%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM529+1 : 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 : n002.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 08:13:02 AM UTC 2026
% Result : Theorem 50.29s 6.97s
% Output : CNFRefutation 50.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 23 unt; 1 def)
% Number of atoms : 178 ( 85 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 207 ( 85 ~; 95 |; 18 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m_MulZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ) ).
fof(mIH_03,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ) ).
fof(mDefQuot,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ) ).
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__2963,hypothesis,
! [X0,X1,X2] :
( ( X2 != sz00
& X1 != sz00
& X0 != sz00
& aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X2,sdtasdt0(X1,X1)) = sdtasdt0(X0,X0)
=> ( iLess0(X0,xn)
=> ~ isPrime0(X2) ) ) ) ).
fof(m__3025,hypothesis,
isPrime0(xp) ).
fof(m__3046,hypothesis,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ) ).
fof(m__3059,hypothesis,
xq = sdtsldt0(xn,xp) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)) ).
fof(m__3124,hypothesis,
( sdtlseqdt0(xm,xn)
& xm != xn ) ).
cnf(c13,plain,
( sdtasdt0(X0,sz00) = sz00
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulZero]) ).
cnf(c46,plain,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X0)
| iLess0(X1,X0)
| X1 = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mIH_03]) ).
cnf(c50,plain,
( X0 = sz00
| ~ doDivides0(X0,X1)
| aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefQuot]) ).
cnf(c51,plain,
( X0 = sz00
| ~ doDivides0(X0,X1)
| X1 = sdtasdt0(X0,X2)
| X2 != sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefQuot]) ).
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(c74,plain,
xn != sz00,
inference(clausification,[status(esa)],[m__2987]) ).
cnf(c75,plain,
xm != sz00,
inference(clausification,[status(esa)],[m__2987]) ).
cnf(c76,plain,
xp != sz00,
inference(clausification,[status(esa)],[m__2987]) ).
cnf(c77,plain,
( ~ aNaturalNumber0(X2)
| X2 = sz00
| ~ aNaturalNumber0(X1)
| X0 = sz00
| sdtasdt0(X0,sdtasdt0(X1,X1)) != sdtasdt0(X2,X2)
| ~ iLess0(X2,xn)
| X1 = sz00
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m__2963]) ).
cnf(c79,plain,
isPrime0(xp),
inference(clausification,[status(esa)],[m__3025]) ).
cnf(c81,plain,
doDivides0(xp,xn),
inference(clausification,[status(esa)],[m__3046]) ).
cnf(c82,plain,
xq = sdtsldt0(xn,xp),
inference(clausification,[status(esa)],[m__3059]) ).
cnf(c83,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(clausification,[status(esa)],[m__3082]) ).
cnf(c84,plain,
xm != xn,
inference(clausification,[status(esa)],[m__3124]) ).
cnf(c85,plain,
sdtlseqdt0(xm,xn),
inference(clausification,[status(esa)],[m__3124]) ).
cnf(d0,plain,
sdtasdt0(xp,sz00) = sz00,
inference(resolution,[status(thm)],[c13,c73]) ).
cnf(d1,plain,
( ~ isPrime0(xp)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(X0)
| xp = sz00
| xq = sz00
| X0 = sz00
| sdtasdt0(xm,xm) != sdtasdt0(X0,X0) ),
inference(superposition,[status(thm)],[c83,c77]) ).
cnf(d2,plain,
( ~ isPrime0(xp)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(X0)
| xq = sz00
| xp = sz00
| sdtasdt0(xm,xm) != sdtasdt0(X0,X0)
| X0 = sz00 ),
inference(resolution,[status(thm)],[c73,d1]) ).
cnf(d3,plain,
( ~ iLess0(X0,xn)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(X0)
| xq = sz00
| xp = sz00
| sdtasdt0(xm,xm) != sdtasdt0(X0,X0)
| X0 = sz00 ),
inference(resolution,[status(thm)],[c79,d2]) ).
cnf(d4,plain,
( ~ iLess0(X0,xn)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(X0)
| xq = sz00
| sdtasdt0(xm,xm) != sdtasdt0(X0,X0)
| X0 = sz00 ),
inference(resolution,[status(thm)],[c76,d3]) ).
cnf(d5,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| xp = sz00
| X0 != xq ),
inference(superposition,[status(thm)],[c82,c50]) ).
cnf(d6,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(X0)
| xp = sz00
| X0 != xq ),
inference(resolution,[status(thm)],[c71,d5]) ).
cnf(d7,plain,
( ~ doDivides0(xp,xn)
| aNaturalNumber0(X0)
| xp = sz00
| X0 != xq ),
inference(resolution,[status(thm)],[c73,d6]) ).
cnf(d8,plain,
( ~ doDivides0(xp,xn)
| aNaturalNumber0(X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c76,d7]) ).
cnf(d9,plain,
( aNaturalNumber0(X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c81,d8]) ).
cnf(d10,plain,
aNaturalNumber0(xq),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| xq = sz00
| sdtasdt0(xm,xm) != sdtasdt0(X0,X0)
| X0 = sz00 ),
inference(resolution,[status(thm)],[d10,d4]) ).
cnf(d12,plain,
( ~ iLess0(xm,xn)
| ~ aNaturalNumber0(xm)
| xq = sz00
| xm = sz00 ),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
( ~ iLess0(xm,xn)
| xq = sz00
| xm = sz00 ),
inference(resolution,[status(thm)],[c72,d12]) ).
cnf(d14,plain,
( ~ iLess0(xm,xn)
| xq = sz00 ),
inference(resolution,[status(thm)],[c75,d13]) ).
cnf(d15,plain,
( iLess0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| xm = xn ),
inference(resolution,[status(thm)],[c46,c85]) ).
cnf(d16,plain,
( iLess0(xm,xn)
| ~ aNaturalNumber0(xm)
| xm = xn ),
inference(resolution,[status(thm)],[c71,d15]) ).
cnf(d17,plain,
( iLess0(xm,xn)
| xm = xn ),
inference(resolution,[status(thm)],[c72,d16]) ).
cnf(d18,plain,
iLess0(xm,xn),
inference(resolution,[status(thm)],[c84,d17]) ).
cnf(d19,plain,
xq = sz00,
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| xn = sdtasdt0(xp,X0)
| xp = sz00
| X0 != xq ),
inference(superposition,[status(thm)],[c82,c51]) ).
cnf(d21,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| xp = sz00
| xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c71,d20]) ).
cnf(d22,plain,
( ~ doDivides0(xp,xn)
| xp = sz00
| xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c73,d21]) ).
cnf(d23,plain,
( ~ doDivides0(xp,xn)
| xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c76,d22]) ).
cnf(d24,plain,
( xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c81,d23]) ).
cnf(d25,plain,
xn = sdtasdt0(xp,xq),
inference(equality_resolution,[status(thm)],[d24]) ).
cnf(d26,plain,
xn = sdtasdt0(xp,sz00),
inference(demodulation,[status(thm)],[d25,d19]) ).
cnf(d27,plain,
xn = sz00,
inference(demodulation,[status(thm)],[d26,d0]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[c74,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM529+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 03:10:21 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.29/6.97 % SZS status Theorem for theBenchmark.p
% 50.29/6.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------