%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COM012+3 : 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 : n019.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 06:58:42 AM UTC 2026
% Result : Theorem 11.46s 2.10s
% Output : CNFRefutation 11.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 108 ( 21 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 110 ( 27 ~; 50 |; 29 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 18 ( 0 sgn 4 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mTCTrans,axiom,
! [X0,X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( ( sdtmndtplgtdt0(X2,X1,X3)
& sdtmndtplgtdt0(X0,X1,X2) )
=> sdtmndtplgtdt0(X0,X1,X3) ) ) ).
fof(m__349,hypothesis,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ) ).
fof(m__,conjecture,
( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xz)
& aReductOfIn0(X0,xy,xR)
& aElement0(X0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xy)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [X0] :
( sdtmndtplgtdt0(X0,xR,xz)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xz)
& aReductOfIn0(X0,xy,xR)
& aElement0(X0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xy)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [X0] :
( sdtmndtplgtdt0(X0,xR,xz)
& aReductOfIn0(X0,xx,xR)
& aElement0(X0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c8,plain,
( ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aElement0(X3)
| ~ aRewritingSystem0(X1)
| ~ sdtmndtplgtdt0(X0,X1,X3)
| ~ sdtmndtplgtdt0(X3,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2) ),
inference(clausification,[status(esa)],[mTCTrans]) ).
cnf(c12,plain,
aElement0(xx),
inference(clausification,[status(esa)],[m__349]) ).
cnf(c13,plain,
aRewritingSystem0(xR),
inference(clausification,[status(esa)],[m__349]) ).
cnf(c14,plain,
aElement0(xy),
inference(clausification,[status(esa)],[m__349]) ).
cnf(c15,plain,
aElement0(xz),
inference(clausification,[status(esa)],[m__349]) ).
cnf(c19,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c24,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c25,plain,
sdtmndtasgtdt0(xy,xR,xz),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c29,plain,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c30,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( xx = xy
| sdtmndtplgtdt0(xx,xR,X0)
| ~ sdtmndtplgtdt0(xy,xR,X0)
| ~ aElement0(xx)
| ~ aElement0(xy)
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[status(thm)],[c8,c19]) ).
cnf(d1,plain,
( ~ sdtmndtplgtdt0(xy,xR,X0)
| sdtmndtplgtdt0(xx,xR,X0)
| ~ aElement0(xy)
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR)
| xx = xy ),
inference(resolution,[status(thm)],[c12,d0]) ).
cnf(d2,plain,
( ~ sdtmndtplgtdt0(xy,xR,X0)
| sdtmndtplgtdt0(xx,xR,X0)
| ~ aElement0(xy)
| ~ aElement0(X0)
| xx = xy ),
inference(resolution,[status(thm)],[c13,d1]) ).
cnf(d3,plain,
( ~ sdtmndtplgtdt0(xy,xR,X0)
| sdtmndtplgtdt0(xx,xR,X0)
| ~ aElement0(X0)
| xx = xy ),
inference(resolution,[status(thm)],[c14,d2]) ).
cnf(d4,plain,
( xy = xz
| sdtmndtplgtdt0(xx,xR,xz)
| ~ aElement0(xz)
| xx = xy ),
inference(resolution,[status(thm)],[d3,c24]) ).
cnf(d5,plain,
( ~ aElement0(xz)
| xy = xz
| xx = xy ),
inference(resolution,[status(thm)],[c29,d4]) ).
cnf(d6,plain,
( xy = xz
| xx = xy ),
inference(resolution,[status(thm)],[c15,d5]) ).
cnf(d7,plain,
( xx = xy
| ~ sdtmndtplgtdt0(xx,xR,xy) ),
inference(superposition,[status(thm)],[d6,c29]) ).
cnf(d8,plain,
( xx = xy
| xx = xy ),
inference(resolution,[status(thm)],[d7,c19]) ).
cnf(d9,plain,
~ sdtmndtasgtdt0(xy,xR,xz),
inference(demodulation,[status(thm)],[c30,d8]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c25,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n019.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Sat Sep 26 23:21:36 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.09/0.55 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.46/2.10 % SZS status Theorem for theBenchmark.p
% 11.46/2.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------