%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM013+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 09:40:08 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of formulae : 99 ( 7 unt; 0 def)
% Number of atoms : 555 ( 8 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 799 ( 343 ~; 346 |; 76 &)
% ( 12 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 243 ( 217 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aRewritingSystem0(X1) )
=> ! [X2] :
( aReductOfIn0(X2,X0,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mTCDef) ).
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/sandbox/benchmark/theBenchmark.p',mTCRDef) ).
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(f14,axiom,
( aRewritingSystem0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__587) ).
fof(f15,conjecture,
! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] : aNormalFormOfIn0(X2,X1,xR) ) )
=> ? [X1] : aNormalFormOfIn0(X1,X0,xR) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f16,negated_conjecture,
~ ! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] : aNormalFormOfIn0(X2,X1,xR) ) )
=> ? [X1] : aNormalFormOfIn0(X1,X0,xR) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f21,plain,
~ ! [X0] :
( aElement0(X0)
=> ( ! [X1] :
( aElement0(X1)
=> ( iLess0(X1,X0)
=> ? [X2] : aNormalFormOfIn0(X2,X1,xR) ) )
=> ? [X3] : aNormalFormOfIn0(X3,X0,xR) ) ),
inference(rectify,[],[f16]) ).
fof(f22,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(flattening,[],[f22]) ).
fof(f24,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(f25,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,[],[f24]) ).
fof(f28,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(f29,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f28]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f36,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ) )
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f37,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ) )
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f36]) ).
fof(f38,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(f39,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,[],[f38]) ).
fof(f40,plain,
? [X0] :
( ! [X3] : ~ aNormalFormOfIn0(X3,X0,xR)
& ! [X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,xR)
| ~ iLess0(X1,X0)
| ~ aElement0(X1) )
& aElement0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f41,plain,
? [X0] :
( ! [X3] : ~ aNormalFormOfIn0(X3,X0,xR)
& ! [X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,xR)
| ~ iLess0(X1,X0)
| ~ aElement0(X1) )
& aElement0(X0) ),
inference(flattening,[],[f40]) ).
fof(f48,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,[],[f25]) ).
fof(f49,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,[],[f48]) ).
fof(f50,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,[],[f49]) ).
fof(f51,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))],[f50]) ).
fof(f52,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,[],[f29]) ).
fof(f53,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,[],[f52]) ).
fof(f62,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,[],[f37]) ).
fof(f63,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,[],[f62]) ).
fof(f64,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))],[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,[],[f39]) ).
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(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))],[f67]) ).
fof(f69,plain,
? [X0] :
( ! [X1] : ~ aNormalFormOfIn0(X1,X0,xR)
& ! [X2] :
( ? [X3] : aNormalFormOfIn0(X3,X2,xR)
| ~ iLess0(X2,X0)
| ~ aElement0(X2) )
& aElement0(X0) ),
inference(rectify,[],[f41]) ).
fof(f70,plain,
( ! [X1] : ~ aNormalFormOfIn0(X1,sK16,xR)
& ! [X2] :
( aNormalFormOfIn0(sK17(X2),X2,xR)
| ~ iLess0(X2,sK16)
| ~ aElement0(X2) )
& aElement0(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X3,sK17(X2))],[f69]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f76,plain,
! [X2,X0,X1] :
( sdtmndtplgtdt0(X0,X1,X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f80,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| X0 != X2
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f81,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,[],[f31]) ).
fof(f106,plain,
! [X3,X0,X4] :
( ~ sdtmndtplgtdt0(X3,X0,X4)
| iLess0(X4,X3)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f111,plain,
! [X2,X0,X1,X4] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aReductOfIn0(X4,X2,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| aElement0(X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| aNormalFormOfIn0(X2,X0,X1)
| aReductOfIn0(sK15(X1,X2),X2,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f115,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f14]) ).
fof(f116,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f14]) ).
fof(f117,plain,
aElement0(sK16),
inference(cnf_transformation,[],[f70]) ).
fof(f118,plain,
! [X2] :
( aNormalFormOfIn0(sK17(X2),X2,xR)
| ~ iLess0(X2,sK16)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f119,plain,
! [X1] : ~ aNormalFormOfIn0(X1,sK16,xR),
inference(cnf_transformation,[],[f70]) ).
fof(f120,plain,
! [X2,X1] :
( sdtmndtasgtdt0(X2,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(equality_resolution,[],[f80]) ).
fof(f121,plain,
! [X2,X1] :
( sdtmndtasgtdt0(X2,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1) ),
inference(duplicate_literal_removal,[],[f120]) ).
fof(f413,plain,
! [X2,X0,X1] :
( ~ aReductOfIn0(X2,X0,X1)
| sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(forward_subsumption_resolution,[],[f76,f71]) ).
fof(f805,plain,
! [X0,X1] :
( ~ aElement0(X0)
| aNormalFormOfIn0(X0,X0,X1)
| aReductOfIn0(sK15(X1,X0),X0,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(resolution,[],[f114,f121]) ).
fof(f806,plain,
! [X0,X1] :
( aReductOfIn0(sK15(X1,X0),X0,X1)
| aNormalFormOfIn0(X0,X0,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(duplicate_literal_removal,[],[f805]) ).
fof(f807,plain,
! [X0,X1] :
( aNormalFormOfIn0(X0,X0,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| sdtmndtplgtdt0(X0,X1,sK15(X1,X0))
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(resolution,[],[f806,f413]) ).
fof(f808,plain,
! [X0,X1] :
( aNormalFormOfIn0(X0,X0,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| aElement0(sK15(X1,X0))
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ),
inference(resolution,[],[f806,f71]) ).
fof(f809,plain,
! [X0,X1] :
( aNormalFormOfIn0(X0,X0,X1)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| aElement0(sK15(X1,X0)) ),
inference(duplicate_literal_removal,[],[f808]) ).
fof(f810,plain,
! [X0,X1] :
( sdtmndtplgtdt0(X0,X1,sK15(X1,X0))
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| aNormalFormOfIn0(X0,X0,X1) ),
inference(duplicate_literal_removal,[],[f807]) ).
fof(f825,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| aNormalFormOfIn0(X0,X0,X1)
| iLess0(sK15(X1,X0),X0)
| ~ aElement0(X0)
| ~ aElement0(sK15(X1,X0))
| ~ isTerminating0(X1)
| ~ aRewritingSystem0(X1) ),
inference(resolution,[],[f810,f106]) ).
fof(f826,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| aNormalFormOfIn0(X0,X0,X1)
| sdtmndtasgtdt0(X0,X1,sK15(X1,X0))
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(sK15(X1,X0)) ),
inference(resolution,[],[f810,f79]) ).
fof(f827,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| aNormalFormOfIn0(X0,X0,X1)
| sdtmndtasgtdt0(X0,X1,sK15(X1,X0))
| ~ aElement0(sK15(X1,X0)) ),
inference(duplicate_literal_removal,[],[f826]) ).
fof(f828,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| aNormalFormOfIn0(X0,X0,X1)
| iLess0(sK15(X1,X0),X0)
| ~ aElement0(sK15(X1,X0))
| ~ isTerminating0(X1) ),
inference(duplicate_literal_removal,[],[f825]) ).
fof(f831,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X0,X1,sK15(X1,X0))
| ~ aRewritingSystem0(X1)
| aNormalFormOfIn0(X0,X0,X1)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f827,f809]) ).
fof(f832,plain,
! [X0,X1] :
( iLess0(sK15(X1,X0),X0)
| ~ aRewritingSystem0(X1)
| aNormalFormOfIn0(X0,X0,X1)
| ~ aElement0(X0)
| ~ isTerminating0(X1) ),
inference(forward_subsumption_resolution,[],[f828,f809]) ).
fof(f1822,plain,
! [X0] :
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| sdtmndtasgtdt0(X0,xR,sK17(X0))
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f118,f112]) ).
fof(f1823,plain,
! [X0] :
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| aElement0(sK17(X0))
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f118,f113]) ).
fof(f1824,plain,
! [X0,X1] :
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| ~ aReductOfIn0(X1,sK17(X0),xR)
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f118,f111]) ).
fof(f1825,plain,
! [X0,X1] :
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| ~ aReductOfIn0(X1,sK17(X0),xR)
| ~ aRewritingSystem0(xR) ),
inference(duplicate_literal_removal,[],[f1824]) ).
fof(f1826,plain,
! [X0] :
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| aElement0(sK17(X0))
| ~ aRewritingSystem0(xR) ),
inference(duplicate_literal_removal,[],[f1823]) ).
fof(f1827,plain,
! [X0] :
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| sdtmndtasgtdt0(X0,xR,sK17(X0))
| ~ aRewritingSystem0(xR) ),
inference(duplicate_literal_removal,[],[f1822]) ).
fof(f1828,plain,
! [X0,X1] :
( ~ aReductOfIn0(X1,sK17(X0),xR)
| ~ aElement0(X0)
| ~ iLess0(X0,sK16) ),
inference(forward_subsumption_resolution,[],[f1825,f116]) ).
fof(f1829,plain,
! [X0] :
( ~ iLess0(X0,sK16)
| ~ aElement0(X0)
| aElement0(sK17(X0)) ),
inference(forward_subsumption_resolution,[],[f1826,f116]) ).
fof(f1830,plain,
! [X0] :
( sdtmndtasgtdt0(X0,xR,sK17(X0))
| ~ aElement0(X0)
| ~ iLess0(X0,sK16) ),
inference(forward_subsumption_resolution,[],[f1827,f116]) ).
fof(f1871,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ iLess0(X0,sK16)
| ~ sdtmndtasgtdt0(X1,xR,X0)
| sdtmndtasgtdt0(X1,xR,sK17(X0))
| ~ aElement0(X1)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0)
| ~ aElement0(sK17(X0)) ),
inference(resolution,[],[f1830,f81]) ).
fof(f1872,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ iLess0(X0,sK16)
| ~ sdtmndtasgtdt0(X1,xR,X0)
| sdtmndtasgtdt0(X1,xR,sK17(X0))
| ~ aElement0(X1)
| ~ aRewritingSystem0(xR)
| ~ aElement0(sK17(X0)) ),
inference(duplicate_literal_removal,[],[f1871]) ).
fof(f1875,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ iLess0(X0,sK16)
| ~ sdtmndtasgtdt0(X1,xR,X0)
| sdtmndtasgtdt0(X1,xR,sK17(X0))
| ~ aElement0(X1)
| ~ aRewritingSystem0(xR) ),
inference(forward_subsumption_resolution,[],[f1872,f1829]) ).
fof(f1878,plain,
! [X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK17(X0))
| ~ iLess0(X0,sK16)
| ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(forward_subsumption_resolution,[],[f1875,f116]) ).
fof(f2555,plain,
! [X0,X1] :
( ~ iLess0(X0,sK16)
| ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(sK17(X0))
| aNormalFormOfIn0(sK17(X0),X1,xR)
| aReductOfIn0(sK15(xR,sK17(X0)),sK17(X0),xR)
| ~ aElement0(X1)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f1878,f114]) ).
fof(f2560,plain,
! [X0,X1] :
( ~ iLess0(X0,sK16)
| ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ aElement0(sK17(X0))
| aNormalFormOfIn0(sK17(X0),X1,xR)
| aReductOfIn0(sK15(xR,sK17(X0)),sK17(X0),xR)
| ~ aRewritingSystem0(xR) ),
inference(duplicate_literal_removal,[],[f2555]) ).
fof(f2563,plain,
! [X0,X1] :
( ~ iLess0(X0,sK16)
| ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| aNormalFormOfIn0(sK17(X0),X1,xR)
| aReductOfIn0(sK15(xR,sK17(X0)),sK17(X0),xR)
| ~ aRewritingSystem0(xR) ),
inference(forward_subsumption_resolution,[],[f2560,f1829]) ).
fof(f2565,plain,
! [X0,X1] :
( ~ iLess0(X0,sK16)
| ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| aNormalFormOfIn0(sK17(X0),X1,xR)
| aReductOfIn0(sK15(xR,sK17(X0)),sK17(X0),xR) ),
inference(forward_subsumption_resolution,[],[f2563,f116]) ).
fof(f2566,plain,
! [X0,X1] :
( aNormalFormOfIn0(sK17(X0),X1,xR)
| ~ sdtmndtasgtdt0(X1,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(X1)
| ~ iLess0(X0,sK16) ),
inference(forward_subsumption_resolution,[],[f2565,f1828]) ).
fof(f2589,plain,
! [X0] :
( ~ sdtmndtasgtdt0(sK16,xR,X0)
| ~ aElement0(X0)
| ~ aElement0(sK16)
| ~ iLess0(X0,sK16) ),
inference(resolution,[],[f2566,f119]) ).
fof(f2596,plain,
! [X0] :
( ~ sdtmndtasgtdt0(sK16,xR,X0)
| ~ aElement0(X0)
| ~ iLess0(X0,sK16) ),
inference(forward_subsumption_resolution,[],[f2589,f117]) ).
fof(f2612,plain,
( ~ aElement0(sK15(xR,sK16))
| ~ iLess0(sK15(xR,sK16),sK16)
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(sK16,sK16,xR)
| ~ aElement0(sK16) ),
inference(resolution,[],[f2596,f831]) ).
fof(f2618,plain,
( ~ iLess0(sK15(xR,sK16),sK16)
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(sK16,sK16,xR)
| ~ aElement0(sK16) ),
inference(forward_subsumption_resolution,[],[f2612,f809]) ).
fof(f2622,plain,
( ~ iLess0(sK15(xR,sK16),sK16)
| aNormalFormOfIn0(sK16,sK16,xR)
| ~ aElement0(sK16) ),
inference(forward_subsumption_resolution,[],[f2618,f116]) ).
fof(f2625,plain,
( ~ iLess0(sK15(xR,sK16),sK16)
| ~ aElement0(sK16) ),
inference(forward_subsumption_resolution,[],[f2622,f119]) ).
fof(f2626,plain,
~ iLess0(sK15(xR,sK16),sK16),
inference(forward_subsumption_resolution,[],[f2625,f117]) ).
fof(f2662,plain,
( ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(sK16,sK16,xR)
| ~ aElement0(sK16)
| ~ isTerminating0(xR) ),
inference(resolution,[],[f2626,f832]) ).
fof(f2663,plain,
( aNormalFormOfIn0(sK16,sK16,xR)
| ~ aElement0(sK16)
| ~ isTerminating0(xR) ),
inference(forward_subsumption_resolution,[],[f2662,f116]) ).
fof(f2664,plain,
( ~ aElement0(sK16)
| ~ isTerminating0(xR) ),
inference(forward_subsumption_resolution,[],[f2663,f119]) ).
fof(f2665,plain,
~ isTerminating0(xR),
inference(forward_subsumption_resolution,[],[f2664,f117]) ).
fof(f2666,plain,
$false,
inference(forward_subsumption_resolution,[],[f2665,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM013+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:46:58 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.31 % (2065277)Will run a generic schedule for satisfiability detection.
% 0.21/0.31 % (2065284)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2791256685:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.31 % (2065283)% WARNING: option uhcvi not known.
% 0.21/0.31 % (2065282)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2026066288_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.31 % (2065283)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2258485843:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.31 % (2065285)dis+10_1_sil=32000:sp=arity:random_seed=768412356:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.31 % (2065286)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4010415690:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.31 % (2065287)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1335360716:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.31 % (2065288)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=503210392:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.31 % TRYING [1]
% 0.21/0.31 % TRYING [2]
% 0.21/0.31 % TRYING [3]
% 0.21/0.31 % TRYING [4]
% 0.21/0.31 % TRYING [5]
% 0.21/0.31 % (2065284) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2065277-2065284"...
% 0.21/0.31 % TRYING [6]
% 0.21/0.31 % (2065284)...printing done.
% 0.21/0.31 % (2065284)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (2065284)------------------------------
% 0.21/0.31 % (2065284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2065284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2065284)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2065284)Termination reason: Refutation
% 0.21/0.31 % (2065284)Time elapsed: 0.036 s
% 0.21/0.31 % (2065284)Peak memory usage: 13 MB
% 0.21/0.31 % (2065284)Instructions burned: 88 (million)
% 0.21/0.31 % (2065277)Success in time 0.068 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------