%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:12:57 AM UTC 2026
% Result : Theorem 6.35s 2.71s
% Output : CNFRefutation 6.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 78 ( 40 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 84 ( 25 ~; 34 |; 22 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 3 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mPrimDiv,axiom,
! [X0] :
( ( X0 != sz10
& X0 != sz00
& aNaturalNumber0(X0) )
=> ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) ) ) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ) ).
fof(m__2315,hypothesis,
~ ( xk = sz10
| xk = sz00 ) ).
fof(m__,conjecture,
? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( X0 = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( X1 = X0
| X1 = sz10 ) )
& X0 != sz10
& X0 != sz00 ) )
& ( doDivides0(X0,xk)
| ? [X1] :
( xk = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( X0 = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( X1 = X0
| X1 = sz10 ) )
& X0 != sz10
& X0 != sz00 ) )
& ( doDivides0(X0,xk)
| ? [X1] :
( xk = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c67,plain,
( aNaturalNumber0(sK85(X0))
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mPrimDiv]) ).
cnf(c68,plain,
( doDivides0(sK85(X0),X0)
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mPrimDiv]) ).
cnf(c69,plain,
( isPrime0(sK85(X0))
| X0 = sz10
| X0 = sz00
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mPrimDiv]) ).
cnf(c109,plain,
aNaturalNumber0(xk),
inference(clausification,[status(esa)],[m__2306]) ).
cnf(c112,plain,
xk != sz00,
inference(clausification,[status(esa)],[m__2315]) ).
cnf(c113,plain,
xk != sz10,
inference(clausification,[status(esa)],[m__2315]) ).
cnf(c119,plain,
( ~ isPrime0(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ isPrime0(sK85(xk))
| ~ aNaturalNumber0(sK85(xk))
| ~ aNaturalNumber0(xk)
| xk = sz10
| xk = sz00 ),
inference(resolution,[status(thm)],[c68,c119]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sK85(xk))
| xk = sz10
| xk = sz00
| ~ aNaturalNumber0(xk)
| xk = sz10
| xk = sz00 ),
inference(resolution,[status(thm)],[c69,d0]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(xk)
| xk = sz10
| xk = sz00
| ~ aNaturalNumber0(xk)
| xk = sz10
| xk = sz00 ),
inference(resolution,[status(thm)],[d1,c67]) ).
cnf(d3,plain,
( xk = sz10
| xk = sz00 ),
inference(resolution,[status(thm)],[c109,d2]) ).
cnf(d4,plain,
xk = sz10,
inference(resolution,[status(thm)],[c112,d3]) ).
cnf(d5,plain,
sz10 != sz10,
inference(demodulation,[status(thm)],[c113,d4]) ).
cnf(d6,plain,
$false,
inference(equality_resolution,[status(thm)],[d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n004.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 03:00:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.35/2.71 % SZS status Theorem for theBenchmark.p
% 6.35/2.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------