%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT028+1 : 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 : 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 0.10s 0.46s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 100 ( 14 unt; 7 def)
% Number of atoms : 412 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 560 ( 248 ~; 241 |; 52 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 8 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 102 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(zero,growth_rate(first_movers,X2)) ) ) )
=> ? [X3] :
( greater(X3,appear(efficient_producers,X0))
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X3) )
=> greater(zero,growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).
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),zero)
& greater(zero,growth_rate(first_movers,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11) ).
fof(f3,conjecture,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> greater(zero,growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> greater(zero,growth_rate(first_movers,X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0] :
( ( environment(X0)
& stable(X0)
& ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> greater(zero,growth_rate(first_movers,X2)) ) ) )
=> ? [X3] :
( greater(X3,appear(efficient_producers,X0))
& ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X0,X4)
& greater_or_equal(X4,X3) )
=> greater(zero,growth_rate(first_movers,X4)) ) ) ),
inference(rectify,[],[f1]) ).
fof(f6,plain,
! [X0] :
( ? [X3] :
( greater(X3,appear(efficient_producers,X0))
& ! [X4] :
( greater(zero,growth_rate(first_movers,X4))
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| ~ greater_or_equal(X4,X3) ) )
| ~ environment(X0)
| ~ stable(X0)
| ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( ~ greater(zero,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] :
( greater(X3,appear(efficient_producers,X0))
& ! [X4] :
( greater(zero,growth_rate(first_movers,X4))
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| ~ greater_or_equal(X4,X3) ) )
| ~ environment(X0)
| ~ stable(X0)
| ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( ~ greater(zero,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),zero)
& greater(zero,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),zero)
& greater(zero,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] :
( ~ greater(X1,appear(efficient_producers,X0))
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) ) )
& environment(X0)
& stable(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,plain,
? [X0] :
( ! [X1] :
( ~ greater(X1,appear(efficient_producers,X0))
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) ) )
& environment(X0)
& stable(X0) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0] :
( ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0)
| ! [X3] :
( ~ in_environment(X0,X3)
| ? [X4] :
( ~ greater(zero,growth_rate(first_movers,X4))
& subpopulations(first_movers,efficient_producers,X0,X4)
& greater_or_equal(X4,X3) ) ) ),
inference(rectify,[],[f7]) ).
fof(f13,plain,
! [X0] :
( ( greater(sK0(X0),appear(efficient_producers,X0))
& ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK0(X0)) ) )
| ~ environment(X0)
| ~ stable(X0)
| ! [X3] :
( ~ in_environment(X0,X3)
| ( ~ greater(zero,growth_rate(first_movers,sK1(X0,X3)))
& subpopulations(first_movers,efficient_producers,X0,sK1(X0,X3))
& greater_or_equal(sK1(X0,X3),X3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X4,sK1(X0,X3))],[f12]) ).
fof(f14,plain,
! [X0] :
( ( in_environment(X0,sK2(X0))
& ! [X2] :
( ( greater(growth_rate(efficient_producers,X2),zero)
& greater(zero,growth_rate(first_movers,X2)) )
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK2(X0)) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f9]) ).
fof(f15,plain,
( ! [X1] :
( ~ greater(X1,appear(efficient_producers,sK3))
| ( ~ greater(zero,growth_rate(first_movers,sK4(X1)))
& subpopulations(first_movers,efficient_producers,sK3,sK4(X1))
& greater_or_equal(sK4(X1),X1) ) )
& environment(sK3)
& stable(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X2,sK4(X1))],[f11]) ).
fof(f16,plain,
! [X2,X3,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK0(X0))
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X3)
| greater_or_equal(sK1(X0,X3),X3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f17,plain,
! [X2,X3,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK0(X0))
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X3)
| subpopulations(first_movers,efficient_producers,X0,sK1(X0,X3)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f18,plain,
! [X2,X3,X0] :
( ~ greater(zero,growth_rate(first_movers,sK1(X0,X3)))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK0(X0))
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X3)
| greater(zero,growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X3,X0] :
( greater(sK0(X0),appear(efficient_producers,X0))
| greater_or_equal(sK1(X0,X3),X3)
| ~ stable(X0)
| ~ in_environment(X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X3,X0] :
( subpopulations(first_movers,efficient_producers,X0,sK1(X0,X3))
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X3)
| greater(sK0(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X3,X0] :
( ~ greater(zero,growth_rate(first_movers,sK1(X0,X3)))
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X3)
| greater(sK0(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK2(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0] :
( in_environment(X0,sK2(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
stable(sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
environment(sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X1] :
( ~ greater(X1,appear(efficient_producers,sK3))
| greater_or_equal(sK4(X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK3,sK4(X1))
| ~ greater(X1,appear(efficient_producers,sK3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X1] :
( ~ greater(zero,growth_rate(first_movers,sK4(X1)))
| ~ greater(X1,appear(efficient_producers,sK3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f44,definition,
( spl5_1
<=> greater_or_equal(sK4(sK0(sK3)),sK0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f48,definition,
( spl5_2
<=> ! [X0] :
( greater_or_equal(sK1(sK3,X0),X0)
| ~ in_environment(sK3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f49,plain,
( ! [X0] :
( greater_or_equal(sK1(sK3,X0),X0)
| ~ in_environment(sK3,X0) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f57,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| greater(sK0(X0),appear(efficient_producers,X0))
| greater(zero,growth_rate(first_movers,sK1(X0,X1)))
| ~ greater_or_equal(sK1(X0,X1),sK2(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(resolution,[],[f20,f22]) ).
fof(f58,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| greater(sK0(X0),appear(efficient_producers,X0))
| greater(zero,growth_rate(first_movers,sK1(X0,X1)))
| ~ greater_or_equal(sK1(X0,X1),sK2(X0)) ),
inference(duplicate_literal_removal,[],[f57]) ).
fof(f60,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,sK4(X0)))
| ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,X1)
| greater_or_equal(sK1(sK3,X1),X1)
| ~ greater(X0,appear(efficient_producers,sK3)) ),
inference(resolution,[],[f16,f28]) ).
fof(f63,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,sK4(X0)))
| ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,X1)
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ greater(X0,appear(efficient_producers,sK3)) ),
inference(resolution,[],[f17,f28]) ).
fof(f66,plain,
! [X0,X1] :
( ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,X1)
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ greater(X0,appear(efficient_producers,sK3)) ),
inference(forward_subsumption_resolution,[],[f63,f29]) ).
fof(f67,plain,
! [X0,X1] :
( ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ stable(sK3)
| ~ in_environment(sK3,X1)
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ greater(X0,appear(efficient_producers,sK3)) ),
inference(forward_subsumption_resolution,[],[f66,f26]) ).
fof(f68,plain,
! [X0,X1] :
( ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ in_environment(sK3,X1)
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ greater(X0,appear(efficient_producers,sK3)) ),
inference(forward_subsumption_resolution,[],[f67,f25]) ).
fof(f70,definition,
( spl5_4
<=> ! [X1] :
( ~ in_environment(sK3,X1)
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f71,plain,
( ! [X1] :
( subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ in_environment(sK3,X1) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl5_5
<=> ! [X0] :
( ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ greater(X0,appear(efficient_producers,sK3)) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f74,plain,
( ! [X0] :
( ~ greater(X0,appear(efficient_producers,sK3))
| ~ greater_or_equal(sK4(X0),sK0(sK3)) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( spl5_4
| spl5_5 ),
inference(avatar_split_clause,[],[f68,f73,f70]) ).
fof(f97,definition,
( spl5_7
<=> ! [X0] :
( ~ in_environment(sK3,X0)
| ~ greater_or_equal(sK1(sK3,X0),sK2(sK3)) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f98,plain,
( ! [X0] :
( ~ greater_or_equal(sK1(sK3,X0),sK2(sK3))
| ~ in_environment(sK3,X0) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl5_8
<=> ! [X1] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X1)
| greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sK0(sK3)) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f102,plain,
( ! [X1] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X1)
| greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sK0(sK3)) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f105,plain,
! [X0,X1] :
( ~ greater_or_equal(sK1(X0,X1),sK2(X0))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| greater(sK0(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f58,f21]) ).
fof(f106,plain,
! [X0] :
( ~ stable(X0)
| ~ in_environment(X0,sK2(X0))
| greater(sK0(X0),appear(efficient_producers,X0))
| ~ environment(X0)
| greater(sK0(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ in_environment(X0,sK2(X0))
| ~ environment(X0) ),
inference(resolution,[],[f105,f19]) ).
fof(f109,plain,
! [X0] :
( ~ stable(X0)
| ~ in_environment(X0,sK2(X0))
| greater(sK0(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(duplicate_literal_removal,[],[f106]) ).
fof(f111,plain,
! [X0] :
( greater(sK0(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f109,f24]) ).
fof(f114,definition,
( spl5_9
<=> in_environment(sK3,sK2(sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
fof(f115,plain,
( in_environment(sK3,sK2(sK3))
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f116,plain,
( ~ in_environment(sK3,sK2(sK3))
| spl5_9 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f118,plain,
( ~ environment(sK3)
| ~ stable(sK3)
| spl5_9 ),
inference(resolution,[],[f116,f24]) ).
fof(f119,plain,
( ~ stable(sK3)
| spl5_9 ),
inference(forward_subsumption_resolution,[],[f118,f26]) ).
fof(f120,plain,
( $false
| spl5_9 ),
inference(forward_subsumption_resolution,[],[f119,f25]) ).
fof(f121,plain,
spl5_9,
inference(avatar_contradiction_clause,[],[f120]) ).
fof(f122,plain,
( ~ stable(sK3)
| ~ environment(sK3)
| ~ greater_or_equal(sK4(sK0(sK3)),sK0(sK3))
| ~ spl5_5 ),
inference(resolution,[],[f111,f74]) ).
fof(f124,plain,
( ~ stable(sK3)
| ~ environment(sK3)
| greater_or_equal(sK4(sK0(sK3)),sK0(sK3)) ),
inference(resolution,[],[f111,f27]) ).
fof(f125,plain,
( ~ environment(sK3)
| greater_or_equal(sK4(sK0(sK3)),sK0(sK3)) ),
inference(forward_subsumption_resolution,[],[f124,f25]) ).
fof(f127,plain,
( ~ environment(sK3)
| ~ greater_or_equal(sK4(sK0(sK3)),sK0(sK3))
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f122,f25]) ).
fof(f128,plain,
greater_or_equal(sK4(sK0(sK3)),sK0(sK3)),
inference(forward_subsumption_resolution,[],[f125,f26]) ).
fof(f130,plain,
( ~ greater_or_equal(sK4(sK0(sK3)),sK0(sK3))
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f127,f26]) ).
fof(f131,plain,
spl5_1,
inference(avatar_split_clause,[],[f128,f44]) ).
fof(f133,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f130,f73,f44]) ).
fof(f137,plain,
( ! [X0] :
( ~ in_environment(sK3,X0)
| greater(zero,growth_rate(first_movers,sK1(sK3,X0)))
| ~ greater_or_equal(sK1(sK3,X0),sK2(sK3))
| ~ environment(sK3)
| ~ stable(sK3) )
| ~ spl5_4 ),
inference(resolution,[],[f71,f22]) ).
fof(f138,plain,
( ! [X0] :
( ~ in_environment(sK3,X0)
| greater(zero,growth_rate(first_movers,sK1(sK3,X0)))
| ~ greater_or_equal(sK1(sK3,X0),sK2(sK3))
| ~ stable(sK3) )
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f137,f26]) ).
fof(f140,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK1(sK3,X0)))
| ~ in_environment(sK3,X0)
| ~ greater_or_equal(sK1(sK3,X0),sK2(sK3)) )
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f138,f25]) ).
fof(f142,plain,
( ! [X0,X1] :
( ~ in_environment(sK3,X0)
| ~ greater_or_equal(sK1(sK3,X0),sK2(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X1)
| ~ greater_or_equal(X1,sK0(sK3))
| ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,X0)
| greater(zero,growth_rate(first_movers,X1)) )
| ~ spl5_4 ),
inference(resolution,[],[f140,f18]) ).
fof(f145,plain,
( ! [X0,X1] :
( ~ in_environment(sK3,X0)
| ~ greater_or_equal(sK1(sK3,X0),sK2(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X1)
| ~ greater_or_equal(X1,sK0(sK3))
| ~ environment(sK3)
| ~ stable(sK3)
| greater(zero,growth_rate(first_movers,X1)) )
| ~ spl5_4 ),
inference(duplicate_literal_removal,[],[f142]) ).
fof(f146,plain,
( ! [X0,X1] :
( ~ in_environment(sK3,X0)
| ~ greater_or_equal(sK1(sK3,X0),sK2(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X1)
| ~ greater_or_equal(X1,sK0(sK3))
| ~ stable(sK3)
| greater(zero,growth_rate(first_movers,X1)) )
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f145,f26]) ).
fof(f147,plain,
( ! [X0,X1] :
( ~ in_environment(sK3,X0)
| ~ greater_or_equal(sK1(sK3,X0),sK2(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X1)
| ~ greater_or_equal(X1,sK0(sK3))
| greater(zero,growth_rate(first_movers,X1)) )
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f146,f25]) ).
fof(f148,plain,
( spl5_8
| spl5_7
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f147,f70,f97,f101]) ).
fof(f152,plain,
( ~ in_environment(sK3,sK2(sK3))
| ~ in_environment(sK3,sK2(sK3))
| ~ spl5_2
| ~ spl5_7 ),
inference(resolution,[],[f98,f49]) ).
fof(f153,plain,
( ~ in_environment(sK3,sK2(sK3))
| ~ spl5_2
| ~ spl5_7 ),
inference(duplicate_literal_removal,[],[f152]) ).
fof(f155,plain,
( $false
| ~ spl5_2
| ~ spl5_7
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f153,f115]) ).
fof(f156,plain,
( ~ spl5_2
| ~ spl5_7
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f157,plain,
! [X0,X1] :
( ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,X1)
| greater_or_equal(sK1(sK3,X1),X1)
| ~ greater(X0,appear(efficient_producers,sK3)) ),
inference(forward_subsumption_resolution,[],[f60,f29]) ).
fof(f159,plain,
! [X0,X1] :
( ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ stable(sK3)
| ~ in_environment(sK3,X1)
| greater_or_equal(sK1(sK3,X1),X1)
| ~ greater(X0,appear(efficient_producers,sK3)) ),
inference(forward_subsumption_resolution,[],[f157,f26]) ).
fof(f161,plain,
! [X0,X1] :
( ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ in_environment(sK3,X1)
| greater_or_equal(sK1(sK3,X1),X1)
| ~ greater(X0,appear(efficient_producers,sK3)) ),
inference(forward_subsumption_resolution,[],[f159,f25]) ).
fof(f166,plain,
( spl5_2
| spl5_5 ),
inference(avatar_split_clause,[],[f161,f73,f48]) ).
fof(f169,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK4(X0)))
| ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ greater(X0,appear(efficient_producers,sK3)) )
| ~ spl5_8 ),
inference(resolution,[],[f102,f28]) ).
fof(f173,plain,
( ! [X0] :
( ~ greater_or_equal(sK4(X0),sK0(sK3))
| ~ greater(X0,appear(efficient_producers,sK3)) )
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f169,f29]) ).
fof(f174,plain,
( spl5_5
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f173,f101,f73]) ).
cnf(s3,plain,
( spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f75]) ).
cnf(s7,plain,
spl5_9,
inference(sat_conversion,[],[f121]) ).
cnf(s8,plain,
spl5_1,
inference(sat_conversion,[],[f131]) ).
cnf(s10,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f133]) ).
cnf(s11,plain,
( ~ spl5_4
| spl5_7
| spl5_8 ),
inference(sat_conversion,[],[f148]) ).
cnf(s12,plain,
( ~ spl5_2
| ~ spl5_7
| ~ spl5_9 ),
inference(sat_conversion,[],[f156]) ).
cnf(s14,plain,
( spl5_2
| spl5_5 ),
inference(sat_conversion,[],[f166]) ).
cnf(s16,plain,
( spl5_5
| ~ spl5_8 ),
inference(sat_conversion,[],[f174]) ).
cnf(s17,plain,
~ spl5_5,
inference(rat,[],[s10,s8]) ).
cnf(s18,plain,
~ spl5_8,
inference(rat,[],[s16,s17]) ).
cnf(s19,plain,
spl5_2,
inference(rat,[],[s14,s17]) ).
cnf(s20,plain,
~ spl5_7,
inference(rat,[],[s12,s19,s7]) ).
cnf(s21,plain,
~ spl5_4,
inference(rat,[],[s11,s18,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s3,s17,s21]) ).
fof(f175,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT028+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n020.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 17:22:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.10/0.46 % (3629289)Will run a generic schedule for satisfiability detection.
% 0.10/0.46 % (3629306)dis+10_1_sil=32000:sp=arity:random_seed=2797803834:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.46 % (3629306) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3629289-3629306"...
% 0.10/0.46 % (3629304)% WARNING: option uhcvi not known.
% 0.10/0.46 % (3629306)...printing done.
% 0.10/0.46 % (3629306)Refutation found. Thanks to Tanya!
% 0.10/0.46 % SZS status Theorem for theBenchmark
% 0.10/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.46 % (3629306)------------------------------
% 0.10/0.46 % (3629306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.46 % (3629306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.46 % (3629306)CaDiCaL version: 2.1.3
% 0.10/0.46 % (3629306)Termination reason: Refutation
% 0.10/0.46 % (3629306)Time elapsed: 0.003 s
% 0.10/0.46 % (3629306)Peak memory usage: 12 MB
% 0.10/0.46 % (3629306)Instructions burned: 6 (million)
% 0.10/0.46 % (3629289)Success in time 0.037 s
% 0.10/0.46 % Vampire exiting
%------------------------------------------------------------------------------