%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM505+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 : 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 08:12:58 AM UTC 2026
% Result : Theorem 15.09s 2.34s
% Output : CNFRefutation 15.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 48 ( 11 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 45 ( 16 ~; 13 |; 12 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 3 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLERefl,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ) ).
fof(mLETotal,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ) ) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ) ).
fof(m__,conjecture,
( ~ ( sdtlseqdt0(xp,xk)
| ? [X0] :
( sdtpldt0(xp,X0) = xk
& aNaturalNumber0(X0) ) )
=> ( ( sdtlseqdt0(xk,xp)
| ? [X0] :
( sdtpldt0(xk,X0) = xp
& aNaturalNumber0(X0) ) )
& xk != xp ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ~ ( sdtlseqdt0(xp,xk)
| ? [X0] :
( sdtpldt0(xp,X0) = xk
& aNaturalNumber0(X0) ) )
=> ( ( sdtlseqdt0(xk,xp)
| ? [X0] :
( sdtpldt0(xk,X0) = xp
& aNaturalNumber0(X0) ) )
& xk != xp ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c30,plain,
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mLERefl]) ).
cnf(c34,plain,
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mLETotal]) ).
cnf(c72,plain,
aNaturalNumber0(xp),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c109,plain,
aNaturalNumber0(xk),
inference(clausification,[status(esa)],[m__2306]) ).
cnf(c131,plain,
~ sdtlseqdt0(xp,xk),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c133,plain,
( ~ sdtlseqdt0(xk,xp)
| xk = xp ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c34,c131]) ).
cnf(d1,plain,
( sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c72,d0]) ).
cnf(d2,plain,
sdtlseqdt0(xk,xp),
inference(resolution,[status(thm)],[c109,d1]) ).
cnf(d3,plain,
xk = xp,
inference(resolution,[status(thm)],[d2,c133]) ).
cnf(d4,plain,
~ sdtlseqdt0(xp,xp),
inference(demodulation,[status(thm)],[c131,d3]) ).
cnf(d5,plain,
~ aNaturalNumber0(xp),
inference(resolution,[status(thm)],[d4,c30]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c72,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM505+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
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 03:03:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.09/2.34 % SZS status Theorem for theBenchmark.p
% 15.09/2.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------