%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM624+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 : n014.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 08:13:22 AM UTC 2026
% Result : Theorem 18.97s 10.28s
% Output : CNFRefutation 18.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 29 unt; 2 def)
% Number of atoms : 125 ( 32 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 118 ( 51 ~; 46 |; 13 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,definition,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ) ).
fof(mLessASymm,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ) ).
fof(mDefMin,definition,
! [X0] :
( ( X0 != slcrc0
& aSubsetOf0(X0,szNzAzT0) )
=> ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) ) ) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ) ).
fof(m__4998,hypothesis,
aSubsetOf0(xO,xS) ).
fof(m__5093,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ) ).
fof(m__5106,hypothesis,
aSubsetOf0(xQ,szNzAzT0) ).
fof(m__5147,hypothesis,
xp = szmzizndt0(xQ) ).
fof(m__5182,hypothesis,
aElementOf0(xp,xO) ).
fof(m__5365,hypothesis,
( aElementOf0(xx,xO)
& aElementOf0(xx,szNzAzT0) ) ).
fof(m__5401,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)) ).
fof(m__5481,hypothesis,
( aElementOf0(xx,xQ)
& aElementOf0(xp,sdtlpdtrp0(xN,xm)) ) ).
fof(m__5518,hypothesis,
( sdtlpdtrp0(xN,xm) != slcrc0
& xQ != slcrc0
& aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
& aSubsetOf0(xQ,szNzAzT0) ) ).
fof(m__,conjecture,
xp = xx ).
fof(negated_conjecture,negated_conjecture,
xp != xx,
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c7,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mDefSub]) ).
cnf(c8,plain,
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mDefSub]) ).
cnf(c52,plain,
aSet0(szNzAzT0),
inference(clausification,[status(esa)],[mNATSet]) ).
cnf(c67,plain,
( ~ aElementOf0(X0,szNzAzT0)
| X1 = X0
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(clausification,[status(esa)],[mLessASymm]) ).
cnf(c82,plain,
( ~ aSubsetOf0(X0,szNzAzT0)
| X2 != szmzizndt0(X0)
| sdtlseqdt0(X2,X1)
| ~ aElementOf0(X1,X0)
| X0 = slcrc0 ),
inference(clausification,[status(esa)],[mDefMin]) ).
cnf(c175,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausification,[status(esa)],[m__3435]) ).
cnf(c227,plain,
aSubsetOf0(xO,xS),
inference(clausification,[status(esa)],[m__4998]) ).
cnf(c230,plain,
xQ != slcrc0,
inference(clausification,[status(esa)],[m__5093]) ).
cnf(c231,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(clausification,[status(esa)],[m__5106]) ).
cnf(c233,plain,
xp = szmzizndt0(xQ),
inference(clausification,[status(esa)],[m__5147]) ).
cnf(c237,plain,
aElementOf0(xp,xO),
inference(clausification,[status(esa)],[m__5182]) ).
cnf(c247,plain,
aElementOf0(xx,szNzAzT0),
inference(clausification,[status(esa)],[m__5365]) ).
cnf(c251,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(clausification,[status(esa)],[m__5401]) ).
cnf(c254,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(clausification,[status(esa)],[m__5481]) ).
cnf(c255,plain,
aElementOf0(xx,xQ),
inference(clausification,[status(esa)],[m__5481]) ).
cnf(c257,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0),
inference(clausification,[status(esa)],[m__5518]) ).
cnf(c259,plain,
sdtlpdtrp0(xN,xm) != slcrc0,
inference(clausification,[status(esa)],[m__5518]) ).
cnf(c260,plain,
xp != xx,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( sdtlseqdt0(X0,X1)
| ~ aSubsetOf0(xQ,szNzAzT0)
| ~ aElementOf0(X1,xQ)
| xQ = slcrc0
| X0 != xp ),
inference(superposition,[status(thm)],[c233,c82]) ).
cnf(d1,plain,
( sdtlseqdt0(X0,X1)
| ~ aSubsetOf0(xQ,szNzAzT0)
| ~ aElementOf0(X1,xQ)
| X0 != xp ),
inference(resolution,[status(thm)],[c230,d0]) ).
cnf(d2,plain,
( sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,xQ)
| X0 != xp ),
inference(resolution,[status(thm)],[c231,d1]) ).
cnf(d3,plain,
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
sdtlseqdt0(xp,xx),
inference(resolution,[status(thm)],[d3,c255]) ).
cnf(d5,plain,
( ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0)
| xx = xp ),
inference(resolution,[status(thm)],[d4,c67]) ).
cnf(d6,plain,
( ~ sdtlseqdt0(xx,xp)
| ~ aElementOf0(xp,szNzAzT0)
| xx = xp ),
inference(resolution,[status(thm)],[c247,d5]) ).
cnf(d7,plain,
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[c175,c8]) ).
cnf(d8,plain,
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[c52,d7]) ).
cnf(d9,plain,
( ~ aElementOf0(X0,xO)
| aElementOf0(X0,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c227,c8]) ).
cnf(d10,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xS) ),
inference(resolution,[status(thm)],[c175,c7]) ).
cnf(d11,plain,
aSet0(xS),
inference(resolution,[status(thm)],[c52,d10]) ).
cnf(d12,plain,
( ~ aElementOf0(X0,xO)
| aElementOf0(X0,xS) ),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
aElementOf0(xp,xS),
inference(resolution,[status(thm)],[d12,c237]) ).
cnf(d14,plain,
aElementOf0(xp,szNzAzT0),
inference(resolution,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
( ~ sdtlseqdt0(xx,xp)
| xx = xp ),
inference(resolution,[status(thm)],[d14,d6]) ).
cnf(d16,plain,
( sdtlseqdt0(X0,X1)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xm))
| sdtlpdtrp0(xN,xm) = slcrc0
| X0 != xx ),
inference(superposition,[status(thm)],[c251,c82]) ).
cnf(d17,plain,
( sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xm))
| sdtlpdtrp0(xN,xm) = slcrc0
| X0 != xx ),
inference(resolution,[status(thm)],[c257,d16]) ).
cnf(d18,plain,
( sdtlseqdt0(X0,X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xm))
| X0 != xx ),
inference(resolution,[status(thm)],[c259,d17]) ).
cnf(d19,plain,
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(equality_resolution,[status(thm)],[d18]) ).
cnf(d20,plain,
sdtlseqdt0(xx,xp),
inference(resolution,[status(thm)],[d19,c254]) ).
cnf(d21,plain,
xx = xp,
inference(resolution,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
xx != xx,
inference(demodulation,[status(thm)],[c260,d21]) ).
cnf(d23,plain,
$false,
inference(equality_resolution,[status(thm)],[d22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM624+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
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 03:29:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.97/10.28 % SZS status Theorem for theBenchmark.p
% 18.97/10.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------