%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM620+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 : n026.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 08:13:21 AM UTC 2026
% Result : Theorem 55.85s 13.47s
% Output : CNFRefutation 55.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 12 unt; 3 def)
% Number of atoms : 175 ( 26 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 209 ( 91 ~; 86 |; 15 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,definition,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ) ).
fof(mCountNFin_01,axiom,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> X0 != slcrc0 ) ).
fof(mDefSub,definition,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ) ).
fof(mSubTrans,axiom,
! [X0,X1,X2] :
( ( aSet0(X2)
& aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X0,X1) )
=> aSubsetOf0(X0,X2) ) ) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ) ).
fof(mSuccNum,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ) ).
fof(mLessRefl,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,X0) ) ).
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__3671,hypothesis,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ) ) ).
fof(m__3754,hypothesis,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ) ) ).
fof(m__5309,hypothesis,
( sdtlpdtrp0(xe,xn) = xp
& aElementOf0(xn,szNzAzT0)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ).
fof(m__5389,hypothesis,
( xx = sdtlpdtrp0(xe,xm)
& aElementOf0(xm,szNzAzT0) ) ).
fof(m__5401,hypothesis,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)) ).
fof(m__,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c1,plain,
( aSet0(X0)
| X0 != slcrc0 ),
inference(clausification,[status(esa)],[mDefEmp]) ).
cnf(c6,plain,
( X0 != slcrc0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(clausification,[status(esa)],[mCountNFin_01]) ).
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(c14,plain,
( ~ aSubsetOf0(X2,X0)
| ~ aSet0(X2)
| ~ aSet0(X0)
| aSubsetOf0(X2,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(clausification,[status(esa)],[mSubTrans]) ).
cnf(c45,plain,
aSet0(szNzAzT0),
inference(clausification,[status(esa)],[mNATSet]) ).
cnf(c48,plain,
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[mSuccNum]) ).
cnf(c59,plain,
( sdtlseqdt0(X0,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[mLessRefl]) ).
cnf(c74,plain,
( aElementOf0(X1,X0)
| szmzizndt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| X0 = slcrc0 ),
inference(clausification,[status(esa)],[mDefMin]) ).
cnf(c177,plain,
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[m__3671]) ).
cnf(c178,plain,
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[m__3671]) ).
cnf(c179,plain,
( ~ sdtlseqdt0(X0,X1)
| aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[m__3754]) ).
cnf(c228,plain,
aElementOf0(xn,szNzAzT0),
inference(clausification,[status(esa)],[m__5309]) ).
cnf(c233,plain,
aElementOf0(xm,szNzAzT0),
inference(clausification,[status(esa)],[m__5389]) ).
cnf(c235,plain,
szmzizndt0(sdtlpdtrp0(xN,xm)) = xx,
inference(clausification,[status(esa)],[m__5401]) ).
cnf(c236,plain,
aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c237,plain,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aSubsetOf0(X0,sdtlpdtrp0(xN,xm))
| aSubsetOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c14,c236]) ).
cnf(d1,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| aSet0(sdtlpdtrp0(xN,xm)) ),
inference(resolution,[status(thm)],[c7,c236]) ).
cnf(d2,plain,
( ~ aSubsetOf0(X0,sdtlpdtrp0(xN,xm))
| aSubsetOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(X0)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ aElementOf0(X1,X0)
| aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSubsetOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(xm,X0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[c179,d3]) ).
cnf(d5,plain,
( ~ sdtlseqdt0(xm,X0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,X0)) ),
inference(resolution,[status(thm)],[c233,d4]) ).
cnf(d6,plain,
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(szmzizndt0(X0),X0)
| X0 = slcrc0 ),
inference(equality_resolution,[status(thm)],[c74]) ).
cnf(d7,plain,
( ~ sdtlseqdt0(xm,X0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| sdtlpdtrp0(xN,X0) = slcrc0 ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ sdtlseqdt0(xm,X0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,X0))
| sdtlpdtrp0(xN,X0) = slcrc0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[c177,d7]) ).
cnf(d9,plain,
( ~ sdtlseqdt0(xm,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| sdtlpdtrp0(xN,xm) = slcrc0
| aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(superposition,[status(thm)],[c235,d8]) ).
cnf(d10,plain,
( ~ sdtlseqdt0(xm,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(resolution,[status(thm)],[c237,d9]) ).
cnf(d11,plain,
( ~ sdtlseqdt0(xm,xm)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(resolution,[status(thm)],[c233,d10]) ).
cnf(d12,plain,
sdtlseqdt0(xm,xm),
inference(resolution,[status(thm)],[c233,c59]) ).
cnf(d13,plain,
( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| sdtlpdtrp0(xN,xm) = slcrc0
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(resolution,[status(thm)],[d1,d13]) ).
cnf(d15,plain,
( ~ aSet0(szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[c177,c7]) ).
cnf(d16,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0)) ),
inference(resolution,[status(thm)],[c45,d15]) ).
cnf(d17,plain,
( sdtlpdtrp0(xN,xm) = slcrc0
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( ~ aElementOf0(xn,szNzAzT0)
| sdtlpdtrp0(xN,xm) = slcrc0 ),
inference(resolution,[status(thm)],[d17,c48]) ).
cnf(d19,plain,
sdtlpdtrp0(xN,xm) = slcrc0,
inference(resolution,[status(thm)],[c228,d18]) ).
cnf(d20,plain,
( ~ aElementOf0(xm,szNzAzT0)
| isCountable0(slcrc0) ),
inference(superposition,[status(thm)],[d19,c178]) ).
cnf(d21,plain,
( ~ isCountable0(X0)
| X0 != slcrc0
| X0 != slcrc0 ),
inference(resolution,[status(thm)],[c1,c6]) ).
cnf(d22,plain,
~ isCountable0(slcrc0),
inference(equality_resolution,[status(thm)],[d21]) ).
cnf(d23,plain,
~ aElementOf0(xm,szNzAzT0),
inference(resolution,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[c233,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM620+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
% 0.11/5.39 % Computer : n026.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 03:31:16 UTC 2026
% 0.15/5.40 % CPUTime :
% 0.15/5.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 55.85/13.47 % SZS status Theorem for theBenchmark.p
% 55.85/13.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------