%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM492+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 : n019.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 08:12:55 AM UTC 2026
% Result : Theorem 115.87s 19.92s
% Output : CNFRefutation 115.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 20 unt; 1 def)
% Number of atoms : 149 ( 23 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 170 ( 71 ~; 67 |; 25 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 10 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ) ).
fof(mMulComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ).
fof(mDefDiv,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ).
fof(mDivMin,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,sdtpldt0(X1,X2))
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__1860,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10
& xp != sz00 ) ).
fof(m__1883,hypothesis,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ) ).
fof(m__1951,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) ).
fof(m__2001,hypothesis,
( doDivides0(xp,sdtasdt0(xp,xm))
& ? [X0] :
( sdtasdt0(xp,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ).
fof(m__,conjecture,
( doDivides0(xp,sdtasdt0(xr,xm))
| ? [X0] :
( sdtasdt0(xr,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( doDivides0(xp,sdtasdt0(xr,xm))
| ? [X0] :
( sdtasdt0(xr,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c4,plain,
( aNaturalNumber0(sdtasdt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
cnf(c9,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
cnf(c49,plain,
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) != X2 ),
inference(clausification,[status(esa)],[mDefDiv]) ).
cnf(c55,plain,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(clausification,[status(esa)],[mDivMin]) ).
cnf(c69,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c70,plain,
aNaturalNumber0(xp),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c71,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c91,plain,
aNaturalNumber0(sK96),
inference(clausification,[status(esa)],[m__1860]) ).
cnf(c92,plain,
sdtasdt0(xp,sK96) = sdtasdt0(xn,xm),
inference(clausification,[status(esa)],[m__1860]) ).
cnf(c99,plain,
aNaturalNumber0(xr),
inference(clausification,[status(esa)],[m__1883]) ).
cnf(c107,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm),
inference(clausification,[status(esa)],[m__1951]) ).
cnf(c112,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(clausification,[status(esa)],[m__2001]) ).
cnf(c113,plain,
aNaturalNumber0(sK100),
inference(clausification,[status(esa)],[m__2001]) ).
cnf(c114,plain,
sdtasdt0(xp,sK100) = sdtasdt0(xp,xm),
inference(clausification,[status(esa)],[m__2001]) ).
cnf(c116,plain,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xm) = sdtasdt0(xm,X0) ),
inference(resolution,[status(thm)],[c71,c9]) ).
cnf(d1,plain,
sdtasdt0(xr,xm) = sdtasdt0(xm,xr),
inference(resolution,[status(thm)],[d0,c99]) ).
cnf(d2,plain,
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(equality_resolution,[status(thm)],[c49]) ).
cnf(d3,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xp,sK96),
inference(demodulation,[status(thm)],[c107,c92]) ).
cnf(d4,plain,
( ~ doDivides0(X0,sdtasdt0(xp,xm))
| doDivides0(X0,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ doDivides0(X0,sdtasdt0(xp,sK96)) ),
inference(superposition,[status(thm)],[d3,c55]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,sK96))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK96)
| doDivides0(xp,sdtasdt0(xr,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sK96)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xp,sK96))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(demodulation,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( doDivides0(xp,sdtasdt0(xm,xr))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sK96)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xp,sK96))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( doDivides0(xp,sdtasdt0(xm,xr))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sK96)
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xp,sK96))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[c70,d7]) ).
cnf(d9,plain,
( doDivides0(xp,sdtasdt0(xm,xr))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xp,sK96))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[c91,d8]) ).
cnf(d10,plain,
( doDivides0(xp,sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xp,sK96))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[c112,d9]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xp,sK96)) ),
inference(superposition,[status(thm)],[c92,c4]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xp,sK96)) ),
inference(resolution,[status(thm)],[c69,d11]) ).
cnf(d13,plain,
aNaturalNumber0(sdtasdt0(xp,sK96)),
inference(resolution,[status(thm)],[c71,d12]) ).
cnf(d14,plain,
( doDivides0(xp,sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(sK100)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c114,c4]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(sK100)
| aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[c70,d15]) ).
cnf(d17,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(resolution,[status(thm)],[c113,d16]) ).
cnf(d18,plain,
( doDivides0(xp,sdtasdt0(xm,xr))
| ~ aNaturalNumber0(sdtasdt0(xm,xr)) ),
inference(resolution,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
~ doDivides0(xp,sdtasdt0(xm,xr)),
inference(demodulation,[status(thm)],[c116,d1]) ).
cnf(d20,plain,
~ aNaturalNumber0(sdtasdt0(xm,xr)),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[d20,c4]) ).
cnf(d22,plain,
~ aNaturalNumber0(xr),
inference(resolution,[status(thm)],[c71,d21]) ).
cnf(d23,plain,
$false,
inference(resolution,[status(thm)],[c99,d22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM492+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n019.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 02:58:33 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 115.87/19.92 % SZS status Theorem for theBenchmark.p
% 115.87/19.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------