%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM621+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 : n010.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 47.52s 21.77s
% Output : CNFRefutation 47.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 49 ( 19 unt; 0 def)
% Number of atoms : 120 ( 22 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 102 ( 31 ~; 24 |; 33 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 13 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLessASymm,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ) ).
fof(m__4660,hypothesis,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ) ).
fof(m__4998,hypothesis,
( aSubsetOf0(xO,xS)
& ! [X0] :
( aElementOf0(X0,xO)
=> aElementOf0(X0,xS) ) ) ).
fof(m__5078,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xO,xK))
& sbrdtbr0(xQ) = xK
& aSubsetOf0(xQ,xO)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& aSet0(xQ) ) ).
fof(m__5147,hypothesis,
( xp = szmzizndt0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& aElementOf0(xp,xQ) ) ).
fof(m__5164,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( X0 != szmzizndt0(xQ)
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& aSet0(xP) ) ).
fof(m__5309,hypothesis,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,szDzozmdt0(xd)) ) ).
fof(m__5348,hypothesis,
( aElementOf0(xx,xP)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xQ)
& aElement0(xx) ) ).
fof(m__5365,hypothesis,
( ? [X0] :
( sdtlpdtrp0(xe,X0) = xx
& aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
& aElementOf0(xx,szNzAzT0) ) ).
fof(m__5389,hypothesis,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ) ).
fof(m__,conjecture,
( ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> aElementOf0(X0,sdtlpdtrp0(xN,xm)) ) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xn))
=> aElementOf0(X0,sdtlpdtrp0(xN,xm)) ) )
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c67,plain,
( ~ aElementOf0(X0,szNzAzT0)
| X1 = X0
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(clausification,[status(esa)],[mLessASymm]) ).
cnf(c176,plain,
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(clausification,[status(esa)],[m__3435]) ).
cnf(c373,plain,
( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[m__4660]) ).
cnf(c374,plain,
( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[m__4660]) ).
cnf(c410,plain,
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xO) ),
inference(clausification,[status(esa)],[m__4998]) ).
cnf(c413,plain,
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) ),
inference(clausification,[status(esa)],[m__5078]) ).
cnf(c427,plain,
aElementOf0(xp,xQ),
inference(clausification,[status(esa)],[m__5147]) ).
cnf(c428,plain,
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) ),
inference(clausification,[status(esa)],[m__5147]) ).
cnf(c429,plain,
xp = szmzizndt0(xQ),
inference(clausification,[status(esa)],[m__5147]) ).
cnf(c434,plain,
( X0 != szmzizndt0(xQ)
| ~ aElementOf0(X0,xP) ),
inference(clausification,[status(esa)],[m__5164]) ).
cnf(c449,plain,
aElementOf0(xn,szNzAzT0),
inference(clausification,[status(esa)],[m__5309]) ).
cnf(c450,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(clausification,[status(esa)],[m__5309]) ).
cnf(c453,plain,
aElementOf0(xx,xQ),
inference(clausification,[status(esa)],[m__5348]) ).
cnf(c455,plain,
aElementOf0(xx,xP),
inference(clausification,[status(esa)],[m__5348]) ).
cnf(c456,plain,
aElementOf0(xx,szNzAzT0),
inference(clausification,[status(esa)],[m__5365]) ).
cnf(c459,plain,
aElementOf0(xm,szNzAzT0),
inference(clausification,[status(esa)],[m__5389]) ).
cnf(c460,plain,
xx = sdtlpdtrp0(xe,xm),
inference(clausification,[status(esa)],[m__5389]) ).
cnf(c465,plain,
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[status(thm)],[c373,c465]) ).
cnf(d1,plain,
( ~ aElementOf0(xn,szNzAzT0)
| aElementOf0(xp,sdtlpdtrp0(xN,xm)) ),
inference(demodulation,[status(thm)],[d0,c450]) ).
cnf(d2,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(resolution,[status(thm)],[c449,d1]) ).
cnf(d3,plain,
( sdtlseqdt0(sdtlpdtrp0(xe,xm),xp)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[c374,d2]) ).
cnf(d4,plain,
( sdtlseqdt0(xx,xp)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(demodulation,[status(thm)],[d3,c460]) ).
cnf(d5,plain,
sdtlseqdt0(xx,xp),
inference(resolution,[status(thm)],[c459,d4]) ).
cnf(d6,plain,
( ~ sdtlseqdt0(xp,xx)
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(xp,szNzAzT0)
| xp = xx ),
inference(resolution,[status(thm)],[d5,c67]) ).
cnf(d7,plain,
( ~ sdtlseqdt0(xp,xx)
| ~ aElementOf0(xp,szNzAzT0)
| xp = xx ),
inference(resolution,[status(thm)],[c456,d6]) ).
cnf(d8,plain,
sdtlseqdt0(xp,xx),
inference(resolution,[status(thm)],[c428,c453]) ).
cnf(d9,plain,
( ~ aElementOf0(xp,szNzAzT0)
| xp = xx ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
aElementOf0(xp,xO),
inference(resolution,[status(thm)],[c413,c427]) ).
cnf(d11,plain,
aElementOf0(xp,xS),
inference(resolution,[status(thm)],[d10,c410]) ).
cnf(d12,plain,
aElementOf0(xp,szNzAzT0),
inference(resolution,[status(thm)],[d11,c176]) ).
cnf(d13,plain,
xp = xx,
inference(resolution,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
( ~ aElementOf0(X0,xP)
| X0 != xp ),
inference(demodulation,[status(thm)],[c434,c429]) ).
cnf(d15,plain,
~ aElementOf0(xp,xP),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
~ aElementOf0(xx,xP),
inference(demodulation,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[c455,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM621+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/15.62 % Computer : n010.cluster.edu
% 0.12/15.62 % Model : x86_64 x86_64
% 0.12/15.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.62 % Memory : 8046.5625MB
% 0.12/15.62 % OS : Linux 6.8.0-71-generic
% 0.12/15.62 % CPULimit : 300
% 0.12/15.62 % WCLimit : 300
% 0.12/15.62 % DateTime : Sat Sep 26 03:29:49 UTC 2026
% 0.12/15.62 % CPUTime :
% 0.12/15.62 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.52/21.77 % SZS status Theorem for theBenchmark.p
% 47.52/21.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------