TSTP Solution File: MGT027+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 17:50:58 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 23
% Syntax : Number of formulae : 157 ( 8 unt; 0 def)
% Number of atoms : 568 ( 12 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 721 ( 310 ~; 315 |; 63 &)
% ( 13 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 12 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 166 ( 154 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f348,plain,
$false,
inference(avatar_sat_refutation,[],[f111,f159,f168,f180,f184,f193,f224,f277,f282,f324,f336,f347]) ).
fof(f347,plain,
( spl3_15
| spl3_12
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f346,f236,f148,f174]) ).
fof(f174,plain,
( spl3_15
<=> ! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sK0(sK2))
| ~ stable(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f148,plain,
( spl3_12
<=> contracts_from(sK0(sK2),first_movers) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f236,plain,
( spl3_21
<=> greater(zero,growth_rate(first_movers,sK1(sK0(sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f346,plain,
( ! [X0] :
( ~ stable(X0)
| ~ in_environment(X0,sK0(sK2))
| ~ environment(X0) )
| spl3_12
| ~ spl3_21 ),
inference(subsumption_resolution,[],[f337,f149]) ).
fof(f149,plain,
( ~ contracts_from(sK0(sK2),first_movers)
| spl3_12 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f337,plain,
( ! [X0] :
( ~ environment(X0)
| contracts_from(sK0(sK2),first_movers)
| ~ in_environment(X0,sK0(sK2))
| ~ stable(X0) )
| ~ spl3_21 ),
inference(resolution,[],[f237,f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(first_movers,sK1(X0)))
| ~ stable(X1)
| ~ in_environment(X1,X0)
| ~ environment(X1)
| contracts_from(X0,first_movers) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( ~ greater(zero,growth_rate(first_movers,sK1(X0)))
& greater(cardinality_at_time(first_movers,sK1(X0)),zero)
& greater_or_equal(sK1(X0),X0) )
| ~ in_environment(X1,X0)
| contracts_from(X0,first_movers)
| ~ environment(X1)
| ~ stable(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f18,f37]) ).
fof(f37,plain,
! [X0] :
( ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater(cardinality_at_time(first_movers,X2),zero)
& greater_or_equal(X2,X0) )
=> ( ~ greater(zero,growth_rate(first_movers,sK1(X0)))
& greater(cardinality_at_time(first_movers,sK1(X0)),zero)
& greater_or_equal(sK1(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater(cardinality_at_time(first_movers,X2),zero)
& greater_or_equal(X2,X0) )
| ~ in_environment(X1,X0)
| contracts_from(X0,first_movers)
| ~ environment(X1)
| ~ stable(X1) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( contracts_from(X0,first_movers)
| ~ in_environment(X1,X0)
| ~ environment(X1)
| ~ stable(X1)
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater(cardinality_at_time(first_movers,X2),zero)
& greater_or_equal(X2,X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( in_environment(X1,X0)
& environment(X1)
& stable(X1)
& ! [X2] :
( ( greater(cardinality_at_time(first_movers,X2),zero)
& greater_or_equal(X2,X0) )
=> greater(zero,growth_rate(first_movers,X2)) ) )
=> contracts_from(X0,first_movers) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ( ! [X2] :
( ( greater_or_equal(X2,X1)
& greater(cardinality_at_time(first_movers,X2),zero) )
=> greater(zero,growth_rate(first_movers,X2)) )
& stable(X0)
& in_environment(X0,X1)
& environment(X0) )
=> contracts_from(X1,first_movers) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from) ).
fof(f237,plain,
( greater(zero,growth_rate(first_movers,sK1(sK0(sK2))))
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f336,plain,
( ~ spl3_14
| ~ spl3_30 ),
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f335,plain,
( $false
| ~ spl3_14
| ~ spl3_30 ),
inference(subsumption_resolution,[],[f331,f158]) ).
fof(f158,plain,
( greater(sK1(sK0(sK2)),sK0(sK2))
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f156,plain,
( spl3_14
<=> greater(sK1(sK0(sK2)),sK0(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f331,plain,
( ~ greater(sK1(sK0(sK2)),sK0(sK2))
| ~ spl3_14
| ~ spl3_30 ),
inference(resolution,[],[f329,f56]) ).
fof(f56,plain,
! [X0,X1] :
( greater_or_equal(X1,X0)
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( greater(X1,X0)
| X0 = X1
| ~ greater_or_equal(X1,X0) )
& ( greater_or_equal(X1,X0)
| ( ~ greater(X1,X0)
& X0 != X1 ) ) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ( greater(X1,X0)
| X0 = X1
| ~ greater_or_equal(X1,X0) )
& ( greater_or_equal(X1,X0)
| ( ~ greater(X1,X0)
& X0 != X1 ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ( greater(X1,X0)
| X0 = X1 )
<=> greater_or_equal(X1,X0) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X6,X5] :
( ( X5 = X6
| greater(X5,X6) )
<=> greater_or_equal(X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f329,plain,
( ~ greater_or_equal(sK1(sK0(sK2)),sK0(sK2))
| ~ spl3_14
| ~ spl3_30 ),
inference(subsumption_resolution,[],[f328,f54]) ).
fof(f54,plain,
stable(sK2),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( stable(sK2)
& environment(sK2)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f28,f39]) ).
fof(f39,plain,
( ? [X0] :
( stable(X0)
& environment(X0)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,X0)) ) )
=> ( stable(sK2)
& environment(sK2)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,X0)) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
? [X0] :
( ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,X0)) )
& stable(X0)
& environment(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& contracts_from(X1,first_movers) ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& contracts_from(X1,first_movers) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9) ).
fof(f328,plain,
( ~ stable(sK2)
| ~ greater_or_equal(sK1(sK0(sK2)),sK0(sK2))
| ~ spl3_14
| ~ spl3_30 ),
inference(subsumption_resolution,[],[f327,f53]) ).
fof(f53,plain,
environment(sK2),
inference(cnf_transformation,[],[f40]) ).
fof(f327,plain,
( ~ greater_or_equal(sK1(sK0(sK2)),sK0(sK2))
| ~ environment(sK2)
| ~ stable(sK2)
| ~ spl3_14
| ~ spl3_30 ),
inference(resolution,[],[f323,f225]) ).
fof(f225,plain,
( in_environment(sK2,sK1(sK0(sK2)))
| ~ spl3_14 ),
inference(resolution,[],[f158,f71]) ).
fof(f71,plain,
! [X0] :
( ~ greater(X0,sK0(sK2))
| in_environment(sK2,X0) ),
inference(resolution,[],[f69,f63]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in_environment(sK2,X0)
| in_environment(sK2,X1)
| ~ greater(X1,X0) ),
inference(subsumption_resolution,[],[f62,f53]) ).
fof(f62,plain,
! [X0,X1] :
( ~ environment(sK2)
| in_environment(sK2,X1)
| ~ in_environment(sK2,X0)
| ~ greater(X1,X0) ),
inference(resolution,[],[f48,f54]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ stable(X0)
| ~ in_environment(X0,X2)
| in_environment(X0,X1)
| ~ greater(X1,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| in_environment(X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X2)
| ~ stable(X0) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X1,X2,X0] :
( ~ greater(X2,X0)
| in_environment(X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ stable(X1) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X1,X2,X0] :
( in_environment(X1,X2)
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X2,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X2,X0] :
( ( stable(X1)
& environment(X1)
& in_environment(X1,X0)
& greater(X2,X0) )
=> in_environment(X1,X2) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X3,X0,X4] :
( ( greater(X4,X3)
& stable(X0)
& environment(X0)
& in_environment(X0,X3) )
=> in_environment(X0,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_long_stable_environments) ).
fof(f69,plain,
in_environment(sK2,sK0(sK2)),
inference(subsumption_resolution,[],[f68,f54]) ).
fof(f68,plain,
( ~ stable(sK2)
| in_environment(sK2,sK0(sK2)) ),
inference(subsumption_resolution,[],[f67,f53]) ).
fof(f67,plain,
( in_environment(sK2,sK0(sK2))
| ~ environment(sK2)
| ~ stable(sK2) ),
inference(resolution,[],[f66,f45]) ).
fof(f45,plain,
! [X0] :
( greater(sK0(X0),appear(efficient_producers,X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ( greater(sK0(X0),appear(efficient_producers,X0))
& ! [X2] :
( ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f30,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ) )
=> ( greater(sK0(X0),appear(efficient_producers,X0))
& ! [X2] :
( ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0] :
( ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f29]) ).
fof(f29,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) ) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( stable(X0)
& environment(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/sandbox2/benchmark/theBenchmark.p',l10) ).
fof(f66,plain,
! [X0] :
( ~ greater(X0,appear(efficient_producers,sK2))
| in_environment(sK2,X0) ),
inference(subsumption_resolution,[],[f65,f53]) ).
fof(f65,plain,
! [X0] :
( ~ environment(sK2)
| ~ greater(X0,appear(efficient_producers,sK2))
| in_environment(sK2,X0) ),
inference(subsumption_resolution,[],[f64,f54]) ).
fof(f64,plain,
! [X0] :
( ~ stable(sK2)
| in_environment(sK2,X0)
| ~ environment(sK2)
| ~ greater(X0,appear(efficient_producers,sK2)) ),
inference(resolution,[],[f63,f58]) ).
fof(f58,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> in_environment(X0,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).
fof(f323,plain,
( ! [X0] :
( ~ in_environment(X0,sK1(sK0(sK2)))
| ~ greater_or_equal(sK1(sK0(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| ~ spl3_30 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f322,plain,
( spl3_30
<=> ! [X0] :
( ~ greater_or_equal(sK1(sK0(sK2)),sK0(X0))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,sK1(sK0(sK2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
fof(f324,plain,
( spl3_30
| spl3_21
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f320,f275,f236,f322]) ).
fof(f275,plain,
( spl3_26
<=> ! [X0] :
( ~ in_environment(X0,sK1(sK0(sK2)))
| subpopulations(first_movers,efficient_producers,X0,sK1(sK0(sK2)))
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
fof(f320,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK1(sK0(sK2))))
| ~ greater_or_equal(sK1(sK0(sK2)),sK0(X0))
| ~ in_environment(X0,sK1(sK0(sK2)))
| ~ environment(X0)
| ~ stable(X0) )
| ~ spl3_26 ),
inference(duplicate_literal_removal,[],[f319]) ).
fof(f319,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK1(sK0(sK2))))
| ~ greater_or_equal(sK1(sK0(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,sK1(sK0(sK2)))
| ~ environment(X0) )
| ~ spl3_26 ),
inference(resolution,[],[f276,f44]) ).
fof(f44,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ stable(X0)
| ~ greater_or_equal(X2,sK0(X0))
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f276,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sK1(sK0(sK2)))
| ~ in_environment(X0,sK1(sK0(sK2)))
| ~ environment(X0) )
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f282,plain,
( spl3_12
| spl3_22 ),
inference(avatar_contradiction_clause,[],[f281]) ).
fof(f281,plain,
( $false
| spl3_12
| spl3_22 ),
inference(subsumption_resolution,[],[f280,f149]) ).
fof(f280,plain,
( contracts_from(sK0(sK2),first_movers)
| spl3_22 ),
inference(subsumption_resolution,[],[f279,f69]) ).
fof(f279,plain,
( ~ in_environment(sK2,sK0(sK2))
| contracts_from(sK0(sK2),first_movers)
| spl3_22 ),
inference(resolution,[],[f243,f117]) ).
fof(f117,plain,
! [X0] :
( greater(cardinality_at_time(first_movers,sK1(X0)),zero)
| ~ in_environment(sK2,X0)
| contracts_from(X0,first_movers) ),
inference(subsumption_resolution,[],[f116,f53]) ).
fof(f116,plain,
! [X0] :
( contracts_from(X0,first_movers)
| greater(cardinality_at_time(first_movers,sK1(X0)),zero)
| ~ environment(sK2)
| ~ in_environment(sK2,X0) ),
inference(resolution,[],[f50,f54]) ).
fof(f50,plain,
! [X0,X1] :
( ~ stable(X1)
| contracts_from(X0,first_movers)
| greater(cardinality_at_time(first_movers,sK1(X0)),zero)
| ~ environment(X1)
| ~ in_environment(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f243,plain,
( ~ greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero)
| spl3_22 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f242,plain,
( spl3_22
<=> greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f277,plain,
( ~ spl3_22
| spl3_26
| ~ spl3_14 ),
inference(avatar_split_clause,[],[f272,f156,f275,f242]) ).
fof(f272,plain,
( ! [X0] :
( ~ in_environment(X0,sK1(sK0(sK2)))
| ~ environment(X0)
| ~ greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero)
| subpopulations(first_movers,efficient_producers,X0,sK1(sK0(sK2))) )
| ~ spl3_14 ),
inference(resolution,[],[f269,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(first_movers,X1),zero)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X1,X0] :
( ~ greater(cardinality_at_time(first_movers,X0),zero)
| subpopulations(first_movers,efficient_producers,X1,X0)
| ~ in_environment(X1,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ environment(X1) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X1)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ in_environment(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( ( environment(X1)
& greater(cardinality_at_time(efficient_producers,X0),zero)
& greater(cardinality_at_time(first_movers,X0),zero)
& in_environment(X1,X0) )
=> subpopulations(first_movers,efficient_producers,X1,X0) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X0] :
( ( in_environment(X0,X2)
& greater(cardinality_at_time(first_movers,X2),zero)
& greater(cardinality_at_time(efficient_producers,X2),zero)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f269,plain,
( greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| ~ spl3_14 ),
inference(resolution,[],[f268,f74]) ).
fof(f74,plain,
! [X0] :
( ~ greater(X0,appear(efficient_producers,sK2))
| greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(subsumption_resolution,[],[f73,f66]) ).
fof(f73,plain,
! [X0] :
( ~ greater(X0,appear(efficient_producers,sK2))
| greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sK2,X0) ),
inference(resolution,[],[f70,f56]) ).
fof(f70,plain,
! [X0] :
( ~ greater_or_equal(X0,appear(efficient_producers,sK2))
| greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sK2,X0) ),
inference(resolution,[],[f46,f53]) ).
fof(f46,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X1,X0] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
! [X1,X0] :
( ( environment(X0)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,X1) )
=> greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X0,X2] :
( ( greater_or_equal(X2,appear(efficient_producers,X0))
& in_environment(X0,X2)
& environment(X0) )
=> greater(cardinality_at_time(efficient_producers,X2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(f268,plain,
( greater(sK1(sK0(sK2)),appear(efficient_producers,sK2))
| ~ spl3_14 ),
inference(subsumption_resolution,[],[f267,f54]) ).
fof(f267,plain,
( greater(sK1(sK0(sK2)),appear(efficient_producers,sK2))
| ~ stable(sK2)
| ~ spl3_14 ),
inference(subsumption_resolution,[],[f266,f53]) ).
fof(f266,plain,
( ~ environment(sK2)
| greater(sK1(sK0(sK2)),appear(efficient_producers,sK2))
| ~ stable(sK2)
| ~ spl3_14 ),
inference(resolution,[],[f226,f45]) ).
fof(f226,plain,
( ! [X0] :
( ~ greater(sK0(sK2),X0)
| greater(sK1(sK0(sK2)),X0) )
| ~ spl3_14 ),
inference(resolution,[],[f158,f47]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ greater(X2,X0)
| greater(X1,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( greater(X1,X0)
| ~ greater(X1,X2)
| ~ greater(X2,X0) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X2,X1,X0] :
( greater(X1,X2)
| ~ greater(X1,X0)
| ~ greater(X0,X2) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X1,X0,X2] :
( greater(X1,X2)
| ~ greater(X1,X0)
| ~ greater(X0,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X1,X0,X2] :
( ( greater(X1,X0)
& greater(X0,X2) )
=> greater(X1,X2) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X6,X5,X7] :
( ( greater(X5,X6)
& greater(X6,X7) )
=> greater(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f224,plain,
~ spl3_15,
inference(avatar_contradiction_clause,[],[f223]) ).
fof(f223,plain,
( $false
| ~ spl3_15 ),
inference(subsumption_resolution,[],[f222,f54]) ).
fof(f222,plain,
( ~ stable(sK2)
| ~ spl3_15 ),
inference(subsumption_resolution,[],[f221,f53]) ).
fof(f221,plain,
( ~ environment(sK2)
| ~ stable(sK2)
| ~ spl3_15 ),
inference(resolution,[],[f175,f69]) ).
fof(f175,plain,
( ! [X0] :
( ~ in_environment(X0,sK0(sK2))
| ~ environment(X0)
| ~ stable(X0) )
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f193,plain,
( ~ spl3_6
| spl3_16 ),
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f192,plain,
( $false
| ~ spl3_6
| spl3_16 ),
inference(subsumption_resolution,[],[f191,f54]) ).
fof(f191,plain,
( ~ stable(sK2)
| ~ spl3_6
| spl3_16 ),
inference(subsumption_resolution,[],[f190,f60]) ).
fof(f60,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( greater_or_equal(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f42]) ).
fof(f190,plain,
( ~ greater_or_equal(sK0(sK2),sK0(sK2))
| ~ stable(sK2)
| ~ spl3_6
| spl3_16 ),
inference(subsumption_resolution,[],[f189,f53]) ).
fof(f189,plain,
( ~ environment(sK2)
| ~ stable(sK2)
| ~ greater_or_equal(sK0(sK2),sK0(sK2))
| ~ spl3_6
| spl3_16 ),
inference(resolution,[],[f188,f69]) ).
fof(f188,plain,
( ! [X0] :
( ~ in_environment(X0,sK0(sK2))
| ~ greater_or_equal(sK0(sK2),sK0(X0))
| ~ stable(X0)
| ~ environment(X0) )
| ~ spl3_6
| spl3_16 ),
inference(subsumption_resolution,[],[f187,f179]) ).
fof(f179,plain,
( ~ greater(zero,growth_rate(first_movers,sK0(sK2)))
| spl3_16 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f177,plain,
( spl3_16
<=> greater(zero,growth_rate(first_movers,sK0(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f187,plain,
( ! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| greater(zero,growth_rate(first_movers,sK0(sK2)))
| ~ in_environment(X0,sK0(sK2))
| ~ greater_or_equal(sK0(sK2),sK0(X0)) )
| ~ spl3_6 ),
inference(duplicate_literal_removal,[],[f186]) ).
fof(f186,plain,
( ! [X0] :
( ~ environment(X0)
| ~ greater_or_equal(sK0(sK2),sK0(X0))
| ~ in_environment(X0,sK0(sK2))
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,sK0(sK2)))
| ~ stable(X0) )
| ~ spl3_6 ),
inference(resolution,[],[f110,f44]) ).
fof(f110,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sK0(sK2))
| ~ in_environment(X0,sK0(sK2))
| ~ environment(X0) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f109,plain,
( spl3_6
<=> ! [X0] :
( ~ in_environment(X0,sK0(sK2))
| subpopulations(first_movers,efficient_producers,X0,sK0(sK2))
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f184,plain,
( spl3_5
| spl3_12
| ~ spl3_13 ),
inference(avatar_contradiction_clause,[],[f183]) ).
fof(f183,plain,
( $false
| spl3_5
| spl3_12
| ~ spl3_13 ),
inference(subsumption_resolution,[],[f182,f107]) ).
fof(f107,plain,
( ~ greater(cardinality_at_time(first_movers,sK0(sK2)),zero)
| spl3_5 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f105,plain,
( spl3_5
<=> greater(cardinality_at_time(first_movers,sK0(sK2)),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f182,plain,
( greater(cardinality_at_time(first_movers,sK0(sK2)),zero)
| spl3_12
| ~ spl3_13 ),
inference(subsumption_resolution,[],[f181,f69]) ).
fof(f181,plain,
( ~ in_environment(sK2,sK0(sK2))
| greater(cardinality_at_time(first_movers,sK0(sK2)),zero)
| spl3_12
| ~ spl3_13 ),
inference(subsumption_resolution,[],[f169,f149]) ).
fof(f169,plain,
( contracts_from(sK0(sK2),first_movers)
| greater(cardinality_at_time(first_movers,sK0(sK2)),zero)
| ~ in_environment(sK2,sK0(sK2))
| ~ spl3_13 ),
inference(superposition,[],[f117,f154]) ).
fof(f154,plain,
( sK0(sK2) = sK1(sK0(sK2))
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f152,plain,
( spl3_13
<=> sK0(sK2) = sK1(sK0(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f180,plain,
( spl3_15
| ~ spl3_16
| spl3_12
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f172,f152,f148,f177,f174]) ).
fof(f172,plain,
( ! [X0] :
( ~ greater(zero,growth_rate(first_movers,sK0(sK2)))
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,sK0(sK2)) )
| spl3_12
| ~ spl3_13 ),
inference(subsumption_resolution,[],[f171,f149]) ).
fof(f171,plain,
( ! [X0] :
( ~ in_environment(X0,sK0(sK2))
| contracts_from(sK0(sK2),first_movers)
| ~ environment(X0)
| ~ greater(zero,growth_rate(first_movers,sK0(sK2)))
| ~ stable(X0) )
| ~ spl3_13 ),
inference(superposition,[],[f51,f154]) ).
fof(f168,plain,
~ spl3_12,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f167,plain,
( $false
| ~ spl3_12 ),
inference(subsumption_resolution,[],[f166,f53]) ).
fof(f166,plain,
( ~ environment(sK2)
| ~ spl3_12 ),
inference(subsumption_resolution,[],[f165,f54]) ).
fof(f165,plain,
( ~ stable(sK2)
| ~ environment(sK2)
| ~ spl3_12 ),
inference(resolution,[],[f164,f45]) ).
fof(f164,plain,
( ~ greater(sK0(sK2),appear(efficient_producers,sK2))
| ~ spl3_12 ),
inference(resolution,[],[f150,f52]) ).
fof(f52,plain,
! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK2)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f150,plain,
( contracts_from(sK0(sK2),first_movers)
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f159,plain,
( spl3_12
| spl3_13
| spl3_14 ),
inference(avatar_split_clause,[],[f135,f156,f152,f148]) ).
fof(f135,plain,
( greater(sK1(sK0(sK2)),sK0(sK2))
| sK0(sK2) = sK1(sK0(sK2))
| contracts_from(sK0(sK2),first_movers) ),
inference(resolution,[],[f119,f69]) ).
fof(f119,plain,
! [X0] :
( ~ in_environment(sK2,X0)
| greater(sK1(X0),X0)
| sK1(X0) = X0
| contracts_from(X0,first_movers) ),
inference(resolution,[],[f115,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,X0)
| X0 = X1
| greater(X1,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f115,plain,
! [X0] :
( greater_or_equal(sK1(X0),X0)
| ~ in_environment(sK2,X0)
| contracts_from(X0,first_movers) ),
inference(subsumption_resolution,[],[f114,f53]) ).
fof(f114,plain,
! [X0] :
( greater_or_equal(sK1(X0),X0)
| ~ in_environment(sK2,X0)
| ~ environment(sK2)
| contracts_from(X0,first_movers) ),
inference(resolution,[],[f49,f54]) ).
fof(f49,plain,
! [X0,X1] :
( ~ stable(X1)
| contracts_from(X0,first_movers)
| greater_or_equal(sK1(X0),X0)
| ~ environment(X1)
| ~ in_environment(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f111,plain,
( ~ spl3_5
| spl3_6 ),
inference(avatar_split_clause,[],[f102,f109,f105]) ).
fof(f102,plain,
! [X0] :
( ~ in_environment(X0,sK0(sK2))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sK0(sK2))
| ~ greater(cardinality_at_time(first_movers,sK0(sK2)),zero) ),
inference(resolution,[],[f101,f59]) ).
fof(f101,plain,
greater(cardinality_at_time(efficient_producers,sK0(sK2)),zero),
inference(subsumption_resolution,[],[f100,f54]) ).
fof(f100,plain,
( greater(cardinality_at_time(efficient_producers,sK0(sK2)),zero)
| ~ stable(sK2) ),
inference(subsumption_resolution,[],[f99,f53]) ).
fof(f99,plain,
( greater(cardinality_at_time(efficient_producers,sK0(sK2)),zero)
| ~ environment(sK2)
| ~ stable(sK2) ),
inference(resolution,[],[f74,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 03:30:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.50 % (16330)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (16336)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.51 % (16330)Refutation not found, incomplete strategy% (16330)------------------------------
% 0.20/0.51 % (16330)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (16336)Refutation not found, incomplete strategy% (16336)------------------------------
% 0.20/0.51 % (16336)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (16330)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (16330)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51
% 0.20/0.51 % (16330)Memory used [KB]: 6012
% 0.20/0.51 % (16330)Time elapsed: 0.098 s
% 0.20/0.51 % (16330)Instructions burned: 2 (million)
% 0.20/0.51 % (16330)------------------------------
% 0.20/0.51 % (16330)------------------------------
% 0.20/0.51 % (16336)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (16352)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.20/0.51 % (16336)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51
% 0.20/0.51 % (16336)Memory used [KB]: 5884
% 0.20/0.51 % (16336)Time elapsed: 0.116 s
% 0.20/0.51 % (16336)Instructions burned: 2 (million)
% 0.20/0.51 % (16336)------------------------------
% 0.20/0.51 % (16336)------------------------------
% 0.20/0.52 % (16352)First to succeed.
% 0.20/0.52 % (16332)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.52 % (16329)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.52 % (16329)Instruction limit reached!
% 0.20/0.52 % (16329)------------------------------
% 0.20/0.52 % (16329)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (16331)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.52 % (16329)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (16329)Termination reason: Unknown
% 0.20/0.52 % (16329)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (16329)Memory used [KB]: 5884
% 0.20/0.52 % (16329)Time elapsed: 0.126 s
% 0.20/0.52 % (16329)Instructions burned: 4 (million)
% 0.20/0.52 % (16329)------------------------------
% 0.20/0.52 % (16329)------------------------------
% 0.20/0.53 % (16331)Refutation not found, incomplete strategy% (16331)------------------------------
% 0.20/0.53 % (16331)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (16331)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (16331)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53
% 0.20/0.53 % (16331)Memory used [KB]: 6012
% 0.20/0.53 % (16331)Time elapsed: 0.124 s
% 0.20/0.53 % (16331)Instructions burned: 3 (million)
% 0.20/0.53 % (16331)------------------------------
% 0.20/0.53 % (16331)------------------------------
% 0.20/0.53 % (16354)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.20/0.53 % (16326)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.53 % (16348)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53 % (16337)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.53 % (16352)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (16352)------------------------------
% 0.20/0.53 % (16352)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (16352)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (16352)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (16352)Memory used [KB]: 6140
% 0.20/0.53 % (16352)Time elapsed: 0.120 s
% 0.20/0.53 % (16352)Instructions burned: 10 (million)
% 0.20/0.53 % (16352)------------------------------
% 0.20/0.53 % (16352)------------------------------
% 0.20/0.53 % (16323)Success in time 0.179 s
%------------------------------------------------------------------------------