%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM465+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 : n003.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 08:12:49 AM UTC 2026
% Result : Theorem 31.48s 4.98s
% Output : CNFRefutation 31.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 19 unt; 0 def)
% Number of atoms : 121 ( 54 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 113 ( 42 ~; 44 |; 17 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ) ).
fof(m_AddZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ) ).
fof(mMulComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ).
fof(m_MulUnit,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ) ).
fof(m_MulZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ) ).
fof(mLERefl,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ) ).
fof(mMonMul,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2
& X0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ) ).
fof(m__987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ) ).
fof(m__1007,hypothesis,
( xm != sz00
=> ( sdtlseqdt0(sz10,xm)
& ? [X0] :
( sdtpldt0(sz10,X0) = xm
& aNaturalNumber0(X0) ) ) ) ).
fof(m__,conjecture,
( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(xn,X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(xn,X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
aNaturalNumber0(sz00),
inference(clausification,[status(esa)],[mSortsC]) ).
cnf(c1,plain,
aNaturalNumber0(sz10),
inference(clausification,[status(esa)],[mSortsC_01]) ).
cnf(c7,plain,
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_AddZero]) ).
cnf(c9,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
cnf(c12,plain,
( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulUnit]) ).
cnf(c13,plain,
( sdtasdt0(X0,sz00) = sz00
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulZero]) ).
cnf(c30,plain,
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mLERefl]) ).
cnf(c42,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X2)
| X2 = sz00
| X1 = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMonMul]) ).
cnf(c45,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__987]) ).
cnf(c46,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__987]) ).
cnf(c49,plain,
( sdtlseqdt0(sz10,xm)
| xm = sz00 ),
inference(clausification,[status(esa)],[m__1007]) ).
cnf(c50,plain,
xm != sz00,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c52,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
xn = sdtasdt0(sz10,xn),
inference(resolution,[status(thm)],[c12,c46]) ).
cnf(d1,plain,
sdtasdt0(xm,sz00) = sz00,
inference(resolution,[status(thm)],[c13,c45]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xm) = sdtasdt0(xm,X0) ),
inference(resolution,[status(thm)],[c9,c45]) ).
cnf(d3,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[d2,c46]) ).
cnf(d4,plain,
~ sdtlseqdt0(xn,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm)],[c52,d3]) ).
cnf(d5,plain,
( ~ sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| sz10 = X0
| xn = sz00
| sdtlseqdt0(xn,sdtasdt0(X0,xn)) ),
inference(superposition,[status(thm)],[d0,c42]) ).
cnf(d6,plain,
( sdtlseqdt0(xn,sdtasdt0(X0,xn))
| ~ sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| xn = sz00
| sz10 = X0 ),
inference(resolution,[status(thm)],[c1,d5]) ).
cnf(d7,plain,
( sdtlseqdt0(xn,sdtasdt0(X0,xn))
| ~ sdtlseqdt0(sz10,X0)
| ~ aNaturalNumber0(X0)
| xn = sz00
| sz10 = X0 ),
inference(resolution,[status(thm)],[c46,d6]) ).
cnf(d8,plain,
( ~ sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(xm)
| xn = sz00
| sz10 = xm ),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
( ~ sdtlseqdt0(sz10,xm)
| xn = sz00
| sz10 = xm ),
inference(resolution,[status(thm)],[c45,d8]) ).
cnf(d10,plain,
sdtlseqdt0(sz10,xm),
inference(resolution,[status(thm)],[c50,c49]) ).
cnf(d11,plain,
( xn = sz00
| sz10 = xm ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( sz10 = xm
| ~ sdtlseqdt0(xn,sdtasdt0(xm,sz00)) ),
inference(superposition,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
( ~ sdtlseqdt0(xn,sz00)
| sz10 = xm ),
inference(demodulation,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(d15,plain,
sdtpldt0(xn,sz00) = xn,
inference(resolution,[status(thm)],[c7,c46]) ).
cnf(d16,plain,
( sz10 = xm
| sdtpldt0(sz00,sz00) = xn ),
inference(superposition,[status(thm)],[d11,d15]) ).
cnf(d17,plain,
( sz00 = xn
| sz10 = xm ),
inference(demodulation,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( sz10 = xm
| sz10 = xm
| ~ sdtlseqdt0(sz00,sz00) ),
inference(superposition,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(sz00)
| sz10 = xm ),
inference(resolution,[status(thm)],[d18,c30]) ).
cnf(d20,plain,
sz10 = xm,
inference(resolution,[status(thm)],[c0,d19]) ).
cnf(d21,plain,
~ sdtlseqdt0(xn,sdtasdt0(sz10,xn)),
inference(demodulation,[status(thm)],[d4,d20]) ).
cnf(d22,plain,
~ sdtlseqdt0(xn,xn),
inference(demodulation,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
~ aNaturalNumber0(xn),
inference(resolution,[status(thm)],[d22,c30]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[c46,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM465+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 02:53:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.48/4.98 % SZS status Theorem for theBenchmark.p
% 31.48/4.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------