TSTP Solution File: NUM534+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM534+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -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 : Thu Aug 31 12:11:04 EDT 2023
% Result : Theorem 6.13s 1.39s
% Output : Refutation 6.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 54
% Syntax : Number of formulae : 253 ( 15 unt; 0 def)
% Number of atoms : 854 ( 72 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 998 ( 397 ~; 437 |; 96 &)
% ( 57 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 47 ( 45 usr; 32 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 286 (; 276 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f43342,plain,
$false,
inference(avatar_sat_refutation,[],[f167,f171,f177,f181,f199,f203,f209,f213,f218,f246,f257,f261,f312,f319,f325,f400,f471,f476,f859,f907,f917,f929,f938,f1861,f1936,f2586,f2596,f42379,f42921,f42969,f42988,f43341]) ).
fof(f43341,plain,
( spl16_215
| spl16_3592 ),
inference(avatar_split_clause,[],[f43340,f42805,f2584]) ).
fof(f2584,plain,
( spl16_215
<=> sP0(sF15,xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_215])]) ).
fof(f42805,plain,
( spl16_3592
<=> aElementOf0(sK10(sF15,xS),xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3592])]) ).
fof(f43340,plain,
( sP0(sF15,xS)
| spl16_3592 ),
inference(subsumption_resolution,[],[f43333,f89]) ).
fof(f89,plain,
aSet0(xS),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
aSet0(xS),
file('/export/starexec/sandbox/tmp/tmp.giK0nLqnlo/Vampire---4.8_30712',m__617) ).
fof(f43333,plain,
( sP0(sF15,xS)
| ~ aSet0(xS)
| spl16_3592 ),
inference(resolution,[],[f43328,f98]) ).
fof(f98,plain,
! [X0,X1] :
( aElementOf0(sK10(X0,X1),X1)
| sP0(X0,X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ aElementOf0(sK10(X0,X1),X0)
& aElementOf0(sK10(X0,X1),X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f58,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK10(X0,X1),X0)
& aElementOf0(sK10(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f43328,plain,
( ~ aElementOf0(sK10(sF15,xS),xS)
| spl16_3592 ),
inference(avatar_component_clause,[],[f42805]) ).
fof(f42988,plain,
( spl16_211
| ~ spl16_63
| ~ spl16_3550
| spl16_3584
| ~ spl16_3592 ),
inference(avatar_split_clause,[],[f42987,f42805,f42702,f42327,f686,f2550]) ).
fof(f2550,plain,
( spl16_211
<=> xx = sK10(sF15,xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_211])]) ).
fof(f686,plain,
( spl16_63
<=> ! [X8] :
( xx = X8
| ~ aElementOf0(X8,xS)
| ~ aElement0(X8)
| aElementOf0(X8,sF14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_63])]) ).
fof(f42327,plain,
( spl16_3550
<=> aElement0(sK10(sF15,xS)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3550])]) ).
fof(f42702,plain,
( spl16_3584
<=> aElementOf0(sK10(sF15,xS),sF14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3584])]) ).
fof(f42987,plain,
( xx = sK10(sF15,xS)
| ~ spl16_63
| ~ spl16_3550
| spl16_3584
| ~ spl16_3592 ),
inference(subsumption_resolution,[],[f42986,f42709]) ).
fof(f42709,plain,
( ~ aElementOf0(sK10(sF15,xS),sF14)
| spl16_3584 ),
inference(avatar_component_clause,[],[f42702]) ).
fof(f42986,plain,
( xx = sK10(sF15,xS)
| aElementOf0(sK10(sF15,xS),sF14)
| ~ spl16_63
| ~ spl16_3550
| ~ spl16_3592 ),
inference(subsumption_resolution,[],[f42976,f42328]) ).
fof(f42328,plain,
( aElement0(sK10(sF15,xS))
| ~ spl16_3550 ),
inference(avatar_component_clause,[],[f42327]) ).
fof(f42976,plain,
( xx = sK10(sF15,xS)
| ~ aElement0(sK10(sF15,xS))
| aElementOf0(sK10(sF15,xS),sF14)
| ~ spl16_63
| ~ spl16_3592 ),
inference(resolution,[],[f42806,f687]) ).
fof(f687,plain,
( ! [X8] :
( ~ aElementOf0(X8,xS)
| xx = X8
| ~ aElement0(X8)
| aElementOf0(X8,sF14) )
| ~ spl16_63 ),
inference(avatar_component_clause,[],[f686]) ).
fof(f42806,plain,
( aElementOf0(sK10(sF15,xS),xS)
| ~ spl16_3592 ),
inference(avatar_component_clause,[],[f42805]) ).
fof(f42969,plain,
( ~ spl16_42
| spl16_3551
| ~ spl16_3584 ),
inference(avatar_contradiction_clause,[],[f42968]) ).
fof(f42968,plain,
( $false
| ~ spl16_42
| spl16_3551
| ~ spl16_3584 ),
inference(subsumption_resolution,[],[f42952,f42338]) ).
fof(f42338,plain,
( ~ aElementOf0(sK10(sF15,xS),sF15)
| spl16_3551 ),
inference(avatar_component_clause,[],[f42331]) ).
fof(f42331,plain,
( spl16_3551
<=> aElementOf0(sK10(sF15,xS),sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3551])]) ).
fof(f42952,plain,
( aElementOf0(sK10(sF15,xS),sF15)
| ~ spl16_42
| ~ spl16_3584 ),
inference(resolution,[],[f42703,f475]) ).
fof(f475,plain,
( ! [X1] :
( ~ aElementOf0(X1,sF14)
| aElementOf0(X1,sF15) )
| ~ spl16_42 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f474,plain,
( spl16_42
<=> ! [X1] :
( aElementOf0(X1,sF15)
| ~ aElementOf0(X1,sF14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_42])]) ).
fof(f42703,plain,
( aElementOf0(sK10(sF15,xS),sF14)
| ~ spl16_3584 ),
inference(avatar_component_clause,[],[f42702]) ).
fof(f42921,plain,
( spl16_215
| ~ spl16_3551 ),
inference(avatar_split_clause,[],[f42920,f42331,f2584]) ).
fof(f42920,plain,
( sP0(sF15,xS)
| ~ spl16_3551 ),
inference(subsumption_resolution,[],[f42902,f89]) ).
fof(f42902,plain,
( sP0(sF15,xS)
| ~ aSet0(xS)
| ~ spl16_3551 ),
inference(resolution,[],[f42332,f99]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aElementOf0(sK10(X0,X1),X0)
| sP0(X0,X1)
| ~ aSet0(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f42332,plain,
( aElementOf0(sK10(sF15,xS),sF15)
| ~ spl16_3551 ),
inference(avatar_component_clause,[],[f42331]) ).
fof(f42379,plain,
( spl16_215
| spl16_3550 ),
inference(avatar_split_clause,[],[f42378,f42327,f2584]) ).
fof(f42378,plain,
( sP0(sF15,xS)
| spl16_3550 ),
inference(subsumption_resolution,[],[f42377,f89]) ).
fof(f42377,plain,
( ~ aSet0(xS)
| sP0(sF15,xS)
| spl16_3550 ),
inference(resolution,[],[f42375,f226]) ).
fof(f226,plain,
! [X2,X1] :
( aElement0(sK10(X1,X2))
| ~ aSet0(X2)
| sP0(X1,X2) ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f225,plain,
! [X2,X1] :
( sP0(X1,X2)
| ~ aSet0(X2)
| aElement0(sK10(X1,X2))
| ~ aSet0(X2) ),
inference(resolution,[],[f98,f93]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.giK0nLqnlo/Vampire---4.8_30712',mEOfElem) ).
fof(f42375,plain,
( ~ aElement0(sK10(sF15,xS))
| spl16_3550 ),
inference(avatar_component_clause,[],[f42327]) ).
fof(f2596,plain,
( ~ spl16_10
| spl16_90
| ~ spl16_215 ),
inference(avatar_contradiction_clause,[],[f2595]) ).
fof(f2595,plain,
( $false
| ~ spl16_10
| spl16_90
| ~ spl16_215 ),
inference(subsumption_resolution,[],[f2594,f217]) ).
fof(f217,plain,
( sP1(sF15)
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f216,plain,
( spl16_10
<=> sP1(sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_10])]) ).
fof(f2594,plain,
( ~ sP1(sF15)
| spl16_90
| ~ spl16_215 ),
inference(subsumption_resolution,[],[f2588,f937]) ).
fof(f937,plain,
( ~ aSubsetOf0(xS,sF15)
| spl16_90 ),
inference(avatar_component_clause,[],[f936]) ).
fof(f936,plain,
( spl16_90
<=> aSubsetOf0(xS,sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_90])]) ).
fof(f2588,plain,
( aSubsetOf0(xS,sF15)
| ~ sP1(sF15)
| ~ spl16_215 ),
inference(resolution,[],[f2585,f95]) ).
fof(f95,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| aSubsetOf0(X1,X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ aSubsetOf0(X1,X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f2585,plain,
( sP0(sF15,xS)
| ~ spl16_215 ),
inference(avatar_component_clause,[],[f2584]) ).
fof(f2586,plain,
( spl16_215
| ~ spl16_41
| ~ spl16_211 ),
inference(avatar_split_clause,[],[f2582,f2550,f469,f2584]) ).
fof(f469,plain,
( spl16_41
<=> aElementOf0(xx,sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_41])]) ).
fof(f2582,plain,
( sP0(sF15,xS)
| ~ spl16_41
| ~ spl16_211 ),
inference(subsumption_resolution,[],[f2581,f89]) ).
fof(f2581,plain,
( sP0(sF15,xS)
| ~ aSet0(xS)
| ~ spl16_41
| ~ spl16_211 ),
inference(subsumption_resolution,[],[f2578,f470]) ).
fof(f470,plain,
( aElementOf0(xx,sF15)
| ~ spl16_41 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f2578,plain,
( ~ aElementOf0(xx,sF15)
| sP0(sF15,xS)
| ~ aSet0(xS)
| ~ spl16_211 ),
inference(superposition,[],[f99,f2551]) ).
fof(f2551,plain,
( xx = sK10(sF15,xS)
| ~ spl16_211 ),
inference(avatar_component_clause,[],[f2550]) ).
fof(f1936,plain,
( spl16_29
| ~ spl16_9
| ~ spl16_24 ),
inference(avatar_split_clause,[],[f1935,f323,f211,f347]) ).
fof(f347,plain,
( spl16_29
<=> ! [X0] :
( aElementOf0(sK10(X0,sF15),sF14)
| xx = sK10(X0,sF15)
| sP0(X0,sF15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_29])]) ).
fof(f211,plain,
( spl16_9
<=> aSet0(sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_9])]) ).
fof(f323,plain,
( spl16_24
<=> ! [X0] :
( ~ aElementOf0(X0,sF15)
| aElementOf0(X0,sF14)
| xx = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_24])]) ).
fof(f1935,plain,
( ! [X1] :
( aElementOf0(sK10(X1,sF15),sF14)
| xx = sK10(X1,sF15)
| sP0(X1,sF15) )
| ~ spl16_9
| ~ spl16_24 ),
inference(subsumption_resolution,[],[f1893,f212]) ).
fof(f212,plain,
( aSet0(sF15)
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f1893,plain,
( ! [X1] :
( aElementOf0(sK10(X1,sF15),sF14)
| xx = sK10(X1,sF15)
| sP0(X1,sF15)
| ~ aSet0(sF15) )
| ~ spl16_24 ),
inference(resolution,[],[f324,f98]) ).
fof(f324,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF15)
| aElementOf0(X0,sF14)
| xx = X0 )
| ~ spl16_24 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f1861,plain,
( spl16_63
| ~ spl16_22 ),
inference(avatar_split_clause,[],[f1759,f310,f686]) ).
fof(f310,plain,
( spl16_22
<=> ! [X0] :
( ~ sP2(X0,xx,xS)
| aElementOf0(X0,sF14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_22])]) ).
fof(f1759,plain,
( ! [X1] :
( aElementOf0(X1,sF14)
| xx = X1
| ~ aElementOf0(X1,xS)
| ~ aElement0(X1) )
| ~ spl16_22 ),
inference(resolution,[],[f311,f117]) ).
fof(f117,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| X0 = X1
| ~ aElementOf0(X0,X2)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| X0 = X1
| ~ aElementOf0(X0,X2)
| ~ aElement0(X0) )
& ( ( X0 != X1
& aElementOf0(X0,X2)
& aElement0(X0) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X3,X1,X0] :
( ( sP2(X3,X1,X0)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| ~ sP2(X3,X1,X0) ) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X3,X1,X0] :
( ( sP2(X3,X1,X0)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| ~ sP2(X3,X1,X0) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X3,X1,X0] :
( sP2(X3,X1,X0)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f311,plain,
( ! [X0] :
( ~ sP2(X0,xx,xS)
| aElementOf0(X0,sF14) )
| ~ spl16_22 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f938,plain,
( ~ spl16_90
| ~ spl16_9
| ~ spl16_89 ),
inference(avatar_split_clause,[],[f934,f927,f211,f936]) ).
fof(f927,plain,
( spl16_89
<=> aSubsetOf0(sF15,xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_89])]) ).
fof(f934,plain,
( ~ aSubsetOf0(xS,sF15)
| ~ spl16_9
| ~ spl16_89 ),
inference(subsumption_resolution,[],[f933,f89]) ).
fof(f933,plain,
( ~ aSubsetOf0(xS,sF15)
| ~ aSet0(xS)
| ~ spl16_9
| ~ spl16_89 ),
inference(subsumption_resolution,[],[f932,f212]) ).
fof(f932,plain,
( ~ aSubsetOf0(xS,sF15)
| ~ aSet0(sF15)
| ~ aSet0(xS)
| ~ spl16_89 ),
inference(subsumption_resolution,[],[f930,f143]) ).
fof(f143,plain,
xS != sF15,
inference(definition_folding,[],[f88,f142,f141]) ).
fof(f141,plain,
sdtmndt0(xS,xx) = sF14,
introduced(function_definition,[]) ).
fof(f142,plain,
sdtpldt0(sF14,xx) = sF15,
introduced(function_definition,[]) ).
fof(f88,plain,
xS != sdtpldt0(sdtmndt0(xS,xx),xx),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
xS != sdtpldt0(sdtmndt0(xS,xx),xx),
inference(flattening,[],[f20]) ).
fof(f20,negated_conjecture,
xS != sdtpldt0(sdtmndt0(xS,xx),xx),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
xS = sdtpldt0(sdtmndt0(xS,xx),xx),
file('/export/starexec/sandbox/tmp/tmp.giK0nLqnlo/Vampire---4.8_30712',m__) ).
fof(f930,plain,
( xS = sF15
| ~ aSubsetOf0(xS,sF15)
| ~ aSet0(sF15)
| ~ aSet0(xS)
| ~ spl16_89 ),
inference(resolution,[],[f928,f133]) ).
fof(f133,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| X0 = X1
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X0)
& aSubsetOf0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.giK0nLqnlo/Vampire---4.8_30712',mSubASymm) ).
fof(f928,plain,
( aSubsetOf0(sF15,xS)
| ~ spl16_89 ),
inference(avatar_component_clause,[],[f927]) ).
fof(f929,plain,
( spl16_89
| ~ spl16_87 ),
inference(avatar_split_clause,[],[f925,f905,f927]) ).
fof(f905,plain,
( spl16_87
<=> sP0(xS,sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_87])]) ).
fof(f925,plain,
( aSubsetOf0(sF15,xS)
| ~ spl16_87 ),
inference(subsumption_resolution,[],[f919,f144]) ).
fof(f144,plain,
sP1(xS),
inference(resolution,[],[f100,f89]) ).
fof(f100,plain,
! [X0] :
( ~ aSet0(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( sP1(X0)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f30,f43,f42]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.giK0nLqnlo/Vampire---4.8_30712',mDefSub) ).
fof(f919,plain,
( aSubsetOf0(sF15,xS)
| ~ sP1(xS)
| ~ spl16_87 ),
inference(resolution,[],[f906,f95]) ).
fof(f906,plain,
( sP0(xS,sF15)
| ~ spl16_87 ),
inference(avatar_component_clause,[],[f905]) ).
fof(f917,plain,
( spl16_87
| ~ spl16_9
| ~ spl16_86 ),
inference(avatar_split_clause,[],[f916,f902,f211,f905]) ).
fof(f902,plain,
( spl16_86
<=> xx = sK10(xS,sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_86])]) ).
fof(f916,plain,
( sP0(xS,sF15)
| ~ spl16_9
| ~ spl16_86 ),
inference(subsumption_resolution,[],[f915,f212]) ).
fof(f915,plain,
( sP0(xS,sF15)
| ~ aSet0(sF15)
| ~ spl16_86 ),
inference(subsumption_resolution,[],[f912,f90]) ).
fof(f90,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/tmp/tmp.giK0nLqnlo/Vampire---4.8_30712',m__617_02) ).
fof(f912,plain,
( ~ aElementOf0(xx,xS)
| sP0(xS,sF15)
| ~ aSet0(sF15)
| ~ spl16_86 ),
inference(superposition,[],[f99,f903]) ).
fof(f903,plain,
( xx = sK10(xS,sF15)
| ~ spl16_86 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f907,plain,
( spl16_86
| spl16_87
| ~ spl16_9
| ~ spl16_83 ),
inference(avatar_split_clause,[],[f900,f857,f211,f905,f902]) ).
fof(f857,plain,
( spl16_83
<=> ! [X1] :
( xx = sK10(X1,sF15)
| sP0(X1,sF15)
| aElementOf0(sK10(X1,sF15),xS) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_83])]) ).
fof(f900,plain,
( sP0(xS,sF15)
| xx = sK10(xS,sF15)
| ~ spl16_9
| ~ spl16_83 ),
inference(subsumption_resolution,[],[f899,f212]) ).
fof(f899,plain,
( sP0(xS,sF15)
| xx = sK10(xS,sF15)
| ~ aSet0(sF15)
| ~ spl16_83 ),
inference(duplicate_literal_removal,[],[f894]) ).
fof(f894,plain,
( sP0(xS,sF15)
| xx = sK10(xS,sF15)
| sP0(xS,sF15)
| ~ aSet0(sF15)
| ~ spl16_83 ),
inference(resolution,[],[f858,f99]) ).
fof(f858,plain,
( ! [X1] :
( aElementOf0(sK10(X1,sF15),xS)
| sP0(X1,sF15)
| xx = sK10(X1,sF15) )
| ~ spl16_83 ),
inference(avatar_component_clause,[],[f857]) ).
fof(f859,plain,
( spl16_83
| ~ spl16_13
| ~ spl16_29 ),
inference(avatar_split_clause,[],[f840,f347,f255,f857]) ).
fof(f255,plain,
( spl16_13
<=> ! [X0] :
( ~ aElementOf0(X0,sF14)
| aElementOf0(X0,xS) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_13])]) ).
fof(f840,plain,
( ! [X1] :
( xx = sK10(X1,sF15)
| sP0(X1,sF15)
| aElementOf0(sK10(X1,sF15),xS) )
| ~ spl16_13
| ~ spl16_29 ),
inference(resolution,[],[f348,f256]) ).
fof(f256,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF14)
| aElementOf0(X0,xS) )
| ~ spl16_13 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f348,plain,
( ! [X0] :
( aElementOf0(sK10(X0,sF15),sF14)
| xx = sK10(X0,sF15)
| sP0(X0,sF15) )
| ~ spl16_29 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f476,plain,
( spl16_42
| ~ spl16_14
| ~ spl16_36 ),
inference(avatar_split_clause,[],[f472,f398,f259,f474]) ).
fof(f259,plain,
( spl16_14
<=> ! [X1] :
( ~ aElementOf0(X1,sF14)
| aElement0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_14])]) ).
fof(f398,plain,
( spl16_36
<=> ! [X0] :
( ~ sP6(X0,xx,sF14)
| aElementOf0(X0,sF15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_36])]) ).
fof(f472,plain,
( ! [X1] :
( aElementOf0(X1,sF15)
| ~ aElementOf0(X1,sF14) )
| ~ spl16_14
| ~ spl16_36 ),
inference(subsumption_resolution,[],[f466,f260]) ).
fof(f260,plain,
( ! [X1] :
( ~ aElementOf0(X1,sF14)
| aElement0(X1) )
| ~ spl16_14 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f466,plain,
( ! [X1] :
( aElementOf0(X1,sF15)
| ~ aElementOf0(X1,sF14)
| ~ aElement0(X1) )
| ~ spl16_36 ),
inference(resolution,[],[f399,f130]) ).
fof(f130,plain,
! [X2,X0,X1] :
( sP6(X0,X1,X2)
| ~ aElementOf0(X0,X2)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( sP6(X0,X1,X2)
| ( X0 != X1
& ~ aElementOf0(X0,X2) )
| ~ aElement0(X0) )
& ( ( ( X0 = X1
| aElementOf0(X0,X2) )
& aElement0(X0) )
| ~ sP6(X0,X1,X2) ) ),
inference(rectify,[],[f86]) ).
fof(f86,plain,
! [X3,X1,X0] :
( ( sP6(X3,X1,X0)
| ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3) )
& ( ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) )
| ~ sP6(X3,X1,X0) ) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X3,X1,X0] :
( ( sP6(X3,X1,X0)
| ( X1 != X3
& ~ aElementOf0(X3,X0) )
| ~ aElement0(X3) )
& ( ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) )
| ~ sP6(X3,X1,X0) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X3,X1,X0] :
( sP6(X3,X1,X0)
<=> ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f399,plain,
( ! [X0] :
( ~ sP6(X0,xx,sF14)
| aElementOf0(X0,sF15) )
| ~ spl16_36 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f471,plain,
( spl16_41
| ~ spl16_36 ),
inference(avatar_split_clause,[],[f467,f398,f469]) ).
fof(f467,plain,
( aElementOf0(xx,sF15)
| ~ spl16_36 ),
inference(subsumption_resolution,[],[f465,f148]) ).
fof(f148,plain,
aElement0(xx),
inference(subsumption_resolution,[],[f147,f89]) ).
fof(f147,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f93,f90]) ).
fof(f465,plain,
( aElementOf0(xx,sF15)
| ~ aElement0(xx)
| ~ spl16_36 ),
inference(resolution,[],[f399,f140]) ).
fof(f140,plain,
! [X2,X1] :
( sP6(X1,X1,X2)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f131]) ).
fof(f131,plain,
! [X2,X0,X1] :
( sP6(X0,X1,X2)
| X0 != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f400,plain,
( spl16_36
| ~ spl16_8 ),
inference(avatar_split_clause,[],[f390,f207,f398]) ).
fof(f207,plain,
( spl16_8
<=> sP7(sF14,xx,sF15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_8])]) ).
fof(f390,plain,
( ! [X0] :
( ~ sP6(X0,xx,sF14)
| aElementOf0(X0,sF15) )
| ~ spl16_8 ),
inference(resolution,[],[f125,f208]) ).
fof(f208,plain,
( sP7(sF14,xx,sF15)
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( ~ sP7(X0,X1,X2)
| ~ sP6(X4,X1,X0)
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ( ( ~ sP6(sK13(X0,X1,X2),X1,X0)
| ~ aElementOf0(sK13(X0,X1,X2),X2) )
& ( sP6(sK13(X0,X1,X2),X1,X0)
| aElementOf0(sK13(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ sP6(X4,X1,X0) )
& ( sP6(X4,X1,X0)
| ~ aElementOf0(X4,X2) ) )
| ~ sP7(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f82,f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP6(X3,X1,X0)
| ~ aElementOf0(X3,X2) )
& ( sP6(X3,X1,X0)
| aElementOf0(X3,X2) ) )
=> ( ( ~ sP6(sK13(X0,X1,X2),X1,X0)
| ~ aElementOf0(sK13(X0,X1,X2),X2) )
& ( sP6(sK13(X0,X1,X2),X1,X0)
| aElementOf0(sK13(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ? [X3] :
( ( ~ sP6(X3,X1,X0)
| ~ aElementOf0(X3,X2) )
& ( sP6(X3,X1,X0)
| aElementOf0(X3,X2) ) ) )
& ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ sP6(X4,X1,X0) )
& ( sP6(X4,X1,X0)
| ~ aElementOf0(X4,X2) ) )
| ~ sP7(X0,X1,X2) ) ),
inference(rectify,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ? [X3] :
( ( ~ sP6(X3,X1,X0)
| ~ aElementOf0(X3,X2) )
& ( sP6(X3,X1,X0)
| aElementOf0(X3,X2) ) ) )
& ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ sP6(X3,X1,X0) )
& ( sP6(X3,X1,X0)
| ~ aElementOf0(X3,X2) ) )
| ~ sP7(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( sP7(X0,X1,X2)
<=> ! [X3] :
( aElementOf0(X3,X2)
<=> sP6(X3,X1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f325,plain,
( spl16_24
| ~ spl16_23 ),
inference(avatar_split_clause,[],[f320,f317,f323]) ).
fof(f317,plain,
( spl16_23
<=> ! [X0] :
( ~ aElementOf0(X0,sF15)
| sP6(X0,xx,sF14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_23])]) ).
fof(f320,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF15)
| aElementOf0(X0,sF14)
| xx = X0 )
| ~ spl16_23 ),
inference(resolution,[],[f318,f129]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1,X2)
| aElementOf0(X0,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f87]) ).
fof(f318,plain,
( ! [X0] :
( sP6(X0,xx,sF14)
| ~ aElementOf0(X0,sF15) )
| ~ spl16_23 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f319,plain,
( spl16_23
| ~ spl16_8 ),
inference(avatar_split_clause,[],[f314,f207,f317]) ).
fof(f314,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF15)
| sP6(X0,xx,sF14) )
| ~ spl16_8 ),
inference(resolution,[],[f124,f208]) ).
fof(f124,plain,
! [X2,X0,X1,X4] :
( ~ sP7(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| sP6(X4,X1,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f312,plain,
( spl16_22
| ~ spl16_3 ),
inference(avatar_split_clause,[],[f307,f175,f310]) ).
fof(f175,plain,
( spl16_3
<=> sP3(xS,xx,sF14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).
fof(f307,plain,
( ! [X0] :
( ~ sP2(X0,xx,xS)
| aElementOf0(X0,sF14) )
| ~ spl16_3 ),
inference(resolution,[],[f111,f176]) ).
fof(f176,plain,
( sP3(xS,xx,sF14)
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f111,plain,
! [X2,X0,X1,X4] :
( ~ sP3(X0,X1,X2)
| ~ sP2(X4,X1,X0)
| aElementOf0(X4,X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ( ~ sP2(sK12(X0,X1,X2),X1,X0)
| ~ aElementOf0(sK12(X0,X1,X2),X2) )
& ( sP2(sK12(X0,X1,X2),X1,X0)
| aElementOf0(sK12(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ sP2(X4,X1,X0) )
& ( sP2(X4,X1,X0)
| ~ aElementOf0(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f71,f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP2(X3,X1,X0)
| ~ aElementOf0(X3,X2) )
& ( sP2(X3,X1,X0)
| aElementOf0(X3,X2) ) )
=> ( ( ~ sP2(sK12(X0,X1,X2),X1,X0)
| ~ aElementOf0(sK12(X0,X1,X2),X2) )
& ( sP2(sK12(X0,X1,X2),X1,X0)
| aElementOf0(sK12(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ( ~ sP2(X3,X1,X0)
| ~ aElementOf0(X3,X2) )
& ( sP2(X3,X1,X0)
| aElementOf0(X3,X2) ) ) )
& ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ sP2(X4,X1,X0) )
& ( sP2(X4,X1,X0)
| ~ aElementOf0(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ( ~ sP2(X3,X1,X0)
| ~ aElementOf0(X3,X2) )
& ( sP2(X3,X1,X0)
| aElementOf0(X3,X2) ) ) )
& ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ sP2(X3,X1,X0) )
& ( sP2(X3,X1,X0)
| ~ aElementOf0(X3,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( sP3(X0,X1,X2)
<=> ! [X3] :
( aElementOf0(X3,X2)
<=> sP2(X3,X1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f261,plain,
( spl16_14
| ~ spl16_11 ),
inference(avatar_split_clause,[],[f249,f244,f259]) ).
fof(f244,plain,
( spl16_11
<=> ! [X0] :
( ~ aElementOf0(X0,sF14)
| sP2(X0,xx,xS) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_11])]) ).
fof(f249,plain,
( ! [X1] :
( ~ aElementOf0(X1,sF14)
| aElement0(X1) )
| ~ spl16_11 ),
inference(resolution,[],[f245,f114]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| aElement0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f245,plain,
( ! [X0] :
( sP2(X0,xx,xS)
| ~ aElementOf0(X0,sF14) )
| ~ spl16_11 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f257,plain,
( spl16_13
| ~ spl16_11 ),
inference(avatar_split_clause,[],[f248,f244,f255]) ).
fof(f248,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF14)
| aElementOf0(X0,xS) )
| ~ spl16_11 ),
inference(resolution,[],[f245,f115]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| aElementOf0(X0,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f246,plain,
( spl16_11
| ~ spl16_3 ),
inference(avatar_split_clause,[],[f241,f175,f244]) ).
fof(f241,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF14)
| sP2(X0,xx,xS) )
| ~ spl16_3 ),
inference(resolution,[],[f110,f176]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( ~ sP3(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| sP2(X4,X1,X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f218,plain,
( spl16_10
| ~ spl16_9 ),
inference(avatar_split_clause,[],[f214,f211,f216]) ).
fof(f214,plain,
( sP1(sF15)
| ~ spl16_9 ),
inference(resolution,[],[f212,f100]) ).
fof(f213,plain,
( spl16_9
| ~ spl16_7 ),
inference(avatar_split_clause,[],[f205,f197,f211]) ).
fof(f197,plain,
( spl16_7
<=> sP8(sF15,xx,sF14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_7])]) ).
fof(f205,plain,
( aSet0(sF15)
| ~ spl16_7 ),
inference(resolution,[],[f198,f121]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( sP8(X0,X1,X2)
| ~ sP7(X2,X1,X0)
| ~ aSet0(X0) )
& ( ( sP7(X2,X1,X0)
& aSet0(X0) )
| ~ sP8(X0,X1,X2) ) ),
inference(rectify,[],[f79]) ).
fof(f79,plain,
! [X2,X1,X0] :
( ( sP8(X2,X1,X0)
| ~ sP7(X0,X1,X2)
| ~ aSet0(X2) )
& ( ( sP7(X0,X1,X2)
& aSet0(X2) )
| ~ sP8(X2,X1,X0) ) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X2,X1,X0] :
( ( sP8(X2,X1,X0)
| ~ sP7(X0,X1,X2)
| ~ aSet0(X2) )
& ( ( sP7(X0,X1,X2)
& aSet0(X2) )
| ~ sP8(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X2,X1,X0] :
( sP8(X2,X1,X0)
<=> ( sP7(X0,X1,X2)
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f198,plain,
( sP8(sF15,xx,sF14)
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f209,plain,
( spl16_8
| ~ spl16_7 ),
inference(avatar_split_clause,[],[f204,f197,f207]) ).
fof(f204,plain,
( sP7(sF14,xx,sF15)
| ~ spl16_7 ),
inference(resolution,[],[f198,f122]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| sP7(X2,X1,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f203,plain,
( ~ spl16_4
| spl16_6 ),
inference(avatar_contradiction_clause,[],[f202]) ).
fof(f202,plain,
( $false
| ~ spl16_4
| spl16_6 ),
inference(subsumption_resolution,[],[f201,f180]) ).
fof(f180,plain,
( aSet0(sF14)
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f179,plain,
( spl16_4
<=> aSet0(sF14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f201,plain,
( ~ aSet0(sF14)
| spl16_6 ),
inference(subsumption_resolution,[],[f200,f148]) ).
fof(f200,plain,
( ~ aElement0(xx)
| ~ aSet0(sF14)
| spl16_6 ),
inference(resolution,[],[f195,f132]) ).
fof(f132,plain,
! [X0,X1] :
( sP9(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( sP9(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f37,f53,f52,f51,f50]) ).
fof(f53,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt0(X0,X1) = X2
<=> sP8(X2,X1,X0) )
| ~ sP9(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f37,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtpldt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ( X1 = X3
| aElementOf0(X3,X0) )
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.giK0nLqnlo/Vampire---4.8_30712',mDefCons) ).
fof(f195,plain,
( ~ sP9(sF14,xx)
| spl16_6 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f194,plain,
( spl16_6
<=> sP9(sF14,xx) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).
fof(f199,plain,
( ~ spl16_6
| spl16_7 ),
inference(avatar_split_clause,[],[f192,f197,f194]) ).
fof(f192,plain,
( sP8(sF15,xx,sF14)
| ~ sP9(sF14,xx) ),
inference(superposition,[],[f139,f142]) ).
fof(f139,plain,
! [X0,X1] :
( sP8(sdtpldt0(X0,X1),X1,X0)
| ~ sP9(X0,X1) ),
inference(equality_resolution,[],[f119]) ).
fof(f119,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sdtpldt0(X0,X1) != X2
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X0,X1) = X2
| ~ sP8(X2,X1,X0) )
& ( sP8(X2,X1,X0)
| sdtpldt0(X0,X1) != X2 ) )
| ~ sP9(X0,X1) ),
inference(nnf_transformation,[],[f53]) ).
fof(f181,plain,
( spl16_4
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f173,f165,f179]) ).
fof(f165,plain,
( spl16_2
<=> sP4(sF14,xx,xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).
fof(f173,plain,
( aSet0(sF14)
| ~ spl16_2 ),
inference(resolution,[],[f166,f107]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ~ sP3(X2,X1,X0)
| ~ aSet0(X0) )
& ( ( sP3(X2,X1,X0)
& aSet0(X0) )
| ~ sP4(X0,X1,X2) ) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X2,X1,X0] :
( ( sP4(X2,X1,X0)
| ~ sP3(X0,X1,X2)
| ~ aSet0(X2) )
& ( ( sP3(X0,X1,X2)
& aSet0(X2) )
| ~ sP4(X2,X1,X0) ) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X2,X1,X0] :
( ( sP4(X2,X1,X0)
| ~ sP3(X0,X1,X2)
| ~ aSet0(X2) )
& ( ( sP3(X0,X1,X2)
& aSet0(X2) )
| ~ sP4(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X2,X1,X0] :
( sP4(X2,X1,X0)
<=> ( sP3(X0,X1,X2)
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f166,plain,
( sP4(sF14,xx,xS)
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f177,plain,
( spl16_3
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f172,f165,f175]) ).
fof(f172,plain,
( sP3(xS,xx,sF14)
| ~ spl16_2 ),
inference(resolution,[],[f166,f108]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| sP3(X2,X1,X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f171,plain,
spl16_1,
inference(avatar_contradiction_clause,[],[f170]) ).
fof(f170,plain,
( $false
| spl16_1 ),
inference(subsumption_resolution,[],[f169,f89]) ).
fof(f169,plain,
( ~ aSet0(xS)
| spl16_1 ),
inference(subsumption_resolution,[],[f168,f148]) ).
fof(f168,plain,
( ~ aElement0(xx)
| ~ aSet0(xS)
| spl16_1 ),
inference(resolution,[],[f163,f118]) ).
fof(f118,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f35,f48,f47,f46,f45]) ).
fof(f48,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> sP4(X2,X1,X0) )
| ~ sP5(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f35,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.giK0nLqnlo/Vampire---4.8_30712',mDefDiff) ).
fof(f163,plain,
( ~ sP5(xS,xx)
| spl16_1 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f162,plain,
( spl16_1
<=> sP5(xS,xx) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).
fof(f167,plain,
( ~ spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f160,f165,f162]) ).
fof(f160,plain,
( sP4(sF14,xx,xS)
| ~ sP5(xS,xx) ),
inference(superposition,[],[f137,f141]) ).
fof(f137,plain,
! [X0,X1] :
( sP4(sdtmndt0(X0,X1),X1,X0)
| ~ sP5(X0,X1) ),
inference(equality_resolution,[],[f105]) ).
fof(f105,plain,
! [X2,X0,X1] :
( sP4(X2,X1,X0)
| sdtmndt0(X0,X1) != X2
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ~ sP4(X2,X1,X0) )
& ( sP4(X2,X1,X0)
| sdtmndt0(X0,X1) != X2 ) )
| ~ sP5(X0,X1) ),
inference(nnf_transformation,[],[f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM534+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.17/0.35 % Computer : n027.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Fri Aug 25 16:28:19 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.17/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.17/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.giK0nLqnlo/Vampire---4.8_30712
% 0.17/0.36 % (30827)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (30834)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.21/0.42 % (30832)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.21/0.42 % (30831)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.21/0.42 % (30830)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.21/0.42 % (30833)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.21/0.43 % (30831)Refutation not found, incomplete strategy% (30831)------------------------------
% 0.21/0.43 % (30831)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.43 % (30831)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.43 % (30831)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.43
% 0.21/0.43 % (30831)Memory used [KB]: 9978
% 0.21/0.43 % (30831)Time elapsed: 0.006 s
% 0.21/0.43 % (30831)------------------------------
% 0.21/0.43 % (30831)------------------------------
% 0.21/0.44 % (30828)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.21/0.46 % (30829)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.21/0.48 % (30830)Refutation not found, incomplete strategy% (30830)------------------------------
% 0.21/0.48 % (30830)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.48 % (30830)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.48 % (30830)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.48
% 0.21/0.48 % (30830)Memory used [KB]: 1023
% 0.21/0.48 % (30830)Time elapsed: 0.056 s
% 0.21/0.48 % (30830)------------------------------
% 0.21/0.48 % (30830)------------------------------
% 0.21/0.49 % (30835)ott+10_5_av=off:bsr=on:br=off:drc=off:fsd=off:fsr=off:fde=unused:gsp=on:lcm=predicate:lma=on:nwc=2.5:sos=all:sp=occurrence:tgt=full:urr=on_375 on Vampire---4 for (375ds/0Mi)
% 0.21/0.51 % (30836)lrs-1010_3_aac=none:anc=none:er=known:fsd=off:fde=unused:gs=on:lcm=predicate:sos=on:sp=weighted_frequency:tgt=ground:stl=62_365 on Vampire---4 for (365ds/0Mi)
% 0.21/0.51 % (30836)Refutation not found, incomplete strategy% (30836)------------------------------
% 0.21/0.51 % (30836)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.51 % (30836)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.51 % (30836)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.51
% 0.21/0.52 % (30836)Memory used [KB]: 9978
% 0.21/0.52 % (30836)Time elapsed: 0.003 s
% 0.21/0.52 % (30836)------------------------------
% 0.21/0.52 % (30836)------------------------------
% 0.21/0.55 % (30837)ott+10_128_aac=none:add=large:afr=on:anc=all_dependent:bsr=on:bce=on:fsd=off:irw=on:nm=2:nwc=1.5:sp=scramble:tgt=full_251 on Vampire---4 for (251ds/0Mi)
% 6.13/1.38 % (30837)First to succeed.
% 6.13/1.39 % (30837)Refutation found. Thanks to Tanya!
% 6.13/1.39 % SZS status Theorem for Vampire---4
% 6.13/1.39 % SZS output start Proof for Vampire---4
% See solution above
% 6.13/1.39 % (30837)------------------------------
% 6.13/1.39 % (30837)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 6.13/1.39 % (30837)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 6.13/1.39 % (30837)Termination reason: Refutation
% 6.13/1.39
% 6.13/1.39 % (30837)Memory used [KB]: 29807
% 6.13/1.39 % (30837)Time elapsed: 0.834 s
% 6.13/1.39 % (30837)------------------------------
% 6.13/1.39 % (30837)------------------------------
% 6.13/1.39 % (30827)Success in time 1.018 s
% 6.13/1.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------