%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM467+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 59.00s 8.82s
% Output : CNFRefutation 59.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 18 unt; 0 def)
% Number of atoms : 83 ( 29 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 27 ~; 23 |; 16 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 9 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(mSortsB,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ) ).
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(mAMDistr,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ) ).
fof(m__1240,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ) ).
fof(m__1240_04,hypothesis,
( doDivides0(xl,xn)
& ? [X0] :
( xn = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ) ).
fof(m__,conjecture,
( doDivides0(xl,sdtpldt0(xm,xn))
| ? [X0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ? [X0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ),
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(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(c15,plain,
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAMDistr]) ).
cnf(c54,plain,
aNaturalNumber0(xl),
inference(clausification,[status(esa)],[m__1240]) ).
cnf(c55,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__1240]) ).
cnf(c56,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__1240]) ).
cnf(c57,plain,
aNaturalNumber0(sK69),
inference(clausification,[status(esa)],[m__1240_04]) ).
cnf(c58,plain,
xm = sdtasdt0(xl,sK69),
inference(clausification,[status(esa)],[m__1240_04]) ).
cnf(c60,plain,
aNaturalNumber0(sK70),
inference(clausification,[status(esa)],[m__1240_04]) ).
cnf(c61,plain,
xn = sdtasdt0(xl,sK70),
inference(clausification,[status(esa)],[m__1240_04]) ).
cnf(c63,plain,
( sdtpldt0(xm,xn) != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xl,sdtpldt0(X0,X1)) = sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X1)) ),
inference(resolution,[status(thm)],[c15,c54]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sdtpldt0(sK69,X0)) = sdtpldt0(sdtasdt0(xl,sK69),sdtasdt0(xl,X0)) ),
inference(resolution,[status(thm)],[d0,c57]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sdtpldt0(sK69,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0)) ),
inference(demodulation,[status(thm)],[d1,c58]) ).
cnf(d3,plain,
sdtasdt0(xl,sdtpldt0(sK69,sK70)) = sdtpldt0(xm,sdtasdt0(xl,sK70)),
inference(resolution,[status(thm)],[d2,c60]) ).
cnf(d4,plain,
sdtasdt0(xl,sdtpldt0(sK69,sK70)) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm)],[d3,c61]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(sdtpldt0(sK69,sK70))
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ),
inference(superposition,[status(thm)],[d4,c63]) ).
cnf(d6,plain,
xn = sdtpldt0(sz00,xn),
inference(resolution,[status(thm)],[c8,c56]) ).
cnf(d7,plain,
sdtpldt0(xm,sz00) = xm,
inference(resolution,[status(thm)],[c7,c55]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X0,sz00),X1) = sdtpldt0(X0,sdtpldt0(sz00,X1)) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xm,sz00),X0) = sdtpldt0(xm,sdtpldt0(sz00,X0)) ),
inference(resolution,[status(thm)],[d8,c55]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,X0) = sdtpldt0(xm,sdtpldt0(sz00,X0)) ),
inference(demodulation,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
sdtpldt0(xm,xn) = sdtpldt0(xm,sdtpldt0(sz00,xn)),
inference(resolution,[status(thm)],[d10,c56]) ).
cnf(d12,plain,
sdtpldt0(xm,xn) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
~ aNaturalNumber0(sdtpldt0(sK69,sK70)),
inference(resolution,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(sK69)
| ~ aNaturalNumber0(sK70) ),
inference(resolution,[status(thm)],[d13,c3]) ).
cnf(d15,plain,
~ aNaturalNumber0(sK70),
inference(resolution,[status(thm)],[c57,d14]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[c60,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM467+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
% 0.09/0.36 % 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 02:53:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 59.00/8.82 % SZS status Theorem for theBenchmark.p
% 59.00/8.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------