%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM459+2 : 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 : n017.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 08:12:48 AM UTC 2026
% Result : Theorem 25.21s 8.62s
% Output : CNFRefutation 25.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 15 unt; 0 def)
% Number of atoms : 171 ( 71 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 191 ( 81 ~; 80 |; 20 &)
% ( 0 <=>; 10 =>; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
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(m_AddZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ) ).
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(mZeroAdd,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ) ).
fof(m__745,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ) ).
fof(m__,conjecture,
( ( sdtlseqdt0(xn,xm)
& ? [X0] :
( sdtpldt0(xn,X0) = xm
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) ) )
=> xm = xn ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( sdtlseqdt0(xn,xm)
& ? [X0] :
( sdtpldt0(xn,X0) = xm
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) ) )
=> xm = xn ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
aNaturalNumber0(sz00),
inference(clausification,[status(esa)],[mSortsC]) ).
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(c7,plain,
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_AddZero]) ).
cnf(c8,plain,
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_AddZero]) ).
cnf(c17,plain,
( X1 = X0
| sdtpldt0(X2,X1) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAddCanc]) ).
cnf(c22,plain,
( X1 = sz00
| sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mZeroAdd]) ).
cnf(c31,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__745]) ).
cnf(c32,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__745]) ).
cnf(c33,plain,
aNaturalNumber0(sK39),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c34,plain,
sdtpldt0(xm,sK39) = xn,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c36,plain,
aNaturalNumber0(sK40),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c37,plain,
sdtpldt0(xn,sK40) = xm,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c39,plain,
xm != xn,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(sK40)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,X0) = sdtpldt0(xn,sdtpldt0(sK40,X0)) ),
inference(superposition,[status(thm)],[c37,c6]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,X0) = sdtpldt0(xn,sdtpldt0(sK40,X0)) ),
inference(resolution,[status(thm)],[c36,d0]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,X0) = sdtpldt0(xn,sdtpldt0(sK40,X0)) ),
inference(resolution,[status(thm)],[c32,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(sK40)
| ~ aNaturalNumber0(sz00)
| sdtpldt0(xm,sz00) = sdtpldt0(xn,sK40) ),
inference(superposition,[status(thm)],[c7,d2]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(sK40)
| ~ aNaturalNumber0(sz00)
| sdtpldt0(xm,sz00) = xm ),
inference(demodulation,[status(thm)],[d3,c37]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(sK40)
| sdtpldt0(xm,sz00) = xm ),
inference(resolution,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
sdtpldt0(xm,sz00) = xm,
inference(resolution,[status(thm)],[c36,d5]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| sz00 = X0
| xm != sdtpldt0(xm,X0) ),
inference(superposition,[status(thm)],[d6,c17]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| xm != sdtpldt0(xm,X0)
| sz00 = X0 ),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(X0)
| xm != sdtpldt0(xm,X0)
| sz00 = X0 ),
inference(resolution,[status(thm)],[c31,d8]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(sK39)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK39,X0)) ),
inference(superposition,[status(thm)],[c34,c6]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK39,X0)) ),
inference(resolution,[status(thm)],[c33,d10]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(sK39,X0)) ),
inference(resolution,[status(thm)],[c31,d11]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(sK39)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(X0,sK39)) ),
inference(superposition,[status(thm)],[c5,d12]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) = sdtpldt0(xm,sdtpldt0(X0,sK39)) ),
inference(resolution,[status(thm)],[c33,d13]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,sK39))
| sz00 = sdtpldt0(X0,sK39)
| xm != sdtpldt0(xn,X0) ),
inference(superposition,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(sdtpldt0(sK40,sK39))
| ~ aNaturalNumber0(sK40)
| sz00 = sdtpldt0(sK40,sK39)
| xm != xm ),
inference(superposition,[status(thm)],[c37,d15]) ).
cnf(d17,plain,
( ~ aNaturalNumber0(sdtpldt0(sK40,sK39))
| xm != xm
| sz00 = sdtpldt0(sK40,sK39) ),
inference(resolution,[status(thm)],[c36,d16]) ).
cnf(d18,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| X0 = sdtpldt0(X0,sz00) ),
inference(superposition,[status(thm)],[c5,c8]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(X0)
| X0 = sdtpldt0(X0,sz00) ),
inference(resolution,[status(thm)],[c0,d18]) ).
cnf(d20,plain,
( ~ aNaturalNumber0(sK40)
| ~ aNaturalNumber0(sz00)
| sdtpldt0(xm,sz00) = sdtpldt0(xn,sK40) ),
inference(superposition,[status(thm)],[d19,d2]) ).
cnf(d21,plain,
( ~ aNaturalNumber0(sK40)
| ~ aNaturalNumber0(sz00)
| xm = sdtpldt0(xn,sK40) ),
inference(demodulation,[status(thm)],[d20,d6]) ).
cnf(d22,plain,
( ~ aNaturalNumber0(sK40)
| ~ aNaturalNumber0(sz00)
| xm = xm ),
inference(demodulation,[status(thm)],[d21,c37]) ).
cnf(d23,plain,
( ~ aNaturalNumber0(sK40)
| xm = xm ),
inference(resolution,[status(thm)],[c0,d22]) ).
cnf(d24,plain,
xm = xm,
inference(resolution,[status(thm)],[c36,d23]) ).
cnf(d25,plain,
( ~ aNaturalNumber0(sdtpldt0(sK40,sK39))
| sz00 = sdtpldt0(sK40,sK39) ),
inference(resolution,[status(thm)],[d24,d17]) ).
cnf(d26,plain,
( ~ aNaturalNumber0(sdtpldt0(sK40,sK39))
| ~ aNaturalNumber0(sK40)
| ~ aNaturalNumber0(sK39)
| sK39 = sz00
| sz00 != sz00 ),
inference(superposition,[status(thm)],[d25,c22]) ).
cnf(d27,plain,
( ~ aNaturalNumber0(sK40)
| ~ aNaturalNumber0(sdtpldt0(sK40,sK39))
| sK39 = sz00
| sz00 != sz00 ),
inference(resolution,[status(thm)],[c33,d26]) ).
cnf(d28,plain,
( ~ aNaturalNumber0(sdtpldt0(sK40,sK39))
| sK39 = sz00
| sz00 != sz00 ),
inference(resolution,[status(thm)],[c36,d27]) ).
cnf(d29,plain,
( ~ aNaturalNumber0(sdtpldt0(sK40,sK39))
| sK39 = sz00 ),
inference(equality_resolution,[status(thm)],[d28]) ).
cnf(d30,plain,
( ~ aNaturalNumber0(sK40)
| ~ aNaturalNumber0(sK39)
| sK39 = sz00 ),
inference(resolution,[status(thm)],[d29,c3]) ).
cnf(d31,plain,
( ~ aNaturalNumber0(sK40)
| sK39 = sz00 ),
inference(resolution,[status(thm)],[c33,d30]) ).
cnf(d32,plain,
sK39 = sz00,
inference(resolution,[status(thm)],[c36,d31]) ).
cnf(d33,plain,
sdtpldt0(xm,sz00) = xn,
inference(demodulation,[status(thm)],[c34,d32]) ).
cnf(d34,plain,
xm = xn,
inference(demodulation,[status(thm)],[d33,d6]) ).
cnf(d35,plain,
$false,
inference(resolution,[status(thm)],[c39,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM459+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n017.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 26 02:45:24 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.21/8.62 % SZS status Theorem for theBenchmark.p
% 25.21/8.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------