%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM622+1 : 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 : n019.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 37.00s 37.88s
% Output : CNFRefutation 37.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 17 unt; 3 def)
% Number of atoms : 137 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 143 ( 60 ~; 56 |; 15 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 13 !; 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(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__4660,hypothesis,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ) ).
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__5461,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ).
fof(m__,conjecture,
aElementOf0(xp,sdtlpdtrp0(xN,xm)) ).
fof(negated_conjecture,negated_conjecture,
~ aElementOf0(xp,sdtlpdtrp0(xN,xm)),
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(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(c196,plain,
( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[m__4660]) ).
cnf(c227,plain,
sdtlpdtrp0(xe,xn) = xp,
inference(clausification,[status(esa)],[m__5309]) ).
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(c237,plain,
aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(clausification,[status(esa)],[m__5461]) ).
cnf(c238,plain,
~ aElementOf0(xp,sdtlpdtrp0(xN,xm)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aSet0(szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[c177,c7]) ).
cnf(d1,plain,
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0)) ),
inference(resolution,[status(thm)],[c45,d0]) ).
cnf(d2,plain,
( ~ aSubsetOf0(X1,sdtlpdtrp0(xN,X0))
| aSubsetOf0(X1,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X0))
| ~ aSet0(szNzAzT0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[status(thm)],[c177,c14]) ).
cnf(d3,plain,
( ~ aSubsetOf0(X0,sdtlpdtrp0(xN,X1))
| aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X1))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c45,d2]) ).
cnf(d4,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xn)) ),
inference(resolution,[status(thm)],[d3,c237]) ).
cnf(d5,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xn)) ),
inference(resolution,[status(thm)],[c233,d4]) ).
cnf(d6,plain,
( ~ aSet0(sdtlpdtrp0(xN,xm))
| aSet0(sdtlpdtrp0(xN,xn)) ),
inference(resolution,[status(thm)],[c237,c7]) ).
cnf(d7,plain,
( aSet0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(xm,szNzAzT0) ),
inference(resolution,[status(thm)],[d1,d6]) ).
cnf(d8,plain,
aSet0(sdtlpdtrp0(xN,xn)),
inference(resolution,[status(thm)],[c233,d7]) ).
cnf(d9,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm)) ),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
szmzizndt0(sdtlpdtrp0(xN,xn)) = sdtlpdtrp0(xe,xn),
inference(resolution,[status(thm)],[c196,c228]) ).
cnf(d11,plain,
szmzizndt0(sdtlpdtrp0(xN,xn)) = xp,
inference(demodulation,[status(thm)],[d10,c227]) ).
cnf(d12,plain,
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| aElementOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm)) ),
inference(resolution,[status(thm)],[c237,c8]) ).
cnf(d13,plain,
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(szmzizndt0(X0),X0)
| X0 = slcrc0 ),
inference(equality_resolution,[status(thm)],[c74]) ).
cnf(d14,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
| aElementOf0(xp,sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(demodulation,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xm))
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(resolution,[status(thm)],[c238,d15]) ).
cnf(d17,plain,
( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(resolution,[status(thm)],[d16,d9]) ).
cnf(d18,plain,
( ~ aElementOf0(xm,szNzAzT0)
| sdtlpdtrp0(xN,xn) = slcrc0 ),
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
sdtlpdtrp0(xN,xn) = slcrc0,
inference(resolution,[status(thm)],[c233,d18]) ).
cnf(d20,plain,
( ~ aElementOf0(xn,szNzAzT0)
| isCountable0(slcrc0) ),
inference(superposition,[status(thm)],[d19,c178]) ).
cnf(d21,plain,
isCountable0(slcrc0),
inference(resolution,[status(thm)],[c228,d20]) ).
cnf(d22,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(d23,plain,
aSet0(slcrc0),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(d24,plain,
~ isCountable0(slcrc0),
inference(resolution,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d24,d21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM622+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.56 % Computer : n019.cluster.edu
% 0.10/5.56 % Model : x86_64 x86_64
% 0.10/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.56 % Memory : 8046.5625MB
% 0.10/5.56 % OS : Linux 6.8.0-71-generic
% 0.10/5.56 % CPULimit : 300
% 0.10/5.56 % WCLimit : 300
% 0.10/5.56 % DateTime : Sat Sep 26 03:29:26 UTC 2026
% 0.10/5.57 % CPUTime :
% 0.10/5.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.00/37.88 % SZS status Theorem for theBenchmark.p
% 37.00/37.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------