%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT027+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 : 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 12:02:33 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 142 ( 19 unt; 8 def)
% Number of atoms : 423 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 487 ( 206 ~; 221 |; 40 &)
% ( 9 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 9 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 104 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( environment(X0)
& stable(X0)
& in_environment(X0,X1)
& ! [X2] :
( ( greater(cardinality_at_time(first_movers,X2),zero)
& greater_or_equal(X2,X1) )
=> greater(zero,growth_rate(first_movers,X2)) ) )
=> contracts_from(X1,first_movers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from) ).
fof(f2,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1)
& greater(cardinality_at_time(first_movers,X1),zero)
& greater(cardinality_at_time(efficient_producers,X1),zero) )
=> subpopulations(first_movers,efficient_producers,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( environment(X0)
& stable(X0)
& in_environment(X0,X1)
& greater(X2,X1) )
=> in_environment(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_long_stable_environments) ).
fof(f4,axiom,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> in_environment(X0,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( greater(X0,X1)
& greater(X1,X2) )
=> greater(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f6,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( greater(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f7,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1)
& greater_or_equal(X1,appear(efficient_producers,X0)) )
=> greater(cardinality_at_time(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6) ).
fof(f8,axiom,
! [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',l10) ).
fof(f9,conjecture,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& contracts_from(X1,first_movers) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9) ).
fof(f10,negated_conjecture,
~ ! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& contracts_from(X1,first_movers) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater(cardinality_at_time(first_movers,X2),zero)
& greater_or_equal(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater(cardinality_at_time(first_movers,X2),zero)
& greater_or_equal(X2,X1) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(ennf_transformation,[],[f2]) ).
fof(f14,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( in_environment(X0,X2)
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ greater(X2,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] :
( in_environment(X0,X2)
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ greater(X2,X1) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f18,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f20,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(flattening,[],[f21]) ).
fof(f23,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,[],[f8]) ).
fof(f24,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,[],[f23]) ).
fof(f25,plain,
? [X0] :
( ! [X1] :
( ~ greater(X1,appear(efficient_producers,X0))
| ~ contracts_from(X1,first_movers) )
& environment(X0)
& stable(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f26,plain,
? [X0] :
( ! [X1] :
( ~ greater(X1,appear(efficient_producers,X0))
| ~ contracts_from(X1,first_movers) )
& environment(X0)
& stable(X0) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ( ~ greater(zero,growth_rate(first_movers,sK0(X1)))
& greater(cardinality_at_time(first_movers,sK0(X1)),zero)
& greater_or_equal(sK0(X1),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X1))],[f12]) ).
fof(f28,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) )
& ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) )
& ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0] :
( ( greater(sK1(X0),appear(efficient_producers,X0))
& ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK1(X0)) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f24]) ).
fof(f31,plain,
( ! [X1] :
( ~ greater(X1,appear(efficient_producers,sK2))
| ~ contracts_from(X1,first_movers) )
& environment(sK2)
& stable(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f26]) ).
fof(f32,plain,
! [X0,X1] :
( ~ stable(X0)
| ~ environment(X0)
| contracts_from(X1,first_movers)
| ~ in_environment(X0,X1)
| greater_or_equal(sK0(X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f33,plain,
! [X0,X1] :
( ~ stable(X0)
| ~ environment(X0)
| contracts_from(X1,first_movers)
| ~ in_environment(X0,X1)
| greater(cardinality_at_time(first_movers,sK0(X1)),zero) ),
inference(cnf_transformation,[],[f27]) ).
fof(f34,plain,
! [X0,X1] :
( ~ stable(X0)
| ~ environment(X0)
| contracts_from(X1,first_movers)
| ~ in_environment(X0,X1)
| ~ greater(zero,growth_rate(first_movers,sK0(X1))) ),
inference(cnf_transformation,[],[f27]) ).
fof(f35,plain,
! [X0,X1] :
( ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(cnf_transformation,[],[f14]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,X2)
| ~ in_environment(X0,X1)
| ~ greater(X2,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ greater(X0,X1)
| greater(X0,X2)
| ~ greater(X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f40,plain,
! [X0,X1] :
( X0 != X1
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
! [X0,X1] :
( ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X2,X0] :
( ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK1(X0))
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f44,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| greater(sK1(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f45,plain,
stable(sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f46,plain,
environment(sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f47,plain,
! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK2)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
! [X0] : greater_or_equal(X0,X0),
inference(equality_resolution,[],[f40]) ).
fof(f49,plain,
( ~ environment(sK2)
| in_environment(sK2,appear(efficient_producers,sK2)) ),
inference(resolution,[],[f37,f45]) ).
fof(f50,plain,
in_environment(sK2,appear(efficient_producers,sK2)),
inference(forward_subsumption_resolution,[],[f49,f46]) ).
fof(f52,plain,
( ~ environment(sK2)
| greater(sK1(sK2),appear(efficient_producers,sK2)) ),
inference(resolution,[],[f44,f45]) ).
fof(f53,plain,
greater(sK1(sK2),appear(efficient_producers,sK2)),
inference(forward_subsumption_resolution,[],[f52,f46]) ).
fof(f54,plain,
! [X0,X1] :
( ~ environment(sK2)
| in_environment(sK2,X0)
| ~ in_environment(sK2,X1)
| ~ greater(X0,X1) ),
inference(resolution,[],[f36,f45]) ).
fof(f55,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ in_environment(sK2,X1)
| in_environment(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f54,f46]) ).
fof(f57,plain,
greater_or_equal(sK1(sK2),appear(efficient_producers,sK2)),
inference(resolution,[],[f53,f41]) ).
fof(f58,plain,
! [X0] :
( ~ environment(sK2)
| contracts_from(X0,first_movers)
| ~ in_environment(sK2,X0)
| greater_or_equal(sK0(X0),X0) ),
inference(resolution,[],[f32,f45]) ).
fof(f59,plain,
! [X0] :
( ~ in_environment(sK2,X0)
| contracts_from(X0,first_movers)
| greater_or_equal(sK0(X0),X0) ),
inference(forward_subsumption_resolution,[],[f58,f46]) ).
fof(f61,plain,
! [X0] :
( ~ greater_or_equal(X0,appear(efficient_producers,sK2))
| ~ in_environment(sK2,X0)
| greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(resolution,[],[f42,f46]) ).
fof(f62,plain,
( ~ in_environment(sK2,appear(efficient_producers,sK2))
| in_environment(sK2,sK1(sK2)) ),
inference(resolution,[],[f55,f53]) ).
fof(f63,plain,
in_environment(sK2,sK1(sK2)),
inference(forward_subsumption_resolution,[],[f62,f50]) ).
fof(f64,plain,
! [X0] :
( ~ environment(sK2)
| contracts_from(X0,first_movers)
| ~ in_environment(sK2,X0)
| greater(cardinality_at_time(first_movers,sK0(X0)),zero) ),
inference(resolution,[],[f33,f45]) ).
fof(f65,plain,
! [X0] :
( ~ in_environment(sK2,X0)
| contracts_from(X0,first_movers)
| greater(cardinality_at_time(first_movers,sK0(X0)),zero) ),
inference(forward_subsumption_resolution,[],[f64,f46]) ).
fof(f66,plain,
! [X0] :
( ~ environment(sK2)
| contracts_from(X0,first_movers)
| ~ in_environment(sK2,X0)
| ~ greater(zero,growth_rate(first_movers,sK0(X0))) ),
inference(resolution,[],[f34,f45]) ).
fof(f67,plain,
! [X0] :
( ~ greater(zero,growth_rate(first_movers,sK0(X0)))
| ~ in_environment(sK2,X0)
| contracts_from(X0,first_movers) ),
inference(forward_subsumption_resolution,[],[f66,f46]) ).
fof(f68,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK2,X0)
| ~ greater_or_equal(X0,sK1(sK2))
| ~ environment(sK2)
| greater(zero,growth_rate(first_movers,X0)) ),
inference(resolution,[],[f43,f45]) ).
fof(f69,plain,
! [X0] :
( ~ greater_or_equal(X0,sK1(sK2))
| ~ subpopulations(first_movers,efficient_producers,sK2,X0)
| greater(zero,growth_rate(first_movers,X0)) ),
inference(forward_subsumption_resolution,[],[f68,f46]) ).
fof(f71,plain,
( contracts_from(sK1(sK2),first_movers)
| greater_or_equal(sK0(sK1(sK2)),sK1(sK2)) ),
inference(resolution,[],[f59,f63]) ).
fof(f73,definition,
( spl3_1
<=> greater_or_equal(sK0(sK1(sK2)),sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f75,plain,
( greater_or_equal(sK0(sK1(sK2)),sK1(sK2))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl3_2
<=> contracts_from(sK1(sK2),first_movers) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f78,plain,
( ~ contracts_from(sK1(sK2),first_movers)
| spl3_2 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( contracts_from(sK1(sK2),first_movers)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f71,f77,f73]) ).
fof(f90,plain,
! [X0] :
( ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sK2,X0)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| subpopulations(first_movers,efficient_producers,sK2,X0) ),
inference(resolution,[],[f35,f46]) ).
fof(f91,plain,
( ~ greater(sK1(sK2),appear(efficient_producers,sK2))
| ~ spl3_2 ),
inference(resolution,[],[f79,f47]) ).
fof(f92,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f91,f53]) ).
fof(f93,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f92]) ).
fof(f95,plain,
( contracts_from(sK1(sK2),first_movers)
| greater(cardinality_at_time(first_movers,sK0(sK1(sK2))),zero) ),
inference(resolution,[],[f65,f63]) ).
fof(f96,plain,
( greater(cardinality_at_time(first_movers,sK0(sK1(sK2))),zero)
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f95,f78]) ).
fof(f102,plain,
( sK1(sK2) = sK0(sK1(sK2))
| greater(sK0(sK1(sK2)),sK1(sK2))
| ~ spl3_1 ),
inference(resolution,[],[f75,f39]) ).
fof(f104,definition,
( spl3_6
<=> greater(sK0(sK1(sK2)),sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f106,plain,
( greater(sK0(sK1(sK2)),sK1(sK2))
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f108,definition,
( spl3_7
<=> sK1(sK2) = sK0(sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f110,plain,
( sK1(sK2) = sK0(sK1(sK2))
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl3_6
| spl3_7
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f102,f73,f108,f104]) ).
fof(f113,plain,
( ~ in_environment(sK2,sK1(sK2))
| greater(cardinality_at_time(efficient_producers,sK1(sK2)),zero) ),
inference(resolution,[],[f61,f57]) ).
fof(f114,plain,
greater(cardinality_at_time(efficient_producers,sK1(sK2)),zero),
inference(forward_subsumption_resolution,[],[f113,f63]) ).
fof(f128,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK1(sK2))
| greater(zero,growth_rate(first_movers,sK1(sK2))) ),
inference(resolution,[],[f69,f48]) ).
fof(f129,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK0(sK1(sK2)))
| greater(zero,growth_rate(first_movers,sK0(sK1(sK2))))
| ~ spl3_1 ),
inference(resolution,[],[f69,f75]) ).
fof(f131,definition,
( spl3_10
<=> greater(zero,growth_rate(first_movers,sK0(sK1(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f133,plain,
( greater(zero,growth_rate(first_movers,sK0(sK1(sK2))))
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f135,definition,
( spl3_11
<=> subpopulations(first_movers,efficient_producers,sK2,sK0(sK1(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f137,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK0(sK1(sK2)))
| spl3_11 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl3_10
| ~ spl3_11
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f129,f73,f135,f131]) ).
fof(f140,definition,
( spl3_12
<=> greater(zero,growth_rate(first_movers,sK1(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f144,definition,
( spl3_13
<=> subpopulations(first_movers,efficient_producers,sK2,sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f146,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK1(sK2))
| spl3_13 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( spl3_12
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f128,f144,f140]) ).
fof(f148,plain,
( ~ in_environment(sK2,sK1(sK2))
| ~ greater(cardinality_at_time(first_movers,sK1(sK2)),zero)
| subpopulations(first_movers,efficient_producers,sK2,sK1(sK2)) ),
inference(resolution,[],[f90,f114]) ).
fof(f149,plain,
( ~ greater(cardinality_at_time(first_movers,sK1(sK2)),zero)
| subpopulations(first_movers,efficient_producers,sK2,sK1(sK2)) ),
inference(forward_subsumption_resolution,[],[f148,f63]) ).
fof(f150,plain,
( ~ greater(cardinality_at_time(first_movers,sK1(sK2)),zero)
| spl3_13 ),
inference(forward_subsumption_resolution,[],[f149,f146]) ).
fof(f165,plain,
( ~ in_environment(sK2,sK1(sK2))
| in_environment(sK2,sK0(sK1(sK2)))
| ~ spl3_6 ),
inference(resolution,[],[f106,f55]) ).
fof(f168,plain,
( in_environment(sK2,sK0(sK1(sK2)))
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f165,f63]) ).
fof(f214,plain,
( greater(cardinality_at_time(first_movers,sK1(sK2)),zero)
| spl3_2
| ~ spl3_7 ),
inference(superposition,[],[f96,f110]) ).
fof(f217,plain,
( ~ greater(zero,growth_rate(first_movers,sK1(sK2)))
| ~ in_environment(sK2,sK1(sK2))
| contracts_from(sK1(sK2),first_movers)
| ~ spl3_7 ),
inference(superposition,[],[f67,f110]) ).
fof(f218,plain,
( ~ greater(zero,growth_rate(first_movers,sK1(sK2)))
| contracts_from(sK1(sK2),first_movers)
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f217,f63]) ).
fof(f219,plain,
( $false
| spl3_2
| ~ spl3_7
| spl3_13 ),
inference(forward_subsumption_resolution,[],[f214,f150]) ).
fof(f220,plain,
( spl3_2
| ~ spl3_7
| spl3_13 ),
inference(avatar_contradiction_clause,[],[f219]) ).
fof(f221,plain,
( ~ greater(zero,growth_rate(first_movers,sK1(sK2)))
| spl3_2
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f218,f78]) ).
fof(f222,plain,
( ~ spl3_12
| spl3_2
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f221,f108,f77,f140]) ).
fof(f227,plain,
( ! [X0] :
( ~ greater(sK1(sK2),X0)
| greater(sK0(sK1(sK2)),X0) )
| ~ spl3_6 ),
inference(resolution,[],[f106,f38]) ).
fof(f252,plain,
( greater(sK0(sK1(sK2)),appear(efficient_producers,sK2))
| ~ spl3_6 ),
inference(resolution,[],[f227,f53]) ).
fof(f255,plain,
( greater_or_equal(sK0(sK1(sK2)),appear(efficient_producers,sK2))
| ~ spl3_6 ),
inference(resolution,[],[f252,f41]) ).
fof(f256,plain,
( ~ in_environment(sK2,sK0(sK1(sK2)))
| greater(cardinality_at_time(efficient_producers,sK0(sK1(sK2))),zero)
| ~ spl3_6 ),
inference(resolution,[],[f255,f61]) ).
fof(f258,plain,
( greater(cardinality_at_time(efficient_producers,sK0(sK1(sK2))),zero)
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f256,f168]) ).
fof(f259,plain,
( ~ in_environment(sK2,sK0(sK1(sK2)))
| ~ greater(cardinality_at_time(first_movers,sK0(sK1(sK2))),zero)
| subpopulations(first_movers,efficient_producers,sK2,sK0(sK1(sK2)))
| ~ spl3_6 ),
inference(resolution,[],[f258,f90]) ).
fof(f263,plain,
( ~ greater(cardinality_at_time(first_movers,sK0(sK1(sK2))),zero)
| subpopulations(first_movers,efficient_producers,sK2,sK0(sK1(sK2)))
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f259,f168]) ).
fof(f264,plain,
( subpopulations(first_movers,efficient_producers,sK2,sK0(sK1(sK2)))
| spl3_2
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f263,f96]) ).
fof(f265,plain,
( $false
| spl3_2
| ~ spl3_6
| spl3_11 ),
inference(forward_subsumption_resolution,[],[f264,f137]) ).
fof(f266,plain,
( spl3_2
| ~ spl3_6
| spl3_11 ),
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f267,plain,
( ~ in_environment(sK2,sK1(sK2))
| contracts_from(sK1(sK2),first_movers)
| ~ spl3_10 ),
inference(resolution,[],[f133,f67]) ).
fof(f276,plain,
( contracts_from(sK1(sK2),first_movers)
| ~ spl3_10 ),
inference(forward_subsumption_resolution,[],[f267,f63]) ).
fof(f277,plain,
( $false
| spl3_2
| ~ spl3_10 ),
inference(forward_subsumption_resolution,[],[f276,f78]) ).
fof(f278,plain,
( spl3_2
| ~ spl3_10 ),
inference(avatar_contradiction_clause,[],[f277]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f80]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f93]) ).
cnf(s5,plain,
( ~ spl3_1
| spl3_6
| spl3_7 ),
inference(sat_conversion,[],[f111]) ).
cnf(s7,plain,
( ~ spl3_1
| spl3_10
| ~ spl3_11 ),
inference(sat_conversion,[],[f138]) ).
cnf(s8,plain,
( spl3_12
| ~ spl3_13 ),
inference(sat_conversion,[],[f147]) ).
cnf(s14,plain,
( spl3_2
| ~ spl3_7
| spl3_13 ),
inference(sat_conversion,[],[f220]) ).
cnf(s15,plain,
( spl3_2
| ~ spl3_7
| ~ spl3_12 ),
inference(sat_conversion,[],[f222]) ).
cnf(s18,plain,
( spl3_2
| ~ spl3_6
| spl3_11 ),
inference(sat_conversion,[],[f266]) ).
cnf(s19,plain,
( spl3_2
| ~ spl3_10 ),
inference(sat_conversion,[],[f278]) ).
cnf(s20,plain,
~ spl3_10,
inference(rat,[],[s19,s3]) ).
cnf(s21,plain,
spl3_1,
inference(rat,[],[s1,s3]) ).
cnf(s22,plain,
~ spl3_11,
inference(rat,[],[s7,s20,s21]) ).
cnf(s23,plain,
~ spl3_6,
inference(rat,[],[s18,s3,s22]) ).
cnf(s24,plain,
spl3_7,
inference(rat,[],[s5,s21,s23]) ).
cnf(s25,plain,
~ spl3_12,
inference(rat,[],[s15,s3,s24]) ).
cnf(s26,plain,
spl3_13,
inference(rat,[],[s14,s3,s24]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s8,s26,s25]) ).
fof(f279,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT027+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 17:18:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.44 % (1037848)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (1037858)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1347617100:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (1037858) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1037848-1037858"...
% 0.10/0.44 % (1037858)...printing done.
% 0.10/0.44 % (1037858)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (1037858)------------------------------
% 0.10/0.44 % (1037858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (1037858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (1037858)CaDiCaL version: 2.1.3
% 0.10/0.44 % (1037858)Termination reason: Refutation
% 0.10/0.44 % (1037858)Time elapsed: 0.004 s
% 0.10/0.44 % (1037858)Peak memory usage: 12 MB
% 0.10/0.44 % (1037858)Instructions burned: 9 (million)
% 0.10/0.44 % (1037848)Success in time 0.031 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------