%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM020+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 0.87s 0.96s
% Output : Refutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 109 ( 21 unt; 3 def)
% Number of atoms : 520 ( 0 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 732 ( 321 ~; 307 |; 83 &)
% ( 12 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 4 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 160 ( 0 sgn 141 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aRewritingSystem0(X1)
& aElement0(X2) )
=> ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCDef) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( aElement0(X0)
& aRewritingSystem0(X1)
& aElement0(X2)
& aElement0(X3) )
=> ( ( sdtmndtasgtdt0(X0,X1,X2)
& sdtmndtasgtdt0(X2,X1,X3) )
=> sdtmndtasgtdt0(X0,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRTrans) ).
fof(f12,axiom,
! [X0] :
( aRewritingSystem0(X0)
=> ( isTerminating0(X0)
<=> ! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( sdtmndtplgtdt0(X1,X0,X2)
=> iLess0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermin) ).
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/sandbox/benchmark/theBenchmark.p',mNFRDef) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f16,axiom,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
fof(f17,axiom,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aElement0(X1)
& aElement0(X2)
& sdtmndtasgtdt0(X0,xR,X1)
& sdtmndtasgtdt0(X0,xR,X2) )
=> ( iLess0(X0,xa)
=> ? [X3] :
( aElement0(X3)
& sdtmndtasgtdt0(X1,xR,X3)
& sdtmndtasgtdt0(X2,xR,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__715) ).
fof(f20,axiom,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__755) ).
fof(f22,axiom,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f23,axiom,
aNormalFormOfIn0(xd,xw,xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(f24,conjecture,
? [X0] :
( aElement0(X0)
& sdtmndtasgtdt0(xb,xR,X0)
& sdtmndtasgtdt0(xd,xR,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f25,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& sdtmndtasgtdt0(xb,xR,X0)
& sdtmndtasgtdt0(xd,xR,X0) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ? [X3] :
( aElement0(X3)
& sdtmndtasgtdt0(X1,xR,X3)
& sdtmndtasgtdt0(X2,xR,X3) )
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,X2) ),
inference(ennf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ? [X3] :
( aElement0(X3)
& sdtmndtasgtdt0(X1,xR,X3)
& sdtmndtasgtdt0(X2,xR,X3) )
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,X2) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ sdtmndtasgtdt0(xd,xR,X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f37,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ) )
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f38,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ) )
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(flattening,[],[f39]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) ) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) ) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f43]) ).
fof(f47,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(f48,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,[],[f47]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( aElement0(sK2(X1,X2))
& sdtmndtasgtdt0(X1,xR,sK2(X1,X2))
& sdtmndtasgtdt0(X2,xR,sK2(X1,X2)) )
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X1,X2))],[f31]) ).
fof(f58,plain,
! [X0] :
( ( ( isTerminating0(X0)
| ? [X1,X2] :
( ~ iLess0(X2,X1)
& sdtmndtplgtdt0(X1,X0,X2)
& aElement0(X1)
& aElement0(X2) ) )
& ( ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) )
| ~ isTerminating0(X0) ) )
| ~ aRewritingSystem0(X0) ),
inference(nnf_transformation,[],[f38]) ).
fof(f59,plain,
! [X0] :
( ( ( isTerminating0(X0)
| ? [X1,X2] :
( ~ iLess0(X2,X1)
& sdtmndtplgtdt0(X1,X0,X2)
& aElement0(X1)
& aElement0(X2) ) )
& ( ! [X3,X4] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X3)
| ~ aElement0(X4) )
| ~ isTerminating0(X0) ) )
| ~ aRewritingSystem0(X0) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ( ( isTerminating0(X0)
| ( ~ iLess0(sK9(X0),sK8(X0))
& sdtmndtplgtdt0(sK8(X0),X0,sK9(X0))
& aElement0(sK8(X0))
& aElement0(sK9(X0)) ) )
& ( ! [X3,X4] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X3)
| ~ aElement0(X4) )
| ~ isTerminating0(X0) ) )
| ~ aRewritingSystem0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X1,sK8(X0)),skolemize(X2,sK9(X0))],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(nnf_transformation,[],[f44]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X0,X1)
& sdtmndtplgtdt0(X4,X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ( aElement0(sK10(X0,X1,X2))
& aReductOfIn0(sK10(X0,X1,X2),X0,X1)
& sdtmndtplgtdt0(sK10(X0,X1,X2),X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X4,sK10(X0,X1,X2))],[f63]) ).
fof(f65,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,[],[f48]) ).
fof(f66,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,[],[f65]) ).
fof(f67,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,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| aReductOfIn0(sK11(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,[sK11]),skolemize(X3,sK11(X1,X2))],[f67]) ).
fof(f69,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f70,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f16]) ).
fof(f73,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f74,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f75,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X2,xR,sK2(X1,X2))
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f76,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK2(X1,X2))
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| aElement0(sK2(X1,X2)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f80,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f20]) ).
fof(f81,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f20]) ).
fof(f82,plain,
aElement0(xu),
inference(cnf_transformation,[],[f20]) ).
fof(f87,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f22]) ).
fof(f88,plain,
aElement0(xw),
inference(cnf_transformation,[],[f22]) ).
fof(f89,plain,
aNormalFormOfIn0(xd,xw,xR),
inference(cnf_transformation,[],[f23]) ).
fof(f90,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xd,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f104,plain,
! [X3,X0,X4] :
( ~ sdtmndtplgtdt0(X3,X0,X4)
| iLess0(X4,X3)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X3)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(cnf_transformation,[],[f40]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ aReductOfIn0(X2,X0,X1)
| sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| aElement0(X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f132,definition,
( spl13_2
<=> aElement0(xd) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f133,plain,
( aElement0(xd)
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f134,plain,
( ~ aElement0(xd)
| spl13_2 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f179,plain,
( sdtmndtplgtdt0(xa,xR,xu)
| ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xu) ),
inference(resolution,[],[f81,f115]) ).
fof(f182,plain,
( sdtmndtplgtdt0(xa,xR,xu)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[],[f179,f74]) ).
fof(f183,plain,
( sdtmndtplgtdt0(xa,xR,xu)
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[],[f182,f69]) ).
fof(f184,plain,
sdtmndtplgtdt0(xa,xR,xu),
inference(forward_subsumption_resolution,[],[f183,f82]) ).
fof(f203,plain,
( sdtmndtasgtdt0(xw,xR,xd)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f89,f118]) ).
fof(f204,plain,
( aElement0(xd)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f89,f119]) ).
fof(f207,plain,
( ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f204,f134]) ).
fof(f208,plain,
( sdtmndtasgtdt0(xw,xR,xd)
| ~ aRewritingSystem0(xR) ),
inference(forward_subsumption_resolution,[],[f203,f88]) ).
fof(f209,plain,
( ~ aRewritingSystem0(xR)
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f207,f88]) ).
fof(f210,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(forward_subsumption_resolution,[],[f208,f69]) ).
fof(f211,plain,
( $false
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f209,f69]) ).
fof(f212,plain,
spl13_2,
inference(avatar_contradiction_clause,[],[f211]) ).
fof(f237,definition,
( spl13_6
<=> iLess0(xu,xa) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f238,plain,
( iLess0(xu,xa)
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f239,plain,
( ~ iLess0(xu,xa)
| spl13_6 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f268,plain,
! [X0,X1] :
( ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(xd)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,xd)
| ~ sdtmndtasgtdt0(xb,xR,sK2(X1,xd))
| ~ aElement0(sK2(X1,xd)) ),
inference(resolution,[],[f75,f90]) ).
fof(f273,plain,
! [X0,X1] :
( ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(xd)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,xd)
| ~ sdtmndtasgtdt0(xb,xR,sK2(X1,xd)) ),
inference(forward_subsumption_resolution,[],[f268,f77]) ).
fof(f276,plain,
( ! [X0,X1] :
( ~ sdtmndtasgtdt0(xb,xR,sK2(X1,xd))
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ sdtmndtasgtdt0(X0,xR,xd)
| ~ iLess0(X0,xa) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f273,f133]) ).
fof(f292,plain,
( ! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(xb)
| ~ sdtmndtasgtdt0(X0,xR,xb)
| ~ sdtmndtasgtdt0(X0,xR,xd)
| ~ iLess0(X0,xa)
| ~ iLess0(X1,xa)
| ~ aElement0(X1)
| ~ aElement0(xb)
| ~ aElement0(xd)
| ~ sdtmndtasgtdt0(X1,xR,xb)
| ~ sdtmndtasgtdt0(X1,xR,xd) )
| ~ spl13_2 ),
inference(resolution,[],[f276,f76]) ).
fof(f293,plain,
( ! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(xb)
| ~ sdtmndtasgtdt0(X0,xR,xb)
| ~ sdtmndtasgtdt0(X0,xR,xd)
| ~ iLess0(X0,xa)
| ~ iLess0(X1,xa)
| ~ aElement0(X1)
| ~ aElement0(xd)
| ~ sdtmndtasgtdt0(X1,xR,xb)
| ~ sdtmndtasgtdt0(X1,xR,xd) )
| ~ spl13_2 ),
inference(duplicate_literal_removal,[],[f292]) ).
fof(f294,plain,
( ! [X0,X1] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,xb)
| ~ sdtmndtasgtdt0(X0,xR,xd)
| ~ iLess0(X0,xa)
| ~ iLess0(X1,xa)
| ~ aElement0(X1)
| ~ aElement0(xd)
| ~ sdtmndtasgtdt0(X1,xR,xb)
| ~ sdtmndtasgtdt0(X1,xR,xd) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f293,f73]) ).
fof(f295,plain,
( ! [X0,X1] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,xb)
| ~ sdtmndtasgtdt0(X0,xR,xd)
| ~ iLess0(X0,xa)
| ~ iLess0(X1,xa)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X1,xR,xb)
| ~ sdtmndtasgtdt0(X1,xR,xd) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f294,f133]) ).
fof(f297,definition,
( spl13_12
<=> ! [X1] :
( ~ iLess0(X1,xa)
| ~ sdtmndtasgtdt0(X1,xR,xd)
| ~ sdtmndtasgtdt0(X1,xR,xb)
| ~ aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f298,plain,
( ! [X1] :
( ~ sdtmndtasgtdt0(X1,xR,xd)
| ~ iLess0(X1,xa)
| ~ sdtmndtasgtdt0(X1,xR,xb)
| ~ aElement0(X1) )
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f299,plain,
( spl13_12
| spl13_12
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f295,f132,f297,f297]) ).
fof(f304,plain,
( iLess0(xu,xa)
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f184,f104]) ).
fof(f305,plain,
( ~ aElement0(xa)
| ~ aElement0(xu)
| ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR)
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f304,f239]) ).
fof(f308,plain,
( ~ aElement0(xu)
| ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR)
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f305,f74]) ).
fof(f311,plain,
( ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR)
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f308,f82]) ).
fof(f314,plain,
( ~ aRewritingSystem0(xR)
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f311,f70]) ).
fof(f315,plain,
( $false
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f314,f69]) ).
fof(f316,plain,
spl13_6,
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f334,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xw)
| ~ aElement0(xd) ),
inference(resolution,[],[f210,f109]) ).
fof(f335,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0)
| ~ aElement0(xw)
| ~ aElement0(xd) ),
inference(forward_subsumption_resolution,[],[f334,f69]) ).
fof(f338,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0)
| ~ aElement0(xd) ),
inference(forward_subsumption_resolution,[],[f335,f88]) ).
fof(f349,plain,
( ! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f338,f133]) ).
fof(f359,plain,
( sdtmndtasgtdt0(xu,xR,xd)
| ~ aElement0(xu)
| ~ spl13_2 ),
inference(resolution,[],[f349,f87]) ).
fof(f360,plain,
( sdtmndtasgtdt0(xu,xR,xd)
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f359,f82]) ).
fof(f362,plain,
( ~ iLess0(xu,xa)
| ~ sdtmndtasgtdt0(xu,xR,xb)
| ~ aElement0(xu)
| ~ spl13_2
| ~ spl13_12 ),
inference(resolution,[],[f360,f298]) ).
fof(f367,plain,
( ~ sdtmndtasgtdt0(xu,xR,xb)
| ~ aElement0(xu)
| ~ spl13_2
| ~ spl13_6
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f362,f238]) ).
fof(f370,plain,
( ~ aElement0(xu)
| ~ spl13_2
| ~ spl13_6
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f367,f80]) ).
fof(f373,plain,
( $false
| ~ spl13_2
| ~ spl13_6
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f370,f82]) ).
fof(f374,plain,
( ~ spl13_2
| ~ spl13_6
| ~ spl13_12 ),
inference(avatar_contradiction_clause,[],[f373]) ).
cnf(s4,plain,
spl13_2,
inference(sat_conversion,[],[f212]) ).
cnf(s11,plain,
( spl13_12
| ~ spl13_2
| spl13_12 ),
inference(sat_conversion,[],[f299]) ).
cnf(s12,plain,
( ~ spl13_2
| spl13_12 ),
inference(rat,[],[s11]) ).
cnf(s13,plain,
spl13_6,
inference(sat_conversion,[],[f316]) ).
cnf(s17,plain,
( ~ spl13_2
| ~ spl13_6
| ~ spl13_12 ),
inference(sat_conversion,[],[f374]) ).
cnf(s22,plain,
~ spl13_12,
inference(rat,[],[s17,s13,s4]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s12,s22,s4]) ).
fof(f375,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM020+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n015.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 21:50:02 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.87/0.96 % (3068177)Detected formulas, will run a generic FOF schedule.
% 0.87/0.96 % (3068185)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3415653017:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.87/0.96 % (3068185)First to succeed.
% 0.87/0.96 % (3068185)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3068177"
% 0.87/0.96 % (3068187)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3584428215:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.87/0.96 % (3068186)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3892819881:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.87/0.96 % (3068184)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=998640605:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.87/0.96 % (3068182)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=3097481292:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.87/0.96 % (3068188)dis-21_1_sil=8000:lcm=predicate:random_seed=607583123: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)
% 0.87/0.96 % (3068183)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=4080173293:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.87/0.96 % (3068186)Also succeeded, but the first one will report.
% 0.87/0.96 % (3068187)Also succeeded, but the first one will report.
% 0.87/0.96 % (3068188)Instruction limit reached!
% 0.87/0.96 % (3068188)------------------------------
% 0.87/0.96 % (3068188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.87/0.96 % (3068188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.96 % (3068188)CaDiCaL version: 2.1.3
% 0.87/0.96 % (3068188)Termination reason: Instruction limit
% 0.87/0.96 % (3068188)Termination phase: Saturation
% 0.87/0.96 % (3068188)Time elapsed: 0.075 s
% 0.87/0.96 % (3068188)Peak memory usage: 89 MB
% 0.87/0.96 % (3068188)Instructions burned: 130 (million)
% 0.87/0.96 % (3068185)Refutation found. Thanks to Tanya!
% 0.87/0.96 % SZS status Theorem for theBenchmark
% 0.87/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 2.85/1.16 % (3068185)------------------------------
% 2.85/1.16 % (3068185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.16 % (3068185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.16 % (3068185)CaDiCaL version: 2.1.3
% 2.85/1.16 % (3068185)Termination reason: Refutation
% 2.85/1.16 % (3068185)Time elapsed: 0.006 s
% 2.85/1.16 % (3068185)Peak memory usage: 89 MB
% 2.85/1.16 % (3068185)Instructions burned: 13 (million)
% 2.85/1.16 % (3068185)------------------------------
% 2.85/1.16 % (3068185)------------------------------
% 2.85/1.16 % (3068177)Success in time 0.309 s
% 2.85/1.16 % Vampire exiting
%------------------------------------------------------------------------------