%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM435+3 : 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 : n007.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 08:12:43 AM UTC 2026
% Result : Theorem 32.62s 4.75s
% Output : CNFRefutation 32.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 15 unt; 0 def)
% Number of atoms : 114 ( 36 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 69 ~; 53 |; 14 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 7 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntMult,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(X0,X1)) ) ).
fof(mMulAsso,axiom,
! [X0,X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) ) ).
fof(mMulComm,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ).
fof(m__979,hypothesis,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ) ).
fof(m__1003,hypothesis,
( sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& ? [X0] :
( sdtasdt0(sdtasdt0(xp,xq),X0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X0) )
& sdtasdt0(xp,xq) != sz00 ) ).
fof(m__1032,hypothesis,
( sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xm) ) ).
fof(m__,conjecture,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)) ).
fof(negated_conjecture,negated_conjecture,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c4,plain,
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mIntMult]) ).
cnf(c11,plain,
( sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(sdtasdt0(X0,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mMulAsso]) ).
cnf(c12,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
cnf(c36,plain,
aInteger0(xp),
inference(clausification,[status(esa)],[m__979]) ).
cnf(c38,plain,
aInteger0(xq),
inference(clausification,[status(esa)],[m__979]) ).
cnf(c41,plain,
aInteger0(sK43),
inference(clausification,[status(esa)],[m__1003]) ).
cnf(c42,plain,
sdtasdt0(sdtasdt0(xp,xq),sK43) = sdtpldt0(xa,smndt0(xb)),
inference(clausification,[status(esa)],[m__1003]) ).
cnf(c45,plain,
aInteger0(xm),
inference(clausification,[status(esa)],[m__1032]) ).
cnf(c46,plain,
sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)),
inference(clausification,[status(esa)],[m__1032]) ).
cnf(c47,plain,
sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xq,sdtasdt0(xp,xm)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ aInteger0(xp)
| sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
inference(superposition,[status(thm)],[c11,c46]) ).
cnf(d1,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
inference(resolution,[status(thm)],[c36,d0]) ).
cnf(d2,plain,
( ~ aInteger0(xm)
| sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)) ),
inference(resolution,[status(thm)],[c38,d1]) ).
cnf(d3,plain,
sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb)),
inference(resolution,[status(thm)],[c45,d2]) ).
cnf(d4,plain,
( ~ aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,sdtasdt0(X1,X2)) = sdtasdt0(X2,sdtasdt0(X0,X1)) ),
inference(superposition,[status(thm)],[c12,c11]) ).
cnf(d5,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| ~ aInteger0(xp)
| ~ aInteger0(xm)
| ~ aInteger0(xq)
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,sdtasdt0(xm,xq)) ),
inference(superposition,[status(thm)],[d4,c47]) ).
cnf(d6,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ aInteger0(sdtasdt0(xp,xm))
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,sdtasdt0(xm,xq)) ),
inference(resolution,[status(thm)],[c36,d5]) ).
cnf(d7,plain,
( ~ aInteger0(xm)
| ~ aInteger0(sdtasdt0(xp,xm))
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,sdtasdt0(xm,xq)) ),
inference(resolution,[status(thm)],[c38,d6]) ).
cnf(d8,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,sdtasdt0(xm,xq)) ),
inference(resolution,[status(thm)],[c45,d7]) ).
cnf(d9,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xm)
| ~ aInteger0(sdtasdt0(xp,xm))
| sdtpldt0(xa,smndt0(xb)) != sdtasdt0(xp,sdtasdt0(xq,xm)) ),
inference(superposition,[status(thm)],[c12,d8]) ).
cnf(d10,plain,
( ~ aInteger0(xm)
| ~ aInteger0(xq)
| ~ aInteger0(sdtasdt0(xp,xm))
| sdtpldt0(xa,smndt0(xb)) != sdtpldt0(xa,smndt0(xb)) ),
inference(demodulation,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
( ~ aInteger0(xm)
| ~ aInteger0(sdtasdt0(xp,xm))
| sdtpldt0(xa,smndt0(xb)) != sdtpldt0(xa,smndt0(xb)) ),
inference(resolution,[status(thm)],[c38,d10]) ).
cnf(d12,plain,
( ~ aInteger0(sdtasdt0(xp,xm))
| sdtpldt0(xa,smndt0(xb)) != sdtpldt0(xa,smndt0(xb)) ),
inference(resolution,[status(thm)],[c45,d11]) ).
cnf(d13,plain,
( ~ aInteger0(sK43)
| ~ aInteger0(xq)
| ~ aInteger0(xp)
| sdtasdt0(xp,sdtasdt0(xq,sK43)) = sdtpldt0(xa,smndt0(xb)) ),
inference(superposition,[status(thm)],[c11,c42]) ).
cnf(d14,plain,
( ~ aInteger0(sK43)
| ~ aInteger0(xq)
| sdtasdt0(xp,sdtasdt0(xq,sK43)) = sdtpldt0(xa,smndt0(xb)) ),
inference(resolution,[status(thm)],[c36,d13]) ).
cnf(d15,plain,
( ~ aInteger0(sK43)
| sdtasdt0(xp,sdtasdt0(xq,sK43)) = sdtpldt0(xa,smndt0(xb)) ),
inference(resolution,[status(thm)],[c38,d14]) ).
cnf(d16,plain,
sdtasdt0(xp,sdtasdt0(xq,sK43)) = sdtpldt0(xa,smndt0(xb)),
inference(resolution,[status(thm)],[c41,d15]) ).
cnf(d17,plain,
( ~ aInteger0(sK43)
| ~ aInteger0(xq)
| ~ aInteger0(xp)
| sdtasdt0(xp,sdtasdt0(xq,sK43)) = sdtpldt0(xa,smndt0(xb)) ),
inference(superposition,[status(thm)],[c42,c11]) ).
cnf(d18,plain,
( ~ aInteger0(sK43)
| ~ aInteger0(xq)
| ~ aInteger0(xp)
| sdtpldt0(xa,smndt0(xb)) = sdtpldt0(xa,smndt0(xb)) ),
inference(demodulation,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
( ~ aInteger0(sK43)
| ~ aInteger0(xq)
| sdtpldt0(xa,smndt0(xb)) = sdtpldt0(xa,smndt0(xb)) ),
inference(resolution,[status(thm)],[c36,d18]) ).
cnf(d20,plain,
( ~ aInteger0(sK43)
| sdtpldt0(xa,smndt0(xb)) = sdtpldt0(xa,smndt0(xb)) ),
inference(resolution,[status(thm)],[c38,d19]) ).
cnf(d21,plain,
sdtpldt0(xa,smndt0(xb)) = sdtpldt0(xa,smndt0(xb)),
inference(resolution,[status(thm)],[c41,d20]) ).
cnf(d22,plain,
~ aInteger0(sdtasdt0(xp,xm)),
inference(resolution,[status(thm)],[d21,d12]) ).
cnf(d23,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xm) ),
inference(resolution,[status(thm)],[d22,c4]) ).
cnf(d24,plain,
~ aInteger0(xm),
inference(resolution,[status(thm)],[c36,d23]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[c45,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM435+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 02:41:55 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.62/4.75 % SZS status Theorem for theBenchmark.p
% 32.62/4.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------