%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM566+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 08:13:10 AM UTC 2026
% Result : Theorem 39.43s 5.27s
% Output : CNFRefutation 39.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 69 ( 19 unt; 2 def)
% Number of atoms : 173 ( 48 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 178 ( 74 ~; 81 |; 13 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 46 ( 5 sgn 10 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefEmp,definition,
! [X0] :
( X0 = slcrc0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ) ).
fof(mDefSub,definition,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ) ).
fof(mSubRefl,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ) ).
fof(mImgRng,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0))) ) ) ).
fof(m__3291,hypothesis,
( isFinite0(xT)
& aSet0(xT) ) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ) ).
fof(m__3453,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ) ).
fof(m__3462,hypothesis,
xK = sz00 ).
fof(m__3476,hypothesis,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ).
fof(m__3507,hypothesis,
! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,sz00))
=> sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ) ).
fof(m__,conjecture,
? [X0] :
( ? [X1] :
( ! [X2] :
( aElementOf0(X2,slbdtsldtrb0(X1,xK))
=> sdtlpdtrp0(xc,X2) = X0 )
& isCountable0(X1)
& aSubsetOf0(X1,xS) )
& aElementOf0(X0,xT) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( ! [X2] :
( aElementOf0(X2,slbdtsldtrb0(X1,xK))
=> sdtlpdtrp0(xc,X2) = X0 )
& isCountable0(X1)
& aSubsetOf0(X1,xS) )
& aElementOf0(X0,xT) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c2,plain,
( ~ aElementOf0(X1,X0)
| X0 != slcrc0 ),
inference(clausification,[status(esa)],[mDefEmp]) ).
cnf(c3,plain,
( ~ aSet0(X0)
| aElementOf0(sK4(X0),X0)
| X0 = slcrc0 ),
inference(clausification,[status(esa)],[mDefEmp]) ).
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(c12,plain,
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mSubRefl]) ).
cnf(c45,plain,
aSet0(szNzAzT0),
inference(clausification,[status(esa)],[mNATSet]) ).
cnf(c143,plain,
( aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(clausification,[status(esa)],[mImgRng]) ).
cnf(c156,plain,
aSet0(xT),
inference(clausification,[status(esa)],[m__3291]) ).
cnf(c159,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausification,[status(esa)],[m__3435]) ).
cnf(c160,plain,
isCountable0(xS),
inference(clausification,[status(esa)],[m__3435]) ).
cnf(c161,plain,
aFunction0(xc),
inference(clausification,[status(esa)],[m__3453]) ).
cnf(c162,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(clausification,[status(esa)],[m__3453]) ).
cnf(c163,plain,
slbdtsldtrb0(xS,xK) = szDzozmdt0(xc),
inference(clausification,[status(esa)],[m__3453]) ).
cnf(c168,plain,
xK = sz00,
inference(clausification,[status(esa)],[m__3462]) ).
cnf(c169,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(clausification,[status(esa)],[m__3476]) ).
cnf(c170,plain,
( sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,X0)
| ~ aElementOf0(X0,slbdtsldtrb0(xS,sz00)) ),
inference(clausification,[status(esa)],[m__3507]) ).
cnf(c171,plain,
( ~ isCountable0(X1)
| aElementOf0(sK166(X0,X1),slbdtsldtrb0(X1,xK))
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,xT) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c172,plain,
( ~ isCountable0(X1)
| sdtlpdtrp0(xc,sK166(X0,X1)) != X0
| ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,xT) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
slbdtsldtrb0(xS,sz00) = szDzozmdt0(xc),
inference(demodulation,[status(thm)],[c163,c168]) ).
cnf(d1,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(demodulation,[status(thm)],[c169,d0]) ).
cnf(d2,plain,
( ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| aElementOf0(sK166(X0,X1),slbdtsldtrb0(X1,sz00))
| ~ aElementOf0(X0,xT) ),
inference(demodulation,[status(thm)],[c171,c168]) ).
cnf(d3,plain,
( ~ aSubsetOf0(xS,xS)
| ~ isCountable0(xS)
| ~ aElementOf0(X0,xT)
| aElementOf0(sK166(X0,xS),szDzozmdt0(xc)) ),
inference(superposition,[status(thm)],[d0,d2]) ).
cnf(d4,plain,
( ~ aSubsetOf0(xS,xS)
| aElementOf0(sK166(X0,xS),szDzozmdt0(xc))
| ~ aElementOf0(X0,xT) ),
inference(resolution,[status(thm)],[c160,d3]) ).
cnf(d5,plain,
( ~ aElementOf0(X0,szDzozmdt0(xc))
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,X0) ),
inference(demodulation,[status(thm)],[c170,d0]) ).
cnf(d6,plain,
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT)
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK166(X0,xS)) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ aSet0(xS)
| ~ aElementOf0(X0,xT)
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK166(X0,xS)) ),
inference(resolution,[status(thm)],[d6,c12]) ).
cnf(d8,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xS) ),
inference(resolution,[status(thm)],[c7,c159]) ).
cnf(d9,plain,
aSet0(xS),
inference(resolution,[status(thm)],[c45,d8]) ).
cnf(d10,plain,
( ~ aElementOf0(X0,xT)
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK166(X0,xS)) ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ aSet0(xT)
| xT = slcrc0
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK166(sK4(xT),xS)) ),
inference(resolution,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
( xT = slcrc0
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK166(sK4(xT),xS)) ),
inference(resolution,[status(thm)],[c156,d11]) ).
cnf(d13,plain,
( xT = slcrc0
| ~ aFunction0(xc)
| ~ aElementOf0(sK166(sK4(xT),xS),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(superposition,[status(thm)],[d12,c143]) ).
cnf(d14,plain,
( ~ aElementOf0(sK166(sK4(xT),xS),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| xT = slcrc0 ),
inference(resolution,[status(thm)],[c161,d13]) ).
cnf(d15,plain,
( ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[c162,c8]) ).
cnf(d16,plain,
( aElementOf0(X0,xT)
| ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(resolution,[status(thm)],[c156,d15]) ).
cnf(d17,plain,
( ~ aElementOf0(sK166(sK4(xT),xS),szDzozmdt0(xc))
| xT = slcrc0
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT) ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(sK4(xT),xT)
| aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| xT = slcrc0 ),
inference(resolution,[status(thm)],[d17,d4]) ).
cnf(d19,plain,
( sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK166(sdtlpdtrp0(xc,slcrc0),xS))
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(sK4(xT),xT)
| xT = slcrc0 ),
inference(resolution,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
( ~ aSet0(xT)
| xT = slcrc0
| ~ aSubsetOf0(xS,xS)
| xT = slcrc0
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK166(sdtlpdtrp0(xc,slcrc0),xS)) ),
inference(resolution,[status(thm)],[d19,c3]) ).
cnf(d21,plain,
( ~ aSubsetOf0(xS,xS)
| xT = slcrc0
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK166(sdtlpdtrp0(xc,slcrc0),xS)) ),
inference(resolution,[status(thm)],[c156,d20]) ).
cnf(d22,plain,
( ~ aSet0(xS)
| xT = slcrc0
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK166(sdtlpdtrp0(xc,slcrc0),xS)) ),
inference(resolution,[status(thm)],[d21,c12]) ).
cnf(d23,plain,
( xT = slcrc0
| sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK166(sdtlpdtrp0(xc,slcrc0),xS)) ),
inference(resolution,[status(thm)],[d9,d22]) ).
cnf(d24,plain,
( xT = slcrc0
| ~ aSubsetOf0(xS,xS)
| ~ isCountable0(xS)
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,slcrc0) ),
inference(superposition,[status(thm)],[d23,c172]) ).
cnf(d25,plain,
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| xT = slcrc0
| sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,slcrc0) ),
inference(resolution,[status(thm)],[c160,d24]) ).
cnf(d26,plain,
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| xT = slcrc0 ),
inference(equality_resolution,[status(thm)],[d25]) ).
cnf(d27,plain,
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(sK4(xT),xT)
| xT = slcrc0
| ~ aSubsetOf0(xS,xS)
| xT = slcrc0 ),
inference(resolution,[status(thm)],[d26,d18]) ).
cnf(d28,plain,
( ~ aSet0(xT)
| xT = slcrc0
| ~ aSubsetOf0(xS,xS)
| xT = slcrc0 ),
inference(resolution,[status(thm)],[d27,c3]) ).
cnf(d29,plain,
( ~ aSubsetOf0(xS,xS)
| xT = slcrc0 ),
inference(resolution,[status(thm)],[c156,d28]) ).
cnf(d30,plain,
( ~ aSet0(xS)
| xT = slcrc0 ),
inference(resolution,[status(thm)],[d29,c12]) ).
cnf(d31,plain,
xT = slcrc0,
inference(resolution,[status(thm)],[d9,d30]) ).
cnf(d32,plain,
( aElementOf0(X0,slcrc0)
| ~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(demodulation,[status(thm)],[d16,d31]) ).
cnf(d33,plain,
~ aElementOf0(X0,slcrc0),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d34,plain,
~ aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(resolution,[status(thm)],[d33,d32]) ).
cnf(d35,plain,
( ~ aFunction0(xc)
| ~ aElementOf0(X0,szDzozmdt0(xc)) ),
inference(resolution,[status(thm)],[d34,c143]) ).
cnf(d36,plain,
~ aElementOf0(X0,szDzozmdt0(xc)),
inference(resolution,[status(thm)],[c161,d35]) ).
cnf(d37,plain,
$false,
inference(resolution,[status(thm)],[d36,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM566+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
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 03:14:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.43/5.27 % SZS status Theorem for theBenchmark.p
% 39.43/5.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------