%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 06:58:44 AM UTC 2026
% Result : Theorem 13.58s 2.33s
% Output : CNFRefutation 13.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 85 ( 6 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 83 ( 13 ~; 26 |; 39 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 1 sgn 7 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mTermNF,axiom,
! [X0] :
( ( isTerminating0(X0)
& aRewritingSystem0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ? [X2] : aNormalFormOfIn0(X2,X1,X0) ) ) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR) ).
fof(m__656_01,hypothesis,
( isTerminating0(xR)
& ! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( ( sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR) )
=> iLess0(X1,X0) ) )
& isLocallyConfluent0(xR)
& ! [X0,X1,X2] :
( ( aReductOfIn0(X2,X0,xR)
& aReductOfIn0(X1,X0,xR)
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& ( ( sdtmndtplgtdt0(X2,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR) ) )
| X2 = X3 )
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) ) ) ) ).
fof(m__799,hypothesis,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xv,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ) ).
fof(m__,conjecture,
? [X0] :
( aNormalFormOfIn0(X0,xw,xR)
| ( ~ ? [X1] : aReductOfIn0(X1,X0,xR)
& ( sdtmndtasgtdt0(xw,xR,X0)
| sdtmndtplgtdt0(xw,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xw,xR)
| xw = X0 )
& aElement0(X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( aNormalFormOfIn0(X0,xw,xR)
| ( ~ ? [X1] : aReductOfIn0(X1,X0,xR)
& ( sdtmndtasgtdt0(xw,xR,X0)
| sdtmndtplgtdt0(xw,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xw,xR)
| xw = X0 )
& aElement0(X0) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c46,plain,
( aNormalFormOfIn0(sK60(X0,X1),X1,X0)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(clausification,[status(esa)],[mTermNF]) ).
cnf(c47,plain,
aRewritingSystem0(xR),
inference(clausification,[status(esa)],[m__656]) ).
cnf(c53,plain,
isTerminating0(xR),
inference(clausification,[status(esa)],[m__656_01]) ).
cnf(c112,plain,
aElement0(xw),
inference(clausification,[status(esa)],[m__799]) ).
cnf(c124,plain,
~ aNormalFormOfIn0(X0,xw,xR),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ isTerminating0(xR)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c46,c124]) ).
cnf(d1,plain,
( ~ isTerminating0(xR)
| ~ aElement0(xw) ),
inference(resolution,[status(thm)],[c47,d0]) ).
cnf(d2,plain,
~ aElement0(xw),
inference(resolution,[status(thm)],[c53,d1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c112,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n006.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sat Sep 26 23:22:16 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.58/2.33 % SZS status Theorem for theBenchmark.p
% 13.58/2.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------