%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM017+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Sun Sep 27 06:59:39 AM UTC 2026
% Result : Theorem 41.39s 7.60s
% Output : CNFRefutation 41.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 44 ( 5 avg)
% Number of connectives : 327 ( 141 ~; 142 |; 41 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 80 ( 0 sgn 33 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mWCRDef,axiom,
! [W0] :
( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1,W2,W3] :
( ( aReductOfIn0(W3,W1,W0)
& aReductOfIn0(W2,W1,W0)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) )
=> ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) ) ) ) ),
file('theBenchmark.p',mWCRDef) ).
fof(m__656_01,axiom,
( isTerminating0(xR)
& isLocallyConfluent0(xR) ),
file('theBenchmark.p',m__656_01) ).
fof(m__731,axiom,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__731) ).
fof(m__755,axiom,
( sdtmndtasgtdt0(xu,xR,xb)
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
file('theBenchmark.p',m__755) ).
fof(m__779,axiom,
( sdtmndtasgtdt0(xv,xR,xc)
& aReductOfIn0(xv,xa,xR)
& aElement0(xv) ),
file('theBenchmark.p',m__779) ).
fof(m__,conjecture,
? [W0] :
( sdtmndtasgtdt0(xv,xR,W0)
& sdtmndtasgtdt0(xu,xR,W0)
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( sdtmndtasgtdt0(xv,xR,W0)
& sdtmndtasgtdt0(xu,xR,W0)
& aElement0(W0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(m__656,axiom,
aRewritingSystem0(xR),
file('theBenchmark.p',m__656) ).
cnf(c_22,plain,
aRewritingSystem0(xR),
inference(clausify,[status(thm)],[m__656]) ).
fof(nnf_11,plain,
! [W0] :
( ( ( ? [W1,W2,W3] :
( ! [W4] :
( ~ sdtmndtasgtdt0(W3,W0,W4)
| ~ sdtmndtasgtdt0(W2,W0,W4)
| ~ aElement0(W4) )
& aReductOfIn0(W3,W1,W0)
& aReductOfIn0(W2,W1,W0)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) )
| isLocallyConfluent0(W0) )
& ( ! [X0,X1,X2] :
( ? [X3] :
( sdtmndtasgtdt0(X2,W0,X3)
& sdtmndtasgtdt0(X1,W0,X3)
& aElement0(X3) )
| ~ aReductOfIn0(X2,X0,W0)
| ~ aReductOfIn0(X1,X0,W0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ isLocallyConfluent0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(fof_nnf,[status(thm)],[mWCRDef]) ).
fof(sk_mWCRDef_sk,plain,
! [W0] :
( ( ( ( ! [W4] :
( ~ sdtmndtasgtdt0(sK3(W0),W0,W4)
| ~ sdtmndtasgtdt0(sK2(W0),W0,W4)
| ~ aElement0(W4) )
& aReductOfIn0(sK3(W0),sK1(W0),W0)
& aReductOfIn0(sK2(W0),sK1(W0),W0)
& aElement0(sK3(W0))
& aElement0(sK2(W0))
& aElement0(sK1(W0)) )
| isLocallyConfluent0(W0) )
& ( ! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X2,W0,sK0(W0,X0,X1,X2))
& sdtmndtasgtdt0(X1,W0,sK0(W0,X0,X1,X2))
& aElement0(sK0(W0,X0,X1,X2)) )
| ~ aReductOfIn0(X2,X0,W0)
| ~ aReductOfIn0(X1,X0,W0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ isLocallyConfluent0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X3,sK0(W0,X0,X1,X2)),skolemize(W1,sK1(W0)),skolemize(W2,sK2(W0)),skolemize(W3,sK3(W0))],[nnf_11]) ).
fof(sk_mWCRDef,plain,
( ! [VAR_0,VAR_1] :
( ~ sdtmndtasgtdt0(sK3(VAR_0),VAR_0,VAR_1)
| ~ sdtmndtasgtdt0(sK2(VAR_0),VAR_0,VAR_1)
| ~ aElement0(VAR_1)
| isLocallyConfluent0(VAR_0)
| ~ aRewritingSystem0(VAR_0) )
& ! [VAR_0] :
( aReductOfIn0(sK3(VAR_0),sK1(VAR_0),VAR_0)
| isLocallyConfluent0(VAR_0)
| ~ aRewritingSystem0(VAR_0) )
& ! [VAR_0] :
( aReductOfIn0(sK2(VAR_0),sK1(VAR_0),VAR_0)
| isLocallyConfluent0(VAR_0)
| ~ aRewritingSystem0(VAR_0) )
& ! [VAR_0] :
( aElement0(sK3(VAR_0))
| isLocallyConfluent0(VAR_0)
| ~ aRewritingSystem0(VAR_0) )
& ! [VAR_0] :
( aElement0(sK2(VAR_0))
| isLocallyConfluent0(VAR_0)
| ~ aRewritingSystem0(VAR_0) )
& ! [VAR_0] :
( aElement0(sK1(VAR_0))
| isLocallyConfluent0(VAR_0)
| ~ aRewritingSystem0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sdtmndtasgtdt0(VAR_3,VAR_0,sK0(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ aReductOfIn0(VAR_3,VAR_1,VAR_0)
| ~ aReductOfIn0(VAR_2,VAR_1,VAR_0)
| ~ aElement0(VAR_3)
| ~ aElement0(VAR_2)
| ~ aElement0(VAR_1)
| ~ isLocallyConfluent0(VAR_0)
| ~ aRewritingSystem0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( sdtmndtasgtdt0(VAR_2,VAR_0,sK0(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ aReductOfIn0(VAR_3,VAR_1,VAR_0)
| ~ aReductOfIn0(VAR_2,VAR_1,VAR_0)
| ~ aElement0(VAR_3)
| ~ aElement0(VAR_2)
| ~ aElement0(VAR_1)
| ~ isLocallyConfluent0(VAR_0)
| ~ aRewritingSystem0(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( aElement0(sK0(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ aReductOfIn0(VAR_3,VAR_1,VAR_0)
| ~ aReductOfIn0(VAR_2,VAR_1,VAR_0)
| ~ aElement0(VAR_3)
| ~ aElement0(VAR_2)
| ~ aElement0(VAR_1)
| ~ isLocallyConfluent0(VAR_0)
| ~ aRewritingSystem0(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mWCRDef_sk]) ).
cnf(c_39,plain,
( sdtmndtasgtdt0(D,A,sK0(A,B,C,D))
| ~ aReductOfIn0(D,B,A)
| ~ aReductOfIn0(C,B,A)
| ~ aElement0(D)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ isLocallyConfluent0(A)
| ~ aRewritingSystem0(A) ),
inference(split_conjunct,[status(thm)],[sk_mWCRDef]) ).
cnf(c_40,plain,
( sdtmndtasgtdt0(C,A,sK0(A,B,C,D))
| ~ aReductOfIn0(D,B,A)
| ~ aReductOfIn0(C,B,A)
| ~ aElement0(D)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ isLocallyConfluent0(A)
| ~ aRewritingSystem0(A) ),
inference(split_conjunct,[status(thm)],[sk_mWCRDef]) ).
cnf(c_41,plain,
( aElement0(sK0(A,B,C,D))
| ~ aReductOfIn0(D,B,A)
| ~ aReductOfIn0(C,B,A)
| ~ aElement0(D)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ isLocallyConfluent0(A)
| ~ aRewritingSystem0(A) ),
inference(split_conjunct,[status(thm)],[sk_mWCRDef]) ).
cnf(c_82,plain,
( aElement0(sK0(xR,A,B,C))
| ~ aReductOfIn0(C,A,xR)
| ~ aReductOfIn0(B,A,xR)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A)
| ~ isLocallyConfluent0(xR) ),
inference(resolve,[status(thm)],[c_22,c_41]) ).
cnf(c_83,plain,
( sdtmndtasgtdt0(B,xR,sK0(xR,A,B,C))
| ~ aReductOfIn0(C,A,xR)
| ~ aReductOfIn0(B,A,xR)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A)
| ~ isLocallyConfluent0(xR) ),
inference(resolve,[status(thm)],[c_22,c_40]) ).
cnf(c_84,plain,
( sdtmndtasgtdt0(C,xR,sK0(xR,A,B,C))
| ~ aReductOfIn0(C,A,xR)
| ~ aReductOfIn0(B,A,xR)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A)
| ~ isLocallyConfluent0(xR) ),
inference(resolve,[status(thm)],[c_22,c_39]) ).
cnf(c_91,negated_conjecture,
( ~ sdtmndtasgtdt0(xv,xR,A)
| ~ sdtmndtasgtdt0(xu,xR,A)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_93,plain,
aReductOfIn0(xv,xa,xR),
inference(clausify,[status(thm)],[m__779]) ).
cnf(c_94,plain,
aElement0(xv),
inference(clausify,[status(thm)],[m__779]) ).
cnf(c_96,plain,
aReductOfIn0(xu,xa,xR),
inference(clausify,[status(thm)],[m__755]) ).
cnf(c_97,plain,
aElement0(xu),
inference(clausify,[status(thm)],[m__755]) ).
cnf(c_105,plain,
aElement0(xa),
inference(clausify,[status(thm)],[m__731]) ).
cnf(c_107,plain,
isLocallyConfluent0(xR),
inference(clausify,[status(thm)],[m__656_01]) ).
cnf(c_143,plain,
( sdtmndtasgtdt0(C,xR,sK0(xR,A,B,C))
| ~ aReductOfIn0(C,A,xR)
| ~ aReductOfIn0(B,A,xR)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_107,c_84]) ).
cnf(c_144,plain,
( sdtmndtasgtdt0(B,xR,sK0(xR,A,B,C))
| ~ aReductOfIn0(C,A,xR)
| ~ aReductOfIn0(B,A,xR)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_107,c_83]) ).
cnf(c_145,plain,
( aElement0(sK0(xR,A,B,C))
| ~ aReductOfIn0(C,A,xR)
| ~ aReductOfIn0(B,A,xR)
| ~ aElement0(C)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_107,c_82]) ).
cnf(c_3850,plain,
( sdtmndtasgtdt0(A,xR,sK0(xR,xa,xu,A))
| ~ aReductOfIn0(A,xa,xR)
| ~ aElement0(A)
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(resolve,[status(thm)],[c_143,c_96]) ).
cnf(c_3851,plain,
( sdtmndtasgtdt0(A,xR,sK0(xR,xa,xu,A))
| ~ aReductOfIn0(A,xa,xR)
| ~ aElement0(A)
| ~ aElement0(xu) ),
inference(resolve,[status(thm)],[c_105,c_3850]) ).
cnf(c_319,plain,
( sdtmndtasgtdt0(A,xR,sK0(xR,xa,xu,A))
| ~ aReductOfIn0(A,xa,xR)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_97,c_3851]) ).
cnf(c_3852,plain,
( sdtmndtasgtdt0(xu,xR,sK0(xR,xa,xu,A))
| ~ aReductOfIn0(A,xa,xR)
| ~ aElement0(A)
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(resolve,[status(thm)],[c_144,c_96]) ).
cnf(c_3853,plain,
( sdtmndtasgtdt0(xu,xR,sK0(xR,xa,xu,A))
| ~ aReductOfIn0(A,xa,xR)
| ~ aElement0(A)
| ~ aElement0(xu) ),
inference(resolve,[status(thm)],[c_105,c_3852]) ).
cnf(c_323,plain,
( sdtmndtasgtdt0(xu,xR,sK0(xR,xa,xu,A))
| ~ aReductOfIn0(A,xa,xR)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_97,c_3853]) ).
cnf(c_3854,plain,
( aElement0(sK0(xR,xa,xu,A))
| ~ aReductOfIn0(A,xa,xR)
| ~ aElement0(A)
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(resolve,[status(thm)],[c_145,c_96]) ).
cnf(c_3855,plain,
( aElement0(sK0(xR,xa,xu,A))
| ~ aReductOfIn0(A,xa,xR)
| ~ aElement0(A)
| ~ aElement0(xu) ),
inference(resolve,[status(thm)],[c_105,c_3854]) ).
cnf(c_327,plain,
( aElement0(sK0(xR,xa,xu,A))
| ~ aReductOfIn0(A,xa,xR)
| ~ aElement0(A) ),
inference(resolve,[status(thm)],[c_97,c_3855]) ).
cnf(c_3856,plain,
( sdtmndtasgtdt0(xv,xR,sK0(xR,xa,xu,xv))
| ~ aElement0(xv) ),
inference(resolve,[status(thm)],[c_319,c_93]) ).
cnf(c_2734,plain,
sdtmndtasgtdt0(xv,xR,sK0(xR,xa,xu,xv)),
inference(resolve,[status(thm)],[c_94,c_3856]) ).
cnf(c_3857,plain,
( sdtmndtasgtdt0(xu,xR,sK0(xR,xa,xu,xv))
| ~ aElement0(xv) ),
inference(resolve,[status(thm)],[c_323,c_93]) ).
cnf(c_2876,plain,
sdtmndtasgtdt0(xu,xR,sK0(xR,xa,xu,xv)),
inference(resolve,[status(thm)],[c_94,c_3857]) ).
cnf(c_3858,plain,
( aElement0(sK0(xR,xa,xu,xv))
| ~ aElement0(xv) ),
inference(resolve,[status(thm)],[c_327,c_93]) ).
cnf(c_2938,plain,
aElement0(sK0(xR,xa,xu,xv)),
inference(resolve,[status(thm)],[c_94,c_3858]) ).
cnf(c_3859,negated_conjecture,
( ~ sdtmndtasgtdt0(xu,xR,sK0(xR,xa,xu,xv))
| ~ aElement0(sK0(xR,xa,xu,xv)) ),
inference(resolve,[status(thm)],[c_2734,c_91]) ).
cnf(c_3860,negated_conjecture,
~ sdtmndtasgtdt0(xu,xR,sK0(xR,xa,xu,xv)),
inference(resolve,[status(thm)],[c_2938,c_3859]) ).
cnf(c_3849,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2876,c_3860]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM017+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.58 % Computer : n018.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Sat Sep 26 23:24:23 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.58 % Process 1706386 was started by sandbox2 on n018,
% 0.11/0.58 % Sat Sep 26 23:24:23 2026
% 0.11/0.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.59
% 0.11/0.59 % From the command line: assign(max_seconds, 300).
% 41.39/7.60
% 41.39/7.60 % given #500 (F,wt=16): 2100 f14(xb,xb,xb) != xa. [back_unit_del(821),unit_del(a,2097)].
% 41.39/7.60
% 41.39/7.60 % SZS status Theorem for theBenchmark
% 41.39/7.60
% 41.39/7.60 % Proof 1 at 6.86 (+ 0.13) seconds.
% 41.39/7.60 % Length of proof is 30.
% 41.39/7.60 % Level of proof is 6.
% 41.39/7.60 % Maximum clause weight is 34.000.
% 41.39/7.60 % Given clauses 697.
% 41.39/7.60
% 41.39/7.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------