%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM490+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 : n014.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 08:12:54 AM UTC 2026
% Result : Theorem 68.67s 29.45s
% Output : CNFRefutation 68.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 21 unt; 2 def)
% Number of atoms : 196 ( 43 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 255 ( 125 ~; 113 |; 9 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ) ).
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ) ).
fof(mMulComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ).
fof(mDefLE,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ).
fof(mDefDiff,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp) ).
fof(m__1951,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) ).
fof(m__,conjecture,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ).
fof(negated_conjecture,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c3,plain,
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB]) ).
cnf(c4,plain,
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
cnf(c9,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
cnf(c26,plain,
( sdtpldt0(X2,X0) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefLE]) ).
cnf(c27,plain,
( aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X1 != sdtmndt0(X2,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiff]) ).
cnf(c29,plain,
( ~ aNaturalNumber0(X2)
| X1 = sdtmndt0(X2,X0)
| sdtpldt0(X0,X1) != X2
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiff]) ).
cnf(c70,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c71,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c72,plain,
aNaturalNumber0(xp),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c76,plain,
sdtlseqdt0(xp,xn),
inference(clausification,[status(esa)],[m__1870]) ).
cnf(c77,plain,
xr = sdtmndt0(xn,xp),
inference(clausification,[status(esa)],[m__1883]) ).
cnf(c81,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(clausification,[status(esa)],[m__1951]) ).
cnf(c82,plain,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xp) = sdtasdt0(xp,X0) ),
inference(resolution,[status(thm)],[c9,c72]) ).
cnf(d1,plain,
sdtasdt0(xm,xp) = sdtasdt0(xp,xm),
inference(resolution,[status(thm)],[d0,c71]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xm) = sdtasdt0(xm,X0) ),
inference(resolution,[status(thm)],[c9,c71]) ).
cnf(d3,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(X0)
| X0 != xr ),
inference(superposition,[status(thm)],[c77,c27]) ).
cnf(d4,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(X0)
| X0 != xr ),
inference(resolution,[status(thm)],[c70,d3]) ).
cnf(d5,plain,
( ~ sdtlseqdt0(xp,xn)
| aNaturalNumber0(X0)
| X0 != xr ),
inference(resolution,[status(thm)],[c72,d4]) ).
cnf(d6,plain,
( aNaturalNumber0(X0)
| X0 != xr ),
inference(resolution,[status(thm)],[c76,d5]) ).
cnf(d7,plain,
aNaturalNumber0(xr),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
sdtasdt0(xr,xm) = sdtasdt0(xm,xr),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xr,xm) = sdtmndt0(X0,sdtasdt0(xp,xm))
| sdtasdt0(xn,xm) != X0 ),
inference(superposition,[status(thm)],[c81,c29]) ).
cnf(d10,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xr) = sdtmndt0(X0,sdtasdt0(xp,xm))
| sdtasdt0(xn,xm) != X0 ),
inference(demodulation,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xr) = sdtmndt0(X0,sdtasdt0(xm,xp))
| sdtasdt0(xn,xm) != X0 ),
inference(demodulation,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xr) = sdtmndt0(X0,sdtasdt0(xm,xp))
| sdtasdt0(xn,xm) != X0 ),
inference(demodulation,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xr) = sdtmndt0(X0,sdtasdt0(xm,xp))
| sdtasdt0(xn,xm) != X0 ),
inference(demodulation,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( ~ sdtlseqdt0(sdtasdt0(xm,xp),X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xr) = sdtmndt0(X0,sdtasdt0(xm,xp))
| sdtasdt0(xn,xm) != X0 ),
inference(demodulation,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
( ~ sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xm,xr) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp)) ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp)),
inference(demodulation,[status(thm)],[c82,d1]) ).
cnf(d17,plain,
sdtasdt0(xm,xr) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp)),
inference(demodulation,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
( ~ sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c81,c3]) ).
cnf(d20,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(demodulation,[status(thm)],[d19,d1]) ).
cnf(d21,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(demodulation,[status(thm)],[d20,d8]) ).
cnf(d22,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[d21,c4]) ).
cnf(d23,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[c71,d22]) ).
cnf(d24,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xp))
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[d7,d23]) ).
cnf(d25,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[d24,c4]) ).
cnf(d26,plain,
( ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[c71,d25]) ).
cnf(d27,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(resolution,[status(thm)],[c72,d26]) ).
cnf(d28,plain,
( ~ sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp)) ),
inference(resolution,[status(thm)],[d27,d18]) ).
cnf(d29,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xm) != X0 ),
inference(superposition,[status(thm)],[c81,c26]) ).
cnf(d30,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xm) != X0 ),
inference(demodulation,[status(thm)],[d29,d1]) ).
cnf(d31,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xm) != X0 ),
inference(demodulation,[status(thm)],[d30,d8]) ).
cnf(d32,plain,
( sdtlseqdt0(sdtasdt0(xm,xp),X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xm) != X0 ),
inference(demodulation,[status(thm)],[d31,d1]) ).
cnf(d33,plain,
( sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(equality_resolution,[status(thm)],[d32]) ).
cnf(d34,plain,
( sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp)) ),
inference(resolution,[status(thm)],[d27,d33]) ).
cnf(d35,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xp)) ),
inference(resolution,[status(thm)],[d34,d28]) ).
cnf(d36,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xm,xp)) ),
inference(resolution,[status(thm)],[d35,c4]) ).
cnf(d37,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xm,xp)) ),
inference(resolution,[status(thm)],[c71,d36]) ).
cnf(d38,plain,
~ aNaturalNumber0(sdtasdt0(xm,xp)),
inference(resolution,[status(thm)],[d7,d37]) ).
cnf(d39,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[d38,c4]) ).
cnf(d40,plain,
~ aNaturalNumber0(xp),
inference(resolution,[status(thm)],[c71,d39]) ).
cnf(d41,plain,
$false,
inference(resolution,[status(thm)],[c72,d40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM490+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n014.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sat Sep 26 02:57:52 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.67/29.45 % SZS status Theorem for theBenchmark.p
% 68.67/29.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------