TSTP Solution File: COM013+4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM013+4 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 : Mon May 20 19:11:20 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 41
% Syntax : Number of formulae : 190 ( 8 unt; 0 def)
% Number of atoms : 932 ( 42 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 1156 ( 414 ~; 435 |; 248 &)
% ( 30 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 21 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 2 con; 0-3 aty)
% Number of variables : 308 ( 233 !; 75 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f497,plain,
$false,
inference(avatar_sat_refutation,[],[f197,f209,f221,f225,f255,f259,f274,f277,f306,f340,f416,f419,f443,f494]) ).
fof(f494,plain,
~ spl27_8,
inference(avatar_contradiction_clause,[],[f493]) ).
fof(f493,plain,
( $false
| ~ spl27_8 ),
inference(subsumption_resolution,[],[f492,f177]) ).
fof(f177,plain,
! [X1] : ~ sP2(X1,X1),
inference(equality_resolution,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( X0 != X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ( ~ sdtmndtasgtdt0(X1,xR,X0)
& ~ sdtmndtplgtdt0(X1,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,X1,xR)
& X0 != X1 )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f60]) ).
fof(f60,plain,
! [X5,X0] :
( ( ~ sdtmndtasgtdt0(X0,xR,X5)
& ~ sdtmndtplgtdt0(X0,xR,X5)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X5)
| ~ aReductOfIn0(X7,X0,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X5,X0,xR)
& X0 != X5 )
| ~ sP2(X5,X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X5,X0] :
( ( ~ sdtmndtasgtdt0(X0,xR,X5)
& ~ sdtmndtplgtdt0(X0,xR,X5)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X5)
| ~ aReductOfIn0(X7,X0,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X5,X0,xR)
& X0 != X5 )
| ~ sP2(X5,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f492,plain,
( sP2(sK13,sK13)
| ~ spl27_8 ),
inference(subsumption_resolution,[],[f489,f118]) ).
fof(f118,plain,
aElement0(sK13),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
( ! [X1] :
( ~ aNormalFormOfIn0(X1,sK13,xR)
& ( aReductOfIn0(sK14(X1),X1,xR)
| sP2(X1,sK13)
| ~ aElement0(X1) ) )
& ! [X3] :
( sP1(X3)
| ~ iLess0(X3,sK13)
| ~ aElement0(X3) )
& aElement0(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f70,f72,f71]) ).
fof(f71,plain,
( ? [X0] :
( ! [X1] :
( ~ aNormalFormOfIn0(X1,X0,xR)
& ( ? [X2] : aReductOfIn0(X2,X1,xR)
| sP2(X1,X0)
| ~ aElement0(X1) ) )
& ! [X3] :
( sP1(X3)
| ~ iLess0(X3,X0)
| ~ aElement0(X3) )
& aElement0(X0) )
=> ( ! [X1] :
( ~ aNormalFormOfIn0(X1,sK13,xR)
& ( ? [X2] : aReductOfIn0(X2,X1,xR)
| sP2(X1,sK13)
| ~ aElement0(X1) ) )
& ! [X3] :
( sP1(X3)
| ~ iLess0(X3,sK13)
| ~ aElement0(X3) )
& aElement0(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X1] :
( ? [X2] : aReductOfIn0(X2,X1,xR)
=> aReductOfIn0(sK14(X1),X1,xR) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
? [X0] :
( ! [X1] :
( ~ aNormalFormOfIn0(X1,X0,xR)
& ( ? [X2] : aReductOfIn0(X2,X1,xR)
| sP2(X1,X0)
| ~ aElement0(X1) ) )
& ! [X3] :
( sP1(X3)
| ~ iLess0(X3,X0)
| ~ aElement0(X3) )
& aElement0(X0) ),
inference(rectify,[],[f47]) ).
fof(f47,plain,
? [X0] :
( ! [X5] :
( ~ aNormalFormOfIn0(X5,X0,xR)
& ( ? [X6] : aReductOfIn0(X6,X5,xR)
| sP2(X5,X0)
| ~ aElement0(X5) ) )
& ! [X1] :
( sP1(X1)
| ~ iLess0(X1,X0)
| ~ aElement0(X1) )
& aElement0(X0) ),
inference(definition_folding,[],[f23,f46,f45,f44]) ).
fof(f44,plain,
! [X2,X1] :
( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X2)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2
| ~ sP0(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f45,plain,
! [X1] :
( ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ! [X3] : ~ aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& sP0(X2,X1)
& aElement0(X2) )
| ~ sP1(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f23,plain,
? [X0] :
( ! [X5] :
( ~ aNormalFormOfIn0(X5,X0,xR)
& ( ? [X6] : aReductOfIn0(X6,X5,xR)
| ( ~ sdtmndtasgtdt0(X0,xR,X5)
& ~ sdtmndtplgtdt0(X0,xR,X5)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X5)
| ~ aReductOfIn0(X7,X0,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X5,X0,xR)
& X0 != X5 )
| ~ aElement0(X5) ) )
& ! [X1] :
( ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ! [X3] : ~ aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X2)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) )
| ~ iLess0(X1,X0)
| ~ aElement0(X1) )
& aElement0(X0) ),
inference(flattening,[],[f22]) ).
fof(f22,plain,
? [X0] :
( ! [X5] :
( ~ aNormalFormOfIn0(X5,X0,xR)
& ( ? [X6] : aReductOfIn0(X6,X5,xR)
| ( ~ sdtmndtasgtdt0(X0,xR,X5)
& ~ sdtmndtplgtdt0(X0,xR,X5)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X5)
| ~ aReductOfIn0(X7,X0,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X5,X0,xR)
& X0 != X5 )
| ~ aElement0(X5) ) )
& ! [X1] :
( ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ! [X3] : ~ aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X2)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) )
| ~ iLess0(X1,X0)
| ~ aElement0(X1) )
& aElement0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
~ ! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ~ ? [X3] : aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X2)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) ) )
=> ? [X5] :
( aNormalFormOfIn0(X5,X0,xR)
| ( ~ ? [X6] : aReductOfIn0(X6,X5,xR)
& ( sdtmndtasgtdt0(X0,xR,X5)
| sdtmndtplgtdt0(X0,xR,X5)
| ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X0,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X0,xR)
| X0 = X5 )
& aElement0(X5) ) ) ) ),
inference(rectify,[],[f16]) ).
fof(f16,negated_conjecture,
~ ! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ~ ? [X3] : aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X1,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) ) )
=> ? [X1] :
( aNormalFormOfIn0(X1,X0,xR)
| ( ~ ? [X2] : aReductOfIn0(X2,X1,xR)
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X1) ) ) ) ),
inference(negated_conjecture,[],[f15]) ).
fof(f15,conjecture,
! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ~ ? [X3] : aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& ( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X1,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2 )
& aElement0(X2) ) ) )
=> ? [X1] :
( aNormalFormOfIn0(X1,X0,xR)
| ( ~ ? [X2] : aReductOfIn0(X2,X1,xR)
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f489,plain,
( ~ aElement0(sK13)
| sP2(sK13,sK13)
| ~ spl27_8 ),
inference(resolution,[],[f478,f183]) ).
fof(f183,plain,
! [X0] :
( ~ sP2(sK14(X0),X0)
| ~ aElement0(X0)
| sP2(X0,sK13) ),
inference(resolution,[],[f120,f105]) ).
fof(f105,plain,
! [X0,X1] :
( ~ aReductOfIn0(X0,X1,xR)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f120,plain,
! [X1] :
( aReductOfIn0(sK14(X1),X1,xR)
| sP2(X1,sK13)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f478,plain,
( sP2(sK14(sK13),sK13)
| ~ spl27_8 ),
inference(subsumption_resolution,[],[f465,f254]) ).
fof(f254,plain,
( sP1(sK14(sK13))
| ~ spl27_8 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f252,plain,
( spl27_8
<=> sP1(sK14(sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_8])]) ).
fof(f465,plain,
( sP2(sK14(sK13),sK13)
| ~ sP1(sK14(sK13))
| ~ spl27_8 ),
inference(superposition,[],[f185,f457]) ).
fof(f457,plain,
( sK14(sK13) = sK11(sK14(sK13))
| ~ spl27_8 ),
inference(subsumption_resolution,[],[f456,f254]) ).
fof(f456,plain,
( sK14(sK13) = sK11(sK14(sK13))
| ~ sP1(sK14(sK13)) ),
inference(subsumption_resolution,[],[f455,f118]) ).
fof(f455,plain,
( sK14(sK13) = sK11(sK14(sK13))
| ~ aElement0(sK13)
| ~ sP1(sK14(sK13)) ),
inference(subsumption_resolution,[],[f454,f177]) ).
fof(f454,plain,
( sK14(sK13) = sK11(sK14(sK13))
| sP2(sK13,sK13)
| ~ aElement0(sK13)
| ~ sP1(sK14(sK13)) ),
inference(duplicate_literal_removal,[],[f453]) ).
fof(f453,plain,
( sK14(sK13) = sK11(sK14(sK13))
| sP2(sK13,sK13)
| ~ aElement0(sK13)
| ~ sP1(sK14(sK13))
| ~ sP1(sK14(sK13)) ),
inference(resolution,[],[f452,f185]) ).
fof(f452,plain,
! [X0] :
( ~ sP2(sK11(sK14(X0)),X0)
| sK14(X0) = sK11(sK14(X0))
| sP2(X0,sK13)
| ~ aElement0(X0)
| ~ sP1(sK14(X0)) ),
inference(resolution,[],[f450,f110]) ).
fof(f110,plain,
! [X0] :
( sP0(sK11(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( aNormalFormOfIn0(sK11(X0),X0,xR)
& ! [X2] : ~ aReductOfIn0(X2,sK11(X0),xR)
& sdtmndtasgtdt0(X0,xR,sK11(X0))
& sP0(sK11(X0),X0)
& aElement0(sK11(X0)) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f63,f64]) ).
fof(f64,plain,
! [X0] :
( ? [X1] :
( aNormalFormOfIn0(X1,X0,xR)
& ! [X2] : ~ aReductOfIn0(X2,X1,xR)
& sdtmndtasgtdt0(X0,xR,X1)
& sP0(X1,X0)
& aElement0(X1) )
=> ( aNormalFormOfIn0(sK11(X0),X0,xR)
& ! [X2] : ~ aReductOfIn0(X2,sK11(X0),xR)
& sdtmndtasgtdt0(X0,xR,sK11(X0))
& sP0(sK11(X0),X0)
& aElement0(sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0] :
( ? [X1] :
( aNormalFormOfIn0(X1,X0,xR)
& ! [X2] : ~ aReductOfIn0(X2,X1,xR)
& sdtmndtasgtdt0(X0,xR,X1)
& sP0(X1,X0)
& aElement0(X1) )
| ~ sP1(X0) ),
inference(rectify,[],[f62]) ).
fof(f62,plain,
! [X1] :
( ? [X2] :
( aNormalFormOfIn0(X2,X1,xR)
& ! [X3] : ~ aReductOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(X1,xR,X2)
& sP0(X2,X1)
& aElement0(X2) )
| ~ sP1(X1) ),
inference(nnf_transformation,[],[f45]) ).
fof(f450,plain,
! [X0,X1] :
( ~ sP0(X1,sK14(X0))
| sK14(X0) = X1
| ~ sP2(X1,X0)
| sP2(X0,sK13)
| ~ aElement0(X0) ),
inference(subsumption_resolution,[],[f445,f235]) ).
fof(f235,plain,
! [X0] :
( aElement0(sK14(X0))
| ~ aElement0(X0)
| sP2(X0,sK13) ),
inference(subsumption_resolution,[],[f234,f122]) ).
fof(f122,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( iLess0(X1,X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| ~ aElement0(X1)
| ~ aElement0(X0) )
& aRewritingSystem0(xR) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( iLess0(X1,X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| ~ aElement0(X1)
| ~ aElement0(X0) )
& aRewritingSystem0(xR) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
( isTerminating0(xR)
& ! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( ( sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR) )
=> iLess0(X1,X0) ) )
& aRewritingSystem0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__587) ).
fof(f234,plain,
! [X0] :
( aElement0(sK14(X0))
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0)
| sP2(X0,sK13) ),
inference(duplicate_literal_removal,[],[f231]) ).
fof(f231,plain,
! [X0] :
( aElement0(sK14(X0))
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0)
| sP2(X0,sK13)
| ~ aElement0(X0) ),
inference(resolution,[],[f159,f120]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( ( aRewritingSystem0(X1)
& aElement0(X0) )
=> ! [X2] :
( aReductOfIn0(X2,X0,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).
fof(f445,plain,
! [X0,X1] :
( ~ aElement0(sK14(X0))
| ~ sP2(X1,X0)
| sK14(X0) = X1
| ~ sP0(X1,sK14(X0))
| sP2(X0,sK13)
| ~ aElement0(X0) ),
inference(resolution,[],[f285,f120]) ).
fof(f285,plain,
! [X2,X0,X1] :
( ~ aReductOfIn0(X0,X1,xR)
| ~ aElement0(X0)
| ~ sP2(X2,X1)
| X0 = X2
| ~ sP0(X2,X0) ),
inference(resolution,[],[f106,f117]) ).
fof(f117,plain,
! [X0,X1] :
( sdtmndtplgtdt0(X1,xR,X0)
| X0 = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ( sdtmndtplgtdt0(X1,xR,X0)
& ( ( sdtmndtplgtdt0(sK12(X0,X1),xR,X0)
& aReductOfIn0(sK12(X0,X1),X1,xR)
& aElement0(sK12(X0,X1)) )
| aReductOfIn0(X0,X1,xR) ) )
| X0 = X1
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f67,f68]) ).
fof(f68,plain,
! [X0,X1] :
( ? [X2] :
( sdtmndtplgtdt0(X2,xR,X0)
& aReductOfIn0(X2,X1,xR)
& aElement0(X2) )
=> ( sdtmndtplgtdt0(sK12(X0,X1),xR,X0)
& aReductOfIn0(sK12(X0,X1),X1,xR)
& aElement0(sK12(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0,X1] :
( ( sdtmndtplgtdt0(X1,xR,X0)
& ( ? [X2] :
( sdtmndtplgtdt0(X2,xR,X0)
& aReductOfIn0(X2,X1,xR)
& aElement0(X2) )
| aReductOfIn0(X0,X1,xR) ) )
| X0 = X1
| ~ sP0(X0,X1) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
! [X2,X1] :
( ( sdtmndtplgtdt0(X1,xR,X2)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X2)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X2,X1,xR) ) )
| X1 = X2
| ~ sP0(X2,X1) ),
inference(nnf_transformation,[],[f44]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(X2)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f185,plain,
! [X0] :
( sP2(sK11(X0),sK13)
| ~ sP1(X0) ),
inference(subsumption_resolution,[],[f184,f109]) ).
fof(f109,plain,
! [X0] :
( aElement0(sK11(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f184,plain,
! [X0] :
( sP2(sK11(X0),sK13)
| ~ aElement0(sK11(X0))
| ~ sP1(X0) ),
inference(resolution,[],[f120,f112]) ).
fof(f112,plain,
! [X2,X0] :
( ~ aReductOfIn0(X2,sK11(X0),xR)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f443,plain,
( ~ spl27_19
| spl27_20
| spl27_18 ),
inference(avatar_split_clause,[],[f432,f413,f440,f436]) ).
fof(f436,plain,
( spl27_19
<=> sP0(sK11(sK17(xR)),sK16(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_19])]) ).
fof(f440,plain,
( spl27_20
<=> sK16(xR) = sK11(sK17(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_20])]) ).
fof(f413,plain,
( spl27_18
<=> sdtmndtplgtdt0(sK16(xR),xR,sK11(sK17(xR))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_18])]) ).
fof(f432,plain,
( sK16(xR) = sK11(sK17(xR))
| ~ sP0(sK11(sK17(xR)),sK16(xR))
| spl27_18 ),
inference(resolution,[],[f415,f117]) ).
fof(f415,plain,
( ~ sdtmndtplgtdt0(sK16(xR),xR,sK11(sK17(xR)))
| spl27_18 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f419,plain,
( spl27_2
| spl27_16 ),
inference(avatar_contradiction_clause,[],[f418]) ).
fof(f418,plain,
( $false
| spl27_2
| spl27_16 ),
inference(subsumption_resolution,[],[f417,f195]) ).
fof(f195,plain,
( ~ sP3(xR)
| spl27_2 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f194,plain,
( spl27_2
<=> sP3(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_2])]) ).
fof(f417,plain,
( sP3(xR)
| spl27_16 ),
inference(resolution,[],[f407,f133]) ).
fof(f133,plain,
! [X0] :
( aElement0(sK16(X0))
| sP3(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ( sP3(X0)
| ( ! [X4] :
( ~ sdtmndtasgtdt0(sK17(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK16(X0),X0,X4)
| ~ aElement0(X4) )
& sdtmndtasgtdt0(sK15(X0),X0,sK17(X0))
& sdtmndtasgtdt0(sK15(X0),X0,sK16(X0))
& aElement0(sK17(X0))
& aElement0(sK16(X0))
& aElement0(sK15(X0)) ) )
& ( ! [X5,X6,X7] :
( ( sdtmndtasgtdt0(X7,X0,sK18(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK18(X0,X6,X7))
& aElement0(sK18(X0,X6,X7)) )
| ~ sdtmndtasgtdt0(X5,X0,X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5) )
| ~ sP3(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18])],[f76,f78,f77]) ).
fof(f77,plain,
! [X0] :
( ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& sdtmndtasgtdt0(X1,X0,X3)
& sdtmndtasgtdt0(X1,X0,X2)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ( ! [X4] :
( ~ sdtmndtasgtdt0(sK17(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK16(X0),X0,X4)
| ~ aElement0(X4) )
& sdtmndtasgtdt0(sK15(X0),X0,sK17(X0))
& sdtmndtasgtdt0(sK15(X0),X0,sK16(X0))
& aElement0(sK17(X0))
& aElement0(sK16(X0))
& aElement0(sK15(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X6,X7] :
( ? [X8] :
( sdtmndtasgtdt0(X7,X0,X8)
& sdtmndtasgtdt0(X6,X0,X8)
& aElement0(X8) )
=> ( sdtmndtasgtdt0(X7,X0,sK18(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK18(X0,X6,X7))
& aElement0(sK18(X0,X6,X7)) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0] :
( ( sP3(X0)
| ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& sdtmndtasgtdt0(X1,X0,X3)
& sdtmndtasgtdt0(X1,X0,X2)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X5,X6,X7] :
( ? [X8] :
( sdtmndtasgtdt0(X7,X0,X8)
& sdtmndtasgtdt0(X6,X0,X8)
& aElement0(X8) )
| ~ sdtmndtasgtdt0(X5,X0,X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5) )
| ~ sP3(X0) ) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ( sP3(X0)
| ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& sdtmndtasgtdt0(X1,X0,X3)
& sdtmndtasgtdt0(X1,X0,X2)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ sdtmndtasgtdt0(X1,X0,X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) )
| ~ sP3(X0) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( sP3(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ sdtmndtasgtdt0(X1,X0,X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f407,plain,
( ~ aElement0(sK16(xR))
| spl27_16 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f405,plain,
( spl27_16
<=> aElement0(sK16(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_16])]) ).
fof(f416,plain,
( ~ spl27_16
| ~ spl27_17
| ~ spl27_18
| spl27_13 ),
inference(avatar_split_clause,[],[f323,f303,f413,f409,f405]) ).
fof(f409,plain,
( spl27_17
<=> aElement0(sK11(sK17(xR))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_17])]) ).
fof(f303,plain,
( spl27_13
<=> sdtmndtasgtdt0(sK16(xR),xR,sK11(sK17(xR))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_13])]) ).
fof(f323,plain,
( ~ sdtmndtplgtdt0(sK16(xR),xR,sK11(sK17(xR)))
| ~ aElement0(sK11(sK17(xR)))
| ~ aElement0(sK16(xR))
| spl27_13 ),
inference(subsumption_resolution,[],[f314,f122]) ).
fof(f314,plain,
( ~ sdtmndtplgtdt0(sK16(xR),xR,sK11(sK17(xR)))
| ~ aElement0(sK11(sK17(xR)))
| ~ aRewritingSystem0(xR)
| ~ aElement0(sK16(xR))
| spl27_13 ),
inference(resolution,[],[f166,f305]) ).
fof(f305,plain,
( ~ sdtmndtasgtdt0(sK16(xR),xR,sK11(sK17(xR)))
| spl27_13 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f166,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 ) )
& ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 ) )
& ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).
fof(f340,plain,
( ~ spl27_14
| spl27_15
| spl27_2 ),
inference(avatar_split_clause,[],[f330,f194,f337,f333]) ).
fof(f333,plain,
( spl27_14
<=> sP0(sK17(xR),sK16(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_14])]) ).
fof(f337,plain,
( spl27_15
<=> sK16(xR) = sK17(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_15])]) ).
fof(f330,plain,
( sK16(xR) = sK17(xR)
| ~ sP0(sK17(xR),sK16(xR))
| spl27_2 ),
inference(subsumption_resolution,[],[f329,f195]) ).
fof(f329,plain,
( sP3(xR)
| sK16(xR) = sK17(xR)
| ~ sP0(sK17(xR),sK16(xR)) ),
inference(subsumption_resolution,[],[f328,f122]) ).
fof(f328,plain,
( ~ aRewritingSystem0(xR)
| sP3(xR)
| sK16(xR) = sK17(xR)
| ~ sP0(sK17(xR),sK16(xR)) ),
inference(resolution,[],[f325,f117]) ).
fof(f325,plain,
! [X0] :
( ~ sdtmndtplgtdt0(sK16(X0),X0,sK17(X0))
| ~ aRewritingSystem0(X0)
| sP3(X0) ),
inference(subsumption_resolution,[],[f324,f133]) ).
fof(f324,plain,
! [X0] :
( ~ sdtmndtplgtdt0(sK16(X0),X0,sK17(X0))
| ~ aRewritingSystem0(X0)
| ~ aElement0(sK16(X0))
| sP3(X0) ),
inference(subsumption_resolution,[],[f318,f134]) ).
fof(f134,plain,
! [X0] :
( aElement0(sK17(X0))
| sP3(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f318,plain,
! [X0] :
( ~ sdtmndtplgtdt0(sK16(X0),X0,sK17(X0))
| ~ aElement0(sK17(X0))
| ~ aRewritingSystem0(X0)
| ~ aElement0(sK16(X0))
| sP3(X0) ),
inference(duplicate_literal_removal,[],[f315]) ).
fof(f315,plain,
! [X0] :
( ~ sdtmndtplgtdt0(sK16(X0),X0,sK17(X0))
| ~ aElement0(sK17(X0))
| ~ aRewritingSystem0(X0)
| ~ aElement0(sK16(X0))
| sP3(X0)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[],[f166,f297]) ).
fof(f297,plain,
! [X0] :
( ~ sdtmndtasgtdt0(sK16(X0),X0,sK17(X0))
| sP3(X0)
| ~ aRewritingSystem0(X0) ),
inference(subsumption_resolution,[],[f294,f134]) ).
fof(f294,plain,
! [X0] :
( sP3(X0)
| ~ sdtmndtasgtdt0(sK16(X0),X0,sK17(X0))
| ~ aElement0(sK17(X0))
| ~ aRewritingSystem0(X0) ),
inference(duplicate_literal_removal,[],[f293]) ).
fof(f293,plain,
! [X0] :
( sP3(X0)
| ~ sdtmndtasgtdt0(sK16(X0),X0,sK17(X0))
| ~ aElement0(sK17(X0))
| ~ aElement0(sK17(X0))
| ~ aRewritingSystem0(X0) ),
inference(resolution,[],[f137,f179]) ).
fof(f179,plain,
! [X2,X1] :
( sdtmndtasgtdt0(X2,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1) ),
inference(duplicate_literal_removal,[],[f178]) ).
fof(f178,plain,
! [X2,X1] :
( sdtmndtasgtdt0(X2,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(equality_resolution,[],[f165]) ).
fof(f165,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| X0 != X2
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f137,plain,
! [X0,X4] :
( ~ sdtmndtasgtdt0(sK17(X0),X0,X4)
| sP3(X0)
| ~ sdtmndtasgtdt0(sK16(X0),X0,X4)
| ~ aElement0(X4) ),
inference(cnf_transformation,[],[f79]) ).
fof(f306,plain,
( ~ spl27_12
| ~ spl27_13
| spl27_2 ),
inference(avatar_split_clause,[],[f296,f194,f303,f299]) ).
fof(f299,plain,
( spl27_12
<=> sP1(sK17(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_12])]) ).
fof(f296,plain,
( ~ sdtmndtasgtdt0(sK16(xR),xR,sK11(sK17(xR)))
| ~ sP1(sK17(xR))
| spl27_2 ),
inference(subsumption_resolution,[],[f295,f109]) ).
fof(f295,plain,
( ~ sdtmndtasgtdt0(sK16(xR),xR,sK11(sK17(xR)))
| ~ aElement0(sK11(sK17(xR)))
| ~ sP1(sK17(xR))
| spl27_2 ),
inference(subsumption_resolution,[],[f292,f195]) ).
fof(f292,plain,
( sP3(xR)
| ~ sdtmndtasgtdt0(sK16(xR),xR,sK11(sK17(xR)))
| ~ aElement0(sK11(sK17(xR)))
| ~ sP1(sK17(xR)) ),
inference(resolution,[],[f137,f111]) ).
fof(f111,plain,
! [X0] :
( sdtmndtasgtdt0(X0,xR,sK11(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f277,plain,
( spl27_4
| spl27_9 ),
inference(avatar_contradiction_clause,[],[f276]) ).
fof(f276,plain,
( $false
| spl27_4
| spl27_9 ),
inference(subsumption_resolution,[],[f275,f207]) ).
fof(f207,plain,
( ~ sP5(xR)
| spl27_4 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f206,plain,
( spl27_4
<=> sP5(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_4])]) ).
fof(f275,plain,
( sP5(xR)
| spl27_9 ),
inference(resolution,[],[f265,f144]) ).
fof(f144,plain,
! [X0] :
( aElement0(sK19(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ( sP5(X0)
| ( ! [X4] :
( ~ sdtmndtasgtdt0(sK21(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK20(X0),X0,X4)
| ~ aElement0(X4) )
& aReductOfIn0(sK21(X0),sK19(X0),X0)
& aReductOfIn0(sK20(X0),sK19(X0),X0)
& aElement0(sK21(X0))
& aElement0(sK20(X0))
& aElement0(sK19(X0)) ) )
& ( ! [X5,X6,X7] :
( ( sdtmndtasgtdt0(X7,X0,sK22(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK22(X0,X6,X7))
& aElement0(sK22(X0,X6,X7)) )
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5) )
| ~ sP5(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22])],[f82,f84,f83]) ).
fof(f83,plain,
! [X0] :
( ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& aReductOfIn0(X3,X1,X0)
& aReductOfIn0(X2,X1,X0)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ( ! [X4] :
( ~ sdtmndtasgtdt0(sK21(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK20(X0),X0,X4)
| ~ aElement0(X4) )
& aReductOfIn0(sK21(X0),sK19(X0),X0)
& aReductOfIn0(sK20(X0),sK19(X0),X0)
& aElement0(sK21(X0))
& aElement0(sK20(X0))
& aElement0(sK19(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0,X6,X7] :
( ? [X8] :
( sdtmndtasgtdt0(X7,X0,X8)
& sdtmndtasgtdt0(X6,X0,X8)
& aElement0(X8) )
=> ( sdtmndtasgtdt0(X7,X0,sK22(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK22(X0,X6,X7))
& aElement0(sK22(X0,X6,X7)) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0] :
( ( sP5(X0)
| ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& aReductOfIn0(X3,X1,X0)
& aReductOfIn0(X2,X1,X0)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X5,X6,X7] :
( ? [X8] :
( sdtmndtasgtdt0(X7,X0,X8)
& sdtmndtasgtdt0(X6,X0,X8)
& aElement0(X8) )
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5) )
| ~ sP5(X0) ) ),
inference(rectify,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ( sP5(X0)
| ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& aReductOfIn0(X3,X1,X0)
& aReductOfIn0(X2,X1,X0)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) )
| ~ sP5(X0) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( sP5(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f265,plain,
( ~ aElement0(sK19(xR))
| spl27_9 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f263,plain,
( spl27_9
<=> aElement0(sK19(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_9])]) ).
fof(f274,plain,
( ~ spl27_9
| ~ spl27_10
| spl27_11
| spl27_4 ),
inference(avatar_split_clause,[],[f242,f206,f271,f267,f263]) ).
fof(f267,plain,
( spl27_10
<=> aElement0(sK20(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_10])]) ).
fof(f271,plain,
( spl27_11
<=> iLess0(sK20(xR),sK19(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_11])]) ).
fof(f242,plain,
( iLess0(sK20(xR),sK19(xR))
| ~ aElement0(sK20(xR))
| ~ aElement0(sK19(xR))
| spl27_4 ),
inference(subsumption_resolution,[],[f238,f207]) ).
fof(f238,plain,
( iLess0(sK20(xR),sK19(xR))
| ~ aElement0(sK20(xR))
| ~ aElement0(sK19(xR))
| sP5(xR) ),
inference(resolution,[],[f123,f147]) ).
fof(f147,plain,
! [X0] :
( aReductOfIn0(sK20(X0),sK19(X0),X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f123,plain,
! [X0,X1] :
( ~ aReductOfIn0(X1,X0,xR)
| iLess0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f259,plain,
spl27_7,
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f258,plain,
( $false
| spl27_7 ),
inference(subsumption_resolution,[],[f257,f177]) ).
fof(f257,plain,
( sP2(sK13,sK13)
| spl27_7 ),
inference(subsumption_resolution,[],[f256,f118]) ).
fof(f256,plain,
( ~ aElement0(sK13)
| sP2(sK13,sK13)
| spl27_7 ),
inference(resolution,[],[f250,f235]) ).
fof(f250,plain,
( ~ aElement0(sK14(sK13))
| spl27_7 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f248,plain,
( spl27_7
<=> aElement0(sK14(sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_7])]) ).
fof(f255,plain,
( ~ spl27_7
| spl27_8 ),
inference(avatar_split_clause,[],[f246,f252,f248]) ).
fof(f246,plain,
( sP1(sK14(sK13))
| ~ aElement0(sK14(sK13)) ),
inference(subsumption_resolution,[],[f245,f177]) ).
fof(f245,plain,
( sP2(sK13,sK13)
| sP1(sK14(sK13))
| ~ aElement0(sK14(sK13)) ),
inference(subsumption_resolution,[],[f244,f118]) ).
fof(f244,plain,
( ~ aElement0(sK13)
| sP2(sK13,sK13)
| sP1(sK14(sK13))
| ~ aElement0(sK14(sK13)) ),
inference(resolution,[],[f241,f119]) ).
fof(f119,plain,
! [X3] :
( ~ iLess0(X3,sK13)
| sP1(X3)
| ~ aElement0(X3) ),
inference(cnf_transformation,[],[f73]) ).
fof(f241,plain,
! [X0] :
( iLess0(sK14(X0),X0)
| ~ aElement0(X0)
| sP2(X0,sK13) ),
inference(subsumption_resolution,[],[f240,f235]) ).
fof(f240,plain,
! [X0] :
( iLess0(sK14(X0),X0)
| ~ aElement0(sK14(X0))
| ~ aElement0(X0)
| sP2(X0,sK13) ),
inference(duplicate_literal_removal,[],[f237]) ).
fof(f237,plain,
! [X0] :
( iLess0(sK14(X0),X0)
| ~ aElement0(sK14(X0))
| ~ aElement0(X0)
| sP2(X0,sK13)
| ~ aElement0(X0) ),
inference(resolution,[],[f123,f120]) ).
fof(f225,plain,
spl27_6,
inference(avatar_contradiction_clause,[],[f224]) ).
fof(f224,plain,
( $false
| spl27_6 ),
inference(subsumption_resolution,[],[f223,f122]) ).
fof(f223,plain,
( ~ aRewritingSystem0(xR)
| spl27_6 ),
inference(subsumption_resolution,[],[f222,f126]) ).
fof(f126,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f25]) ).
fof(f222,plain,
( ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR)
| spl27_6 ),
inference(resolution,[],[f219,f180]) ).
fof(f180,plain,
! [X0] :
( sP7(X0)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[],[f151,f158]) ).
fof(f158,plain,
! [X0] :
( sP8(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( sP8(X0)
| ~ aRewritingSystem0(X0) ),
inference(definition_folding,[],[f31,f55,f54]) ).
fof(f54,plain,
! [X0] :
( sP7(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f55,plain,
! [X0] :
( ( isTerminating0(X0)
<=> sP7(X0) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f31,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ) )
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ) )
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aRewritingSystem0(X0)
=> ( isTerminating0(X0)
<=> ! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> ( sdtmndtplgtdt0(X1,X0,X2)
=> iLess0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTermin) ).
fof(f151,plain,
! [X0] :
( ~ sP8(X0)
| ~ isTerminating0(X0)
| sP7(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ( ( isTerminating0(X0)
| ~ sP7(X0) )
& ( sP7(X0)
| ~ isTerminating0(X0) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f55]) ).
fof(f219,plain,
( ~ sP7(xR)
| spl27_6 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f218,plain,
( spl27_6
<=> sP7(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_6])]) ).
fof(f221,plain,
( ~ spl27_5
| spl27_6 ),
inference(avatar_split_clause,[],[f212,f218,f214]) ).
fof(f214,plain,
( spl27_5
<=> sP2(sK24(xR),sK23(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_5])]) ).
fof(f212,plain,
( sP7(xR)
| ~ sP2(sK24(xR),sK23(xR)) ),
inference(resolution,[],[f156,f107]) ).
fof(f107,plain,
! [X0,X1] :
( ~ sdtmndtplgtdt0(X1,xR,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f156,plain,
! [X0] :
( sdtmndtplgtdt0(sK23(X0),X0,sK24(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( sP7(X0)
| ( ~ iLess0(sK24(X0),sK23(X0))
& sdtmndtplgtdt0(sK23(X0),X0,sK24(X0))
& aElement0(sK24(X0))
& aElement0(sK23(X0)) ) )
& ( ! [X3,X4] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ~ sP7(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f88,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1,X2] :
( ~ iLess0(X2,X1)
& sdtmndtplgtdt0(X1,X0,X2)
& aElement0(X2)
& aElement0(X1) )
=> ( ~ iLess0(sK24(X0),sK23(X0))
& sdtmndtplgtdt0(sK23(X0),X0,sK24(X0))
& aElement0(sK24(X0))
& aElement0(sK23(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0] :
( ( sP7(X0)
| ? [X1,X2] :
( ~ iLess0(X2,X1)
& sdtmndtplgtdt0(X1,X0,X2)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X3,X4] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ~ sP7(X0) ) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ( sP7(X0)
| ? [X1,X2] :
( ~ iLess0(X2,X1)
& sdtmndtplgtdt0(X1,X0,X2)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) )
| ~ sP7(X0) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f209,plain,
( ~ spl27_3
| spl27_4 ),
inference(avatar_split_clause,[],[f200,f206,f202]) ).
fof(f202,plain,
( spl27_3
<=> sP2(sK20(xR),sK19(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_3])]) ).
fof(f200,plain,
( sP5(xR)
| ~ sP2(sK20(xR),sK19(xR)) ),
inference(resolution,[],[f147,f105]) ).
fof(f197,plain,
( ~ spl27_1
| spl27_2 ),
inference(avatar_split_clause,[],[f188,f194,f190]) ).
fof(f190,plain,
( spl27_1
<=> sP2(sK16(xR),sK15(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_1])]) ).
fof(f188,plain,
( sP3(xR)
| ~ sP2(sK16(xR),sK15(xR)) ),
inference(resolution,[],[f135,f108]) ).
fof(f108,plain,
! [X0,X1] :
( ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f135,plain,
! [X0] :
( sdtmndtasgtdt0(sK15(X0),X0,sK16(X0))
| sP3(X0) ),
inference(cnf_transformation,[],[f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM013+4 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n023.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 : Sun May 19 10:09:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (3012)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (3015)WARNING: value z3 for option sas not known
% 0.14/0.36 % (3015)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)
% 0.14/0.37 % (3013)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (3016)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (3014)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (3017)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)
% 0.14/0.37 % (3018)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)
% 0.14/0.37 % (3019)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)
% 0.14/0.37 % (3015)First to succeed.
% 0.14/0.37 % (3015)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3012"
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (3015)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (3015)------------------------------
% 0.14/0.38 % (3015)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (3015)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (3015)Memory used [KB]: 1046
% 0.14/0.38 % (3015)Time elapsed: 0.013 s
% 0.14/0.38 % (3015)Instructions burned: 27 (million)
% 0.14/0.38 % (3012)Success in time 0.011 s
%------------------------------------------------------------------------------