%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM523+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 : n007.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 08:13:01 AM UTC 2026
% Result : Theorem 25.90s 23.37s
% Output : CNFRefutation 25.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 10 unt; 1 def)
% Number of atoms : 120 ( 17 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 142 ( 59 ~; 56 |; 21 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ) ).
fof(mDefDiv,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ).
fof(mPDP,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X2,sdtasdt0(X0,X1))
& isPrime0(X2) )
=> ( doDivides0(X2,X1)
| doDivides0(X2,X0) ) ) ) ).
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn) ).
fof(m__3025,hypothesis,
( isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10 ) ).
fof(m__,conjecture,
( ( doDivides0(xp,xn)
| ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) )
& ( doDivides0(xp,sdtasdt0(xn,xn))
| ? [X0] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( doDivides0(xp,xn)
| ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) )
& ( doDivides0(xp,sdtasdt0(xn,xn))
| ? [X0] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c4,plain,
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
cnf(c49,plain,
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiv]) ).
cnf(c70,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X1,sdtasdt0(X2,X0))
| doDivides0(X1,X0)
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mPDP]) ).
cnf(c71,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__2987]) ).
cnf(c72,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__2987]) ).
cnf(c73,plain,
aNaturalNumber0(xp),
inference(clausification,[status(esa)],[m__2987]) ).
cnf(c85,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(clausification,[status(esa)],[m__3014]) ).
cnf(c89,plain,
isPrime0(xp),
inference(clausification,[status(esa)],[m__3025]) ).
cnf(c91,plain,
( ~ doDivides0(xp,xn)
| sdtasdt0(xn,xn) != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( doDivides0(X1,sdtasdt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X1,X0))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[status(thm)],[c49]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(superposition,[status(thm)],[c85,d0]) ).
cnf(d2,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(demodulation,[status(thm)],[d1,c85]) ).
cnf(d3,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(resolution,[status(thm)],[c73,d2]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(superposition,[status(thm)],[c85,c4]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolution,[status(thm)],[c73,d4]) ).
cnf(d6,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(resolution,[status(thm)],[c72,d6]) ).
cnf(d8,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( ~ isPrime0(xp)
| doDivides0(xp,xn)
| doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(resolution,[status(thm)],[d8,c70]) ).
cnf(d10,plain,
( ~ isPrime0(xp)
| doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(resolution,[status(thm)],[c71,d9]) ).
cnf(d11,plain,
( ~ isPrime0(xp)
| doDivides0(xp,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(resolution,[status(thm)],[c73,d10]) ).
cnf(d12,plain,
( doDivides0(xp,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(resolution,[status(thm)],[c89,d11]) ).
cnf(d13,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xn,xn) != sdtasdt0(xn,xn) ),
inference(superposition,[status(thm)],[c85,c91]) ).
cnf(d14,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ doDivides0(xp,xn) ),
inference(resolution,[status(thm)],[d14,c4]) ).
cnf(d16,plain,
~ doDivides0(xp,xn),
inference(resolution,[status(thm)],[c72,d15]) ).
cnf(d17,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(resolution,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[d17,c4]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c72,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM523+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
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 03:04:08 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.90/23.37 % SZS status Theorem for theBenchmark.p
% 25.90/23.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------