%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM524+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 : 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 08:13:01 AM UTC 2026
% Result : Theorem 98.59s 16.90s
% Output : CNFRefutation 98.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 64 ( 21 unt; 1 def)
% Number of atoms : 201 ( 80 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 243 ( 106 ~; 115 |; 14 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ) ).
fof(mMulAsso,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ) ).
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(mDivAsso,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),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__3046,hypothesis,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ) ).
fof(m__3059,hypothesis,
xq = sdtsldt0(xn,xp) ).
fof(m__,conjecture,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)) ).
fof(negated_conjecture,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c4,plain,
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
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(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(c52,plain,
( X0 = sz00
| ~ doDivides0(X0,X1)
| X1 != sdtasdt0(X0,X2)
| X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefQuot]) ).
cnf(c57,plain,
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X0,X1) ),
inference(clausification,[status(esa)],[mDivAsso]) ).
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(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(c80,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(clausification,[status(esa)],[m__3046]) ).
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)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(X0,xn),xp)
| xp = sz00 ),
inference(resolution,[status(thm)],[c57,c81]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| xp = sz00
| sdtasdt0(X0,xq) = sdtsldt0(sdtasdt0(X0,xn),xp) ),
inference(demodulation,[status(thm)],[d0,c82]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| xp = sz00
| sdtasdt0(X0,xq) = sdtsldt0(sdtasdt0(X0,xn),xp) ),
inference(resolution,[status(thm)],[c71,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(X0)
| xp = sz00
| sdtasdt0(X0,xq) = sdtsldt0(sdtasdt0(X0,xn),xp) ),
inference(resolution,[status(thm)],[c73,d2]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xq) = sdtsldt0(sdtasdt0(X0,xn),xp) ),
inference(resolution,[status(thm)],[c76,d3]) ).
cnf(d5,plain,
sdtasdt0(xn,xq) = sdtsldt0(sdtasdt0(xn,xn),xp),
inference(resolution,[status(thm)],[d4,c71]) ).
cnf(d6,plain,
( ~ doDivides0(X1,sdtasdt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X1,X0))
| X1 = sz00
| X0 = sdtsldt0(sdtasdt0(X1,X0),X1) ),
inference(equality_resolution,[status(thm)],[c52]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xp,sdtasdt0(xm,xm)),xp)
| xp = sz00
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(superposition,[status(thm)],[c78,d6]) ).
cnf(d8,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| xp = sz00
| sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp) ),
inference(demodulation,[status(thm)],[d7,c78]) ).
cnf(d9,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| xp = sz00
| sdtasdt0(xm,xm) = sdtasdt0(xn,xq) ),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| xp = sz00
| sdtasdt0(xm,xm) = sdtasdt0(xn,xq) ),
inference(demodulation,[status(thm)],[d9,c78]) ).
cnf(d11,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| xp = sz00
| sdtasdt0(xm,xm) = sdtasdt0(xn,xq) ),
inference(resolution,[status(thm)],[c73,d10]) ).
cnf(d12,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| sdtasdt0(xm,xm) = sdtasdt0(xn,xq) ),
inference(resolution,[status(thm)],[c76,d11]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| sdtasdt0(xm,xm) = sdtasdt0(xn,xq) ),
inference(resolution,[status(thm)],[c80,d12]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(superposition,[status(thm)],[c78,c4]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolution,[status(thm)],[c73,d14]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolution,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(resolution,[status(thm)],[c72,d16]) ).
cnf(d18,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sdtasdt0(xm,xm) = sdtasdt0(xn,xq) ),
inference(resolution,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| xp = sz00
| X0 != xq ),
inference(superposition,[status(thm)],[c82,c50]) ).
cnf(d20,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(X0)
| xp = sz00
| X0 != xq ),
inference(resolution,[status(thm)],[c71,d19]) ).
cnf(d21,plain,
( ~ doDivides0(xp,xn)
| aNaturalNumber0(X0)
| xp = sz00
| X0 != xq ),
inference(resolution,[status(thm)],[c73,d20]) ).
cnf(d22,plain,
( ~ doDivides0(xp,xn)
| aNaturalNumber0(X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c76,d21]) ).
cnf(d23,plain,
( aNaturalNumber0(X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c81,d22]) ).
cnf(d24,plain,
aNaturalNumber0(xq),
inference(equality_resolution,[status(thm)],[d23]) ).
cnf(d25,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| xn = sdtasdt0(xp,X0)
| xp = sz00
| X0 != xq ),
inference(superposition,[status(thm)],[c82,c51]) ).
cnf(d26,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| xp = sz00
| xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c71,d25]) ).
cnf(d27,plain,
( ~ doDivides0(xp,xn)
| xp = sz00
| xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c73,d26]) ).
cnf(d28,plain,
( ~ doDivides0(xp,xn)
| xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c76,d27]) ).
cnf(d29,plain,
( xn = sdtasdt0(xp,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c81,d28]) ).
cnf(d30,plain,
xn = sdtasdt0(xp,xq),
inference(equality_resolution,[status(thm)],[d29]) ).
cnf(d31,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(xp,X0),X1) = sdtasdt0(xp,sdtasdt0(X0,X1)) ),
inference(resolution,[status(thm)],[c10,c73]) ).
cnf(d32,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(xp,xq),X0) = sdtasdt0(xp,sdtasdt0(xq,X0)) ),
inference(resolution,[status(thm)],[d24,d31]) ).
cnf(d33,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xn,X0) = sdtasdt0(xp,sdtasdt0(xq,X0)) ),
inference(demodulation,[status(thm)],[d32,d30]) ).
cnf(d34,plain,
sdtasdt0(xn,xq) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(resolution,[status(thm)],[d33,d24]) ).
cnf(d35,plain,
sdtasdt0(xm,xm) != sdtasdt0(xn,xq),
inference(demodulation,[status(thm)],[c83,d34]) ).
cnf(d36,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(resolution,[status(thm)],[d35,d18]) ).
cnf(d37,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[d36,c4]) ).
cnf(d38,plain,
$false,
inference(resolution,[status(thm)],[c72,d37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM524+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n016.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 03:11:15 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 98.59/16.90 % SZS status Theorem for theBenchmark.p
% 98.59/16.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------