TSTP Solution File: SET766+4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 Apr 30 15:13:08 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 57
% Syntax : Number of formulae : 196 ( 45 unt; 0 def)
% Number of atoms : 607 ( 25 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 651 ( 240 ~; 233 |; 89 &)
% ( 63 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 46 ( 44 usr; 41 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 406 ( 386 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f360,plain,
$false,
inference(avatar_sat_refutation,[],[f108,f113,f118,f122,f126,f130,f134,f138,f142,f146,f152,f156,f160,f164,f168,f172,f176,f180,f194,f200,f204,f208,f212,f216,f220,f240,f256,f260,f264,f268,f290,f294,f298,f302,f326,f330,f340,f344,f348,f357,f359]) ).
fof(f359,plain,
( ~ spl6_2
| ~ spl6_35
| spl6_40 ),
inference(avatar_split_clause,[],[f358,f354,f324,f110]) ).
fof(f110,plain,
( spl6_2
<=> member(sK2,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f324,plain,
( spl6_35
<=> ! [X0] :
( ~ member(X0,sK0)
| apply(sK1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_35])]) ).
fof(f354,plain,
( spl6_40
<=> apply(sK1,sK2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_40])]) ).
fof(f358,plain,
( ~ member(sK2,sK0)
| ~ spl6_35
| spl6_40 ),
inference(resolution,[],[f356,f325]) ).
fof(f325,plain,
( ! [X0] :
( apply(sK1,X0,X0)
| ~ member(X0,sK0) )
| ~ spl6_35 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f356,plain,
( ~ apply(sK1,sK2,sK2)
| spl6_40 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f357,plain,
( ~ spl6_2
| ~ spl6_40
| spl6_3
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f331,f328,f115,f354,f110]) ).
fof(f115,plain,
( spl6_3
<=> member(sK2,equivalence_class(sK2,sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
fof(f328,plain,
( spl6_36
<=> ! [X0,X3,X2,X1] :
( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_36])]) ).
fof(f331,plain,
( ~ apply(sK1,sK2,sK2)
| ~ member(sK2,sK0)
| spl6_3
| ~ spl6_36 ),
inference(resolution,[],[f329,f117]) ).
fof(f117,plain,
( ~ member(sK2,equivalence_class(sK2,sK0,sK1))
| spl6_3 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f329,plain,
( ! [X2,X3,X0,X1] :
( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
| ~ spl6_36 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f348,plain,
( spl6_39
| ~ spl6_2
| ~ spl6_29 ),
inference(avatar_split_clause,[],[f280,f262,f110,f346]) ).
fof(f346,plain,
( spl6_39
<=> ! [X0] :
( ~ member(X0,sK2)
| member(X0,sum(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_39])]) ).
fof(f262,plain,
( spl6_29
<=> ! [X2,X0,X1] :
( member(X0,sum(X1))
| ~ member(X0,X2)
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_29])]) ).
fof(f280,plain,
( ! [X0] :
( ~ member(X0,sK2)
| member(X0,sum(sK0)) )
| ~ spl6_2
| ~ spl6_29 ),
inference(resolution,[],[f263,f112]) ).
fof(f112,plain,
( member(sK2,sK0)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f263,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X0,X2)
| member(X0,sum(X1)) )
| ~ spl6_29 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f344,plain,
spl6_38,
inference(avatar_split_clause,[],[f75,f342]) ).
fof(f342,plain,
( spl6_38
<=> ! [X4,X0,X3,X2,X1] :
( apply(X1,X2,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X2,X3)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0)
| ~ equivalence(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_38])]) ).
fof(f75,plain,
! [X2,X3,X0,X1,X4] :
( apply(X1,X2,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X2,X3)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X1,X2,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X2,X3)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X5,X6] :
( apply(X1,X6,X5)
| ~ apply(X1,X5,X6)
| ~ member(X6,X0)
| ~ member(X5,X0) )
& ! [X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0) ) )
| ~ equivalence(X1,X0) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X1,X2,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X2,X3)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X5,X6] :
( apply(X1,X6,X5)
| ~ apply(X1,X5,X6)
| ~ member(X6,X0)
| ~ member(X5,X0) )
& ! [X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0) ) )
| ~ equivalence(X1,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( equivalence(X1,X0)
=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( apply(X1,X5,X6)
=> apply(X1,X6,X5) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) ) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( apply(X1,X5,X6)
=> apply(X1,X6,X5) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X6] :
( equivalence(X6,X0)
<=> ( ! [X2,X4,X5] :
( ( member(X5,X0)
& member(X4,X0)
& member(X2,X0) )
=> ( ( apply(X6,X4,X5)
& apply(X6,X2,X4) )
=> apply(X6,X2,X5) ) )
& ! [X2,X4] :
( ( member(X4,X0)
& member(X2,X0) )
=> ( apply(X6,X2,X4)
=> apply(X6,X4,X2) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X6,X2,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).
fof(f340,plain,
spl6_37,
inference(avatar_split_clause,[],[f74,f338]) ).
fof(f338,plain,
( spl6_37
<=> ! [X5,X0,X6,X1] :
( apply(X1,X6,X5)
| ~ apply(X1,X5,X6)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ equivalence(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_37])]) ).
fof(f74,plain,
! [X0,X1,X6,X5] :
( apply(X1,X6,X5)
| ~ apply(X1,X5,X6)
| ~ member(X6,X0)
| ~ member(X5,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f330,plain,
spl6_36,
inference(avatar_split_clause,[],[f100,f328]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
& ( ( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
& ( ( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( member(X3,equivalence_class(X2,X1,X0))
<=> ( apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X6,X3,X0,X2] :
( member(X2,equivalence_class(X0,X3,X6))
<=> ( apply(X6,X0,X2)
& member(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).
fof(f326,plain,
( spl6_35
| ~ spl6_1
| ~ spl6_27 ),
inference(avatar_split_clause,[],[f269,f254,f105,f324]) ).
fof(f105,plain,
( spl6_1
<=> equivalence(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f254,plain,
( spl6_27
<=> ! [X0,X1,X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0)
| ~ equivalence(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_27])]) ).
fof(f269,plain,
( ! [X0] :
( ~ member(X0,sK0)
| apply(sK1,X0,X0) )
| ~ spl6_1
| ~ spl6_27 ),
inference(resolution,[],[f255,f107]) ).
fof(f107,plain,
( equivalence(sK1,sK0)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f255,plain,
( ! [X0,X1,X7] :
( ~ equivalence(X1,X0)
| ~ member(X7,X0)
| apply(X1,X7,X7) )
| ~ spl6_27 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f302,plain,
spl6_34,
inference(avatar_split_clause,[],[f95,f300]) ).
fof(f300,plain,
( spl6_34
<=> ! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_34])]) ).
fof(f95,plain,
! [X2,X0,X1] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f298,plain,
spl6_33,
inference(avatar_split_clause,[],[f92,f296]) ).
fof(f296,plain,
( spl6_33
<=> ! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_33])]) ).
fof(f92,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 ) )
& ( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 ) )
& ( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( X0 = X2
| X0 = X1 ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( X1 = X2
| X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f294,plain,
spl6_32,
inference(avatar_split_clause,[],[f91,f292]) ).
fof(f292,plain,
( spl6_32
<=> ! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_32])]) ).
fof(f91,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f290,plain,
spl6_31,
inference(avatar_split_clause,[],[f88,f288]) ).
fof(f288,plain,
( spl6_31
<=> ! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_31])]) ).
fof(f88,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0,X3] :
( member(X1,difference(X3,X0))
<=> ( ~ member(X1,X0)
& member(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
fof(f268,plain,
spl6_30,
inference(avatar_split_clause,[],[f99,f266]) ).
fof(f266,plain,
( spl6_30
<=> ! [X0,X3,X2,X1] :
( apply(X0,X2,X3)
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_30])]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( apply(X0,X2,X3)
| ~ member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f264,plain,
spl6_29,
inference(avatar_split_clause,[],[f85,f262]) ).
fof(f85,plain,
! [X2,X0,X1] :
( member(X0,sum(X1))
| ~ member(X0,X2)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ( member(X0,sK5(X0,X1))
& member(sK5(X0,X1),X1) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f53,f54]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
=> ( member(X0,sK5(X0,X1))
& member(sK5(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X0,X2)
& member(X2,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X2,X0] :
( member(X2,sum(X0))
<=> ? [X4] :
( member(X2,X4)
& member(X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
fof(f260,plain,
spl6_28,
inference(avatar_split_clause,[],[f80,f258]) ).
fof(f258,plain,
( spl6_28
<=> ! [X0,X1,X3] :
( member(X0,X3)
| ~ member(X3,X1)
| ~ member(X0,product(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_28])]) ).
fof(f80,plain,
! [X3,X0,X1] :
( member(X0,X3)
| ~ member(X3,X1)
| ~ member(X0,product(X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ( ~ member(X0,sK4(X0,X1))
& member(sK4(X0,X1),X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f49,f50]) ).
fof(f50,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) )
=> ( ~ member(X0,sK4(X0,X1))
& member(sK4(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(rectify,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) )
| ~ member(X0,product(X1)) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X2,X1)
=> member(X0,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X2,X0] :
( member(X2,product(X0))
<=> ! [X4] :
( member(X4,X0)
=> member(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
fof(f256,plain,
spl6_27,
inference(avatar_split_clause,[],[f73,f254]) ).
fof(f73,plain,
! [X0,X1,X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f240,plain,
( spl6_26
| ~ spl6_2
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f221,f198,f110,f238]) ).
fof(f238,plain,
( spl6_26
<=> ! [X0] :
( member(sK2,X0)
| ~ subset(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_26])]) ).
fof(f198,plain,
( spl6_20
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_20])]) ).
fof(f221,plain,
( ! [X0] :
( member(sK2,X0)
| ~ subset(sK0,X0) )
| ~ spl6_2
| ~ spl6_20 ),
inference(resolution,[],[f199,f112]) ).
fof(f199,plain,
( ! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) )
| ~ spl6_20 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f220,plain,
spl6_25,
inference(avatar_split_clause,[],[f98,f218]) ).
fof(f218,plain,
( spl6_25
<=> ! [X0,X3,X2,X1] :
( member(X3,X1)
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_25])]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f216,plain,
spl6_24,
inference(avatar_split_clause,[],[f84,f214]) ).
fof(f214,plain,
( spl6_24
<=> ! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_24])]) ).
fof(f84,plain,
! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f212,plain,
spl6_23,
inference(avatar_split_clause,[],[f83,f210]) ).
fof(f210,plain,
( spl6_23
<=> ! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_23])]) ).
fof(f83,plain,
! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f208,plain,
spl6_22,
inference(avatar_split_clause,[],[f82,f206]) ).
fof(f206,plain,
( spl6_22
<=> ! [X0,X1] :
( member(X0,product(X1))
| ~ member(X0,sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_22])]) ).
fof(f82,plain,
! [X0,X1] :
( member(X0,product(X1))
| ~ member(X0,sK4(X0,X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f204,plain,
spl6_21,
inference(avatar_split_clause,[],[f81,f202]) ).
fof(f202,plain,
( spl6_21
<=> ! [X0,X1] :
( member(X0,product(X1))
| member(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_21])]) ).
fof(f81,plain,
! [X0,X1] :
( member(X0,product(X1))
| member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f200,plain,
spl6_20,
inference(avatar_split_clause,[],[f70,f198]) ).
fof(f70,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f43,f44]) ).
fof(f44,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f194,plain,
( spl6_19
| ~ spl6_4
| ~ spl6_11 ),
inference(avatar_split_clause,[],[f181,f150,f120,f192]) ).
fof(f192,plain,
( spl6_19
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_19])]) ).
fof(f120,plain,
( spl6_4
<=> ! [X0] : ~ member(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
fof(f150,plain,
( spl6_11
<=> ! [X0,X1] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
fof(f181,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl6_4
| ~ spl6_11 ),
inference(resolution,[],[f151,f121]) ).
fof(f121,plain,
( ! [X0] : ~ member(X0,empty_set)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f151,plain,
( ! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f180,plain,
spl6_18,
inference(avatar_split_clause,[],[f97,f178]) ).
fof(f178,plain,
( spl6_18
<=> ! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).
fof(f97,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f176,plain,
spl6_17,
inference(avatar_split_clause,[],[f96,f174]) ).
fof(f174,plain,
( spl6_17
<=> ! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_17])]) ).
fof(f96,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f172,plain,
spl6_16,
inference(avatar_split_clause,[],[f90,f170]) ).
fof(f170,plain,
( spl6_16
<=> ! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).
fof(f90,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f168,plain,
spl6_15,
inference(avatar_split_clause,[],[f89,f166]) ).
fof(f166,plain,
( spl6_15
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).
fof(f89,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f164,plain,
spl6_14,
inference(avatar_split_clause,[],[f87,f162]) ).
fof(f162,plain,
( spl6_14
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f160,plain,
spl6_13,
inference(avatar_split_clause,[],[f86,f158]) ).
fof(f158,plain,
( spl6_13
<=> ! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,difference(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
fof(f86,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f156,plain,
spl6_12,
inference(avatar_split_clause,[],[f72,f154]) ).
fof(f154,plain,
( spl6_12
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
fof(f72,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f152,plain,
spl6_11,
inference(avatar_split_clause,[],[f71,f150]) ).
fof(f71,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f146,plain,
spl6_10,
inference(avatar_split_clause,[],[f79,f144]) ).
fof(f144,plain,
( spl6_10
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
fof(f79,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X0] :
( member(X2,power_set(X0))
<=> subset(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
fof(f142,plain,
spl6_9,
inference(avatar_split_clause,[],[f78,f140]) ).
fof(f140,plain,
( spl6_9
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
fof(f78,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f138,plain,
spl6_8,
inference(avatar_split_clause,[],[f76,f136]) ).
fof(f136,plain,
( spl6_8
<=> ! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
fof(f76,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2,X0] :
( member(X2,singleton(X0))
<=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f134,plain,
spl6_7,
inference(avatar_split_clause,[],[f103,f132]) ).
fof(f132,plain,
( spl6_7
<=> ! [X2,X1] : member(X1,unordered_pair(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
fof(f103,plain,
! [X2,X1] : member(X1,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f93]) ).
fof(f93,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f130,plain,
spl6_6,
inference(avatar_split_clause,[],[f102,f128]) ).
fof(f128,plain,
( spl6_6
<=> ! [X2,X1] : member(X2,unordered_pair(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
fof(f102,plain,
! [X2,X1] : member(X2,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f94]) ).
fof(f94,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f126,plain,
spl6_5,
inference(avatar_split_clause,[],[f101,f124]) ).
fof(f124,plain,
( spl6_5
<=> ! [X1] : member(X1,singleton(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
fof(f101,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f46]) ).
fof(f122,plain,
spl6_4,
inference(avatar_split_clause,[],[f69,f120]) ).
fof(f69,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f118,plain,
~ spl6_3,
inference(avatar_split_clause,[],[f68,f115]) ).
fof(f68,plain,
~ member(sK2,equivalence_class(sK2,sK0,sK1)),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
( ~ member(sK2,equivalence_class(sK2,sK0,sK1))
& member(sK2,sK0)
& equivalence(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f35,f40]) ).
fof(f40,plain,
( ? [X0,X1,X2] :
( ~ member(X2,equivalence_class(X2,X0,X1))
& member(X2,X0)
& equivalence(X1,X0) )
=> ( ~ member(sK2,equivalence_class(sK2,sK0,sK1))
& member(sK2,sK0)
& equivalence(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
? [X0,X1,X2] :
( ~ member(X2,equivalence_class(X2,X0,X1))
& member(X2,X0)
& equivalence(X1,X0) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
? [X0,X1,X2] :
( ~ member(X2,equivalence_class(X2,X0,X1))
& member(X2,X0)
& equivalence(X1,X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X1,X2] :
( ( member(X2,X0)
& equivalence(X1,X0) )
=> member(X2,equivalence_class(X2,X0,X1)) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X3,X6,X0] :
( ( member(X0,X3)
& equivalence(X6,X3) )
=> member(X0,equivalence_class(X0,X3,X6)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X3,X6,X0] :
( ( member(X0,X3)
& equivalence(X6,X3) )
=> member(X0,equivalence_class(X0,X3,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII02) ).
fof(f113,plain,
spl6_2,
inference(avatar_split_clause,[],[f67,f110]) ).
fof(f67,plain,
member(sK2,sK0),
inference(cnf_transformation,[],[f41]) ).
fof(f108,plain,
spl6_1,
inference(avatar_split_clause,[],[f66,f105]) ).
fof(f66,plain,
equivalence(sK1,sK0),
inference(cnf_transformation,[],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 01:37:55 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (32549)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (32551)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (32553)WARNING: value z3 for option sas not known
% 0.21/0.38 % (32552)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (32553)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38 % (32556)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.38 % (32557)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.38 % (32555)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.38 % (32554)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.38 % (32555)First to succeed.
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [4]
% 0.21/0.39 % (32555)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39 % (32555)------------------------------
% 0.21/0.39 % (32555)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.39 % (32555)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (32555)Memory used [KB]: 1001
% 0.21/0.39 % (32555)Time elapsed: 0.012 s
% 0.21/0.39 % (32555)Instructions burned: 15 (million)
% 0.21/0.39 % (32555)------------------------------
% 0.21/0.39 % (32555)------------------------------
% 0.21/0.39 % (32549)Success in time 0.028 s
%------------------------------------------------------------------------------