%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM482+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 : n016.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 08:12:53 AM UTC 2026
% Result : Theorem 19.22s 2.88s
% Output : CNFRefutation 19.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 67 ( 28 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 72 ( 21 ~; 20 |; 24 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 5 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ) ).
fof(m_MulUnit,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ) ).
fof(m__1716,hypothesis,
aNaturalNumber0(xk) ).
fof(m__,conjecture,
( ( isPrime0(xk)
& ! [X0] :
( ( ( doDivides0(X0,xk)
| ? [X1] :
( xk = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xk
| X0 = sz10 ) ) )
=> ? [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,
~ ( ( isPrime0(xk)
& ! [X0] :
( ( ( doDivides0(X0,xk)
| ? [X1] :
( xk = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xk
| X0 = sz10 ) ) )
=> ? [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(c1,plain,
aNaturalNumber0(sz10),
inference(clausification,[status(esa)],[mSortsC_01]) ).
cnf(c11,plain,
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulUnit]) ).
cnf(c67,plain,
aNaturalNumber0(xk),
inference(clausification,[status(esa)],[m__1716]) ).
cnf(c82,plain,
isPrime0(xk),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c84,plain,
( ~ isPrime0(X0)
| xk != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
sdtasdt0(xk,sz10) = xk,
inference(resolution,[status(thm)],[c67,c11]) ).
cnf(d1,plain,
( ~ isPrime0(xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sz10)
| xk != xk ),
inference(superposition,[status(thm)],[d0,c84]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sz10)
| xk != xk ),
inference(resolution,[status(thm)],[c82,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(xk)
| xk != xk ),
inference(resolution,[status(thm)],[c1,d2]) ).
cnf(d4,plain,
xk != xk,
inference(resolution,[status(thm)],[c67,d3]) ).
cnf(d5,plain,
$false,
inference(equality_resolution,[status(thm)],[d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM482+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
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 03:00:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.22/2.88 % SZS status Theorem for theBenchmark.p
% 19.22/2.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------