%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM469+1 : 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 : n011.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 08:12:50 AM UTC 2026
% Result : Theorem 124.21s 18.42s
% Output : CNFRefutation 124.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 80 ( 21 unt; 2 def)
% Number of atoms : 230 ( 62 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 273 ( 123 ~; 120 |; 17 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 2 sgn 18 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(mSortsB,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ) ).
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ) ).
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(mMulComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ).
fof(m_MulZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ) ).
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(mDefDiv,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ).
fof(mDefQuot,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ) ).
fof(m__1240,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ) ).
fof(m__1240_04,hypothesis,
( doDivides0(xl,xn)
& doDivides0(xl,xm) ) ).
fof(m__1298,hypothesis,
( xl != sz00
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ).
fof(m__,conjecture,
doDivides0(xl,sdtpldt0(xm,xn)) ).
fof(negated_conjecture,negated_conjecture,
~ doDivides0(xl,sdtpldt0(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(c4,plain,
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
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(c9,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
cnf(c14,plain,
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulZero]) ).
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(c47,plain,
( aNaturalNumber0(sK61(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiv]) ).
cnf(c48,plain,
( X1 = sdtasdt0(X0,sK61(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiv]) ).
cnf(c49,plain,
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiv]) ).
cnf(c50,plain,
( X0 = sz00
| ~ doDivides0(X0,X1)
| aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefQuot]) ).
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,
doDivides0(xl,xm),
inference(clausification,[status(esa)],[m__1240_04]) ).
cnf(c58,plain,
doDivides0(xl,xn),
inference(clausification,[status(esa)],[m__1240_04]) ).
cnf(c59,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| xl = sz00 ),
inference(clausification,[status(esa)],[m__1298]) ).
cnf(c60,plain,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK61(sz00,X0))
| sz00 = X0 ),
inference(superposition,[status(thm)],[c48,c14]) ).
cnf(d1,plain,
( ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(sK61(sz00,X0))
| ~ aNaturalNumber0(X0)
| sz00 = X0 ),
inference(resolution,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
( ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(X0)
| sz00 = X0 ),
inference(resolution,[status(thm)],[d1,c47]) ).
cnf(d3,plain,
( ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(X0)
| sz00 = X0 ),
inference(resolution,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtsldt0(X1,X0))
| ~ aNaturalNumber0(X0)
| X0 = sz00 ),
inference(equality_resolution,[status(thm)],[c50]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X1,X0) ),
inference(superposition,[status(thm)],[c9,c49]) ).
cnf(d6,plain,
( doDivides0(X1,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X0)) ),
inference(superposition,[status(thm)],[c9,d6]) ).
cnf(d8,plain,
( xl = sz00
| ~ aNaturalNumber0(sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ aNaturalNumber0(xl)
| doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c59,d7]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| xl = sz00 ),
inference(resolution,[status(thm)],[c60,d8]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| xl = sz00 ),
inference(resolution,[status(thm)],[c54,d9]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| xl = sz00 ),
inference(resolution,[status(thm)],[d10,c4]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| xl = sz00 ),
inference(resolution,[status(thm)],[c54,d11]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| xl = sz00 ),
inference(resolution,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
( ~ doDivides0(xl,xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| xl = sz00
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| xl = sz00 ),
inference(resolution,[status(thm)],[d13,d4]) ).
cnf(d15,plain,
( ~ doDivides0(xl,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| xl = sz00 ),
inference(resolution,[status(thm)],[c54,d14]) ).
cnf(d16,plain,
( ~ doDivides0(xl,xn)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| xl = sz00 ),
inference(resolution,[status(thm)],[c56,d15]) ).
cnf(d17,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| xl = sz00 ),
inference(resolution,[status(thm)],[c58,d16]) ).
cnf(d18,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| xl = sz00
| xl = sz00 ),
inference(resolution,[status(thm)],[d17,d4]) ).
cnf(d19,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| xl = sz00 ),
inference(resolution,[status(thm)],[c54,d18]) ).
cnf(d20,plain,
( ~ doDivides0(xl,xm)
| xl = sz00 ),
inference(resolution,[status(thm)],[c55,d19]) ).
cnf(d21,plain,
xl = sz00,
inference(resolution,[status(thm)],[c57,d20]) ).
cnf(d22,plain,
doDivides0(sz00,xn),
inference(demodulation,[status(thm)],[c58,d21]) ).
cnf(d23,plain,
( ~ aNaturalNumber0(xn)
| sz00 = xn ),
inference(resolution,[status(thm)],[d22,d3]) ).
cnf(d24,plain,
sz00 = xn,
inference(resolution,[status(thm)],[c56,d23]) ).
cnf(d25,plain,
doDivides0(sz00,xm),
inference(demodulation,[status(thm)],[c57,d21]) ).
cnf(d26,plain,
( ~ aNaturalNumber0(xm)
| sz00 = xm ),
inference(resolution,[status(thm)],[d25,d3]) ).
cnf(d27,plain,
sz00 = xm,
inference(resolution,[status(thm)],[c55,d26]) ).
cnf(d28,plain,
~ doDivides0(sz00,sdtpldt0(xm,xn)),
inference(demodulation,[status(thm)],[c60,d21]) ).
cnf(d29,plain,
~ doDivides0(sz00,sdtpldt0(sz00,xn)),
inference(demodulation,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
~ doDivides0(sz00,sdtpldt0(sz00,sz00)),
inference(demodulation,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c9,c14]) ).
cnf(d32,plain,
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(resolution,[status(thm)],[c0,d31]) ).
cnf(d33,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,sdtpldt0(sz00,X1)) = sdtpldt0(sz00,sdtasdt0(X0,X1)) ),
inference(superposition,[status(thm)],[d32,c15]) ).
cnf(d34,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,sdtpldt0(sz00,X1)) = sdtpldt0(sz00,sdtasdt0(X0,X1)) ),
inference(resolution,[status(thm)],[c0,d33]) ).
cnf(d35,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| sdtasdt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sz00,sz00) ),
inference(superposition,[status(thm)],[d32,d34]) ).
cnf(d36,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtpldt0(sz00,sz00)) = sdtpldt0(sz00,sz00) ),
inference(resolution,[status(thm)],[c0,d35]) ).
cnf(d37,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(superposition,[status(thm)],[c5,c7]) ).
cnf(d38,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(resolution,[status(thm)],[c0,d37]) ).
cnf(d39,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sdtpldt0(sz00,sz00) ),
inference(superposition,[status(thm)],[d38,d36]) ).
cnf(d40,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sdtpldt0(sz00,sz00) ),
inference(resolution,[status(thm)],[c0,d39]) ).
cnf(d41,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sz00 = sdtpldt0(sz00,sz00) ),
inference(superposition,[status(thm)],[d40,d32]) ).
cnf(d42,plain,
( ~ aNaturalNumber0(X0)
| ~ doDivides0(sz00,sz00) ),
inference(superposition,[status(thm)],[d41,d30]) ).
cnf(d43,plain,
doDivides0(sz00,sz00),
inference(demodulation,[status(thm)],[d25,d27]) ).
cnf(d44,plain,
~ aNaturalNumber0(X0),
inference(resolution,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
$false,
inference(resolution,[status(thm)],[d44,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM469+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n011.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sat Sep 26 02:52:13 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 124.21/18.42 % SZS status Theorem for theBenchmark.p
% 124.21/18.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------