%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM421+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 : n018.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 08:12:41 AM UTC 2026
% Result : Theorem 35.45s 8.19s
% Output : CNFRefutation 35.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 26 unt; 0 def)
% Number of atoms : 129 ( 55 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 111 ( 47 ~; 42 |; 13 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 16 !; 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(mIntMult,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(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(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(mMulComm,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ).
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(m__419,hypothesis,
aInteger0(xa) ).
fof(m__,conjecture,
( sz00 = sdtasdt0(sz00,xa)
& sdtasdt0(xa,sz00) = sz00 ) ).
fof(negated_conjecture,negated_conjecture,
~ ( sz00 = sdtasdt0(sz00,xa)
& sdtasdt0(xa,sz00) = sz00 ),
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(c4,plain,
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mIntMult]) ).
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(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(c10,plain,
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mAddNeg]) ).
cnf(c12,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
cnf(c13,plain,
( sdtasdt0(X0,sz10) = X0
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mMulOne]) ).
cnf(c15,plain,
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mDistrib]) ).
cnf(c17,plain,
aInteger0(xa),
inference(clausification,[status(esa)],[m__419]) ).
cnf(c18,plain,
( sz00 != sdtasdt0(sz00,xa)
| sdtasdt0(xa,sz00) != sz00 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
sz00 = sdtpldt0(smndt0(xa),xa),
inference(resolution,[status(thm)],[c10,c17]) ).
cnf(d1,plain,
( ~ aInteger0(X0)
| sdtasdt0(sz00,X0) = sdtasdt0(X0,sz00) ),
inference(resolution,[status(thm)],[c12,c0]) ).
cnf(d2,plain,
sdtasdt0(sz00,xa) = sdtasdt0(xa,sz00),
inference(resolution,[status(thm)],[d1,c17]) ).
cnf(d3,plain,
sdtasdt0(xa,sz10) = xa,
inference(resolution,[status(thm)],[c13,c17]) ).
cnf(d4,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d5,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtasdt0(X0,sdtpldt0(sz10,X1)) = sdtpldt0(sdtasdt0(X0,sz10),sdtasdt0(X0,X1)) ),
inference(resolution,[status(thm)],[c15,c1]) ).
cnf(d6,plain,
( ~ aInteger0(X0)
| sdtasdt0(xa,sdtpldt0(sz10,X0)) = sdtpldt0(sdtasdt0(xa,sz10),sdtasdt0(xa,X0)) ),
inference(resolution,[status(thm)],[d5,c17]) ).
cnf(d7,plain,
( ~ aInteger0(X0)
| sdtasdt0(xa,sdtpldt0(sz10,X0)) = sdtpldt0(xa,sdtasdt0(xa,X0)) ),
inference(demodulation,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
sdtasdt0(xa,sdtpldt0(sz10,sz00)) = sdtpldt0(xa,sdtasdt0(xa,sz00)),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
sdtasdt0(xa,sz10) = sdtpldt0(xa,sdtasdt0(xa,sz00)),
inference(demodulation,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
xa = sdtpldt0(xa,sdtasdt0(xa,sz00)),
inference(demodulation,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
xa = sdtpldt0(xa,sdtasdt0(sz00,xa)),
inference(demodulation,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtasdt0(X0,X1) = sdtpldt0(sz00,sdtasdt0(X0,X1)) ),
inference(resolution,[status(thm)],[c8,c4]) ).
cnf(d13,plain,
( ~ aInteger0(X0)
| sdtasdt0(sz00,X0) = sdtpldt0(sz00,sdtasdt0(sz00,X0)) ),
inference(resolution,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
sdtasdt0(sz00,xa) = sdtpldt0(sz00,sdtasdt0(sz00,xa)),
inference(resolution,[status(thm)],[d13,c17]) ).
cnf(d15,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(resolution,[status(thm)],[c13,c0]) ).
cnf(d16,plain,
( ~ aInteger0(X0)
| sdtasdt0(sz00,sdtpldt0(sz10,X0)) = sdtpldt0(sdtasdt0(sz00,sz10),sdtasdt0(sz00,X0)) ),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d17,plain,
( ~ aInteger0(X0)
| sdtasdt0(sz00,sdtpldt0(sz10,X0)) = sdtpldt0(sz00,sdtasdt0(sz00,X0)) ),
inference(demodulation,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
sdtasdt0(sz00,sdtpldt0(sz10,xa)) = sdtpldt0(sz00,sdtasdt0(sz00,xa)),
inference(resolution,[status(thm)],[d17,c17]) ).
cnf(d19,plain,
sdtasdt0(sz00,sdtpldt0(sz10,xa)) = sdtasdt0(sz00,xa),
inference(demodulation,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(sdtpldt0(sz10,xa))
| aInteger0(sdtasdt0(sz00,xa)) ),
inference(superposition,[status(thm)],[d19,c4]) ).
cnf(d21,plain,
( aInteger0(sdtasdt0(sz00,xa))
| ~ aInteger0(sdtpldt0(sz10,xa)) ),
inference(resolution,[status(thm)],[c0,d20]) ).
cnf(d22,plain,
( ~ aInteger0(xa)
| ~ aInteger0(sz10)
| aInteger0(sdtasdt0(sz00,xa)) ),
inference(resolution,[status(thm)],[d21,c3]) ).
cnf(d23,plain,
( ~ aInteger0(xa)
| aInteger0(sdtasdt0(sz00,xa)) ),
inference(resolution,[status(thm)],[c1,d22]) ).
cnf(d24,plain,
aInteger0(sdtasdt0(sz00,xa)),
inference(resolution,[status(thm)],[c17,d23]) ).
cnf(d25,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(smndt0(X0),sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(smndt0(X0),X1),X2) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d26,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(smndt0(xa),sdtpldt0(X0,X1)) = sdtpldt0(sdtpldt0(smndt0(xa),X0),X1) ),
inference(resolution,[status(thm)],[d25,c17]) ).
cnf(d27,plain,
( ~ aInteger0(X0)
| sdtpldt0(smndt0(xa),sdtpldt0(xa,X0)) = sdtpldt0(sdtpldt0(smndt0(xa),xa),X0) ),
inference(resolution,[status(thm)],[d26,c17]) ).
cnf(d28,plain,
( ~ aInteger0(X0)
| sdtpldt0(smndt0(xa),sdtpldt0(xa,X0)) = sdtpldt0(sz00,X0) ),
inference(demodulation,[status(thm)],[d27,d0]) ).
cnf(d29,plain,
sdtpldt0(smndt0(xa),sdtpldt0(xa,sdtasdt0(sz00,xa))) = sdtpldt0(sz00,sdtasdt0(sz00,xa)),
inference(resolution,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
sdtpldt0(smndt0(xa),xa) = sdtpldt0(sz00,sdtasdt0(sz00,xa)),
inference(demodulation,[status(thm)],[d29,d11]) ).
cnf(d31,plain,
sz00 = sdtpldt0(sz00,sdtasdt0(sz00,xa)),
inference(demodulation,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
sdtasdt0(sz00,xa) = sz00,
inference(demodulation,[status(thm)],[d14,d31]) ).
cnf(d33,plain,
( sdtasdt0(sz00,xa) != sz00
| sz00 != sdtasdt0(sz00,xa) ),
inference(demodulation,[status(thm)],[c18,d2]) ).
cnf(d34,plain,
sz00 != sdtasdt0(sz00,xa),
inference(resolution,[status(thm)],[d32,d33]) ).
cnf(d35,plain,
sz00 != sz00,
inference(demodulation,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
$false,
inference(equality_resolution,[status(thm)],[d35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM421+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 02:42:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.45/8.19 % SZS status Theorem for theBenchmark.p
% 35.45/8.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------