%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM525+1 : 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 : n011.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 6.09s 22.02s
% Output : CNFRefutation 6.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 28 unt; 1 def)
% Number of atoms : 140 ( 73 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 141 ( 62 ~; 59 |; 14 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ) ).
fof(mMulComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,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_MulUnit,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ) ).
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__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn) ).
fof(m__3046,hypothesis,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ) ).
fof(m__3059,hypothesis,
xq = sdtsldt0(xn,xp) ).
fof(m__,conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) ).
fof(negated_conjecture,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c1,plain,
aNaturalNumber0(sz10),
inference(clausification,[status(esa)],[mSortsC_01]) ).
cnf(c9,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
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(c11,plain,
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulUnit]) ).
cnf(c12,plain,
( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulUnit]) ).
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(c73,plain,
aNaturalNumber0(xp),
inference(clausification,[status(esa)],[m__2987]) ).
cnf(c76,plain,
xp != sz00,
inference(clausification,[status(esa)],[m__2987]) ).
cnf(c78,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(clausification,[status(esa)],[m__3014]) ).
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(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| xn = sdtasdt0(xp,X0)
| xp = sz00
| X0 != xq ),
inference(superposition,[status(thm)],[c82,c51]) ).
cnf(d1,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| xp = sz00
| xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c71,d0]) ).
cnf(d2,plain,
( ~ doDivides0(xp,xn)
| xp = sz00
| xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c73,d1]) ).
cnf(d3,plain,
( ~ doDivides0(xp,xn)
| xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c76,d2]) ).
cnf(d4,plain,
( xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c81,d3]) ).
cnf(d5,plain,
xn = sdtasdt0(xp,xq),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| xp = sz00
| X0 != xq ),
inference(superposition,[status(thm)],[c82,c50]) ).
cnf(d7,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(X0)
| xp = sz00
| X0 != xq ),
inference(resolution,[status(thm)],[c71,d6]) ).
cnf(d8,plain,
( ~ doDivides0(xp,xn)
| aNaturalNumber0(X0)
| xp = sz00
| X0 != xq ),
inference(resolution,[status(thm)],[c73,d7]) ).
cnf(d9,plain,
( ~ doDivides0(xp,xn)
| aNaturalNumber0(X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c76,d8]) ).
cnf(d10,plain,
( aNaturalNumber0(X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c81,d9]) ).
cnf(d11,plain,
aNaturalNumber0(xq),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xn) = sdtasdt0(xn,X0) ),
inference(resolution,[status(thm)],[c9,c71]) ).
cnf(d13,plain,
sdtasdt0(xp,xn) = sdtasdt0(xn,xp),
inference(resolution,[status(thm)],[d12,c73]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(xn,X0),X1) = sdtasdt0(xn,sdtasdt0(X0,X1)) ),
inference(resolution,[status(thm)],[c10,c71]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(xn,xp),X0) = sdtasdt0(xn,sdtasdt0(xp,X0)) ),
inference(resolution,[status(thm)],[d14,c73]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(xp,xn),X0) = sdtasdt0(xn,sdtasdt0(xp,X0)) ),
inference(demodulation,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
sdtasdt0(sdtasdt0(xp,xn),xq) = sdtasdt0(xn,sdtasdt0(xp,xq)),
inference(resolution,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
sdtasdt0(sdtasdt0(xp,xn),xq) = sdtasdt0(xn,xn),
inference(demodulation,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(xp,X0),X1) = sdtasdt0(xp,sdtasdt0(X0,X1)) ),
inference(resolution,[status(thm)],[c10,c73]) ).
cnf(d20,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(xp,xn),X0) = sdtasdt0(xp,sdtasdt0(xn,X0)) ),
inference(resolution,[status(thm)],[d19,c71]) ).
cnf(d21,plain,
sdtasdt0(sdtasdt0(xp,xn),xq) = sdtasdt0(xp,sdtasdt0(xn,xq)),
inference(resolution,[status(thm)],[d20,d11]) ).
cnf(d22,plain,
sdtasdt0(xn,xn) = sdtasdt0(xp,sdtasdt0(xn,xq)),
inference(demodulation,[status(thm)],[d21,d18]) ).
cnf(d23,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(xp,xq),X0) = sdtasdt0(xp,sdtasdt0(xq,X0)) ),
inference(resolution,[status(thm)],[d11,d19]) ).
cnf(d24,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xn,X0) = sdtasdt0(xp,sdtasdt0(xq,X0)) ),
inference(demodulation,[status(thm)],[d23,d5]) ).
cnf(d25,plain,
sdtasdt0(xn,xq) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(resolution,[status(thm)],[d24,d11]) ).
cnf(d26,plain,
sdtasdt0(xn,xn) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
inference(demodulation,[status(thm)],[c83,c78]) ).
cnf(d27,plain,
sdtasdt0(xn,xn) != sdtasdt0(xp,sdtasdt0(xn,xq)),
inference(demodulation,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
sdtasdt0(xn,xn) != sdtasdt0(xn,xn),
inference(demodulation,[status(thm)],[d27,d22]) ).
cnf(d29,plain,
xn = sdtasdt0(sz10,xn),
inference(resolution,[status(thm)],[c12,c71]) ).
cnf(d30,plain,
sdtasdt0(xn,sz10) = xn,
inference(resolution,[status(thm)],[c11,c71]) ).
cnf(d31,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(xn,sz10),X0) = sdtasdt0(xn,sdtasdt0(sz10,X0)) ),
inference(resolution,[status(thm)],[d14,c1]) ).
cnf(d32,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xn,X0) = sdtasdt0(xn,sdtasdt0(sz10,X0)) ),
inference(demodulation,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
sdtasdt0(xn,xn) = sdtasdt0(xn,sdtasdt0(sz10,xn)),
inference(resolution,[status(thm)],[d32,c71]) ).
cnf(d34,plain,
sdtasdt0(xn,xn) = sdtasdt0(xn,xn),
inference(demodulation,[status(thm)],[d33,d29]) ).
cnf(d35,plain,
$false,
inference(resolution,[status(thm)],[d34,d28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM525+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n011.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 03:06:14 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.09/22.02 % SZS status Theorem for theBenchmark.p
% 6.09/22.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------