%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM487+3 : 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 : n006.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 16.72s 13.94s
% Output : CNFRefutation 16.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 89 ( 47 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 87 ( 32 ~; 30 |; 20 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 7 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(mAddComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ) ).
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(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10
& xp != sz00 ) ).
fof(m__1883,hypothesis,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ) ).
fof(m__,conjecture,
( ( sdtlseqdt0(xr,xn)
| ? [X0] :
( sdtpldt0(xr,X0) = xn
& aNaturalNumber0(X0) ) )
& xr != xn ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( sdtlseqdt0(xr,xn)
| ? [X0] :
( sdtpldt0(xr,X0) = xn
& aNaturalNumber0(X0) ) )
& xr != xn ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
aNaturalNumber0(sz00),
inference(clausification,[status(esa)],[mSortsC]) ).
cnf(c5,plain,
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAddComm]) ).
cnf(c7,plain,
( sdtpldt0(X0,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(c70,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c72,plain,
aNaturalNumber0(xp),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c89,plain,
xp != sz00,
inference(clausification,[status(esa)],[m__1860]) ).
cnf(c100,plain,
aNaturalNumber0(xr),
inference(clausification,[status(esa)],[m__1883]) ).
cnf(c101,plain,
sdtpldt0(xp,xr) = xn,
inference(clausification,[status(esa)],[m__1883]) ).
cnf(c103,plain,
( sdtpldt0(xr,X0) != xn
| ~ aNaturalNumber0(X0)
| xr = xn ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
sdtpldt0(xn,sz00) = xn,
inference(resolution,[status(thm)],[c7,c70]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| sdtpldt0(xn,X0) != xn ),
inference(superposition,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) != xn
| X0 = sz00 ),
inference(resolution,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) != xn
| X0 = sz00 ),
inference(resolution,[status(thm)],[c70,d2]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xp,X0) = sdtpldt0(X0,xp) ),
inference(resolution,[status(thm)],[c5,c72]) ).
cnf(d5,plain,
sdtpldt0(xp,xr) = sdtpldt0(xr,xp),
inference(resolution,[status(thm)],[d4,c100]) ).
cnf(d6,plain,
xn = sdtpldt0(xr,xp),
inference(demodulation,[status(thm)],[d5,c101]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(xp)
| xr = xn
| xn != xn ),
inference(superposition,[status(thm)],[d6,c103]) ).
cnf(d8,plain,
( xr = xn
| xn != xn ),
inference(resolution,[status(thm)],[c72,d7]) ).
cnf(d9,plain,
xr = xn,
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
xn = sdtpldt0(xn,xp),
inference(demodulation,[status(thm)],[d6,d9]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(xp)
| xp = sz00
| xn != xn ),
inference(superposition,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
( xp = sz00
| xn != xn ),
inference(resolution,[status(thm)],[c72,d11]) ).
cnf(d13,plain,
xn != xn,
inference(resolution,[status(thm)],[c89,d12]) ).
cnf(d14,plain,
$false,
inference(equality_resolution,[status(thm)],[d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM487+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.61 % Computer : n006.cluster.edu
% 0.10/10.61 % Model : x86_64 x86_64
% 0.10/10.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.61 % Memory : 8046.5625MB
% 0.10/10.61 % OS : Linux 6.8.0-71-generic
% 0.10/10.61 % CPULimit : 300
% 0.10/10.61 % WCLimit : 300
% 0.10/10.61 % DateTime : Sat Sep 26 02:56:37 UTC 2026
% 0.10/10.61 % CPUTime :
% 0.10/10.61 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.72/13.94 % SZS status Theorem for theBenchmark.p
% 16.72/13.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------