%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM453+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 08:12:46 AM UTC 2026
% Result : Theorem 40.79s 10.06s
% Output : CNFRefutation 40.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 9 unt; 0 def)
% Number of atoms : 215 ( 82 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 271 ( 122 ~; 135 |; 9 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntZero,axiom,
aInteger0(sz00) ).
fof(mIntOne,axiom,
aInteger0(sz10) ).
fof(mIntNeg,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ) ).
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(m__2171,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ) ).
fof(m__,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ) ).
fof(negated_conjecture,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != 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(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(c8,plain,
( X0 = sdtpldt0(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(c138,plain,
aInteger0(xp),
inference(clausification,[status(esa)],[m__2171]) ).
cnf(c139,plain,
xp != sz00,
inference(clausification,[status(esa)],[m__2171]) ).
cnf(c143,plain,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aInteger0(X0)
| ~ aInteger0(smndt0(X0))
| ~ aInteger0(X0)
| sz00 = sdtpldt0(X0,smndt0(X0)) ),
inference(superposition,[status(thm)],[c6,c10]) ).
cnf(d1,plain,
( sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(sz10)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0)) = sdtpldt0(sz10,X0) ),
inference(superposition,[status(thm)],[c143,c5]) ).
cnf(d2,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0)) = sdtpldt0(sz10,X0) ),
inference(resolution,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz00)
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,sz00) ),
inference(superposition,[status(thm)],[c7,d2]) ).
cnf(d4,plain,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,sz00) ),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
( sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| sz10 = sdtpldt0(sz10,sz00) ),
inference(superposition,[status(thm)],[c143,d4]) ).
cnf(d6,plain,
( ~ aInteger0(smndt0(xp))
| sz10 = sdtpldt0(sz10,sz00)
| ~ aInteger0(sz10)
| ~ aInteger0(xp)
| ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(xp,X0)) = sdtpldt0(sz10,X0) ),
inference(superposition,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(xp,X0)) = sdtpldt0(sz10,X0)
| sz10 = sdtpldt0(sz10,sz00) ),
inference(resolution,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(xp,X0)) = sdtpldt0(sz10,X0)
| sz10 = sdtpldt0(sz10,sz00) ),
inference(resolution,[status(thm)],[c138,d7]) ).
cnf(d9,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz00)
| sz10 = sdtpldt0(sz10,sz00)
| sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00) ),
inference(superposition,[status(thm)],[c7,d8]) ).
cnf(d10,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00)
| sz10 = sdtpldt0(sz10,sz00) ),
inference(resolution,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00)
| sz10 = sdtpldt0(sz10,sz00) ),
inference(resolution,[status(thm)],[c138,d10]) ).
cnf(d12,plain,
( ~ aInteger0(smndt0(xp))
| sz10 = sdtpldt0(sz10,sz00)
| ~ aInteger0(smndt0(xp))
| sz10 = sdtpldt0(sz10,sz00)
| sz10 = sdtpldt0(sz10,sz00) ),
inference(superposition,[status(thm)],[d5,d11]) ).
cnf(d13,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10)
| ~ aInteger0(sz00)
| sdtpldt0(sz00,sz10) = sz10 ),
inference(superposition,[status(thm)],[d12,c6]) ).
cnf(d14,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10)
| sdtpldt0(sz00,sz10) = sz10 ),
inference(resolution,[status(thm)],[c0,d13]) ).
cnf(d15,plain,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz00,sz10) = sz10 ),
inference(resolution,[status(thm)],[c1,d14]) ).
cnf(d16,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz00)
| ~ aInteger0(sz10)
| ~ aInteger0(X0)
| sdtpldt0(sz00,sdtpldt0(sz10,X0)) = sdtpldt0(sz10,X0) ),
inference(superposition,[status(thm)],[d15,c5]) ).
cnf(d17,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10)
| ~ aInteger0(X0)
| sdtpldt0(sz00,sdtpldt0(sz10,X0)) = sdtpldt0(sz10,X0) ),
inference(resolution,[status(thm)],[c0,d16]) ).
cnf(d18,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sdtpldt0(sz00,sdtpldt0(sz10,X0)) = sdtpldt0(sz10,X0) ),
inference(resolution,[status(thm)],[c1,d17]) ).
cnf(d19,plain,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(smndt0(xp))
| sdtpldt0(sz00,sdtpldt0(sz10,sz00)) = sdtpldt0(sz10,smndt0(xp)) ),
inference(superposition,[status(thm)],[d4,d18]) ).
cnf(d20,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(xp)
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,sz00) = sdtpldt0(sz10,xp) ),
inference(superposition,[status(thm)],[c10,d2]) ).
cnf(d21,plain,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,sz00) = sdtpldt0(sz10,xp) ),
inference(resolution,[status(thm)],[c138,d20]) ).
cnf(d22,plain,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(xp)
| sdtpldt0(sz00,sdtpldt0(sz10,sz00)) = sdtpldt0(sz10,xp) ),
inference(superposition,[status(thm)],[d21,d18]) ).
cnf(d23,plain,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz00,sdtpldt0(sz10,sz00)) = sdtpldt0(sz10,xp) ),
inference(resolution,[status(thm)],[c138,d22]) ).
cnf(d24,plain,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,xp) = sdtpldt0(sz10,smndt0(xp)) ),
inference(superposition,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(superposition,[status(thm)],[d24,c143]) ).
cnf(d26,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10)
| ~ aInteger0(xp)
| ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(xp,X0)) = sdtpldt0(sz10,X0) ),
inference(superposition,[status(thm)],[d25,c5]) ).
cnf(d27,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(xp,X0)) = sdtpldt0(sz10,X0) ),
inference(resolution,[status(thm)],[c1,d26]) ).
cnf(d28,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(xp,X0)) = sdtpldt0(sz10,X0) ),
inference(resolution,[status(thm)],[c138,d27]) ).
cnf(d29,plain,
( ~ aInteger0(xp)
| ~ aInteger0(X0)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(X0,xp)) = sdtpldt0(sz10,X0) ),
inference(superposition,[status(thm)],[c6,d28]) ).
cnf(d30,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0)
| sdtpldt0(sz10,sdtpldt0(X0,xp)) = sdtpldt0(sz10,X0) ),
inference(resolution,[status(thm)],[c138,d29]) ).
cnf(d31,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X0)
| ~ aInteger0(smndt0(X0))
| ~ aInteger0(X1)
| sdtpldt0(X0,sdtpldt0(smndt0(X0),X1)) = sdtpldt0(sz00,X1) ),
inference(superposition,[status(thm)],[c9,c5]) ).
cnf(d32,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(sz10)
| ~ aInteger0(xp)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(smndt0(sz10))
| sdtpldt0(sz00,xp) = sdtpldt0(sz10,smndt0(sz10)) ),
inference(superposition,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(smndt0(sz10))
| sdtpldt0(sz00,xp) = sdtpldt0(sz10,smndt0(sz10)) ),
inference(resolution,[status(thm)],[c1,d32]) ).
cnf(d34,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(smndt0(sz10))
| sdtpldt0(sz00,xp) = sdtpldt0(sz10,smndt0(sz10)) ),
inference(resolution,[status(thm)],[c138,d33]) ).
cnf(d35,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(sz10)
| sz00 = sdtpldt0(sz00,xp) ),
inference(superposition,[status(thm)],[d34,d0]) ).
cnf(d36,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(smndt0(sz10))
| sz00 = sdtpldt0(sz00,xp) ),
inference(resolution,[status(thm)],[c1,d35]) ).
cnf(d37,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(xp)
| xp = sz00 ),
inference(superposition,[status(thm)],[d36,c8]) ).
cnf(d38,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(smndt0(sz10))
| xp = sz00 ),
inference(resolution,[status(thm)],[c138,d37]) ).
cnf(d39,plain,
( ~ aInteger0(smndt0(xp))
| ~ aInteger0(smndt0(sz10)) ),
inference(resolution,[status(thm)],[c139,d38]) ).
cnf(d40,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(sz10)) ),
inference(resolution,[status(thm)],[d39,c2]) ).
cnf(d41,plain,
~ aInteger0(smndt0(sz10)),
inference(resolution,[status(thm)],[c138,d40]) ).
cnf(d42,plain,
~ aInteger0(sz10),
inference(resolution,[status(thm)],[d41,c2]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[c1,d42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM453+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n016.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 02:52:45 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.79/10.06 % SZS status Theorem for theBenchmark.p
% 40.79/10.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------