TSTP Solution File: MGT027+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : MGT027+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n020.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 : Tue May 21 00:42:11 EDT 2024
% Result : Theorem 0.56s 0.74s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 20
% Syntax : Number of formulae : 134 ( 4 unt; 0 def)
% Number of atoms : 542 ( 13 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 753 ( 345 ~; 321 |; 59 &)
% ( 10 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 170 ( 158 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f481,plain,
$false,
inference(avatar_sat_refutation,[],[f158,f164,f185,f215,f224,f376,f416,f431,f480]) ).
fof(f480,plain,
( ~ spl3_5
| spl3_24
| ~ spl3_27 ),
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f479,plain,
( $false
| ~ spl3_5
| spl3_24
| ~ spl3_27 ),
inference(subsumption_resolution,[],[f478,f148]) ).
fof(f148,plain,
( greater(sK0(sK1),appear(efficient_producers,sK1))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f147,plain,
( spl3_5
<=> greater(sK0(sK1),appear(efficient_producers,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f478,plain,
( ~ greater(sK0(sK1),appear(efficient_producers,sK1))
| spl3_24
| ~ spl3_27 ),
inference(forward_demodulation,[],[f375,f415]) ).
fof(f415,plain,
( sK0(sK1) = sK2(sK0(sK1))
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f413,plain,
( spl3_27
<=> sK0(sK1) = sK2(sK0(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
fof(f375,plain,
( ~ greater(sK2(sK0(sK1)),appear(efficient_producers,sK1))
| spl3_24 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f373,plain,
( spl3_24
<=> greater(sK2(sK0(sK1)),appear(efficient_producers,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f431,plain,
( ~ spl3_4
| ~ spl3_24 ),
inference(avatar_contradiction_clause,[],[f430]) ).
fof(f430,plain,
( $false
| ~ spl3_4
| ~ spl3_24 ),
inference(subsumption_resolution,[],[f429,f43]) ).
fof(f43,plain,
environment(sK1),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
( ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK1)) )
& stable(sK1)
& environment(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f21,f34]) ).
fof(f34,plain,
( ? [X0] :
( ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,X0)) )
& stable(X0)
& environment(X0) )
=> ( ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK1)) )
& stable(sK1)
& environment(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
? [X0] :
( ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,X0)) )
& stable(X0)
& environment(X0) ),
inference(flattening,[],[f20]) ).
fof(f20,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] :
( contracts_from(X1,first_movers)
& greater(X1,appear(efficient_producers,X0)) ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( contracts_from(X1,first_movers)
& greater(X1,appear(efficient_producers,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9) ).
fof(f429,plain,
( ~ environment(sK1)
| ~ spl3_4
| ~ spl3_24 ),
inference(subsumption_resolution,[],[f427,f44]) ).
fof(f44,plain,
stable(sK1),
inference(cnf_transformation,[],[f35]) ).
fof(f427,plain,
( ~ stable(sK1)
| ~ environment(sK1)
| ~ spl3_4
| ~ spl3_24 ),
inference(resolution,[],[f420,f46]) ).
fof(f46,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f22]) ).
fof(f22,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).
fof(f420,plain,
( ~ in_environment(sK1,appear(efficient_producers,sK1))
| ~ spl3_4
| ~ spl3_24 ),
inference(resolution,[],[f374,f145]) ).
fof(f145,plain,
( ! [X0] :
( ~ greater(sK2(sK0(sK1)),X0)
| ~ in_environment(sK1,X0) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f144,plain,
( spl3_4
<=> ! [X0] :
( ~ greater(sK2(sK0(sK1)),X0)
| ~ in_environment(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f374,plain,
( greater(sK2(sK0(sK1)),appear(efficient_producers,sK1))
| ~ spl3_24 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f416,plain,
( spl3_3
| spl3_27
| ~ spl3_5
| spl3_10
| spl3_24 ),
inference(avatar_split_clause,[],[f411,f373,f182,f147,f413,f141]) ).
fof(f141,plain,
( spl3_3
<=> ! [X1] :
( ~ in_environment(X1,sK0(sK1))
| ~ environment(X1)
| ~ stable(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f182,plain,
( spl3_10
<=> contracts_from(sK0(sK1),first_movers) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f411,plain,
( ! [X0] :
( sK0(sK1) = sK2(sK0(sK1))
| ~ in_environment(X0,sK0(sK1))
| ~ stable(X0)
| ~ environment(X0) )
| ~ spl3_5
| spl3_10
| spl3_24 ),
inference(subsumption_resolution,[],[f410,f183]) ).
fof(f183,plain,
( ~ contracts_from(sK0(sK1),first_movers)
| spl3_10 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f410,plain,
( ! [X0] :
( sK0(sK1) = sK2(sK0(sK1))
| contracts_from(sK0(sK1),first_movers)
| ~ in_environment(X0,sK0(sK1))
| ~ stable(X0)
| ~ environment(X0) )
| ~ spl3_5
| spl3_24 ),
inference(subsumption_resolution,[],[f407,f148]) ).
fof(f407,plain,
( ! [X0] :
( sK0(sK1) = sK2(sK0(sK1))
| ~ greater(sK0(sK1),appear(efficient_producers,sK1))
| contracts_from(sK0(sK1),first_movers)
| ~ in_environment(X0,sK0(sK1))
| ~ stable(X0)
| ~ environment(X0) )
| spl3_24 ),
inference(resolution,[],[f396,f50]) ).
fof(f50,plain,
! [X0,X1] :
( greater_or_equal(sK2(X1),X1)
| contracts_from(X1,first_movers)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| ( ~ greater(zero,growth_rate(first_movers,sK2(X1)))
& greater_or_equal(sK2(X1),X1)
& greater(cardinality_at_time(first_movers,sK2(X1)),zero) )
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f29,f36]) ).
fof(f36,plain,
! [X1] :
( ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater_or_equal(X2,X1)
& greater(cardinality_at_time(first_movers,X2),zero) )
=> ( ~ greater(zero,growth_rate(first_movers,sK2(X1)))
& greater_or_equal(sK2(X1),X1)
& greater(cardinality_at_time(first_movers,sK2(X1)),zero) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater_or_equal(X2,X1)
& greater(cardinality_at_time(first_movers,X2),zero) )
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater_or_equal(X2,X1)
& greater(cardinality_at_time(first_movers,X2),zero) )
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( ! [X2] :
( ( greater_or_equal(X2,X1)
& greater(cardinality_at_time(first_movers,X2),zero) )
=> greater(zero,growth_rate(first_movers,X2)) )
& in_environment(X0,X1)
& stable(X0)
& environment(X0) )
=> contracts_from(X1,first_movers) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from) ).
fof(f396,plain,
( ! [X0] :
( ~ greater_or_equal(sK2(sK0(sK1)),X0)
| sK2(sK0(sK1)) = X0
| ~ greater(X0,appear(efficient_producers,sK1)) )
| spl3_24 ),
inference(resolution,[],[f379,f52]) ).
fof(f52,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( X0 != X1
& ~ greater(X0,X1) ) )
& ( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( X0 != X1
& ~ greater(X0,X1) ) )
& ( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( X0 = X1
| greater(X0,X1) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X5,X6] :
( greater_or_equal(X5,X6)
<=> ( X5 = X6
| greater(X5,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f379,plain,
( ! [X0] :
( ~ greater(sK2(sK0(sK1)),X0)
| ~ greater(X0,appear(efficient_producers,sK1)) )
| spl3_24 ),
inference(resolution,[],[f375,f55]) ).
fof(f55,plain,
! [X2,X0,X1] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( greater(X1,X2)
& greater(X0,X1) )
=> greater(X0,X2) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X5,X6,X7] :
( ( greater(X6,X7)
& greater(X5,X6) )
=> greater(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f376,plain,
( spl3_4
| ~ spl3_24
| spl3_7 ),
inference(avatar_split_clause,[],[f371,f155,f373,f144]) ).
fof(f155,plain,
( spl3_7
<=> greater(cardinality_at_time(efficient_producers,sK2(sK0(sK1))),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f371,plain,
( ! [X0] :
( ~ greater(sK2(sK0(sK1)),appear(efficient_producers,sK1))
| ~ greater(sK2(sK0(sK1)),X0)
| ~ in_environment(sK1,X0) )
| spl3_7 ),
inference(subsumption_resolution,[],[f370,f43]) ).
fof(f370,plain,
( ! [X0] :
( ~ greater(sK2(sK0(sK1)),appear(efficient_producers,sK1))
| ~ greater(sK2(sK0(sK1)),X0)
| ~ in_environment(sK1,X0)
| ~ environment(sK1) )
| spl3_7 ),
inference(resolution,[],[f334,f44]) ).
fof(f334,plain,
( ! [X0,X1] :
( ~ stable(X0)
| ~ greater(sK2(sK0(sK1)),appear(efficient_producers,X0))
| ~ greater(sK2(sK0(sK1)),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) )
| spl3_7 ),
inference(duplicate_literal_removal,[],[f333]) ).
fof(f333,plain,
( ! [X0,X1] :
( ~ environment(X0)
| ~ greater(sK2(sK0(sK1)),appear(efficient_producers,X0))
| ~ greater(sK2(sK0(sK1)),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) )
| spl3_7 ),
inference(resolution,[],[f304,f47]) ).
fof(f47,plain,
! [X2,X0,X1] :
( in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( greater(X2,X1)
& in_environment(X0,X1)
& stable(X0)
& environment(X0) )
=> in_environment(X0,X2) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X3,X4] :
( ( greater(X4,X3)
& in_environment(X0,X3)
& stable(X0)
& environment(X0) )
=> in_environment(X0,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_long_stable_environments) ).
fof(f304,plain,
( ! [X0] :
( ~ in_environment(X0,sK2(sK0(sK1)))
| ~ environment(X0)
| ~ greater(sK2(sK0(sK1)),appear(efficient_producers,X0)) )
| spl3_7 ),
inference(resolution,[],[f231,f53]) ).
fof(f53,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f231,plain,
( ! [X0] :
( ~ greater_or_equal(sK2(sK0(sK1)),appear(efficient_producers,X0))
| ~ in_environment(X0,sK2(sK0(sK1)))
| ~ environment(X0) )
| spl3_7 ),
inference(resolution,[],[f157,f40]) ).
fof(f40,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( ( greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,X1)
& environment(X0) )
=> 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(f157,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK2(sK0(sK1))),zero)
| spl3_7 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f224,plain,
( ~ spl3_5
| ~ spl3_10 ),
inference(avatar_contradiction_clause,[],[f223]) ).
fof(f223,plain,
( $false
| ~ spl3_5
| ~ spl3_10 ),
inference(subsumption_resolution,[],[f222,f148]) ).
fof(f222,plain,
( ~ greater(sK0(sK1),appear(efficient_producers,sK1))
| ~ spl3_10 ),
inference(resolution,[],[f184,f45]) ).
fof(f45,plain,
! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f184,plain,
( contracts_from(sK0(sK1),first_movers)
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f215,plain,
( ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f214]) ).
fof(f214,plain,
( $false
| ~ spl3_3
| ~ spl3_5 ),
inference(subsumption_resolution,[],[f213,f43]) ).
fof(f213,plain,
( ~ environment(sK1)
| ~ spl3_3
| ~ spl3_5 ),
inference(subsumption_resolution,[],[f212,f44]) ).
fof(f212,plain,
( ~ stable(sK1)
| ~ environment(sK1)
| ~ spl3_3
| ~ spl3_5 ),
inference(subsumption_resolution,[],[f210,f148]) ).
fof(f210,plain,
( ~ greater(sK0(sK1),appear(efficient_producers,sK1))
| ~ stable(sK1)
| ~ environment(sK1)
| ~ spl3_3 ),
inference(resolution,[],[f207,f46]) ).
fof(f207,plain,
( ! [X0] :
( ~ in_environment(sK1,X0)
| ~ greater(sK0(sK1),X0) )
| ~ spl3_3 ),
inference(subsumption_resolution,[],[f206,f43]) ).
fof(f206,plain,
( ! [X0] :
( ~ environment(sK1)
| ~ greater(sK0(sK1),X0)
| ~ in_environment(sK1,X0) )
| ~ spl3_3 ),
inference(resolution,[],[f196,f44]) ).
fof(f196,plain,
( ! [X0,X1] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater(sK0(sK1),X1)
| ~ in_environment(X0,X1) )
| ~ spl3_3 ),
inference(duplicate_literal_removal,[],[f195]) ).
fof(f195,plain,
( ! [X0,X1] :
( ~ environment(X0)
| ~ stable(X0)
| ~ greater(sK0(sK1),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) )
| ~ spl3_3 ),
inference(resolution,[],[f142,f47]) ).
fof(f142,plain,
( ! [X1] :
( ~ in_environment(X1,sK0(sK1))
| ~ environment(X1)
| ~ stable(X1) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f185,plain,
( spl3_3
| spl3_10
| spl3_6 ),
inference(avatar_split_clause,[],[f178,f151,f182,f141]) ).
fof(f151,plain,
( spl3_6
<=> greater(cardinality_at_time(first_movers,sK2(sK0(sK1))),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f178,plain,
( ! [X0] :
( contracts_from(sK0(sK1),first_movers)
| ~ in_environment(X0,sK0(sK1))
| ~ stable(X0)
| ~ environment(X0) )
| spl3_6 ),
inference(resolution,[],[f153,f49]) ).
fof(f49,plain,
! [X0,X1] :
( greater(cardinality_at_time(first_movers,sK2(X1)),zero)
| contracts_from(X1,first_movers)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f153,plain,
( ~ greater(cardinality_at_time(first_movers,sK2(sK0(sK1))),zero)
| spl3_6 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f164,plain,
spl3_5,
inference(avatar_contradiction_clause,[],[f163]) ).
fof(f163,plain,
( $false
| spl3_5 ),
inference(subsumption_resolution,[],[f162,f43]) ).
fof(f162,plain,
( ~ environment(sK1)
| spl3_5 ),
inference(subsumption_resolution,[],[f159,f44]) ).
fof(f159,plain,
( ~ stable(sK1)
| ~ environment(sK1)
| spl3_5 ),
inference(resolution,[],[f149,f41]) ).
fof(f41,plain,
! [X0] :
( greater(sK0(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ( ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& greater(sK0(X0),appear(efficient_producers,X0)) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f32]) ).
fof(f32,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& greater(X1,appear(efficient_producers,X0)) )
=> ( ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& greater(sK0(X0),appear(efficient_producers,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& greater(X1,appear(efficient_producers,X0)) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& greater(X1,appear(efficient_producers,X0)) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) )
& greater(X1,appear(efficient_producers,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10) ).
fof(f149,plain,
( ~ greater(sK0(sK1),appear(efficient_producers,sK1))
| spl3_5 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f158,plain,
( spl3_3
| spl3_4
| ~ spl3_5
| ~ spl3_6
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f139,f155,f151,f147,f144,f141]) ).
fof(f139,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,sK2(sK0(sK1))),zero)
| ~ greater(cardinality_at_time(first_movers,sK2(sK0(sK1))),zero)
| ~ greater(sK0(sK1),appear(efficient_producers,sK1))
| ~ greater(sK2(sK0(sK1)),X0)
| ~ in_environment(sK1,X0)
| ~ in_environment(X1,sK0(sK1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(subsumption_resolution,[],[f137,f45]) ).
fof(f137,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,sK2(sK0(sK1))),zero)
| ~ greater(cardinality_at_time(first_movers,sK2(sK0(sK1))),zero)
| ~ greater(sK0(sK1),appear(efficient_producers,sK1))
| ~ greater(sK2(sK0(sK1)),X0)
| ~ in_environment(sK1,X0)
| contracts_from(sK0(sK1),first_movers)
| ~ in_environment(X1,sK0(sK1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(resolution,[],[f125,f50]) ).
fof(f125,plain,
! [X0,X1] :
( ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK2(X0)),zero)
| ~ greater(cardinality_at_time(first_movers,sK2(X0)),zero)
| ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(sK2(X0),X1)
| ~ in_environment(sK1,X1) ),
inference(subsumption_resolution,[],[f124,f43]) ).
fof(f124,plain,
! [X0,X1] :
( ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK2(X0)),zero)
| ~ greater(cardinality_at_time(first_movers,sK2(X0)),zero)
| ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ greater(sK2(X0),X1)
| ~ in_environment(sK1,X1)
| ~ environment(sK1) ),
inference(subsumption_resolution,[],[f123,f44]) ).
fof(f123,plain,
! [X0,X1] :
( ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK2(X0)),zero)
| ~ greater(cardinality_at_time(first_movers,sK2(X0)),zero)
| ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ greater(sK2(X0),X1)
| ~ in_environment(sK1,X1)
| ~ stable(sK1)
| ~ environment(sK1) ),
inference(resolution,[],[f100,f47]) ).
fof(f100,plain,
! [X0] :
( ~ in_environment(sK1,sK2(X0))
| ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK2(X0)),zero)
| ~ greater(cardinality_at_time(first_movers,sK2(X0)),zero)
| ~ greater_or_equal(sK2(X0),sK0(sK1)) ),
inference(subsumption_resolution,[],[f99,f43]) ).
fof(f99,plain,
! [X0] :
( ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK2(X0)),zero)
| ~ greater(cardinality_at_time(first_movers,sK2(X0)),zero)
| ~ in_environment(sK1,sK2(X0))
| ~ environment(sK1) ),
inference(resolution,[],[f98,f48]) ).
fof(f48,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( ( greater(cardinality_at_time(efficient_producers,X1),zero)
& greater(cardinality_at_time(first_movers,X1),zero)
& in_environment(X0,X1)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X2] :
( ( greater(cardinality_at_time(efficient_producers,X2),zero)
& greater(cardinality_at_time(first_movers,X2),zero)
& in_environment(X0,X2)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f98,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2(X0))
| ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ greater(X0,appear(efficient_producers,sK1)) ),
inference(subsumption_resolution,[],[f97,f43]) ).
fof(f97,plain,
! [X0] :
( ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2(X0))
| ~ greater(X0,appear(efficient_producers,sK1))
| ~ environment(sK1) ),
inference(resolution,[],[f84,f44]) ).
fof(f84,plain,
! [X0,X1] :
( ~ stable(X1)
| ~ greater_or_equal(sK2(X0),sK0(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
| ~ greater(X0,appear(efficient_producers,sK1))
| ~ environment(X1) ),
inference(resolution,[],[f81,f42]) ).
fof(f42,plain,
! [X2,X0] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f81,plain,
! [X0] :
( ~ greater(zero,growth_rate(first_movers,sK2(X0)))
| ~ greater(X0,appear(efficient_producers,sK1)) ),
inference(subsumption_resolution,[],[f80,f43]) ).
fof(f80,plain,
! [X0] :
( ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(zero,growth_rate(first_movers,sK2(X0)))
| ~ environment(sK1) ),
inference(subsumption_resolution,[],[f79,f44]) ).
fof(f79,plain,
! [X0] :
( ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(zero,growth_rate(first_movers,sK2(X0)))
| ~ stable(sK1)
| ~ environment(sK1) ),
inference(duplicate_literal_removal,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(zero,growth_rate(first_movers,sK2(X0)))
| ~ stable(sK1)
| ~ environment(sK1) ),
inference(resolution,[],[f74,f46]) ).
fof(f74,plain,
! [X0,X1] :
( ~ in_environment(sK1,X1)
| ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(X0,X1)
| ~ greater(zero,growth_rate(first_movers,sK2(X0))) ),
inference(subsumption_resolution,[],[f73,f43]) ).
fof(f73,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(first_movers,sK2(X0)))
| ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(X0,X1)
| ~ in_environment(sK1,X1)
| ~ environment(sK1) ),
inference(subsumption_resolution,[],[f61,f44]) ).
fof(f61,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(first_movers,sK2(X0)))
| ~ greater(X0,appear(efficient_producers,sK1))
| ~ greater(X0,X1)
| ~ in_environment(sK1,X1)
| ~ stable(sK1)
| ~ environment(sK1) ),
inference(resolution,[],[f59,f47]) ).
fof(f59,plain,
! [X0] :
( ~ in_environment(sK1,X0)
| ~ greater(zero,growth_rate(first_movers,sK2(X0)))
| ~ greater(X0,appear(efficient_producers,sK1)) ),
inference(subsumption_resolution,[],[f58,f43]) ).
fof(f58,plain,
! [X0] :
( ~ in_environment(sK1,X0)
| ~ greater(zero,growth_rate(first_movers,sK2(X0)))
| ~ environment(sK1)
| ~ greater(X0,appear(efficient_producers,sK1)) ),
inference(resolution,[],[f57,f44]) ).
fof(f57,plain,
! [X0,X1] :
( ~ stable(X1)
| ~ in_environment(X1,X0)
| ~ greater(zero,growth_rate(first_movers,sK2(X0)))
| ~ environment(X1)
| ~ greater(X0,appear(efficient_producers,sK1)) ),
inference(resolution,[],[f51,f45]) ).
fof(f51,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| ~ greater(zero,growth_rate(first_movers,sK2(X1)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : MGT027+1 : TPTP v8.2.0. Released v2.0.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 00:10:08 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 This is a FOF_THM_RFO_SEQ problem
% 0.12/0.34 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.50/0.73 % (8665)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.50/0.73 % (8666)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2996ds/33Mi)
% 0.50/0.73 % (8667)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2996ds/34Mi)
% 0.50/0.73 % (8668)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2996ds/45Mi)
% 0.50/0.73 % (8670)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2996ds/56Mi)
% 0.50/0.73 % (8669)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2996ds/83Mi)
% 0.50/0.73 % (8663)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2996ds/34Mi)
% 0.50/0.73 % (8669)Refutation not found, incomplete strategy% (8669)------------------------------
% 0.50/0.73 % (8669)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.50/0.73 % (8669)Termination reason: Refutation not found, incomplete strategy
% 0.50/0.73
% 0.50/0.73 % (8669)Memory used [KB]: 1068
% 0.50/0.73 % (8669)Time elapsed: 0.005 s
% 0.50/0.73 % (8669)Instructions burned: 6 (million)
% 0.50/0.73 % (8669)------------------------------
% 0.50/0.73 % (8669)------------------------------
% 0.56/0.73 % (8671)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on theBenchmark for (2996ds/55Mi)
% 0.56/0.73 % (8664)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2996ds/51Mi)
% 0.56/0.74 % (8671)Refutation not found, incomplete strategy% (8671)------------------------------
% 0.56/0.74 % (8671)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74 % (8671)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74
% 0.56/0.74 % (8671)Memory used [KB]: 1041
% 0.56/0.74 % (8671)Time elapsed: 0.004 s
% 0.56/0.74 % (8671)Instructions burned: 4 (million)
% 0.56/0.74 % (8671)------------------------------
% 0.56/0.74 % (8671)------------------------------
% 0.56/0.74 % (8665)First to succeed.
% 0.56/0.74 % (8666)Instruction limit reached!
% 0.56/0.74 % (8666)------------------------------
% 0.56/0.74 % (8666)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74 % (8666)Termination reason: Unknown
% 0.56/0.74 % (8666)Termination phase: Saturation
% 0.56/0.74
% 0.56/0.74 % (8666)Memory used [KB]: 1255
% 0.56/0.74 % (8666)Time elapsed: 0.017 s
% 0.56/0.74 % (8666)Instructions burned: 34 (million)
% 0.56/0.74 % (8666)------------------------------
% 0.56/0.74 % (8666)------------------------------
% 0.56/0.74 % (8665)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8662"
% 0.56/0.74 % (8664)Also succeeded, but the first one will report.
% 0.56/0.74 % (8665)Refutation found. Thanks to Tanya!
% 0.56/0.74 % SZS status Theorem for theBenchmark
% 0.56/0.74 % SZS output start Proof for theBenchmark
% See solution above
% 0.56/0.74 % (8665)------------------------------
% 0.56/0.74 % (8665)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74 % (8665)Termination reason: Refutation
% 0.56/0.74
% 0.56/0.74 % (8665)Memory used [KB]: 1251
% 0.56/0.74 % (8665)Time elapsed: 0.017 s
% 0.56/0.74 % (8665)Instructions burned: 47 (million)
% 0.56/0.74 % (8662)Success in time 0.386 s
% 0.56/0.74 % Vampire---4.8 exiting
%------------------------------------------------------------------------------