%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : COM017+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Jul 24 10:54:56 AM UTC 2025
% Result : Theorem 23.27s 3.25s
% Output : CNFRefutation 23.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 32 unt; 0 def)
% Number of atoms : 193 ( 8 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 198 ( 57 ~; 80 |; 53 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 46 ( 4 sgn 12 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
? [W0] :
( aElement0(W0)
& ( xu = W0
| aReductOfIn0(W0,xu,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xu,xR,W0)
| sdtmndtasgtdt0(xu,xR,W0) )
& ( xv = W0
| aReductOfIn0(W0,xv,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xv,xR,W0)
| sdtmndtasgtdt0(xv,xR,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ? [W0] :
( aElement0(W0)
& ( xu = W0
| aReductOfIn0(W0,xu,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xu,xR,W0)
| sdtmndtasgtdt0(xu,xR,W0) )
& ( xv = W0
| aReductOfIn0(W0,xv,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xv,xR,W0)
| sdtmndtasgtdt0(xv,xR,W0) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(106,plain,
( ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0)
| sP2(X0,X1) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ sdtmndtasgtdt0(xu,xR,sK8(xR,xa,xv,xu))
| ~ aElement0(sK8(xR,xa,xv,xu))
| sP2(sK8(xR,xa,xv,xu),X1_13) ),
inference(instantiation,[status(thm)],[106]) ).
cnf(107,plain,
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sP2(X0,X1) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l13,plain,
( ~ sdtmndtasgtdt0(xv,xR,sK8(xR,xa,xv,xu))
| ~ sP2(sK8(xR,xa,xv,xu),X1_13) ),
inference(instantiation,[status(thm)],[107]) ).
fof(mWCRDef,plain,
! [W0] :
( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1,W2,W3] :
( ( aElement0(W1)
& aElement0(W2)
& aElement0(W3)
& aReductOfIn0(W2,W1,W0)
& aReductOfIn0(W3,W1,W0) )
=> ? [W4] :
( aElement0(W4)
& sdtmndtasgtdt0(W2,W0,W4)
& sdtmndtasgtdt0(W3,W0,W4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWCRDef) ).
cnf(21,plain,
( ~ aReductOfIn0(X0,X1,X2)
| ~ aReductOfIn0(X3,X1,X2)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aElement0(X3)
| ~ isLocallyConfluent0(X2)
| sdtmndtasgtdt0(X0,X2,sK8(X2,X1,X0,X3)) ),
inference(cnf,[status(esa)],[mWCRDef]) ).
cnf(l37,plain,
( ~ aReductOfIn0(xv,xa,xR)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xa)
| ~ aElement0(xv)
| ~ aElement0(xu)
| ~ isLocallyConfluent0(xR)
| sdtmndtasgtdt0(xv,xR,sK8(xR,xa,xv,xu)) ),
inference(instantiation,[status(thm)],[21]) ).
cnf(22,plain,
( ~ aReductOfIn0(X0,X1,X2)
| ~ aReductOfIn0(X3,X1,X2)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aElement0(X3)
| ~ isLocallyConfluent0(X2)
| sdtmndtasgtdt0(X3,X2,sK8(X2,X1,X0,X3)) ),
inference(cnf,[status(esa)],[mWCRDef]) ).
cnf(l2,plain,
( ~ aReductOfIn0(xv,xa,xR)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xa)
| ~ aElement0(xv)
| ~ aElement0(xu)
| ~ isLocallyConfluent0(xR)
| sdtmndtasgtdt0(xu,xR,sK8(xR,xa,xv,xu)) ),
inference(instantiation,[status(thm)],[22]) ).
fof(m__779,plain,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR)
& ( xv = xc
| ( ( aReductOfIn0(xc,xv,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xv,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) )
& sdtmndtplgtdt0(xv,xR,xc) ) )
& sdtmndtasgtdt0(xv,xR,xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__779) ).
cnf(95,plain,
aElement0(xv),
inference(cnf,[status(esa)],[m__779]) ).
cnf(l243,plain,
aElement0(xv),
inference(instantiation,[status(thm)],[95]) ).
fof(m__755,plain,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& ( xu = xb
| ( ( aReductOfIn0(xb,xu,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xu,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtplgtdt0(xu,xR,xb) ) )
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
cnf(89,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf,[status(esa)],[m__755]) ).
cnf(l53,plain,
aReductOfIn0(xu,xa,xR),
inference(instantiation,[status(thm)],[89]) ).
cnf(l47,plain,
aElement0(xv),
inference(instantiation,[status(thm)],[95]) ).
cnf(l8,plain,
aReductOfIn0(xu,xa,xR),
inference(instantiation,[status(thm)],[89]) ).
cnf(96,plain,
aReductOfIn0(xv,xa,xR),
inference(cnf,[status(esa)],[m__779]) ).
cnf(l44,plain,
aReductOfIn0(xv,xa,xR),
inference(instantiation,[status(thm)],[96]) ).
fof(m__731,plain,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
cnf(56,plain,
aElement0(xa),
inference(cnf,[status(esa)],[m__731]) ).
cnf(l41,plain,
aElement0(xa),
inference(instantiation,[status(thm)],[56]) ).
cnf(20,plain,
( ~ aReductOfIn0(X0,X1,X2)
| ~ aReductOfIn0(X3,X1,X2)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aElement0(X3)
| ~ isLocallyConfluent0(X2)
| aElement0(sK8(X2,X1,X0,X3)) ),
inference(cnf,[status(esa)],[mWCRDef]) ).
cnf(l1,plain,
( ~ aReductOfIn0(xv,xa,xR)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xa)
| ~ aElement0(xv)
| ~ aElement0(xu)
| ~ isLocallyConfluent0(xR)
| aElement0(sK8(xR,xa,xv,xu)) ),
inference(instantiation,[status(thm)],[20]) ).
cnf(l247,plain,
aElement0(xa),
inference(instantiation,[status(thm)],[56]) ).
fof(m__656,plain,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
cnf(39,plain,
aRewritingSystem0(xR),
inference(cnf,[status(esa)],[m__656]) ).
cnf(l81,plain,
aRewritingSystem0(xR),
inference(instantiation,[status(thm)],[39]) ).
cnf(l49,plain,
aReductOfIn0(xv,xa,xR),
inference(instantiation,[status(thm)],[96]) ).
cnf(l32,plain,
aReductOfIn0(xv,xa,xR),
inference(instantiation,[status(thm)],[96]) ).
cnf(l4,plain,
aReductOfIn0(xu,xa,xR),
inference(instantiation,[status(thm)],[89]) ).
fof(mReduct,plain,
! [W0,W1] :
( ( aElement0(W0)
& aRewritingSystem0(W1) )
=> ! [W2] :
( aReductOfIn0(W2,W0,W1)
=> aElement0(W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).
cnf(0,plain,
( ~ aReductOfIn0(X0,X1,X2)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| aElement0(X0) ),
inference(cnf,[status(esa)],[mReduct]) ).
cnf(l5,plain,
( ~ aReductOfIn0(xv,xa,xR)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xa)
| aElement0(xv) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l3,plain,
aRewritingSystem0(xR),
inference(instantiation,[status(thm)],[39]) ).
cnf(88,plain,
aElement0(xu),
inference(cnf,[status(esa)],[m__755]) ).
cnf(l262,plain,
aElement0(xu),
inference(instantiation,[status(thm)],[88]) ).
cnf(l15,plain,
aReductOfIn0(xv,xa,xR),
inference(instantiation,[status(thm)],[96]) ).
cnf(l69,plain,
aElement0(xu),
inference(instantiation,[status(thm)],[88]) ).
fof(m__656_01,plain,
( ! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3] :
( aElement0(W3)
& ( W1 = W3
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( W2 = W3
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
& isLocallyConfluent0(xR)
& ! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( aReductOfIn0(W1,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1) )
=> iLess0(W1,W0) ) )
& isTerminating0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
cnf(51,plain,
isLocallyConfluent0(xR),
inference(cnf,[status(esa)],[m__656_01]) ).
cnf(l127,plain,
isLocallyConfluent0(xR),
inference(instantiation,[status(thm)],[51]) ).
cnf(l11,plain,
aRewritingSystem0(xR),
inference(instantiation,[status(thm)],[39]) ).
cnf(l86,plain,
aElement0(xa),
inference(instantiation,[status(thm)],[56]) ).
cnf(l38,plain,
aRewritingSystem0(xR),
inference(instantiation,[status(thm)],[39]) ).
cnf(l149,plain,
isLocallyConfluent0(xR),
inference(instantiation,[status(thm)],[51]) ).
cnf(l283,plain,
isLocallyConfluent0(xR),
inference(instantiation,[status(thm)],[51]) ).
cnf(l100,plain,
aElement0(xu),
inference(instantiation,[status(thm)],[88]) ).
cnf(l16,plain,
aElement0(xa),
inference(instantiation,[status(thm)],[56]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l13,l37,l2,l243,l53,l47,l8,l44,l41,l1,l247,l81,l49,l32,l4,l5,l3,l262,l15,l69,l127,l11,l86,l38,l149,l283,l100,l16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COM017+4 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jul 20 06:09:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.18/0.53 % launching worker at depth: 10
% 23.27/3.25 % SZS status Theorem for theBenchmark
% 23.27/3.25 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------