%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM017+4 : 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 : n001.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 09:39:24 AM UTC 2026
% Result : Theorem 3.00s 1.12s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 77 ( 18 unt; 9 def)
% Number of atoms : 500 ( 28 equ)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 641 ( 218 ~; 233 |; 177 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 8 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 78 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
( ! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& aReductOfIn0(X1,X0,xR)
& aReductOfIn0(X2,X0,xR) )
=> ? [X3] :
( aElement0(X3)
& ( X1 = X3
| ( ( aReductOfIn0(X3,X1,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X1,xR,X3) ) )
& sdtmndtasgtdt0(X1,xR,X3)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X2,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3) ) )
& isLocallyConfluent0(xR)
& ! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> ( ( aReductOfIn0(X1,X0,xR)
| ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,X0,xR)
& sdtmndtplgtdt0(X2,xR,X1) )
| sdtmndtplgtdt0(X0,xR,X1) )
=> iLess0(X1,X0) ) )
& isTerminating0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
fof(f17,axiom,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
fof(f20,axiom,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& ( xu = xb
| ( ( aReductOfIn0(xb,xu,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xu,xR)
& sdtmndtplgtdt0(X0,xR,xb) ) )
& sdtmndtplgtdt0(xu,xR,xb) ) )
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
fof(f21,axiom,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR)
& ( xv = xc
| ( ( aReductOfIn0(xc,xv,xR)
| ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xv,xR)
& sdtmndtplgtdt0(X0,xR,xc) ) )
& sdtmndtplgtdt0(xv,xR,xc) ) )
& sdtmndtasgtdt0(xv,xR,xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__779) ).
fof(f22,conjecture,
? [X0] :
( aElement0(X0)
& ( xu = X0
| aReductOfIn0(X0,xu,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xu,xR)
& sdtmndtplgtdt0(X1,xR,X0) )
| sdtmndtplgtdt0(xu,xR,X0)
| sdtmndtasgtdt0(xu,xR,X0) )
& ( xv = X0
| aReductOfIn0(X0,xv,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xv,xR)
& sdtmndtplgtdt0(X1,xR,X0) )
| sdtmndtplgtdt0(xv,xR,X0)
| sdtmndtasgtdt0(xv,xR,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f23,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& ( xu = X0
| aReductOfIn0(X0,xu,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xu,xR)
& sdtmndtplgtdt0(X1,xR,X0) )
| sdtmndtplgtdt0(xu,xR,X0)
| sdtmndtasgtdt0(xu,xR,X0) )
& ( xv = X0
| aReductOfIn0(X0,xv,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xv,xR)
& sdtmndtplgtdt0(X1,xR,X0) )
| sdtmndtplgtdt0(xv,xR,X0)
| sdtmndtasgtdt0(xv,xR,X0) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f28,plain,
( ! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& aReductOfIn0(X1,X0,xR)
& aReductOfIn0(X2,X0,xR) )
=> ? [X3] :
( aElement0(X3)
& ( X1 = X3
| ( ( aReductOfIn0(X3,X1,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X1,xR,X3) ) )
& sdtmndtasgtdt0(X1,xR,X3)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X2,xR)
& sdtmndtplgtdt0(X5,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3) ) )
& isLocallyConfluent0(xR)
& ! [X6,X7] :
( ( aElement0(X6)
& aElement0(X7) )
=> ( ( aReductOfIn0(X7,X6,xR)
| ? [X8] :
( aElement0(X8)
& aReductOfIn0(X8,X6,xR)
& sdtmndtplgtdt0(X8,xR,X7) )
| sdtmndtplgtdt0(X6,xR,X7) )
=> iLess0(X7,X6) ) )
& isTerminating0(xR) ),
inference(rectify,[],[f16]) ).
fof(f31,plain,
~ ? [X0] :
( aElement0(X0)
& ( xu = X0
| aReductOfIn0(X0,xu,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xu,xR)
& sdtmndtplgtdt0(X1,xR,X0) )
| sdtmndtplgtdt0(xu,xR,X0)
| sdtmndtasgtdt0(xu,xR,X0) )
& ( xv = X0
| aReductOfIn0(X0,xv,xR)
| ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xv,xR)
& sdtmndtplgtdt0(X2,xR,X0) )
| sdtmndtplgtdt0(xv,xR,X0)
| sdtmndtasgtdt0(xv,xR,X0) ) ),
inference(rectify,[],[f23]) ).
fof(f52,plain,
( ! [X0,X1,X2] :
( ? [X3] :
( aElement0(X3)
& ( X1 = X3
| ( ( aReductOfIn0(X3,X1,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X1,xR,X3) ) )
& sdtmndtasgtdt0(X1,xR,X3)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X2,xR)
& sdtmndtplgtdt0(X5,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) )
& isLocallyConfluent0(xR)
& ! [X6,X7] :
( iLess0(X7,X6)
| ( ~ aReductOfIn0(X7,X6,xR)
& ! [X8] :
( ~ aElement0(X8)
| ~ aReductOfIn0(X8,X6,xR)
| ~ sdtmndtplgtdt0(X8,xR,X7) )
& ~ sdtmndtplgtdt0(X6,xR,X7) )
| ~ aElement0(X6)
| ~ aElement0(X7) )
& isTerminating0(xR) ),
inference(ennf_transformation,[],[f28]) ).
fof(f53,plain,
( ! [X0,X1,X2] :
( ? [X3] :
( aElement0(X3)
& ( X1 = X3
| ( ( aReductOfIn0(X3,X1,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X1,xR,X3) ) )
& sdtmndtasgtdt0(X1,xR,X3)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X2,xR)
& sdtmndtplgtdt0(X5,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) )
& isLocallyConfluent0(xR)
& ! [X6,X7] :
( iLess0(X7,X6)
| ( ~ aReductOfIn0(X7,X6,xR)
& ! [X8] :
( ~ aElement0(X8)
| ~ aReductOfIn0(X8,X6,xR)
| ~ sdtmndtplgtdt0(X8,xR,X7) )
& ~ sdtmndtplgtdt0(X6,xR,X7) )
| ~ aElement0(X6)
| ~ aElement0(X7) )
& isTerminating0(xR) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0] :
( ~ aElement0(X0)
| ( xu != X0
& ~ aReductOfIn0(X0,xu,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xu,xR)
| ~ sdtmndtplgtdt0(X1,xR,X0) )
& ~ sdtmndtplgtdt0(xu,xR,X0)
& ~ sdtmndtasgtdt0(xu,xR,X0) )
| ( xv != X0
& ~ aReductOfIn0(X0,xv,xR)
& ! [X2] :
( ~ aElement0(X2)
| ~ aReductOfIn0(X2,xv,xR)
| ~ sdtmndtplgtdt0(X2,xR,X0) )
& ~ sdtmndtplgtdt0(xv,xR,X0)
& ~ sdtmndtasgtdt0(xv,xR,X0) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f63,definition,
! [X3,X2] :
( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X2,xR)
& sdtmndtplgtdt0(X5,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) )
| ~ sP4(X3,X2) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f64,plain,
( ! [X0,X1,X2] :
( ? [X3] :
( aElement0(X3)
& ( X1 = X3
| ( ( aReductOfIn0(X3,X1,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X1,xR,X3) ) )
& sdtmndtasgtdt0(X1,xR,X3)
& sP4(X3,X2)
& sdtmndtasgtdt0(X2,xR,X3) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) )
& isLocallyConfluent0(xR)
& ! [X6,X7] :
( iLess0(X7,X6)
| ( ~ aReductOfIn0(X7,X6,xR)
& ! [X8] :
( ~ aElement0(X8)
| ~ aReductOfIn0(X8,X6,xR)
| ~ sdtmndtplgtdt0(X8,xR,X7) )
& ~ sdtmndtplgtdt0(X6,xR,X7) )
| ~ aElement0(X6)
| ~ aElement0(X7) )
& isTerminating0(xR) ),
inference(definition_folding,[],[f53,f63]) ).
fof(f69,definition,
! [X0] :
( ( xv != X0
& ~ aReductOfIn0(X0,xv,xR)
& ! [X2] :
( ~ aElement0(X2)
| ~ aReductOfIn0(X2,xv,xR)
| ~ sdtmndtplgtdt0(X2,xR,X0) )
& ~ sdtmndtplgtdt0(xv,xR,X0)
& ~ sdtmndtasgtdt0(xv,xR,X0) )
| ~ sP8(X0) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f70,plain,
! [X0] :
( ~ aElement0(X0)
| ( xu != X0
& ~ aReductOfIn0(X0,xu,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xu,xR)
| ~ sdtmndtplgtdt0(X1,xR,X0) )
& ~ sdtmndtplgtdt0(xu,xR,X0)
& ~ sdtmndtasgtdt0(xu,xR,X0) )
| sP8(X0) ),
inference(definition_folding,[],[f56,f69]) ).
fof(f96,plain,
( ! [X0,X1,X2] :
( ? [X3] :
( aElement0(X3)
& ( X1 = X3
| ( ( aReductOfIn0(X3,X1,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X1,xR,X3) ) )
& sdtmndtasgtdt0(X1,xR,X3)
& sP4(X3,X2)
& sdtmndtasgtdt0(X2,xR,X3) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) )
& isLocallyConfluent0(xR)
& ! [X5,X6] :
( iLess0(X6,X5)
| ( ~ aReductOfIn0(X6,X5,xR)
& ! [X7] :
( ~ aElement0(X7)
| ~ aReductOfIn0(X7,X5,xR)
| ~ sdtmndtplgtdt0(X7,xR,X6) )
& ~ sdtmndtplgtdt0(X5,xR,X6) )
| ~ aElement0(X5)
| ~ aElement0(X6) )
& isTerminating0(xR) ),
inference(rectify,[],[f64]) ).
fof(f97,plain,
( ! [X0,X1,X2] :
( ( aElement0(sK23(X1,X2))
& ( sK23(X1,X2) = X1
| ( ( aReductOfIn0(sK23(X1,X2),X1,xR)
| ( aElement0(sK24(X1,X2))
& aReductOfIn0(sK24(X1,X2),X1,xR)
& sdtmndtplgtdt0(sK24(X1,X2),xR,sK23(X1,X2)) ) )
& sdtmndtplgtdt0(X1,xR,sK23(X1,X2)) ) )
& sdtmndtasgtdt0(X1,xR,sK23(X1,X2))
& sP4(sK23(X1,X2),X2)
& sdtmndtasgtdt0(X2,xR,sK23(X1,X2)) )
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) )
& isLocallyConfluent0(xR)
& ! [X5,X6] :
( iLess0(X6,X5)
| ( ~ aReductOfIn0(X6,X5,xR)
& ! [X7] :
( ~ aElement0(X7)
| ~ aReductOfIn0(X7,X5,xR)
| ~ sdtmndtplgtdt0(X7,xR,X6) )
& ~ sdtmndtplgtdt0(X5,xR,X6) )
| ~ aElement0(X5)
| ~ aElement0(X6) )
& isTerminating0(xR) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23,sK24]),skolemize(X3,sK23(X1,X2)),skolemize(X4,sK24(X1,X2))],[f96]) ).
fof(f107,plain,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& ( xu = xb
| ( ( aReductOfIn0(xb,xu,xR)
| ( aElement0(sK30)
& aReductOfIn0(sK30,xu,xR)
& sdtmndtplgtdt0(sK30,xR,xb) ) )
& sdtmndtplgtdt0(xu,xR,xb) ) )
& sdtmndtasgtdt0(xu,xR,xb) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(X0,sK30)],[f20]) ).
fof(f108,plain,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR)
& ( xv = xc
| ( ( aReductOfIn0(xc,xv,xR)
| ( aElement0(sK31)
& aReductOfIn0(sK31,xv,xR)
& sdtmndtplgtdt0(sK31,xR,xc) ) )
& sdtmndtplgtdt0(xv,xR,xc) ) )
& sdtmndtasgtdt0(xv,xR,xc) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X0,sK31)],[f21]) ).
fof(f109,plain,
! [X0] :
( ( xv != X0
& ~ aReductOfIn0(X0,xv,xR)
& ! [X2] :
( ~ aElement0(X2)
| ~ aReductOfIn0(X2,xv,xR)
| ~ sdtmndtplgtdt0(X2,xR,X0) )
& ~ sdtmndtplgtdt0(xv,xR,X0)
& ~ sdtmndtasgtdt0(xv,xR,X0) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f69]) ).
fof(f110,plain,
! [X0] :
( ( xv != X0
& ~ aReductOfIn0(X0,xv,xR)
& ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(X1,xv,xR)
| ~ sdtmndtplgtdt0(X1,xR,X0) )
& ~ sdtmndtplgtdt0(xv,xR,X0)
& ~ sdtmndtasgtdt0(xv,xR,X0) )
| ~ sP8(X0) ),
inference(rectify,[],[f109]) ).
fof(f166,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X2,xR,sK23(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) ),
inference(cnf_transformation,[],[f97]) ).
fof(f168,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK23(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) ),
inference(cnf_transformation,[],[f97]) ).
fof(f173,plain,
! [X2,X0,X1] :
( aElement0(sK23(X1,X2))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(X2,X0,xR) ),
inference(cnf_transformation,[],[f97]) ).
fof(f176,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f212,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f107]) ).
fof(f213,plain,
aElement0(xu),
inference(cnf_transformation,[],[f107]) ).
fof(f219,plain,
aReductOfIn0(xv,xa,xR),
inference(cnf_transformation,[],[f108]) ).
fof(f220,plain,
aElement0(xv),
inference(cnf_transformation,[],[f108]) ).
fof(f221,plain,
! [X0] :
( ~ sP8(X0)
| ~ sdtmndtasgtdt0(xv,xR,X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f226,plain,
! [X0] :
( sP8(X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f270,definition,
( spl33_2
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[spl33_2])],[avatar_definition]) ).
fof(f271,plain,
( ~ aElement0(xu)
| spl33_2 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f347,plain,
( $false
| spl33_2 ),
inference(resolution,[],[f213,f271]) ).
fof(f348,plain,
spl33_2,
inference(avatar_contradiction_clause,[],[f347]) ).
fof(f354,definition,
( spl33_23
<=> aElement0(xv) ),
introduced(definition,[new_symbols(definition,[spl33_23])],[avatar_definition]) ).
fof(f355,plain,
( ~ aElement0(xv)
| spl33_23 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f372,plain,
( $false
| spl33_23 ),
inference(resolution,[],[f355,f220]) ).
fof(f373,plain,
spl33_23,
inference(avatar_contradiction_clause,[],[f372]) ).
fof(f381,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) ),
inference(resolution,[],[f221,f226]) ).
fof(f438,definition,
( spl33_37
<=> aElement0(xa) ),
introduced(definition,[new_symbols(definition,[spl33_37])],[avatar_definition]) ).
fof(f439,plain,
( ~ aElement0(xa)
| spl33_37 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f521,plain,
( $false
| spl33_37 ),
inference(resolution,[],[f439,f176]) ).
fof(f522,plain,
spl33_37,
inference(avatar_contradiction_clause,[],[f521]) ).
fof(f630,definition,
( spl33_59
<=> aReductOfIn0(xu,xa,xR) ),
introduced(definition,[new_symbols(definition,[spl33_59])],[avatar_definition]) ).
fof(f631,plain,
( ~ aReductOfIn0(xu,xa,xR)
| spl33_59 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f637,plain,
( $false
| spl33_59 ),
inference(resolution,[],[f631,f212]) ).
fof(f638,plain,
spl33_59,
inference(avatar_contradiction_clause,[],[f637]) ).
fof(f917,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(xv)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aReductOfIn0(xv,X0,xR)
| ~ sdtmndtasgtdt0(xu,xR,sK23(X1,xv))
| ~ aElement0(sK23(X1,xv)) ),
inference(resolution,[],[f166,f381]) ).
fof(f929,definition,
( spl33_83
<=> ! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(sK23(X1,xv))
| ~ sdtmndtasgtdt0(xu,xR,sK23(X1,xv))
| ~ aReductOfIn0(xv,X0,xR)
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,X0,xR) ) ),
introduced(definition,[new_symbols(definition,[spl33_83])],[avatar_definition]) ).
fof(f930,plain,
( ! [X0,X1] :
( ~ sdtmndtasgtdt0(xu,xR,sK23(X1,xv))
| ~ aElement0(sK23(X1,xv))
| ~ aElement0(X0)
| ~ aReductOfIn0(xv,X0,xR)
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,X0,xR) )
| ~ spl33_83 ),
inference(avatar_component_clause,[],[f929]) ).
fof(f931,plain,
( ~ spl33_23
| spl33_83 ),
inference(avatar_split_clause,[],[f917,f929,f354]) ).
fof(f1133,plain,
( ! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,X0,xR)
| ~ aReductOfIn0(xv,X0,xR)
| ~ aElement0(sK23(xu,xv))
| ~ aElement0(X1)
| ~ aReductOfIn0(xv,X1,xR)
| ~ aElement0(xu)
| ~ aReductOfIn0(xu,X1,xR) )
| ~ spl33_83 ),
inference(resolution,[],[f168,f930]) ).
fof(f1141,plain,
( ! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,X0,xR)
| ~ aReductOfIn0(xv,X0,xR)
| ~ aElement0(sK23(xu,xv))
| ~ aElement0(X1)
| ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR) )
| ~ spl33_83 ),
inference(duplicate_literal_removal,[],[f1133]) ).
fof(f1171,definition,
( spl33_123
<=> ! [X1] :
( ~ aElement0(X1)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aReductOfIn0(xv,X1,xR) ) ),
introduced(definition,[new_symbols(definition,[spl33_123])],[avatar_definition]) ).
fof(f1172,plain,
( ! [X1] :
( ~ aReductOfIn0(xv,X1,xR)
| ~ aReductOfIn0(xu,X1,xR)
| ~ aElement0(X1) )
| ~ spl33_123 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f1174,definition,
( spl33_124
<=> aElement0(sK23(xu,xv)) ),
introduced(definition,[new_symbols(definition,[spl33_124])],[avatar_definition]) ).
fof(f1175,plain,
( ~ aElement0(sK23(xu,xv))
| spl33_124 ),
inference(avatar_component_clause,[],[f1174]) ).
fof(f1176,plain,
( spl33_123
| ~ spl33_124
| ~ spl33_23
| ~ spl33_2
| spl33_123
| ~ spl33_83 ),
inference(avatar_split_clause,[],[f1141,f929,f1171,f270,f354,f1174,f1171]) ).
fof(f1178,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,X0,xR)
| ~ aReductOfIn0(xv,X0,xR) )
| spl33_124 ),
inference(resolution,[],[f1175,f173]) ).
fof(f1179,plain,
( ~ spl33_23
| ~ spl33_2
| spl33_123
| spl33_124 ),
inference(avatar_split_clause,[],[f1178,f1174,f1171,f270,f354]) ).
fof(f1182,plain,
( ~ aReductOfIn0(xu,xa,xR)
| ~ aElement0(xa)
| ~ spl33_123 ),
inference(resolution,[],[f1172,f219]) ).
fof(f1183,plain,
( ~ spl33_37
| ~ spl33_59
| ~ spl33_123 ),
inference(avatar_split_clause,[],[f1182,f1171,f630,f438]) ).
cnf(s16,plain,
spl33_2,
inference(sat_conversion,[],[f348]) ).
cnf(s21,plain,
spl33_23,
inference(sat_conversion,[],[f373]) ).
cnf(s37,plain,
spl33_37,
inference(sat_conversion,[],[f522]) ).
cnf(s60,plain,
spl33_59,
inference(sat_conversion,[],[f638]) ).
cnf(s87,plain,
( ~ spl33_23
| spl33_83 ),
inference(sat_conversion,[],[f931]) ).
cnf(s134,plain,
( spl33_123
| ~ spl33_23
| ~ spl33_83
| ~ spl33_2
| spl33_123
| ~ spl33_124 ),
inference(sat_conversion,[],[f1176]) ).
cnf(s135,plain,
( ~ spl33_2
| ~ spl33_23
| ~ spl33_83
| spl33_123
| ~ spl33_124 ),
inference(rat,[],[s134]) ).
cnf(s136,plain,
( ~ spl33_2
| ~ spl33_23
| spl33_123
| spl33_124 ),
inference(sat_conversion,[],[f1179]) ).
cnf(s137,plain,
( ~ spl33_37
| ~ spl33_59
| ~ spl33_123 ),
inference(sat_conversion,[],[f1183]) ).
cnf(s145,plain,
~ spl33_123,
inference(rat,[],[s137,s60,s37]) ).
cnf(s189,plain,
spl33_83,
inference(rat,[],[s87,s21]) ).
cnf(s215,plain,
spl33_124,
inference(rat,[],[s136,s21,s145,s16]) ).
cnf(s216,plain,
$false,
inference(rat,[],[s135,s189,s145,s21,s215,s16]) ).
fof(f1184,plain,
$false,
inference(avatar_sat_refutation,[],[s216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM017+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:51:49 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.00/1.12 % (785884)Detected formulas, will run a generic FOF schedule.
% 3.00/1.12 % (785893)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3644473277:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.00/1.12 % (785890)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=3034367042:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.00/1.12 % (785889)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=3643071485:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.00/1.12 % (785891)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=3029712847:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.00/1.12 % (785892)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2101247779:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.00/1.12 % (785893)Instruction limit reached!
% 3.00/1.12 % (785893)------------------------------
% 3.00/1.12 % (785893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.12 % (785893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.12 % (785893)CaDiCaL version: 2.1.3
% 3.00/1.12 % (785893)Termination reason: Instruction limit
% 3.00/1.12 % (785893)Termination phase: Saturation
% 3.00/1.12 % (785893)Time elapsed: 0.039 s
% 3.00/1.12 % (785893)Peak memory usage: 88 MB
% 3.00/1.12 % (785893)Instructions burned: 121 (million)
% 3.00/1.12 % (785895)dis-21_1_sil=8000:lcm=predicate:random_seed=1733281253: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)
% 3.00/1.12 % (785894)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2245644834:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.00/1.12 % (785895)First to succeed.
% 3.00/1.12 % (785895)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-785884"
% 3.00/1.12 % (785892)Instruction limit reached!
% 3.00/1.12 % (785892)------------------------------
% 3.00/1.12 % (785892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.12 % (785892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.12 % (785892)CaDiCaL version: 2.1.3
% 3.00/1.12 % (785892)Termination reason: Instruction limit
% 3.00/1.12 % (785892)Termination phase: Saturation
% 3.00/1.12 % (785892)Time elapsed: 0.068 s
% 3.00/1.12 % (785892)Peak memory usage: 89 MB
% 3.00/1.12 % (785892)Instructions burned: 110 (million)
% 3.00/1.12 % (785894)Instruction limit reached!
% 3.00/1.12 % (785894)------------------------------
% 3.00/1.12 % (785894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.12 % (785894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.12 % (785894)CaDiCaL version: 2.1.3
% 3.00/1.12 % (785894)Termination reason: Instruction limit
% 3.00/1.12 % (785894)Termination phase: Saturation
% 3.00/1.12 % (785894)Time elapsed: 0.099 s
% 3.00/1.12 % (785894)Peak memory usage: 89 MB
% 3.00/1.12 % (785894)Instructions burned: 139 (million)
% 3.00/1.12 % (785901)lrs+10_1_sil=8000:sp=occurrence:random_seed=3088734829:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.00/1.12 % (785901)Also succeeded, but the first one will report.
% 3.00/1.12 % (785904)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1832901130:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.00/1.12 % (785904)Refutation not found, incomplete strategy
% 3.00/1.12 % (785904)------------------------------
% 3.00/1.12 % (785904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.12 % (785904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.12 % (785904)CaDiCaL version: 2.1.3
% 3.00/1.12 % (785904)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.12 % (785904)Time elapsed: 0.008 s
% 3.00/1.12 % (785904)Peak memory usage: 89 MB
% 3.00/1.12 % (785904)Instructions burned: 11 (million)
% 3.00/1.12 % (785905)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1012143253:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.00/1.12 % (785895)Refutation found. Thanks to Tanya!
% 3.00/1.12 % SZS status Theorem for theBenchmark
% 3.00/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.33 % (785895)------------------------------
% 3.89/1.33 % (785895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.33 % (785895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.33 % (785895)CaDiCaL version: 2.1.3
% 3.89/1.33 % (785895)Termination reason: Refutation
% 3.89/1.33 % (785895)Time elapsed: 0.019 s
% 3.89/1.33 % (785895)Peak memory usage: 90 MB
% 3.89/1.33 % (785895)Instructions burned: 26 (million)
% 3.89/1.33 % (785895)------------------------------
% 3.89/1.33 % (785895)------------------------------
% 3.89/1.33 % (785884)Success in time 0.455 s
% 3.89/1.33 % Vampire exiting
%------------------------------------------------------------------------------