%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM022+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:39:25 AM UTC 2026
% Result : Theorem 2.24s 0.83s
% Output : Refutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 90 ( 18 unt; 5 def)
% Number of atoms : 415 ( 20 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 495 ( 170 ~; 162 |; 142 &)
% ( 10 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 123 ( 0 sgn 88 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aRewritingSystem0(X1)
& aElement0(X2) )
=> ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).
fof(f13,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aRewritingSystem0(X1) )
=> ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ~ ? [X3] : aReductOfIn0(X3,X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNFRDef) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
fof(f17,axiom,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
fof(f19,conjecture,
( ( ( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) )
=> ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtasgtdt0(X0,xR,xb)
& ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& sdtmndtasgtdt0(X1,xR,xc)
& ? [X2] :
( aElement0(X2)
& sdtmndtasgtdt0(X0,xR,X2)
& sdtmndtasgtdt0(X1,xR,X2)
& ? [X3] :
( aNormalFormOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(xb,xR,X3)
& sdtmndtasgtdt0(xc,xR,X3) ) ) ) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [X0] :
( aElement0(X0)
& sdtmndtasgtdt0(xb,xR,X0)
& sdtmndtasgtdt0(xc,xR,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f20,negated_conjecture,
~ ( ( ( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) )
=> ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtasgtdt0(X0,xR,xb)
& ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& sdtmndtasgtdt0(X1,xR,xc)
& ? [X2] :
( aElement0(X2)
& sdtmndtasgtdt0(X0,xR,X2)
& sdtmndtasgtdt0(X1,xR,X2)
& ? [X3] :
( aNormalFormOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(xb,xR,X3)
& sdtmndtasgtdt0(xc,xR,X3) ) ) ) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [X0] :
( aElement0(X0)
& sdtmndtasgtdt0(xb,xR,X0)
& sdtmndtasgtdt0(xc,xR,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
~ ( ( ( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) )
=> ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtasgtdt0(X0,xR,xb)
& ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& sdtmndtasgtdt0(X1,xR,xc)
& ? [X2] :
( aElement0(X2)
& sdtmndtasgtdt0(X0,xR,X2)
& sdtmndtasgtdt0(X1,xR,X2)
& ? [X3] :
( aNormalFormOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(xb,xR,X3)
& sdtmndtasgtdt0(xc,xR,X3) ) ) ) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(xb,xR,X4)
& sdtmndtasgtdt0(xc,xR,X4) ) ) ),
inference(rectify,[],[f20]) ).
fof(f28,plain,
( ! [X4] :
( ~ aElement0(X4)
| ~ sdtmndtasgtdt0(xb,xR,X4)
| ~ sdtmndtasgtdt0(xc,xR,X4) )
& sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc)
& ( ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtasgtdt0(X0,xR,xb)
& ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& sdtmndtasgtdt0(X1,xR,xc)
& ? [X2] :
( aElement0(X2)
& sdtmndtasgtdt0(X0,xR,X2)
& sdtmndtasgtdt0(X1,xR,X2)
& ? [X3] :
( aNormalFormOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(xb,xR,X3)
& sdtmndtasgtdt0(xc,xR,X3) ) ) ) )
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f29,plain,
( ! [X4] :
( ~ aElement0(X4)
| ~ sdtmndtasgtdt0(xb,xR,X4)
| ~ sdtmndtasgtdt0(xc,xR,X4) )
& sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc)
& ( ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtasgtdt0(X0,xR,xb)
& ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& sdtmndtasgtdt0(X1,xR,xc)
& ? [X2] :
( aElement0(X2)
& sdtmndtasgtdt0(X0,xR,X2)
& sdtmndtasgtdt0(X1,xR,X2)
& ? [X3] :
( aNormalFormOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(xb,xR,X3)
& sdtmndtasgtdt0(xc,xR,X3) ) ) ) )
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ) ),
inference(flattening,[],[f28]) ).
fof(f36,plain,
! [X0,X1] :
( ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X3] : ~ aReductOfIn0(X3,X2,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f37,plain,
! [X0,X1] :
( ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X3] : ~ aReductOfIn0(X3,X2,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(flattening,[],[f36]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f42]) ).
fof(f50,definition,
! [X0,X1] :
( ? [X2] :
( aElement0(X2)
& sdtmndtasgtdt0(X0,xR,X2)
& sdtmndtasgtdt0(X1,xR,X2)
& ? [X3] :
( aNormalFormOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(xb,xR,X3)
& sdtmndtasgtdt0(xc,xR,X3) ) )
| ~ sP0(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f51,plain,
( ! [X4] :
( ~ aElement0(X4)
| ~ sdtmndtasgtdt0(xb,xR,X4)
| ~ sdtmndtasgtdt0(xc,xR,X4) )
& sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc)
& ( ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtasgtdt0(X0,xR,xb)
& ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& sdtmndtasgtdt0(X1,xR,xc)
& sP0(X0,X1) ) )
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ) ),
inference(definition_folding,[],[f29,f50]) ).
fof(f59,plain,
! [X0,X1] :
( ? [X2] :
( aElement0(X2)
& sdtmndtasgtdt0(X0,xR,X2)
& sdtmndtasgtdt0(X1,xR,X2)
& ? [X3] :
( aNormalFormOfIn0(X3,X2,xR)
& sdtmndtasgtdt0(xb,xR,X3)
& sdtmndtasgtdt0(xc,xR,X3) ) )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f50]) ).
fof(f60,plain,
! [X0,X1] :
( ( aElement0(sK6(X0,X1))
& sdtmndtasgtdt0(X0,xR,sK6(X0,X1))
& sdtmndtasgtdt0(X1,xR,sK6(X0,X1))
& aNormalFormOfIn0(sK7(X0,X1),sK6(X0,X1),xR)
& sdtmndtasgtdt0(xb,xR,sK7(X0,X1))
& sdtmndtasgtdt0(xc,xR,sK7(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X2,sK6(X0,X1)),skolemize(X3,sK7(X0,X1))],[f59]) ).
fof(f61,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ sdtmndtasgtdt0(xc,xR,X0) )
& sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc)
& ( ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& sdtmndtasgtdt0(X1,xR,xb)
& ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xa,xR)
& sdtmndtasgtdt0(X2,xR,xc)
& sP0(X1,X2) ) )
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ) ),
inference(rectify,[],[f51]) ).
fof(f62,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ sdtmndtasgtdt0(xc,xR,X0) )
& sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc)
& ( ( aElement0(sK8)
& aReductOfIn0(sK8,xa,xR)
& sdtmndtasgtdt0(sK8,xR,xb)
& aElement0(sK9)
& aReductOfIn0(sK9,xa,xR)
& sdtmndtasgtdt0(sK9,xR,xc)
& sP0(sK8,sK9) )
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X1,sK8),skolemize(X2,sK9)],[f61]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ? [X3] : aReductOfIn0(X3,X2,X1) )
& ( ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X3] : ~ aReductOfIn0(X3,X2,X1) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(nnf_transformation,[],[f37]) ).
fof(f72,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ? [X3] : aReductOfIn0(X3,X2,X1) )
& ( ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X3] : ~ aReductOfIn0(X3,X2,X1) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ? [X3] : aReductOfIn0(X3,X2,X1) )
& ( ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X4] : ~ aReductOfIn0(X4,X2,X1) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| aReductOfIn0(sK17(X1,X2),X2,X1) )
& ( ( aElement0(X2)
& sdtmndtasgtdt0(X0,X1,X2)
& ! [X4] : ~ aReductOfIn0(X4,X2,X1) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X3,sK17(X1,X2))],[f73]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( X0 != X2
& ~ sdtmndtplgtdt0(X0,X1,X2) ) )
& ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(nnf_transformation,[],[f43]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( X0 != X2
& ~ sdtmndtplgtdt0(X0,X1,X2) ) )
& ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f79]) ).
fof(f85,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f88,plain,
aElement0(xc),
inference(cnf_transformation,[],[f17]) ).
fof(f89,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f90,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f94,plain,
! [X0,X1] :
( sdtmndtasgtdt0(xc,xR,sK7(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f95,plain,
! [X0,X1] :
( sdtmndtasgtdt0(xb,xR,sK7(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f96,plain,
! [X0,X1] :
( aNormalFormOfIn0(sK7(X0,X1),sK6(X0,X1),xR)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f99,plain,
! [X0,X1] :
( aElement0(sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f100,plain,
( sP0(sK8,sK9)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(cnf_transformation,[],[f62]) ).
fof(f107,plain,
sdtmndtasgtdt0(xa,xR,xc),
inference(cnf_transformation,[],[f62]) ).
fof(f108,plain,
sdtmndtasgtdt0(xa,xR,xb),
inference(cnf_transformation,[],[f62]) ).
fof(f109,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xc,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| aElement0(X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f147,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| X0 != X2
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f155,plain,
! [X2,X1] :
( sdtmndtasgtdt0(X2,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(equality_resolution,[],[f147]) ).
fof(f156,plain,
! [X2,X1] :
( sdtmndtasgtdt0(X2,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1) ),
inference(duplicate_literal_removal,[],[f155]) ).
fof(f160,definition,
( spl23_1
<=> sdtmndtplgtdt0(xa,xR,xc) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
fof(f162,plain,
( ~ sdtmndtplgtdt0(xa,xR,xc)
| spl23_1 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f164,definition,
( spl23_2
<=> sdtmndtplgtdt0(xa,xR,xb) ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
fof(f168,definition,
( spl23_3
<=> sP0(sK8,sK9) ),
introduced(definition,[new_symbols(definition,[spl23_3])],[avatar_definition]) ).
fof(f170,plain,
( sP0(sK8,sK9)
| ~ spl23_3 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f171,plain,
( ~ spl23_1
| ~ spl23_2
| spl23_3 ),
inference(avatar_split_clause,[],[f100,f168,f164,f160]) ).
fof(f220,plain,
( ~ aElement0(xc)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xb,xR,xc)
| ~ aElement0(xc) ),
inference(resolution,[],[f156,f109]) ).
fof(f221,plain,
( ~ aElement0(xc)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xb,xR,xc) ),
inference(duplicate_literal_removal,[],[f220]) ).
fof(f222,plain,
( ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xb,xR,xc) ),
inference(forward_subsumption_resolution,[],[f221,f88]) ).
fof(f223,plain,
~ sdtmndtasgtdt0(xb,xR,xc),
inference(forward_subsumption_resolution,[],[f222,f85]) ).
fof(f224,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ sdtmndtasgtdt0(xb,xR,sK7(X0,X1))
| ~ aElement0(sK7(X0,X1)) ),
inference(resolution,[],[f94,f109]) ).
fof(f225,plain,
! [X0,X1] :
( ~ aElement0(sK7(X0,X1))
| ~ sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f224,f95]) ).
fof(f236,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| aElement0(sK7(X0,X1))
| ~ aElement0(sK6(X0,X1))
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f96,f130]) ).
fof(f237,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| aElement0(sK7(X0,X1))
| ~ aElement0(sK6(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f236,f85]) ).
fof(f238,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ aElement0(sK6(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f237,f225]) ).
fof(f239,plain,
! [X0,X1] : ~ sP0(X0,X1),
inference(forward_subsumption_resolution,[],[f238,f99]) ).
fof(f287,plain,
( sdtmndtplgtdt0(xa,xR,xc)
| xa = xc
| ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xc) ),
inference(resolution,[],[f145,f107]) ).
fof(f288,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| xa = xb
| ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb) ),
inference(resolution,[],[f145,f108]) ).
fof(f298,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| xa = xb
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb) ),
inference(forward_subsumption_resolution,[],[f288,f90]) ).
fof(f299,plain,
( xa = xc
| ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xc)
| spl23_1 ),
inference(forward_subsumption_resolution,[],[f287,f162]) ).
fof(f302,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| xa = xb
| ~ aElement0(xb) ),
inference(forward_subsumption_resolution,[],[f298,f85]) ).
fof(f303,plain,
( xa = xc
| ~ aRewritingSystem0(xR)
| ~ aElement0(xc)
| spl23_1 ),
inference(forward_subsumption_resolution,[],[f299,f90]) ).
fof(f304,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| xa = xb ),
inference(forward_subsumption_resolution,[],[f302,f89]) ).
fof(f305,plain,
( xa = xc
| ~ aElement0(xc)
| spl23_1 ),
inference(forward_subsumption_resolution,[],[f303,f85]) ).
fof(f307,definition,
( spl23_12
<=> xa = xb ),
introduced(definition,[new_symbols(definition,[spl23_12])],[avatar_definition]) ).
fof(f309,plain,
( xa = xb
| ~ spl23_12 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f310,plain,
( spl23_12
| spl23_2 ),
inference(avatar_split_clause,[],[f304,f164,f307]) ).
fof(f311,plain,
( xa = xc
| spl23_1 ),
inference(forward_subsumption_resolution,[],[f305,f88]) ).
fof(f405,plain,
( ~ sdtmndtasgtdt0(xa,xR,xc)
| ~ spl23_12 ),
inference(superposition,[],[f223,f309]) ).
fof(f410,plain,
( $false
| ~ spl23_12 ),
inference(forward_subsumption_resolution,[],[f405,f107]) ).
fof(f411,plain,
~ spl23_12,
inference(avatar_contradiction_clause,[],[f410]) ).
fof(f412,plain,
( $false
| ~ spl23_3 ),
inference(forward_subsumption_resolution,[],[f170,f239]) ).
fof(f413,plain,
~ spl23_3,
inference(avatar_contradiction_clause,[],[f412]) ).
fof(f422,plain,
( ! [X0] :
( ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ sdtmndtasgtdt0(xa,xR,X0)
| ~ aElement0(X0) )
| spl23_1 ),
inference(superposition,[],[f109,f311]) ).
fof(f1865,plain,
( ~ sdtmndtasgtdt0(xa,xR,xb)
| ~ aElement0(xb)
| ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| spl23_1 ),
inference(resolution,[],[f422,f156]) ).
fof(f1870,plain,
( ~ sdtmndtasgtdt0(xa,xR,xb)
| ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| spl23_1 ),
inference(duplicate_literal_removal,[],[f1865]) ).
fof(f1873,plain,
( ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| spl23_1 ),
inference(forward_subsumption_resolution,[],[f1870,f108]) ).
fof(f1880,plain,
( ~ aRewritingSystem0(xR)
| spl23_1 ),
inference(forward_subsumption_resolution,[],[f1873,f89]) ).
fof(f1886,plain,
( $false
| spl23_1 ),
inference(forward_subsumption_resolution,[],[f1880,f85]) ).
fof(f1887,plain,
spl23_1,
inference(avatar_contradiction_clause,[],[f1886]) ).
cnf(s1,plain,
( ~ spl23_1
| ~ spl23_2
| spl23_3 ),
inference(sat_conversion,[],[f171]) ).
cnf(s10,plain,
( spl23_2
| spl23_12 ),
inference(sat_conversion,[],[f310]) ).
cnf(s16,plain,
~ spl23_12,
inference(sat_conversion,[],[f411]) ).
cnf(s17,plain,
~ spl23_3,
inference(sat_conversion,[],[f413]) ).
cnf(s40,plain,
spl23_1,
inference(sat_conversion,[],[f1887]) ).
cnf(s42,plain,
spl23_2,
inference(rat,[],[s10,s16]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s1,s17,s42,s40]) ).
fof(f1899,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM022+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:48:53 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.24/0.83 % (3814394)Detected formulas, will run a generic FOF schedule.
% 2.24/0.83 % (3814404)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3326253110:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.24/0.83 % (3814402)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1306161423:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.24/0.83 % (3814403)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2660068766:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.24/0.83 % (3814399)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1740721977:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.24/0.83 % (3814405)dis-21_1_sil=8000:lcm=predicate:random_seed=4085415777:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.24/0.83 % (3814401)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3551370532:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.24/0.83 % (3814400)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3082899140:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.24/0.83 % (3814404)Instruction limit reached!
% 2.24/0.83 % (3814404)------------------------------
% 2.24/0.83 % (3814404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/0.83 % (3814404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.83 % (3814404)CaDiCaL version: 2.1.3
% 2.24/0.83 % (3814404)Termination reason: Instruction limit
% 2.24/0.83 % (3814404)Termination phase: Saturation
% 2.24/0.83 % (3814404)Time elapsed: 0.050 s
% 2.24/0.83 % (3814404)Peak memory usage: 89 MB
% 2.24/0.83 % (3814404)Instructions burned: 141 (million)
% 2.24/0.83 % (3814402)Instruction limit reached!
% 2.24/0.83 % (3814402)------------------------------
% 2.24/0.83 % (3814402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/0.83 % (3814402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.83 % (3814402)CaDiCaL version: 2.1.3
% 2.24/0.83 % (3814402)Termination reason: Instruction limit
% 2.24/0.83 % (3814402)Termination phase: Saturation
% 2.24/0.83 % (3814402)Time elapsed: 0.054 s
% 2.24/0.83 % (3814402)Peak memory usage: 88 MB
% 2.24/0.83 % (3814402)Instructions burned: 110 (million)
% 2.24/0.83 % (3814403)Instruction limit reached!
% 2.24/0.83 % (3814403)------------------------------
% 2.24/0.83 % (3814403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/0.83 % (3814403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.83 % (3814403)CaDiCaL version: 2.1.3
% 2.24/0.83 % (3814403)Termination reason: Instruction limit
% 2.24/0.83 % (3814403)Termination phase: Saturation
% 2.24/0.83 % (3814403)Time elapsed: 0.068 s
% 2.24/0.83 % (3814403)Peak memory usage: 88 MB
% 2.24/0.83 % (3814403)Instructions burned: 120 (million)
% 2.24/0.83 % (3814405)Instruction limit reached!
% 2.24/0.83 % (3814405)------------------------------
% 2.24/0.83 % (3814405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.24/0.83 % (3814405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.83 % (3814405)CaDiCaL version: 2.1.3
% 2.24/0.83 % (3814405)Termination reason: Instruction limit
% 2.24/0.83 % (3814405)Termination phase: Saturation
% 2.24/0.83 % (3814405)Time elapsed: 0.077 s
% 2.24/0.83 % (3814405)Peak memory usage: 89 MB
% 2.24/0.83 % (3814405)Instructions burned: 129 (million)
% 2.24/0.83 % (3814413)lrs+10_1_sil=8000:sp=occurrence:random_seed=351957563:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.24/0.83 % (3814413)First to succeed.
% 2.24/0.83 % (3814413)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3814394"
% 2.24/0.83 % (3814414)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1931035426:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 2.24/0.83 % (3814415)lrs+1011_1_sil=32000:sp=occurrence:random_seed=491946990:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.24/0.83 % (3814414)Also succeeded, but the first one will report.
% 2.24/0.83 % (3814415)Also succeeded, but the first one will report.
% 2.24/0.83 % (3814416)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2782171919:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 2.24/0.83 % (3814413)Refutation found. Thanks to Tanya!
% 2.24/0.83 % SZS status Theorem for theBenchmark
% 2.24/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 3.29/0.92 % (3814413)------------------------------
% 3.29/0.92 % (3814413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/0.92 % (3814413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/0.92 % (3814413)CaDiCaL version: 2.1.3
% 3.29/0.92 % (3814413)Termination reason: Refutation
% 3.29/0.92 % (3814413)Time elapsed: 0.022 s
% 3.29/0.92 % (3814413)Peak memory usage: 90 MB
% 3.29/0.92 % (3814413)Instructions burned: 60 (million)
% 3.29/0.92 % (3814413)------------------------------
% 3.29/0.92 % (3814413)------------------------------
% 3.29/0.92 % (3814394)Success in time 0.421 s
% 3.29/0.92 % Vampire exiting
%------------------------------------------------------------------------------