%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM020+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:40:09 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 20
% Syntax : Number of formulae : 134 ( 27 unt; 7 def)
% Number of atoms : 562 ( 0 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 751 ( 323 ~; 317 |; 84 &)
% ( 16 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 8 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 174 ( 0 sgn 155 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aRewritingSystem0(X1) )
=> ! [X2] :
( aReductOfIn0(X2,X0,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mNFRDef) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
fof(f16,axiom,
( isLocallyConfluent0(xR)
& 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(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/sandbox2/benchmark/theBenchmark.p',m__715) ).
fof(f20,axiom,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
fof(f22,axiom,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__799) ).
fof(f23,axiom,
aNormalFormOfIn0(xd,xw,xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
fof(f24,conjecture,
? [X0] :
( aElement0(X0)
& sdtmndtasgtdt0(xb,xR,X0)
& sdtmndtasgtdt0(xd,xR,X0) ),
file('/export/starexec/sandbox2/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] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f31,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(flattening,[],[f30]) ).
fof(f32,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(f33,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,[],[f32]) ).
fof(f38,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(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(flattening,[],[f38]) ).
fof(f44,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ) )
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f45,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ) )
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f44]) ).
fof(f46,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(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(flattening,[],[f46]) ).
fof(f50,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(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ sdtmndtasgtdt0(xd,xR,X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f59,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,[],[f33]) ).
fof(f60,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,[],[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)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X0,X1)
& sdtmndtplgtdt0(X4,X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(rectify,[],[f60]) ).
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)
| ( aElement0(sK4(X0,X1,X2))
& aReductOfIn0(sK4(X0,X1,X2),X0,X1)
& sdtmndtplgtdt0(sK4(X0,X1,X2),X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X4,sK4(X0,X1,X2))],[f61]) ).
fof(f73,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,[],[f45]) ).
fof(f74,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,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ( ( isTerminating0(X0)
| ( ~ iLess0(sK14(X0),sK13(X0))
& sdtmndtplgtdt0(sK13(X0),X0,sK14(X0))
& aElement0(sK13(X0))
& aElement0(sK14(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,[sK13,sK14]),skolemize(X1,sK13(X0)),skolemize(X2,sK14(X0))],[f74]) ).
fof(f76,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,[],[f47]) ).
fof(f77,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,[],[f76]) ).
fof(f78,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,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| aReductOfIn0(sK15(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,[sK15]),skolemize(X3,sK15(X1,X2))],[f78]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( aElement0(sK17(X1,X2))
& sdtmndtasgtdt0(X1,xR,sK17(X1,X2))
& sdtmndtasgtdt0(X2,xR,sK17(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,[sK17]),skolemize(X3,sK17(X1,X2))],[f51]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f87,plain,
! [X2,X0,X1] :
( sdtmndtplgtdt0(X0,X1,X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f62]) ).
fof(f92,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,[],[f39]) ).
fof(f117,plain,
! [X3,X0,X4] :
( ~ sdtmndtplgtdt0(X3,X0,X4)
| iLess0(X4,X3)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| aElement0(X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f127,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f128,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f16]) ).
fof(f131,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f132,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtasgtdt0(X2,xR,sK17(X1,X2)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtasgtdt0(X1,xR,sK17(X1,X2)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ iLess0(X0,xa)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| aElement0(sK17(X1,X2)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f138,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f20]) ).
fof(f139,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f20]) ).
fof(f140,plain,
aElement0(xu),
inference(cnf_transformation,[],[f20]) ).
fof(f145,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f22]) ).
fof(f146,plain,
aElement0(xw),
inference(cnf_transformation,[],[f22]) ).
fof(f147,plain,
aNormalFormOfIn0(xd,xw,xR),
inference(cnf_transformation,[],[f23]) ).
fof(f148,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xd,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f177,definition,
( spl18_4
<=> aElement0(xd) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
fof(f178,plain,
( aElement0(xd)
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f185,plain,
( aElement0(xd)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f124,f147]) ).
fof(f186,plain,
( aElement0(xd)
| ~ aRewritingSystem0(xR) ),
inference(forward_subsumption_resolution,[],[f185,f146]) ).
fof(f187,plain,
aElement0(xd),
inference(forward_subsumption_resolution,[],[f186,f127]) ).
fof(f188,plain,
spl18_4,
inference(avatar_split_clause,[],[f187,f177]) ).
fof(f192,plain,
( sdtmndtasgtdt0(xw,xR,xd)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f123,f147]) ).
fof(f193,plain,
( sdtmndtasgtdt0(xw,xR,xd)
| ~ aRewritingSystem0(xR) ),
inference(forward_subsumption_resolution,[],[f192,f146]) ).
fof(f194,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(forward_subsumption_resolution,[],[f193,f127]) ).
fof(f201,plain,
! [X2,X0,X1] :
( ~ aReductOfIn0(X2,X0,X1)
| sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(forward_subsumption_resolution,[],[f87,f82]) ).
fof(f202,plain,
( sdtmndtplgtdt0(xa,xR,xu)
| ~ aElement0(xa)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f201,f139]) ).
fof(f209,plain,
( sdtmndtplgtdt0(xa,xR,xu)
| ~ aRewritingSystem0(xR) ),
inference(forward_subsumption_resolution,[],[f202,f132]) ).
fof(f211,plain,
sdtmndtplgtdt0(xa,xR,xu),
inference(forward_subsumption_resolution,[],[f209,f127]) ).
fof(f240,plain,
( iLess0(xu,xa)
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f117,f211]) ).
fof(f245,plain,
( iLess0(xu,xa)
| ~ aElement0(xu)
| ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR) ),
inference(forward_subsumption_resolution,[],[f240,f132]) ).
fof(f249,plain,
( iLess0(xu,xa)
| ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR) ),
inference(forward_subsumption_resolution,[],[f245,f140]) ).
fof(f253,plain,
( iLess0(xu,xa)
| ~ aRewritingSystem0(xR) ),
inference(forward_subsumption_resolution,[],[f249,f128]) ).
fof(f257,plain,
iLess0(xu,xa),
inference(forward_subsumption_resolution,[],[f253,f127]) ).
fof(f388,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xw)
| ~ aElement0(xd) ),
inference(resolution,[],[f92,f194]) ).
fof(f397,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0)
| ~ aElement0(xw)
| ~ aElement0(xd) ),
inference(forward_subsumption_resolution,[],[f388,f127]) ).
fof(f405,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0)
| ~ aElement0(xd) ),
inference(forward_subsumption_resolution,[],[f397,f146]) ).
fof(f411,plain,
( ! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xw)
| sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0) )
| ~ spl18_4 ),
inference(forward_subsumption_resolution,[],[f405,f178]) ).
fof(f478,plain,
! [X0] :
( ~ iLess0(xu,xa)
| ~ aElement0(xu)
| ~ aElement0(X0)
| ~ aElement0(xb)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| aElement0(sK17(X0,xb)) ),
inference(resolution,[],[f135,f138]) ).
fof(f497,plain,
! [X0] :
( ~ iLess0(xu,xa)
| ~ aElement0(X0)
| ~ aElement0(xb)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| aElement0(sK17(X0,xb)) ),
inference(forward_subsumption_resolution,[],[f478,f140]) ).
fof(f513,plain,
! [X0] :
( ~ iLess0(xu,xa)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| aElement0(sK17(X0,xb)) ),
inference(forward_subsumption_resolution,[],[f497,f131]) ).
fof(f534,definition,
( spl18_26
<=> iLess0(xu,xa) ),
introduced(definition,[new_symbols(definition,[spl18_26])],[avatar_definition]) ).
fof(f536,plain,
( ~ iLess0(xu,xa)
| spl18_26 ),
inference(avatar_component_clause,[],[f534]) ).
fof(f539,definition,
( spl18_27
<=> ! [X0] :
( ~ aElement0(X0)
| aElement0(sK17(X0,xb))
| ~ sdtmndtasgtdt0(xu,xR,X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_27])],[avatar_definition]) ).
fof(f540,plain,
( ! [X0] :
( ~ sdtmndtasgtdt0(xu,xR,X0)
| aElement0(sK17(X0,xb))
| ~ aElement0(X0) )
| ~ spl18_27 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f541,plain,
( spl18_27
| ~ spl18_26 ),
inference(avatar_split_clause,[],[f513,f534,f539]) ).
fof(f621,plain,
! [X0] :
( ~ iLess0(xu,xa)
| ~ aElement0(xu)
| ~ aElement0(X0)
| ~ aElement0(xb)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| sdtmndtasgtdt0(xb,xR,sK17(X0,xb)) ),
inference(resolution,[],[f133,f138]) ).
fof(f638,plain,
! [X0] :
( ~ iLess0(xu,xa)
| ~ aElement0(X0)
| ~ aElement0(xb)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| sdtmndtasgtdt0(xb,xR,sK17(X0,xb)) ),
inference(forward_subsumption_resolution,[],[f621,f140]) ).
fof(f645,plain,
! [X0] :
( ~ iLess0(xu,xa)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| sdtmndtasgtdt0(xb,xR,sK17(X0,xb)) ),
inference(forward_subsumption_resolution,[],[f638,f131]) ).
fof(f662,definition,
( spl18_36
<=> ! [X0] :
( ~ aElement0(X0)
| sdtmndtasgtdt0(xb,xR,sK17(X0,xb))
| ~ sdtmndtasgtdt0(xu,xR,X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_36])],[avatar_definition]) ).
fof(f663,plain,
( ! [X0] :
( sdtmndtasgtdt0(xb,xR,sK17(X0,xb))
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xu,xR,X0) )
| ~ spl18_36 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f664,plain,
( spl18_36
| ~ spl18_26 ),
inference(avatar_split_clause,[],[f645,f534,f662]) ).
fof(f678,plain,
! [X0] :
( ~ iLess0(xu,xa)
| ~ aElement0(xu)
| ~ aElement0(X0)
| ~ aElement0(xb)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| sdtmndtasgtdt0(X0,xR,sK17(X0,xb)) ),
inference(resolution,[],[f134,f138]) ).
fof(f695,plain,
! [X0] :
( ~ iLess0(xu,xa)
| ~ aElement0(X0)
| ~ aElement0(xb)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| sdtmndtasgtdt0(X0,xR,sK17(X0,xb)) ),
inference(forward_subsumption_resolution,[],[f678,f140]) ).
fof(f702,plain,
! [X0] :
( ~ iLess0(xu,xa)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| sdtmndtasgtdt0(X0,xR,sK17(X0,xb)) ),
inference(forward_subsumption_resolution,[],[f695,f131]) ).
fof(f719,definition,
( spl18_43
<=> ! [X0] :
( ~ aElement0(X0)
| sdtmndtasgtdt0(X0,xR,sK17(X0,xb))
| ~ sdtmndtasgtdt0(xu,xR,X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_43])],[avatar_definition]) ).
fof(f720,plain,
( ! [X0] :
( sdtmndtasgtdt0(X0,xR,sK17(X0,xb))
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xu,xR,X0) )
| ~ spl18_43 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f721,plain,
( spl18_43
| ~ spl18_26 ),
inference(avatar_split_clause,[],[f702,f534,f719]) ).
fof(f1363,plain,
( sdtmndtasgtdt0(xu,xR,xd)
| ~ aElement0(xu)
| ~ spl18_4 ),
inference(resolution,[],[f411,f145]) ).
fof(f1368,plain,
( sdtmndtasgtdt0(xu,xR,xd)
| ~ spl18_4 ),
inference(forward_subsumption_resolution,[],[f1363,f140]) ).
fof(f3128,plain,
( aElement0(sK17(xd,xb))
| ~ aElement0(xd)
| ~ spl18_4
| ~ spl18_27 ),
inference(resolution,[],[f540,f1368]) ).
fof(f3150,plain,
( aElement0(sK17(xd,xb))
| ~ spl18_4
| ~ spl18_27 ),
inference(forward_subsumption_resolution,[],[f3128,f178]) ).
fof(f3235,plain,
( ~ aElement0(xd)
| ~ sdtmndtasgtdt0(xu,xR,xd)
| ~ sdtmndtasgtdt0(xb,xR,sK17(xd,xb))
| ~ aElement0(sK17(xd,xb))
| ~ spl18_43 ),
inference(resolution,[],[f720,f148]) ).
fof(f3258,plain,
( ~ sdtmndtasgtdt0(xu,xR,xd)
| ~ sdtmndtasgtdt0(xb,xR,sK17(xd,xb))
| ~ aElement0(sK17(xd,xb))
| ~ spl18_4
| ~ spl18_43 ),
inference(forward_subsumption_resolution,[],[f3235,f178]) ).
fof(f3268,plain,
( ~ sdtmndtasgtdt0(xb,xR,sK17(xd,xb))
| ~ aElement0(sK17(xd,xb))
| ~ spl18_4
| ~ spl18_43 ),
inference(forward_subsumption_resolution,[],[f3258,f1368]) ).
fof(f3319,definition,
( spl18_163
<=> aElement0(sK17(xd,xb)) ),
introduced(definition,[new_symbols(definition,[spl18_163])],[avatar_definition]) ).
fof(f3323,definition,
( spl18_164
<=> sdtmndtasgtdt0(xb,xR,sK17(xd,xb)) ),
introduced(definition,[new_symbols(definition,[spl18_164])],[avatar_definition]) ).
fof(f3325,plain,
( ~ sdtmndtasgtdt0(xb,xR,sK17(xd,xb))
| spl18_164 ),
inference(avatar_component_clause,[],[f3323]) ).
fof(f3326,plain,
( ~ spl18_163
| ~ spl18_164
| ~ spl18_4
| ~ spl18_43 ),
inference(avatar_split_clause,[],[f3268,f719,f177,f3323,f3319]) ).
fof(f3636,plain,
( spl18_163
| ~ spl18_4
| ~ spl18_27 ),
inference(avatar_split_clause,[],[f3150,f539,f177,f3319]) ).
fof(f3679,plain,
( ~ aElement0(xd)
| ~ sdtmndtasgtdt0(xu,xR,xd)
| ~ spl18_36
| spl18_164 ),
inference(resolution,[],[f3325,f663]) ).
fof(f3681,plain,
( ~ sdtmndtasgtdt0(xu,xR,xd)
| ~ spl18_4
| ~ spl18_36
| spl18_164 ),
inference(forward_subsumption_resolution,[],[f3679,f178]) ).
fof(f3682,plain,
( $false
| ~ spl18_4
| ~ spl18_36
| spl18_164 ),
inference(forward_subsumption_resolution,[],[f3681,f1368]) ).
fof(f3683,plain,
( ~ spl18_4
| ~ spl18_36
| spl18_164 ),
inference(avatar_contradiction_clause,[],[f3682]) ).
fof(f4230,plain,
( $false
| spl18_26 ),
inference(forward_subsumption_resolution,[],[f257,f536]) ).
fof(f4231,plain,
spl18_26,
inference(avatar_contradiction_clause,[],[f4230]) ).
cnf(s4,plain,
spl18_4,
inference(sat_conversion,[],[f188]) ).
cnf(s17,plain,
( ~ spl18_26
| spl18_27 ),
inference(sat_conversion,[],[f541]) ).
cnf(s25,plain,
( ~ spl18_26
| spl18_36 ),
inference(sat_conversion,[],[f664]) ).
cnf(s32,plain,
( ~ spl18_26
| spl18_43 ),
inference(sat_conversion,[],[f721]) ).
cnf(s179,plain,
( ~ spl18_4
| ~ spl18_43
| ~ spl18_163
| ~ spl18_164 ),
inference(sat_conversion,[],[f3326]) ).
cnf(s219,plain,
( ~ spl18_4
| ~ spl18_27
| spl18_163 ),
inference(sat_conversion,[],[f3636]) ).
cnf(s221,plain,
( ~ spl18_4
| ~ spl18_36
| spl18_164 ),
inference(sat_conversion,[],[f3683]) ).
cnf(s272,plain,
spl18_26,
inference(sat_conversion,[],[f4231]) ).
cnf(s310,plain,
spl18_43,
inference(rat,[],[s32,s272]) ).
cnf(s314,plain,
spl18_36,
inference(rat,[],[s25,s272]) ).
cnf(s318,plain,
spl18_27,
inference(rat,[],[s17,s272]) ).
cnf(s331,plain,
spl18_164,
inference(rat,[],[s221,s314,s4]) ).
cnf(s332,plain,
spl18_163,
inference(rat,[],[s219,s318,s4]) ).
cnf(s334,plain,
$false,
inference(rat,[],[s179,s331,s310,s332,s4]) ).
fof(f4232,plain,
$false,
inference(avatar_sat_refutation,[],[s334]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n011.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 21:46:46 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.29 % (3813526)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (3813534)dis+10_1_sil=32000:sp=arity:random_seed=1474367135:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (3813532)% WARNING: option uhcvi not known.
% 0.19/0.29 % (3813531)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2592603522_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (3813532)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1885294414:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (3813533)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3925407307:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (3813535)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3244560387:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (3813536)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=313895676:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (3813537)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=502314044:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % TRYING [1]
% 0.19/0.29 % TRYING [2]
% 0.19/0.29 % TRYING [3]
% 0.19/0.29 % TRYING [4]
% 0.19/0.29 % TRYING [5]
% 0.19/0.29 % (3813534) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3813526-3813534"...
% 0.19/0.29 % (3813534)...printing done.
% 0.19/0.29 % (3813534)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (3813534)------------------------------
% 0.19/0.29 % (3813534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (3813534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (3813534)CaDiCaL version: 2.1.3
% 0.19/0.29 % (3813534)Termination reason: Refutation
% 0.19/0.29 % (3813534)Time elapsed: 0.036 s
% 0.19/0.29 % (3813534)Peak memory usage: 14 MB
% 0.19/0.29 % (3813534)Instructions burned: 103 (million)
% 0.19/0.29 % (3813526)Success in time 0.066 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------