%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM454+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 : n026.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 08:12:47 AM UTC 2026
% Result : Theorem 13.45s 16.87s
% Output : CNFRefutation 13.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 90 ( 43 unt; 0 def)
% Number of atoms : 169 ( 92 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 136 ( 57 ~; 54 |; 14 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntZero,axiom,
aInteger0(sz00) ).
fof(mIntOne,axiom,
aInteger0(sz10) ).
fof(mIntNeg,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ) ).
fof(mIntPlus,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtpldt0(X0,X1)) ) ).
fof(mAddAsso,axiom,
! [X0,X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ) ).
fof(mAddComm,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ) ).
fof(mAddZero,axiom,
! [X0] :
( aInteger0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ) ).
fof(mAddNeg,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sdtpldt0(X0,smndt0(X0)) = sz00 ) ) ).
fof(mMulOne,axiom,
! [X0] :
( aInteger0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ) ).
fof(mDistrib,axiom,
! [X0,X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ) ).
fof(mMulZero,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ) ).
fof(mZeroDiv,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ) ).
fof(m__2171,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ) ).
fof(m__,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
aInteger0(sz00),
inference(clausification,[status(esa)],[mIntZero]) ).
cnf(c1,plain,
aInteger0(sz10),
inference(clausification,[status(esa)],[mIntOne]) ).
cnf(c2,plain,
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mIntNeg]) ).
cnf(c3,plain,
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mIntPlus]) ).
cnf(c5,plain,
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mAddAsso]) ).
cnf(c6,plain,
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mAddComm]) ).
cnf(c7,plain,
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mAddZero]) ).
cnf(c9,plain,
( sdtpldt0(X0,smndt0(X0)) = sz00
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mAddNeg]) ).
cnf(c10,plain,
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mAddNeg]) ).
cnf(c14,plain,
( X0 = sdtasdt0(sz10,X0)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mMulOne]) ).
cnf(c16,plain,
( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mDistrib]) ).
cnf(c17,plain,
( sdtasdt0(X0,sz00) = sz00
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mMulZero]) ).
cnf(c21,plain,
( X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,X1) != sz00
| X0 = sz00 ),
inference(clausification,[status(esa)],[mZeroDiv]) ).
cnf(c138,plain,
aInteger0(xp),
inference(clausification,[status(esa)],[m__2171]) ).
cnf(c139,plain,
xp != sz00,
inference(clausification,[status(esa)],[m__2171]) ).
cnf(c145,plain,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c146,plain,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
sdtpldt0(xp,sz00) = xp,
inference(resolution,[status(thm)],[c7,c138]) ).
cnf(d1,plain,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d2,plain,
( ~ aInteger0(X0)
| sdtpldt0(X0,xp) = sdtpldt0(xp,X0) ),
inference(resolution,[status(thm)],[c6,c138]) ).
cnf(d3,plain,
sdtpldt0(sz10,xp) = sdtpldt0(xp,sz10),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
smndt0(sz10) = sdtpldt0(xp,sz10),
inference(demodulation,[status(thm)],[d3,c145]) ).
cnf(d5,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(xp,sdtpldt0(X0,X1)) = sdtpldt0(sdtpldt0(xp,X0),X1) ),
inference(resolution,[status(thm)],[c5,c138]) ).
cnf(d6,plain,
( ~ aInteger0(X0)
| sdtpldt0(xp,sdtpldt0(sz10,X0)) = sdtpldt0(sdtpldt0(xp,sz10),X0) ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
( ~ aInteger0(X0)
| sdtpldt0(xp,sdtpldt0(sz10,X0)) = sdtpldt0(smndt0(sz10),X0) ),
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
( ~ aInteger0(X0)
| sdtpldt0(xp,sdtpldt0(sz10,smndt0(X0))) = sdtpldt0(smndt0(sz10),smndt0(X0)) ),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
sdtpldt0(xp,sdtpldt0(sz10,smndt0(sz10))) = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(resolution,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
sdtpldt0(xp,sz00) = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(demodulation,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
xp = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(demodulation,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d13,plain,
sdtpldt0(xp,smndt0(xp)) = sz00,
inference(resolution,[status(thm)],[c9,c138]) ).
cnf(d14,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(sz10,sdtpldt0(X0,X1)) = sdtpldt0(sdtpldt0(sz10,X0),X1) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d15,plain,
( ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(xp,X0)) = sdtpldt0(sdtpldt0(sz10,xp),X0) ),
inference(resolution,[status(thm)],[d14,c138]) ).
cnf(d16,plain,
( ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(xp,X0)) = sdtpldt0(smndt0(sz10),X0) ),
inference(demodulation,[status(thm)],[d15,c145]) ).
cnf(d17,plain,
( ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(xp,smndt0(X0))) = sdtpldt0(smndt0(sz10),smndt0(X0)) ),
inference(resolution,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
sdtpldt0(sz10,sdtpldt0(xp,smndt0(xp))) = sdtpldt0(smndt0(sz10),smndt0(xp)),
inference(resolution,[status(thm)],[d17,c138]) ).
cnf(d19,plain,
sdtpldt0(sz10,sz00) = sdtpldt0(smndt0(sz10),smndt0(xp)),
inference(demodulation,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
sz10 = sdtpldt0(smndt0(sz10),smndt0(xp)),
inference(demodulation,[status(thm)],[d19,d12]) ).
cnf(d21,plain,
sdtpldt0(xp,sdtpldt0(sz10,smndt0(xp))) = sdtpldt0(smndt0(sz10),smndt0(xp)),
inference(resolution,[status(thm)],[d8,c138]) ).
cnf(d22,plain,
sdtpldt0(xp,smndt0(sz10)) = sdtpldt0(smndt0(sz10),smndt0(xp)),
inference(demodulation,[status(thm)],[d21,c146]) ).
cnf(d23,plain,
sdtpldt0(xp,smndt0(sz10)) = sz10,
inference(demodulation,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))) = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(resolution,[status(thm)],[d17,c1]) ).
cnf(d25,plain,
sdtpldt0(sz10,sz10) = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(demodulation,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
sdtpldt0(sz10,sz10) = xp,
inference(demodulation,[status(thm)],[d25,d11]) ).
cnf(d27,plain,
sz00 = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[status(thm)],[c10,c1]) ).
cnf(d28,plain,
sdtpldt0(xp,sdtpldt0(sz10,sz10)) = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d29,plain,
sdtpldt0(xp,sdtpldt0(sz10,sz10)) = sz00,
inference(demodulation,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
sdtpldt0(xp,xp) = sz00,
inference(demodulation,[status(thm)],[d29,d26]) ).
cnf(d31,plain,
xp = sdtasdt0(sz10,xp),
inference(resolution,[status(thm)],[c14,c138]) ).
cnf(d32,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtasdt0(sdtpldt0(X0,sz10),X1) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(sz10,X1)) ),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(d33,plain,
( ~ aInteger0(X0)
| sdtasdt0(sdtpldt0(sz10,sz10),X0) = sdtpldt0(sdtasdt0(sz10,X0),sdtasdt0(sz10,X0)) ),
inference(resolution,[status(thm)],[d32,c1]) ).
cnf(d34,plain,
( ~ aInteger0(X0)
| sdtasdt0(xp,X0) = sdtpldt0(sdtasdt0(sz10,X0),sdtasdt0(sz10,X0)) ),
inference(demodulation,[status(thm)],[d33,d26]) ).
cnf(d35,plain,
sdtasdt0(xp,xp) = sdtpldt0(sdtasdt0(sz10,xp),sdtasdt0(sz10,xp)),
inference(resolution,[status(thm)],[d34,c138]) ).
cnf(d36,plain,
sdtasdt0(xp,xp) = sdtpldt0(xp,sdtasdt0(sz10,xp)),
inference(demodulation,[status(thm)],[d35,d31]) ).
cnf(d37,plain,
sdtasdt0(xp,xp) = sdtpldt0(xp,xp),
inference(demodulation,[status(thm)],[d36,d31]) ).
cnf(d38,plain,
sdtasdt0(xp,xp) = sz00,
inference(demodulation,[status(thm)],[d37,d30]) ).
cnf(d39,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xp)
| xp = sz00
| xp = sz00
| sz00 != sz00 ),
inference(superposition,[status(thm)],[d38,c21]) ).
cnf(d40,plain,
( xp = sz00
| sz00 != sz00 ),
inference(resolution,[status(thm)],[c138,d39]) ).
cnf(d41,plain,
sz00 != sz00,
inference(resolution,[status(thm)],[c139,d40]) ).
cnf(d42,plain,
sdtasdt0(xp,sz00) = sz00,
inference(resolution,[status(thm)],[c17,c138]) ).
cnf(d43,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(sdtpldt0(X0,X1),sz00) = sz00 ),
inference(resolution,[status(thm)],[c17,c3]) ).
cnf(d44,plain,
( ~ aInteger0(X0)
| sdtasdt0(sdtpldt0(sz10,X0),sz00) = sz00 ),
inference(resolution,[status(thm)],[d43,c1]) ).
cnf(d45,plain,
sdtpldt0(xp,sdtpldt0(sz10,xp)) = sdtpldt0(smndt0(sz10),xp),
inference(resolution,[status(thm)],[d7,c138]) ).
cnf(d46,plain,
sdtpldt0(xp,smndt0(sz10)) = sdtpldt0(smndt0(sz10),xp),
inference(demodulation,[status(thm)],[d45,c145]) ).
cnf(d47,plain,
sdtpldt0(sz10,sdtpldt0(xp,xp)) = sdtpldt0(smndt0(sz10),xp),
inference(resolution,[status(thm)],[d16,c138]) ).
cnf(d48,plain,
sdtpldt0(sz10,sdtpldt0(xp,xp)) = sdtpldt0(xp,smndt0(sz10)),
inference(demodulation,[status(thm)],[d47,d46]) ).
cnf(d49,plain,
( ~ aInteger0(sdtpldt0(xp,xp))
| ~ aInteger0(sz10)
| aInteger0(sdtpldt0(xp,smndt0(sz10))) ),
inference(superposition,[status(thm)],[d48,c3]) ).
cnf(d50,plain,
( ~ aInteger0(sdtpldt0(xp,xp))
| aInteger0(sdtpldt0(xp,smndt0(sz10))) ),
inference(resolution,[status(thm)],[c1,d49]) ).
cnf(d51,plain,
( sdtasdt0(sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))),sz00) = sz00
| ~ aInteger0(sdtpldt0(xp,xp)) ),
inference(resolution,[status(thm)],[d50,d44]) ).
cnf(d52,plain,
( ~ aInteger0(sdtpldt0(xp,xp))
| sdtasdt0(sdtpldt0(sz10,sz10),sz00) = sz00 ),
inference(demodulation,[status(thm)],[d51,d23]) ).
cnf(d53,plain,
( ~ aInteger0(sdtpldt0(xp,xp))
| sdtasdt0(xp,sz00) = sz00 ),
inference(demodulation,[status(thm)],[d52,d26]) ).
cnf(d54,plain,
( ~ aInteger0(sdtpldt0(xp,xp))
| sz00 = sz00 ),
inference(demodulation,[status(thm)],[d53,d42]) ).
cnf(d55,plain,
( ~ aInteger0(sz00)
| sz00 = sz00 ),
inference(demodulation,[status(thm)],[d54,d30]) ).
cnf(d56,plain,
sz00 = sz00,
inference(resolution,[status(thm)],[c0,d55]) ).
cnf(d57,plain,
$false,
inference(resolution,[status(thm)],[d56,d41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM454+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.53 % Computer : n026.cluster.edu
% 0.09/10.53 % Model : x86_64 x86_64
% 0.09/10.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.53 % Memory : 8046.5625MB
% 0.09/10.53 % OS : Linux 6.8.0-71-generic
% 0.09/10.53 % CPULimit : 300
% 0.09/10.53 % WCLimit : 300
% 0.09/10.53 % DateTime : Sat Sep 26 02:51:38 UTC 2026
% 0.09/10.53 % CPUTime :
% 0.09/10.53 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.45/16.87 % SZS status Theorem for theBenchmark.p
% 13.45/16.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------