%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM501+3 : 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 : n002.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 08:12:57 AM UTC 2026
% Result : Theorem 24.13s 4.37s
% Output : CNFRefutation 24.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 109 ( 35 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 130 ( 56 ~; 42 |; 27 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 9 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 9 !; 6 ?)
% 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(mMulAsso,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,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__2306,hypothesis,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ) ).
fof(m__2342,hypothesis,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( xr = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xr
| X0 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ) ).
fof(m__,conjecture,
( doDivides0(xr,sdtasdt0(xn,xm))
| ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( doDivides0(xr,sdtasdt0(xn,xm))
| ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c4,plain,
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ 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(c10,plain,
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulAsso]) ).
cnf(c72,plain,
aNaturalNumber0(xp),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c95,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK99),
inference(clausification,[status(esa)],[m__1860]) ).
cnf(c110,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(clausification,[status(esa)],[m__2306]) ).
cnf(c116,plain,
aNaturalNumber0(xr),
inference(clausification,[status(esa)],[m__2342]) ).
cnf(c117,plain,
aNaturalNumber0(sK104),
inference(clausification,[status(esa)],[m__2342]) ).
cnf(c118,plain,
xk = sdtasdt0(xr,sK104),
inference(clausification,[status(esa)],[m__2342]) ).
cnf(c125,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xr,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
sdtasdt0(xp,xk) = sdtasdt0(xp,sK99),
inference(demodulation,[status(thm)],[c95,c110]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,sK99) != sdtasdt0(xr,X0) ),
inference(demodulation,[status(thm)],[c125,c95]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xk) != sdtasdt0(xr,X0) ),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xk) != sdtasdt0(X0,xr) ),
inference(superposition,[status(thm)],[c9,d2]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xk) != sdtasdt0(X0,xr) ),
inference(resolution,[status(thm)],[c116,d3]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| sdtasdt0(xp,xk) != sdtasdt0(X0,sdtasdt0(X1,xr)) ),
inference(superposition,[status(thm)],[c10,d4]) ).
cnf(d6,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xp,xk) != sdtasdt0(X0,sdtasdt0(X1,xr)) ),
inference(resolution,[status(thm)],[c116,d5]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xk) != sdtasdt0(X1,sdtasdt0(xr,X0)) ),
inference(superposition,[status(thm)],[c9,d6]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xk) != sdtasdt0(X0,sdtasdt0(xr,X1)) ),
inference(resolution,[status(thm)],[c116,d7]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,sK104))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK104)
| sdtasdt0(xp,xk) != sdtasdt0(X0,xk) ),
inference(superposition,[status(thm)],[c118,d8]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,sK104))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xp,xk) != sdtasdt0(X0,xk) ),
inference(resolution,[status(thm)],[c117,d9]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,sK104))
| ~ aNaturalNumber0(xp) ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
~ aNaturalNumber0(sdtasdt0(xp,sK104)),
inference(resolution,[status(thm)],[c72,d11]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK104) ),
inference(resolution,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
~ aNaturalNumber0(sK104),
inference(resolution,[status(thm)],[c72,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[c117,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM501+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 03:03:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.13/4.37 % SZS status Theorem for theBenchmark.p
% 24.13/4.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------