%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM508+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 : n015.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 08:12:58 AM UTC 2026
% Result : Theorem 62.64s 23.97s
% Output : CNFRefutation 62.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 80 ( 28 unt; 0 def)
% Number of atoms : 213 ( 38 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 253 ( 120 ~; 110 |; 15 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 42 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ) ).
fof(mAddComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ) ).
fof(mAddAsso,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ).
fof(mIH_03,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__1799,hypothesis,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X2,sdtasdt0(X0,X1))
& isPrime0(X2) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X2,X1)
| doDivides0(X2,X0) ) ) ) ) ).
fof(m__2342,hypothesis,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ) ).
fof(m__2362,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ) ).
fof(m__2478,hypothesis,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ).
fof(m__,conjecture,
( doDivides0(xr,xm)
| doDivides0(xr,xn) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( doDivides0(xr,xm)
| doDivides0(xr,xn) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c3,plain,
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB]) ).
cnf(c5,plain,
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAddComm]) ).
cnf(c6,plain,
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAddAsso]) ).
cnf(c46,plain,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X0)
| iLess0(X1,X0)
| X1 = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mIH_03]) ).
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(c73,plain,
( doDivides0(X1,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X2,X0),X1),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X1,sdtasdt0(X2,X0))
| doDivides0(X1,X0)
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m__1799]) ).
cnf(c87,plain,
aNaturalNumber0(xr),
inference(clausification,[status(esa)],[m__2342]) ).
cnf(c89,plain,
isPrime0(xr),
inference(clausification,[status(esa)],[m__2342]) ).
cnf(c91,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(clausification,[status(esa)],[m__2362]) ).
cnf(c94,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(clausification,[status(esa)],[m__2478]) ).
cnf(c95,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(clausification,[status(esa)],[m__2478]) ).
cnf(c96,plain,
~ doDivides0(xr,xn),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c97,plain,
~ doDivides0(xr,xm),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,X0) = sdtpldt0(X0,xm) ),
inference(resolution,[status(thm)],[c5,c71]) ).
cnf(d1,plain,
sdtpldt0(xm,xr) = sdtpldt0(xr,xm),
inference(resolution,[status(thm)],[d0,c87]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X0,xr),X1) = sdtpldt0(X0,sdtpldt0(xr,X1)) ),
inference(resolution,[status(thm)],[c6,c87]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xr),X0) = sdtpldt0(xn,sdtpldt0(xr,X0)) ),
inference(resolution,[status(thm)],[d2,c70]) ).
cnf(d4,plain,
sdtpldt0(sdtpldt0(xn,xr),xm) = sdtpldt0(xn,sdtpldt0(xr,xm)),
inference(resolution,[status(thm)],[d3,c71]) ).
cnf(d5,plain,
sdtpldt0(sdtpldt0(xn,xr),xm) = sdtpldt0(xn,sdtpldt0(xm,xr)),
inference(demodulation,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) = sdtpldt0(X0,xn) ),
inference(resolution,[status(thm)],[c5,c70]) ).
cnf(d7,plain,
sdtpldt0(xn,xr) = sdtpldt0(xr,xn),
inference(resolution,[status(thm)],[d6,c87]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X0,xn),X1) = sdtpldt0(X0,sdtpldt0(xn,X1)) ),
inference(resolution,[status(thm)],[c6,c70]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xr,xn),X0) = sdtpldt0(xr,sdtpldt0(xn,X0)) ),
inference(resolution,[status(thm)],[d8,c87]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xr),X0) = sdtpldt0(xr,sdtpldt0(xn,X0)) ),
inference(demodulation,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
sdtpldt0(sdtpldt0(xn,xr),xm) = sdtpldt0(xr,sdtpldt0(xn,xm)),
inference(resolution,[status(thm)],[d10,c71]) ).
cnf(d12,plain,
sdtpldt0(xn,sdtpldt0(xm,xr)) = sdtpldt0(xr,sdtpldt0(xn,xm)),
inference(demodulation,[status(thm)],[d11,d5]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xr,sdtpldt0(xn,xm))) ),
inference(superposition,[status(thm)],[d11,c3]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr)))
| ~ aNaturalNumber0(sdtpldt0(xn,xr)) ),
inference(demodulation,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr)))
| ~ aNaturalNumber0(sdtpldt0(xn,xr)) ),
inference(resolution,[status(thm)],[c71,d14]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xp,xn),X0) = sdtpldt0(xp,sdtpldt0(xn,X0)) ),
inference(resolution,[status(thm)],[d8,c72]) ).
cnf(d17,plain,
sdtpldt0(sdtpldt0(xp,xn),xm) = sdtpldt0(xp,sdtpldt0(xn,xm)),
inference(resolution,[status(thm)],[d16,c71]) ).
cnf(d18,plain,
( ~ aNaturalNumber0(sdtpldt0(xp,xn))
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(superposition,[status(thm)],[d17,c3]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(sdtpldt0(xp,xn))
| aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(resolution,[status(thm)],[c71,d18]) ).
cnf(d20,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X0,xm),X1) = sdtpldt0(X0,sdtpldt0(xm,X1)) ),
inference(resolution,[status(thm)],[c6,c71]) ).
cnf(d21,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),X0) = sdtpldt0(xn,sdtpldt0(xm,X0)) ),
inference(resolution,[status(thm)],[d20,c70]) ).
cnf(d22,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(xn,sdtpldt0(xm,xr)),
inference(resolution,[status(thm)],[d21,c87]) ).
cnf(d23,plain,
sdtpldt0(xn,xp) = sdtpldt0(xp,xn),
inference(resolution,[status(thm)],[d6,c72]) ).
cnf(d24,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X0,xp),X1) = sdtpldt0(X0,sdtpldt0(xp,X1)) ),
inference(resolution,[status(thm)],[c6,c72]) ).
cnf(d25,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xp),X0) = sdtpldt0(xn,sdtpldt0(xp,X0)) ),
inference(resolution,[status(thm)],[d24,c70]) ).
cnf(d26,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xp,xn),X0) = sdtpldt0(xn,sdtpldt0(xp,X0)) ),
inference(demodulation,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
sdtpldt0(sdtpldt0(xp,xn),xm) = sdtpldt0(xn,sdtpldt0(xp,xm)),
inference(resolution,[status(thm)],[d26,c71]) ).
cnf(d28,plain,
sdtpldt0(xp,sdtpldt0(xn,xm)) = sdtpldt0(xn,sdtpldt0(xp,xm)),
inference(demodulation,[status(thm)],[d27,d17]) ).
cnf(d29,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xp,X0) = sdtpldt0(X0,xp) ),
inference(resolution,[status(thm)],[c5,c72]) ).
cnf(d30,plain,
sdtpldt0(xp,xm) = sdtpldt0(xm,xp),
inference(resolution,[status(thm)],[d29,c71]) ).
cnf(d31,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)),
inference(resolution,[status(thm)],[d21,c72]) ).
cnf(d32,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xp,xm)),
inference(demodulation,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xp,sdtpldt0(xn,xm)),
inference(demodulation,[status(thm)],[d32,d28]) ).
cnf(d34,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c95,c46]) ).
cnf(d35,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolution,[status(thm)],[c94,d34]) ).
cnf(d36,plain,
( ~ isPrime0(xr)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| doDivides0(xr,xm)
| doDivides0(xr,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolution,[status(thm)],[d35,c73]) ).
cnf(d37,plain,
( ~ isPrime0(xr)
| doDivides0(xr,xm)
| doDivides0(xr,xn)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(demodulation,[status(thm)],[d36,d33]) ).
cnf(d38,plain,
( ~ isPrime0(xr)
| doDivides0(xr,xm)
| doDivides0(xr,xn)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr)))
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(demodulation,[status(thm)],[d37,d22]) ).
cnf(d39,plain,
( ~ isPrime0(xr)
| doDivides0(xr,xm)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr)))
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(resolution,[status(thm)],[c96,d38]) ).
cnf(d40,plain,
( ~ isPrime0(xr)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(resolution,[status(thm)],[c97,d39]) ).
cnf(d41,plain,
( ~ isPrime0(xr)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(resolution,[status(thm)],[c70,d40]) ).
cnf(d42,plain,
( ~ isPrime0(xr)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(resolution,[status(thm)],[c71,d41]) ).
cnf(d43,plain,
( ~ isPrime0(xr)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(resolution,[status(thm)],[c87,d42]) ).
cnf(d44,plain,
( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(resolution,[status(thm)],[c89,d43]) ).
cnf(d45,plain,
( ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(resolution,[status(thm)],[c91,d44]) ).
cnf(d46,plain,
( ~ aNaturalNumber0(sdtpldt0(xp,xn))
| ~ aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(resolution,[status(thm)],[d45,d19]) ).
cnf(d47,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xr))
| ~ aNaturalNumber0(sdtpldt0(xp,xn)) ),
inference(resolution,[status(thm)],[d46,d15]) ).
cnf(d48,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(xn,xr)) ),
inference(resolution,[status(thm)],[d47,c3]) ).
cnf(d49,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xr)) ),
inference(resolution,[status(thm)],[c70,d48]) ).
cnf(d50,plain,
~ aNaturalNumber0(sdtpldt0(xn,xr)),
inference(resolution,[status(thm)],[c72,d49]) ).
cnf(d51,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[d50,c3]) ).
cnf(d52,plain,
~ aNaturalNumber0(xr),
inference(resolution,[status(thm)],[c70,d51]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[c87,d52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM508+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 03:05:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 62.64/23.97 % SZS status Theorem for theBenchmark.p
% 62.64/23.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------