%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM504+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 : n020.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 37.33s 5.17s
% Output : CNFRefutation 37.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 16 unt; 0 def)
% Number of atoms : 86 ( 21 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 82 ( 30 ~; 24 |; 23 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 7 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ) ).
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ) ).
fof(mLEAsym,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ) ).
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__2414,hypothesis,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ? [X0] :
( sdtpldt0(sdtasdt0(xp,xm),X0) = sdtasdt0(xp,xk)
& aNaturalNumber0(X0) )
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ? [X0] :
( sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm)
& aNaturalNumber0(X0) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ) ).
cnf(c3,plain,
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB]) ).
cnf(c4,plain,
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
cnf(c31,plain,
( ~ aNaturalNumber0(X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(clausification,[status(esa)],[mLEAsym]) ).
cnf(c70,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c71,plain,
aNaturalNumber0(xm),
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(c134,plain,
aNaturalNumber0(sK110),
inference(clausification,[status(esa)],[m__2414]) ).
cnf(c135,plain,
sdtpldt0(sdtasdt0(xn,xm),sK110) = sdtasdt0(xp,xm),
inference(clausification,[status(esa)],[m__2414]) ).
cnf(c136,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(clausification,[status(esa)],[m__2414]) ).
cnf(c137,plain,
sdtasdt0(xp,xm) != sdtasdt0(xp,xk),
inference(clausification,[status(esa)],[m__2414]) ).
cnf(c140,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(clausification,[status(esa)],[m__2414]) ).
cnf(d0,plain,
sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)),
inference(demodulation,[status(thm)],[c136,c110]) ).
cnf(d1,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(resolution,[status(thm)],[d0,c31]) ).
cnf(d2,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[c137,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[c140,d2]) ).
cnf(d4,plain,
sdtasdt0(xp,xk) = sdtasdt0(xp,sK99),
inference(demodulation,[status(thm)],[c95,c110]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xp,sK99)) ),
inference(superposition,[status(thm)],[c95,c4]) ).
cnf(d6,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(demodulation,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(resolution,[status(thm)],[c70,d6]) ).
cnf(d8,plain,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(resolution,[status(thm)],[c71,d7]) ).
cnf(d9,plain,
~ aNaturalNumber0(sdtasdt0(xp,xm)),
inference(resolution,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
sdtpldt0(sdtasdt0(xp,xk),sK110) = sdtasdt0(xp,xm),
inference(demodulation,[status(thm)],[c135,c110]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sK110)
| aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolution,[status(thm)],[c134,d11]) ).
cnf(d13,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(resolution,[status(thm)],[d8,d12]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM504+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
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 03:02:19 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.33/5.17 % SZS status Theorem for theBenchmark.p
% 37.33/5.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------