%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM529+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 : n026.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 29.51s 15.89s
% Output : CNFRefutation 29.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 69 ( 26 unt; 1 def)
% Number of atoms : 217 ( 88 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 238 ( 90 ~; 98 |; 34 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(m_AddZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ) ).
fof(mMulAsso,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ) ).
fof(m_MulZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ) ).
fof(mDefLE,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ).
fof(mLEAsym,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ) ).
fof(mMonMul2,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ) ).
fof(mIH_03,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ) ).
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)
| ( ! [X3] :
( ( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) )
=> ( X3 = X2
| X3 = sz10 ) )
& X2 != sz10 ) ) ) ) ) ).
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__3059,hypothesis,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)) ).
fof(m__3124,hypothesis,
( sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) )
& xm != xn ) ).
cnf(c0,plain,
aNaturalNumber0(sz00),
inference(clausification,[status(esa)],[mSortsC]) ).
cnf(c8,plain,
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_AddZero]) ).
cnf(c10,plain,
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulAsso]) ).
cnf(c13,plain,
( sdtasdt0(X0,sz00) = sz00
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulZero]) ).
cnf(c26,plain,
( sdtpldt0(X2,X0) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefLE]) ).
cnf(c31,plain,
( ~ aNaturalNumber0(X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(clausification,[status(esa)],[mLEAsym]) ).
cnf(c45,plain,
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| X0 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMonMul2]) ).
cnf(c46,plain,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X0)
| iLess0(X1,X0)
| X1 = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mIH_03]) ).
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(c75,plain,
xm != sz00,
inference(clausification,[status(esa)],[m__2987]) ).
cnf(c76,plain,
xp != sz00,
inference(clausification,[status(esa)],[m__2987]) ).
cnf(c78,plain,
( sdtasdt0(X1,sdtasdt0(X0,X0)) != sdtasdt0(X2,X2)
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X2)
| X0 = sz00
| ~ iLess0(X2,xn)
| X2 = sz00
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m__2963]) ).
cnf(c89,plain,
isPrime0(xp),
inference(clausification,[status(esa)],[m__3025]) ).
cnf(c96,plain,
aNaturalNumber0(xq),
inference(clausification,[status(esa)],[m__3059]) ).
cnf(c97,plain,
xn = sdtasdt0(xp,xq),
inference(clausification,[status(esa)],[m__3059]) ).
cnf(c99,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(clausification,[status(esa)],[m__3082]) ).
cnf(c100,plain,
xm != xn,
inference(clausification,[status(esa)],[m__3124]) ).
cnf(c103,plain,
sdtlseqdt0(xm,xn),
inference(clausification,[status(esa)],[m__3124]) ).
cnf(d0,plain,
sdtasdt0(xn,sz00) = sz00,
inference(resolution,[status(thm)],[c13,c71]) ).
cnf(d1,plain,
( ~ isPrime0(xp)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| xq = sz00
| xp = sz00
| X0 = sz00
| sdtasdt0(xm,xm) != sdtasdt0(X0,X0) ),
inference(superposition,[status(thm)],[c99,c78]) ).
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)],[c89,d2]) ).
cnf(d4,plain,
( ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| xq = sz00
| xp = sz00
| sdtasdt0(xm,xm) != sdtasdt0(X0,X0)
| X0 = sz00 ),
inference(resolution,[status(thm)],[c96,d3]) ).
cnf(d5,plain,
( ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| xq = sz00
| sdtasdt0(xm,xm) != sdtasdt0(X0,X0)
| X0 = sz00 ),
inference(resolution,[status(thm)],[c76,d4]) ).
cnf(d6,plain,
( ~ iLess0(xm,xn)
| ~ aNaturalNumber0(xm)
| xq = sz00
| xm = sz00 ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( ~ iLess0(xm,xn)
| xq = sz00
| xm = sz00 ),
inference(resolution,[status(thm)],[c72,d6]) ).
cnf(d8,plain,
( ~ iLess0(xm,xn)
| xq = sz00 ),
inference(resolution,[status(thm)],[c75,d7]) ).
cnf(d9,plain,
( iLess0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| xm = xn ),
inference(resolution,[status(thm)],[c46,c103]) ).
cnf(d10,plain,
( iLess0(xm,xn)
| ~ aNaturalNumber0(xm)
| xm = xn ),
inference(resolution,[status(thm)],[c71,d9]) ).
cnf(d11,plain,
( iLess0(xm,xn)
| xm = xn ),
inference(resolution,[status(thm)],[c72,d10]) ).
cnf(d12,plain,
iLess0(xm,xn),
inference(resolution,[status(thm)],[c100,d11]) ).
cnf(d13,plain,
xq = sz00,
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(xp,X0),X1) = sdtasdt0(xp,sdtasdt0(X0,X1)) ),
inference(resolution,[status(thm)],[c10,c73]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(xp,xq),X0) = sdtasdt0(xp,sdtasdt0(xq,X0)) ),
inference(resolution,[status(thm)],[d14,c96]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xn,X0) = sdtasdt0(xp,sdtasdt0(xq,X0)) ),
inference(demodulation,[status(thm)],[d15,c97]) ).
cnf(d17,plain,
sdtasdt0(xn,xq) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(resolution,[status(thm)],[d16,c96]) ).
cnf(d18,plain,
sdtasdt0(xm,xm) = sdtasdt0(xn,xq),
inference(demodulation,[status(thm)],[c99,d17]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| xm = sz00
| sdtlseqdt0(xm,sdtasdt0(xn,xq)) ),
inference(superposition,[status(thm)],[d18,c45]) ).
cnf(d20,plain,
( sdtlseqdt0(xm,sdtasdt0(xn,xq))
| xm = sz00 ),
inference(resolution,[status(thm)],[c72,d19]) ).
cnf(d21,plain,
sdtlseqdt0(xm,sdtasdt0(xn,xq)),
inference(resolution,[status(thm)],[c75,d20]) ).
cnf(d22,plain,
sdtlseqdt0(xm,sdtasdt0(xn,sz00)),
inference(demodulation,[status(thm)],[d21,d13]) ).
cnf(d23,plain,
sdtlseqdt0(xm,sz00),
inference(demodulation,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
xm = sdtpldt0(sz00,xm),
inference(resolution,[status(thm)],[c8,c72]) ).
cnf(d25,plain,
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| xm != X0 ),
inference(superposition,[status(thm)],[d24,c26]) ).
cnf(d26,plain,
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| xm != X0 ),
inference(resolution,[status(thm)],[c0,d25]) ).
cnf(d27,plain,
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| xm != X0 ),
inference(resolution,[status(thm)],[c72,d26]) ).
cnf(d28,plain,
( sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(xm) ),
inference(equality_resolution,[status(thm)],[d27]) ).
cnf(d29,plain,
sdtlseqdt0(sz00,xm),
inference(resolution,[status(thm)],[c72,d28]) ).
cnf(d30,plain,
( ~ sdtlseqdt0(xm,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| xm = sz00 ),
inference(resolution,[status(thm)],[d29,c31]) ).
cnf(d31,plain,
( ~ sdtlseqdt0(xm,sz00)
| ~ aNaturalNumber0(xm)
| xm = sz00 ),
inference(resolution,[status(thm)],[c0,d30]) ).
cnf(d32,plain,
( ~ sdtlseqdt0(xm,sz00)
| xm = sz00 ),
inference(resolution,[status(thm)],[c72,d31]) ).
cnf(d33,plain,
~ sdtlseqdt0(xm,sz00),
inference(resolution,[status(thm)],[c75,d32]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[d33,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM529+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
% 0.10/5.38 % Computer : n026.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.39 % DateTime : Sat Sep 26 03:10:31 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.51/15.89 % SZS status Theorem for theBenchmark.p
% 29.51/15.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------