(sK4,sK3(sK4))
| ~ environment(sK4)
| ~ greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4)))
| ~ in_environment(sK4,sK3(sK4))
| ~ environment(sK4)
| ~ greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4))) ),
inference(resolution,[],[f50,f22]) ).
fof(f146,plain,
( ~ in_environment(sK4,sK3(sK4))
| ~ environment(sK4)
| ~ greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4))) ),
inference(duplicate_literal_removal,[],[f143]) ).
fof(f149,plain,
( ~ environment(sK4)
| ~ greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4))) ),
inference(forward_subsumption_resolution,[],[f146,f33]) ).
fof(f152,plain,
~ greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4))),
inference(forward_subsumption_resolution,[],[f149,f30]) ).
fof(f155,plain,
( $false
| ~ spl5_3 ),
inference(forward_subsumption_resolution,[],[f152,f62]) ).
fof(f156,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f167,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK4,X0)
| ~ greater(X0,sK0(sK4))
| ~ in_environment(sK4,sK3(sK4))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ environment(sK4)
| ~ subpopulations(first_movers,efficient_producers,sK4,X1)
| ~ environment(sK4)
| ~ greater(X1,sK0(sK4))
| ~ in_environment(sK4,sK3(sK4))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(resolution,[],[f68,f16]) ).
fof(f172,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK4,X0)
| ~ greater(X0,sK0(sK4))
| ~ in_environment(sK4,sK3(sK4))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ environment(sK4)
| ~ subpopulations(first_movers,efficient_producers,sK4,X1)
| ~ greater(X1,sK0(sK4))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(duplicate_literal_removal,[],[f167]) ).
fof(f179,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK4,X0)
| ~ greater(X0,sK0(sK4))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ environment(sK4)
| ~ subpopulations(first_movers,efficient_producers,sK4,X1)
| ~ greater(X1,sK0(sK4))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(forward_subsumption_resolution,[],[f172,f33]) ).
fof(f184,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK4,X0)
| ~ greater(X0,sK0(sK4))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sK4,X1)
| ~ greater(X1,sK0(sK4))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(forward_subsumption_resolution,[],[f179,f30]) ).
fof(f187,definition,
( spl5_10
<=> ! [X1] :
( ~ subpopulations(first_movers,efficient_producers,sK4,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sK0(sK4)) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f188,plain,
( ! [X1] :
( ~ subpopulations(first_movers,efficient_producers,sK4,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sK0(sK4)) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f189,plain,
( spl5_10
| spl5_10 ),
inference(avatar_split_clause,[],[f184,f187,f187]) ).
fof(f191,definition,
( spl5_11
<=> ! [X1] :
( ~ greater(sK2(sK4,X1),sK0(sK4))
| critical_point(sK4) = X1
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(sK4,X1) ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
fof(f192,plain,
( ! [X1] :
( ~ in_environment(sK4,X1)
| critical_point(sK4) = X1
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(sK2(sK4,X1),sK0(sK4)) )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f198,plain,
( ! [X0] :
( greater(growth_rate(efficient_producers,sK2(sK4,X0)),growth_rate(first_movers,sK2(sK4,X0)))
| ~ greater(sK2(sK4,X0),sK0(sK4))
| ~ in_environment(sK4,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ environment(sK4)
| critical_point(sK4) = X0 )
| ~ spl5_10 ),
inference(resolution,[],[f188,f25]) ).
fof(f199,plain,
( ! [X0] :
( ~ greater(sK2(sK4,X0),sK0(sK4))
| ~ in_environment(sK4,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ environment(sK4)
| critical_point(sK4) = X0 )
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f198,f26]) ).
fof(f203,plain,
( ! [X0] :
( ~ greater(sK2(sK4,X0),sK0(sK4))
| ~ in_environment(sK4,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| critical_point(sK4) = X0 )
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f199,f30]) ).
fof(f205,plain,
( spl5_11
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f203,f187,f191]) ).
fof(f211,plain,
( critical_point(sK4) = sK0(sK4)
| greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4)))
| ~ greater(sK2(sK4,sK0(sK4)),sK0(sK4))
| ~ spl5_1
| ~ spl5_11 ),
inference(resolution,[],[f192,f40]) ).
fof(f212,plain,
( greater(growth_rate(efficient_producers,sK0(sK4)),growth_rate(first_movers,sK0(sK4)))
| ~ greater(sK2(sK4,sK0(sK4)),sK0(sK4))
| ~ spl5_1
| spl5_4
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f211,f74]) ).
fof(f214,plain,
( ~ greater(sK2(sK4,sK0(sK4)),sK0(sK4))
| ~ spl5_1
| spl5_3
| spl5_4
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f212,f63]) ).
fof(f220,plain,
( $false
| ~ spl5_1
| spl5_3
| spl5_4
| ~ spl5_5
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f214,f79]) ).
fof(f221,plain,
( ~ spl5_1
| spl5_3
| spl5_4
| ~ spl5_5
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f220]) ).
cnf(s2,plain,
spl5_1,
inference(sat_conversion,[],[f59]) ).
cnf(s4,plain,
( ~ spl5_1
| spl5_3
| spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f80]) ).
cnf(s6,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f110]) ).
cnf(s9,plain,
~ spl5_3,
inference(sat_conversion,[],[f156]) ).
cnf(s10,plain,
( spl5_10
| spl5_10 ),
inference(sat_conversion,[],[f189]) ).
cnf(s11,plain,
spl5_10,
inference(rat,[],[s10]) ).
cnf(s13,plain,
( ~ spl5_10
| spl5_11 ),
inference(sat_conversion,[],[f205]) ).
cnf(s16,plain,
( ~ spl5_1
| spl5_3
| spl5_4
| ~ spl5_5
| ~ spl5_11 ),
inference(sat_conversion,[],[f221]) ).
cnf(s17,plain,
spl5_11,
inference(rat,[],[s13,s11]) ).
cnf(s19,plain,
( ~ spl5_1
| spl5_4
| spl5_5 ),
inference(rat,[],[s4,s9]) ).
cnf(s20,plain,
~ spl5_4,
inference(rat,[],[s6,s2]) ).
cnf(s21,plain,
~ spl5_5,
inference(rat,[],[s16,s17,s2,s9,s20]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s19,s2,s21,s20]) ).
fof(f222,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n014.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 17:16:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.15/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.45 % (1036260)Will run a generic schedule for satisfiability detection.
% 0.15/0.45 % (1036269)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1211457975:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.45 % (1036266)% WARNING: option uhcvi not known.
% 0.15/0.45 % (1036269) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1036260-1036269"...
% 0.15/0.45 % (1036269)...printing done.
% 0.15/0.45 % (1036269)Refutation found. Thanks to Tanya!
% 0.15/0.45 % SZS status Theorem for theBenchmark
% 0.15/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.45 % (1036269)------------------------------
% 0.15/0.45 % (1036269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.45 % (1036269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.45 % (1036269)CaDiCaL version: 2.1.3
% 0.15/0.45 % (1036269)Termination reason: Refutation
% 0.15/0.45 % (1036269)Time elapsed: 0.005 s
% 0.15/0.45 % (1036269)Peak memory usage: 12 MB
% 0.15/0.45 % (1036269)Instructions burned: 10 (million)
% 0.15/0.45 % (1036260)Success in time 0.035 s
% 0.15/0.45 % Vampire exiting
%------------------------------------------------------------------------------