%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n001.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 : Theorem 1.78s 1.15s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 112 ( 11 unt; 8 def)
% Number of atoms : 457 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 611 ( 266 ~; 273 |; 52 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 9 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 86 !; 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] :
( ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK0(X0))
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,X2))
| ~ 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,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(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))
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X3)
| greater_or_equal(sK1(X0,X3),X3) ),
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] :
( ~ greater_or_equal(X2,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2))
| ~ 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(f30,plain,
! [X0] :
( ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,X0)
| greater_or_equal(sK1(sK3,X0),X0)
| greater_or_equal(sK4(sK0(sK3)),sK0(sK3)) ),
inference(resolution,[],[f19,f27]) ).
fof(f31,plain,
! [X0] :
( ~ stable(sK3)
| ~ in_environment(sK3,X0)
| greater_or_equal(sK1(sK3,X0),X0)
| greater_or_equal(sK4(sK0(sK3)),sK0(sK3)) ),
inference(forward_subsumption_resolution,[],[f30,f26]) ).
fof(f32,plain,
! [X0] :
( ~ in_environment(sK3,X0)
| greater_or_equal(sK1(sK3,X0),X0)
| greater_or_equal(sK4(sK0(sK3)),sK0(sK3)) ),
inference(forward_subsumption_resolution,[],[f31,f25]) ).
fof(f34,definition,
( spl5_1
<=> greater_or_equal(sK4(sK0(sK3)),sK0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f36,plain,
( greater_or_equal(sK4(sK0(sK3)),sK0(sK3))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f38,definition,
( spl5_2
<=> ! [X0] :
( ~ in_environment(sK3,X0)
| greater_or_equal(sK1(sK3,X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f39,plain,
( ! [X0] :
( greater_or_equal(sK1(sK3,X0),X0)
| ~ in_environment(sK3,X0) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f32,f38,f34]) ).
fof(f41,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK1(sK3,sK2(X0))))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1(sK3,sK2(X0)))
| ~ in_environment(sK3,sK2(X0))
| ~ environment(X0)
| ~ stable(X0) )
| ~ spl5_2 ),
inference(resolution,[],[f39,f22]) ).
fof(f42,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1(sK3,sK2(X0)))
| ~ in_environment(sK3,sK2(X0))
| ~ environment(X0)
| ~ stable(X0)
| ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,sK2(X0))
| greater(sK0(sK3),appear(efficient_producers,sK3)) )
| ~ spl5_2 ),
inference(resolution,[],[f41,f21]) ).
fof(f43,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1(sK3,sK2(X0)))
| ~ in_environment(sK3,sK2(X0))
| ~ environment(X0)
| ~ stable(X0)
| ~ environment(sK3)
| ~ stable(sK3)
| greater(sK0(sK3),appear(efficient_producers,sK3)) )
| ~ spl5_2 ),
inference(duplicate_literal_removal,[],[f42]) ).
fof(f44,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1(sK3,sK2(X0)))
| ~ in_environment(sK3,sK2(X0))
| ~ environment(X0)
| ~ stable(X0)
| ~ stable(sK3)
| greater(sK0(sK3),appear(efficient_producers,sK3)) )
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f43,f26]) ).
fof(f45,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1(sK3,sK2(X0)))
| ~ in_environment(sK3,sK2(X0))
| ~ environment(X0)
| ~ stable(X0)
| greater(sK0(sK3),appear(efficient_producers,sK3)) )
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f44,f25]) ).
fof(f47,definition,
( spl5_3
<=> greater(sK0(sK3),appear(efficient_producers,sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f48,plain,
( ~ greater(sK0(sK3),appear(efficient_producers,sK3))
| spl5_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,definition,
( spl5_4
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1(sK3,sK2(X0)))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(sK3,sK2(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f52,plain,
( ! [X0] :
( ~ in_environment(sK3,sK2(X0))
| ~ stable(X0)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1(sK3,sK2(X0))) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f53,plain,
( spl5_3
| spl5_4
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f45,f38,f51,f47]) ).
fof(f54,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ environment(sK3)
| greater(zero,growth_rate(first_movers,X0))
| ~ in_environment(sK3,X1)
| greater_or_equal(sK1(sK3,X1),X1) ),
inference(resolution,[],[f16,f25]) ).
fof(f55,plain,
( greater_or_equal(sK4(sK0(sK3)),sK0(sK3))
| ~ spl5_3 ),
inference(resolution,[],[f49,f27]) ).
fof(f56,plain,
( spl5_1
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f55,f47,f34]) ).
fof(f58,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,sK2(X1))
| greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,X1,sK1(sK3,sK2(X1)))
| ~ in_environment(sK3,sK2(X1))
| ~ environment(X1)
| ~ stable(X1) )
| ~ spl5_2 ),
inference(resolution,[],[f18,f41]) ).
fof(f59,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,sK2(X1))
| greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,X1,sK1(sK3,sK2(X1)))
| ~ environment(X1)
| ~ stable(X1) )
| ~ spl5_2 ),
inference(duplicate_literal_removal,[],[f58]) ).
fof(f60,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ stable(sK3)
| ~ in_environment(sK3,sK2(X1))
| greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,X1,sK1(sK3,sK2(X1)))
| ~ environment(X1)
| ~ stable(X1) )
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f59,f26]) ).
fof(f61,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ in_environment(sK3,sK2(X1))
| greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,X1,sK1(sK3,sK2(X1)))
| ~ environment(X1)
| ~ stable(X1) )
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f60,f25]) ).
fof(f63,definition,
( spl5_5
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK0(sK3)) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f64,plain,
( ! [X0] :
( ~ greater_or_equal(X0,sK0(sK3))
| greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( spl5_4
| spl5_5
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f61,f38,f63,f51]) ).
fof(f66,plain,
( ~ stable(sK3)
| ~ environment(sK3)
| ~ subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,sK2(sK3)))
| ~ environment(sK3)
| ~ stable(sK3)
| ~ spl5_4 ),
inference(resolution,[],[f52,f24]) ).
fof(f67,plain,
( ~ stable(sK3)
| ~ environment(sK3)
| ~ subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,sK2(sK3)))
| ~ spl5_4 ),
inference(duplicate_literal_removal,[],[f66]) ).
fof(f68,plain,
( ~ environment(sK3)
| ~ subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,sK2(sK3)))
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f67,f25]) ).
fof(f69,plain,
( ~ subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,sK2(sK3)))
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f68,f26]) ).
fof(f70,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,sK2(sK3))
| greater(zero,growth_rate(first_movers,X0)) )
| ~ spl5_4 ),
inference(resolution,[],[f69,f17]) ).
fof(f71,plain,
( ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,sK2(sK3))
| greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ spl5_4 ),
inference(resolution,[],[f69,f20]) ).
fof(f72,plain,
( ~ stable(sK3)
| ~ in_environment(sK3,sK2(sK3))
| greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f71,f26]) ).
fof(f73,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ stable(sK3)
| ~ in_environment(sK3,sK2(sK3))
| greater(zero,growth_rate(first_movers,X0)) )
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f70,f26]) ).
fof(f74,plain,
( ~ in_environment(sK3,sK2(sK3))
| greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f72,f25]) ).
fof(f75,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ in_environment(sK3,sK2(sK3))
| greater(zero,growth_rate(first_movers,X0)) )
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f73,f25]) ).
fof(f78,definition,
( spl5_6
<=> in_environment(sK3,sK2(sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f80,plain,
( ~ in_environment(sK3,sK2(sK3))
| spl5_6 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( ~ spl5_6
| spl5_5
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f75,f51,f63,f78]) ).
fof(f83,plain,
( ~ environment(sK3)
| ~ stable(sK3)
| spl5_6 ),
inference(resolution,[],[f80,f24]) ).
fof(f84,plain,
( ~ stable(sK3)
| spl5_6 ),
inference(forward_subsumption_resolution,[],[f83,f26]) ).
fof(f85,plain,
( $false
| spl5_6 ),
inference(forward_subsumption_resolution,[],[f84,f25]) ).
fof(f86,plain,
spl5_6,
inference(avatar_contradiction_clause,[],[f85]) ).
fof(f87,plain,
( spl5_3
| ~ spl5_6
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f74,f51,f78,f47]) ).
fof(f91,plain,
( greater(zero,growth_rate(first_movers,sK4(sK0(sK3))))
| ~ subpopulations(first_movers,efficient_producers,sK3,sK4(sK0(sK3)))
| ~ spl5_1
| ~ spl5_5 ),
inference(resolution,[],[f64,f36]) ).
fof(f93,definition,
( spl5_7
<=> subpopulations(first_movers,efficient_producers,sK3,sK4(sK0(sK3))) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f95,plain,
( ~ subpopulations(first_movers,efficient_producers,sK3,sK4(sK0(sK3)))
| spl5_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl5_8
<=> greater(zero,growth_rate(first_movers,sK4(sK0(sK3)))) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f99,plain,
( greater(zero,growth_rate(first_movers,sK4(sK0(sK3))))
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f114,plain,
( ~ greater(sK0(sK3),appear(efficient_producers,sK3))
| spl5_7 ),
inference(resolution,[],[f95,f28]) ).
fof(f117,plain,
( ~ greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ spl5_8 ),
inference(resolution,[],[f99,f29]) ).
fof(f118,plain,
( $false
| ~ spl5_3
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f117,f49]) ).
fof(f119,plain,
( ~ spl5_3
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| greater(zero,growth_rate(first_movers,X0))
| ~ in_environment(sK3,X1)
| greater_or_equal(sK1(sK3,X1),X1) ),
inference(forward_subsumption_resolution,[],[f54,f26]) ).
fof(f121,plain,
( spl5_2
| spl5_5 ),
inference(avatar_split_clause,[],[f120,f63,f38]) ).
fof(f122,plain,
( ~ spl5_7
| spl5_8
| ~ spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f91,f63,f34,f97,f93]) ).
fof(f123,plain,
( ~ spl5_3
| spl5_7 ),
inference(avatar_split_clause,[],[f114,f93,f47]) ).
fof(f124,plain,
( ! [X0] :
( ~ environment(sK3)
| ~ stable(sK3)
| ~ in_environment(sK3,X0)
| greater_or_equal(sK1(sK3,X0),X0) )
| spl5_3 ),
inference(resolution,[],[f48,f19]) ).
fof(f125,plain,
( ! [X0] :
( ~ stable(sK3)
| ~ in_environment(sK3,X0)
| greater_or_equal(sK1(sK3,X0),X0) )
| spl5_3 ),
inference(forward_subsumption_resolution,[],[f124,f26]) ).
fof(f126,plain,
( ! [X0] :
( ~ in_environment(sK3,X0)
| greater_or_equal(sK1(sK3,X0),X0) )
| spl5_3 ),
inference(forward_subsumption_resolution,[],[f125,f25]) ).
fof(f127,plain,
( spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f126,f47,f38]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s2,plain,
( ~ spl5_2
| spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f53]) ).
cnf(s3,plain,
( spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( ~ spl5_2
| spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f65]) ).
cnf(s5,plain,
( ~ spl5_4
| spl5_5
| ~ spl5_6 ),
inference(sat_conversion,[],[f81]) ).
cnf(s7,plain,
spl5_6,
inference(sat_conversion,[],[f86]) ).
cnf(s9,plain,
( spl5_3
| ~ spl5_4
| ~ spl5_6 ),
inference(sat_conversion,[],[f87]) ).
cnf(s13,plain,
( ~ spl5_3
| ~ spl5_8 ),
inference(sat_conversion,[],[f119]) ).
cnf(s14,plain,
( spl5_2
| spl5_5 ),
inference(sat_conversion,[],[f121]) ).
cnf(s15,plain,
( ~ spl5_1
| ~ spl5_5
| ~ spl5_7
| spl5_8 ),
inference(sat_conversion,[],[f122]) ).
cnf(s16,plain,
( ~ spl5_3
| spl5_7 ),
inference(sat_conversion,[],[f123]) ).
cnf(s17,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f127]) ).
cnf(s19,plain,
( ~ spl5_4
| spl5_5 ),
inference(rat,[],[s5,s7]) ).
cnf(s20,plain,
spl5_1,
inference(rat,[],[s2,s9,s1,s3,s7]) ).
cnf(s21,plain,
spl5_2,
inference(rat,[],[s15,s13,s16,s14,s17,s20]) ).
cnf(s22,plain,
spl5_5,
inference(rat,[],[s4,s19,s21]) ).
cnf(s23,plain,
~ spl5_3,
inference(rat,[],[s15,s13,s16,s20,s22]) ).
cnf(s24,plain,
~ spl5_4,
inference(rat,[],[s9,s7,s23]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s2,s21,s24,s23]) ).
fof(f128,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT028+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 17:27:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 1.78/1.15 % (3824188)Detected formulas, will run a generic FOF schedule.
% 1.78/1.15 % (3824198)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=864093328:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.78/1.15 % (3824198)First to succeed.
% 1.78/1.15 % (3824198)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3824188"
% 1.78/1.15 % (3824199)dis-21_1_sil=8000:lcm=predicate:random_seed=4083266913:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.78/1.15 % (3824196)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3759243854:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.78/1.15 % (3824194)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=763109974:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.78/1.15 % (3824195)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2911684228:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.78/1.15 % (3824193)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=217979757:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.78/1.15 % (3824196)Also succeeded, but the first one will report.
% 1.78/1.15 % (3824199)Also succeeded, but the first one will report.
% 1.78/1.15 % (3824197)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2515872955:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.78/1.15 % (3824197)Also succeeded, but the first one will report.
% 1.78/1.15 % (3824198)Refutation found. Thanks to Tanya!
% 1.78/1.15 % SZS status Theorem for theBenchmark
% 1.78/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.34 % (3824198)------------------------------
% 2.62/1.34 % (3824198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.34 % (3824198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.34 % (3824198)CaDiCaL version: 2.1.3
% 2.62/1.34 % (3824198)Termination reason: Refutation
% 2.62/1.34 % (3824198)Time elapsed: 0.003 s
% 2.62/1.34 % (3824198)Peak memory usage: 89 MB
% 2.62/1.34 % (3824198)Instructions burned: 6 (million)
% 2.62/1.34 % (3824198)------------------------------
% 2.62/1.34 % (3824198)------------------------------
% 2.62/1.34 % (3824188)Success in time 0.287 s
% 2.62/1.34 % Vampire exiting
%------------------------------------------------------------------------------