%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM507+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 : n010.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 32.83s 11.56s
% Output : CNFRefutation 32.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 16 unt; 1 def)
% Number of atoms : 244 ( 82 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 313 ( 136 ~; 133 |; 34 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 15 !; 8 ?)
% 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(mAddCanc,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ) ).
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(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ) ).
fof(m__2342,hypothesis,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( xr = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xr
| X0 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ) ).
fof(m__2362,hypothesis,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X0] :
( sdtpldt0(xr,X0) = xk
& aNaturalNumber0(X0) ) ) ).
fof(m__2377,hypothesis,
( sdtlseqdt0(xk,xp)
& ? [X0] :
( sdtpldt0(xk,X0) = xp
& aNaturalNumber0(X0) )
& xk != xp ) ).
fof(m__,conjecture,
( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X0] :
( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X0) ) )
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X0] :
( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X0) ) )
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
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(c17,plain,
( X1 = X0
| sdtpldt0(X2,X1) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAddCanc]) ).
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(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(c109,plain,
aNaturalNumber0(xk),
inference(clausification,[status(esa)],[m__2306]) ).
cnf(c116,plain,
aNaturalNumber0(xr),
inference(clausification,[status(esa)],[m__2342]) ).
cnf(c125,plain,
aNaturalNumber0(sK107),
inference(clausification,[status(esa)],[m__2362]) ).
cnf(c126,plain,
sdtpldt0(xr,sK107) = xk,
inference(clausification,[status(esa)],[m__2362]) ).
cnf(c130,plain,
xk != xp,
inference(clausification,[status(esa)],[m__2377]) ).
cnf(c131,plain,
aNaturalNumber0(sK109),
inference(clausification,[status(esa)],[m__2377]) ).
cnf(c132,plain,
sdtpldt0(xk,sK109) = xp,
inference(clausification,[status(esa)],[m__2377]) ).
cnf(c133,plain,
sdtlseqdt0(xk,xp),
inference(clausification,[status(esa)],[m__2377]) ).
cnf(c134,plain,
( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0) != sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(xr,X0)) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(superposition,[status(thm)],[c6,c134]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(xr,X0)) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c116,d0]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(X0,xr)) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(superposition,[status(thm)],[c5,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(X0,xr)) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c116,d2]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(X0,sdtpldt0(X1,xr))) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(superposition,[status(thm)],[c6,d3]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(X0,sdtpldt0(X1,xr))) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c116,d4]) ).
cnf(d6,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(X1,sdtpldt0(xr,X0))) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(superposition,[status(thm)],[c5,d5]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(X0,sdtpldt0(xr,X1))) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c116,d6]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,sK107))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK107)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(X0,xk)) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(superposition,[status(thm)],[c126,d7]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,sK107))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(X0,xk)) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c125,d8]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,sK107))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(xk,X0)) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(superposition,[status(thm)],[c5,d9]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,sK107))
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),sdtpldt0(xk,X0)) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c109,d10]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sK109,sK107))
| ~ aNaturalNumber0(sK109)
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(superposition,[status(thm)],[c132,d11]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(sdtpldt0(sK109,sK107))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp)
| sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c131,d12]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(sdtpldt0(sK109,sK107))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(sdtpldt0(sK109,sK107))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr)
| xr = X0
| sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),X0) ),
inference(superposition,[status(thm)],[d14,c17]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(sdtpldt0(sK109,sK107))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X0)
| xr = X0
| sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),X0) ),
inference(resolution,[status(thm)],[c116,d15]) ).
cnf(d17,plain,
( ~ aNaturalNumber0(sdtpldt0(sK109,sK107))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| xr = xp ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( ~ aNaturalNumber0(sdtpldt0(sK109,sK107))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xr = xp ),
inference(resolution,[status(thm)],[c72,d17]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(sK109)
| ~ aNaturalNumber0(sK107)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xr = xp ),
inference(resolution,[status(thm)],[d18,c3]) ).
cnf(d20,plain,
( ~ aNaturalNumber0(sK109)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xr = xp ),
inference(resolution,[status(thm)],[c125,d19]) ).
cnf(d21,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xr = xp ),
inference(resolution,[status(thm)],[c131,d20]) ).
cnf(d22,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| xr = xp ),
inference(resolution,[status(thm)],[d21,c3]) ).
cnf(d23,plain,
( ~ aNaturalNumber0(xm)
| xr = xp ),
inference(resolution,[status(thm)],[c70,d22]) ).
cnf(d24,plain,
xr = xp,
inference(resolution,[status(thm)],[c71,d23]) ).
cnf(d25,plain,
sdtpldt0(xp,sK107) = xk,
inference(demodulation,[status(thm)],[c126,d24]) ).
cnf(d26,plain,
( sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(sK107)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| xk != X0 ),
inference(superposition,[status(thm)],[d25,c26]) ).
cnf(d27,plain,
( sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(sK107)
| ~ aNaturalNumber0(X0)
| xk != X0 ),
inference(resolution,[status(thm)],[c72,d26]) ).
cnf(d28,plain,
( sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| xk != X0 ),
inference(resolution,[status(thm)],[c125,d27]) ).
cnf(d29,plain,
( sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk) ),
inference(equality_resolution,[status(thm)],[d28]) ).
cnf(d30,plain,
sdtlseqdt0(xp,xk),
inference(resolution,[status(thm)],[c109,d29]) ).
cnf(d31,plain,
( ~ sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xk = xp ),
inference(resolution,[status(thm)],[d30,c31]) ).
cnf(d32,plain,
( ~ sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xk)
| xk = xp ),
inference(resolution,[status(thm)],[c72,d31]) ).
cnf(d33,plain,
( ~ sdtlseqdt0(xk,xp)
| xk = xp ),
inference(resolution,[status(thm)],[c109,d32]) ).
cnf(d34,plain,
~ sdtlseqdt0(xk,xp),
inference(resolution,[status(thm)],[c130,d33]) ).
cnf(d35,plain,
$false,
inference(resolution,[status(thm)],[c133,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM507+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
% 0.09/5.37 % Computer : n010.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 03:02:22 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.83/11.56 % SZS status Theorem for theBenchmark.p
% 32.83/11.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------