%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM613+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 : n013.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 08:13:20 AM UTC 2026
% Result : Theorem 30.56s 10.46s
% Output : CNFRefutation 30.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 30 unt; 1 def)
% Number of atoms : 115 ( 48 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 94 ( 39 ~; 34 |; 10 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,definition,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ) ).
fof(mSuccNum,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ) ).
fof(mSuccEquSucc,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
=> X0 = X1 ) ) ).
fof(mCardNum,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ) ).
fof(mCardDiff,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( ( aElementOf0(X1,X0)
& isFinite0(X0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ) ).
fof(mCardSeg,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sbrdtbr0(slbdtrb0(X0)) = X0 ) ).
fof(m__3418,hypothesis,
aElementOf0(xK,szNzAzT0) ).
fof(m__3533,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ) ).
fof(m__4891,hypothesis,
( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aSet0(xO) ) ).
fof(m__5093,hypothesis,
( xQ != slcrc0
& aSubsetOf0(xQ,xO) ) ).
fof(m__5147,hypothesis,
xp = szmzizndt0(xQ) ).
fof(m__5164,hypothesis,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ) ).
fof(m__5173,hypothesis,
aElementOf0(xp,xQ) ).
fof(m__5255,hypothesis,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
& szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ)
& sbrdtbr0(xQ) = szszuzczcdt0(xk) ) ).
fof(m__,conjecture,
sbrdtbr0(xP) = xk ).
fof(negated_conjecture,negated_conjecture,
sbrdtbr0(xP) != xk,
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c7,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mDefSub]) ).
cnf(c55,plain,
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[mSuccNum]) ).
cnf(c57,plain,
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[mSuccEquSucc]) ).
cnf(c72,plain,
( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mCardNum]) ).
cnf(c77,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mCardDiff]) ).
cnf(c111,plain,
( sbrdtbr0(slbdtrb0(X0)) = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(clausification,[status(esa)],[mCardSeg]) ).
cnf(c174,plain,
aElementOf0(xK,szNzAzT0),
inference(clausification,[status(esa)],[m__3418]) ).
cnf(c186,plain,
aElementOf0(xk,szNzAzT0),
inference(clausification,[status(esa)],[m__3533]) ).
cnf(c187,plain,
szszuzczcdt0(xk) = xK,
inference(clausification,[status(esa)],[m__3533]) ).
cnf(c220,plain,
aSet0(xO),
inference(clausification,[status(esa)],[m__4891]) ).
cnf(c229,plain,
aSubsetOf0(xQ,xO),
inference(clausification,[status(esa)],[m__5093]) ).
cnf(c233,plain,
xp = szmzizndt0(xQ),
inference(clausification,[status(esa)],[m__5147]) ).
cnf(c235,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(clausification,[status(esa)],[m__5164]) ).
cnf(c236,plain,
aElementOf0(xp,xQ),
inference(clausification,[status(esa)],[m__5173]) ).
cnf(c240,plain,
sbrdtbr0(xQ) = szszuzczcdt0(xk),
inference(clausification,[status(esa)],[m__5255]) ).
cnf(c241,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(clausification,[status(esa)],[m__5255]) ).
cnf(c242,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(clausification,[status(esa)],[m__5255]) ).
cnf(c243,plain,
sbrdtbr0(xP) != xk,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
sbrdtbr0(xQ) = xK,
inference(demodulation,[status(thm)],[c240,c187]) ).
cnf(d1,plain,
szszuzczcdt0(sbrdtbr0(xP)) = xK,
inference(demodulation,[status(thm)],[c241,d0]) ).
cnf(d2,plain,
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| X0 = sbrdtbr0(xP)
| szszuzczcdt0(X0) != xK ),
inference(superposition,[status(thm)],[d1,c57]) ).
cnf(d3,plain,
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != xK
| X0 = sbrdtbr0(xP) ),
inference(resolution,[status(thm)],[c242,d2]) ).
cnf(d4,plain,
sbrdtbr0(slbdtrb0(xK)) = xK,
inference(resolution,[status(thm)],[c111,c174]) ).
cnf(d5,plain,
( ~ aElementOf0(X0,szNzAzT0)
| sbrdtbr0(slbdtrb0(szszuzczcdt0(X0))) = szszuzczcdt0(X0) ),
inference(resolution,[status(thm)],[c111,c55]) ).
cnf(d6,plain,
sbrdtbr0(slbdtrb0(szszuzczcdt0(xk))) = szszuzczcdt0(xk),
inference(resolution,[status(thm)],[d5,c186]) ).
cnf(d7,plain,
sbrdtbr0(slbdtrb0(xK)) = szszuzczcdt0(xk),
inference(demodulation,[status(thm)],[d6,c187]) ).
cnf(d8,plain,
xK = szszuzczcdt0(xk),
inference(demodulation,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
( ~ aElementOf0(xk,szNzAzT0)
| xk = sbrdtbr0(xP)
| xK != xK ),
inference(superposition,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
( xk = sbrdtbr0(xP)
| xK != xK ),
inference(resolution,[status(thm)],[c186,d9]) ).
cnf(d11,plain,
xP = sdtmndt0(xQ,xp),
inference(demodulation,[status(thm)],[c235,c233]) ).
cnf(d12,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xp))) = sbrdtbr0(xQ) ),
inference(resolution,[status(thm)],[c77,c236]) ).
cnf(d13,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ),
inference(demodulation,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| xK = sbrdtbr0(xQ) ),
inference(demodulation,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| xK = xK ),
inference(demodulation,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
( ~ aSet0(xO)
| aSet0(xQ) ),
inference(resolution,[status(thm)],[c229,c7]) ).
cnf(d17,plain,
aSet0(xQ),
inference(resolution,[status(thm)],[c220,d16]) ).
cnf(d18,plain,
( ~ isFinite0(xQ)
| xK = xK ),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
( isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(superposition,[status(thm)],[d0,c72]) ).
cnf(d20,plain,
( isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(resolution,[status(thm)],[c174,d19]) ).
cnf(d21,plain,
isFinite0(xQ),
inference(resolution,[status(thm)],[d17,d20]) ).
cnf(d22,plain,
xK = xK,
inference(resolution,[status(thm)],[d21,d18]) ).
cnf(d23,plain,
xk = sbrdtbr0(xP),
inference(resolution,[status(thm)],[d22,d10]) ).
cnf(d24,plain,
xk != xk,
inference(demodulation,[status(thm)],[c243,d23]) ).
cnf(d25,plain,
$false,
inference(equality_resolution,[status(thm)],[d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM613+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
% 0.10/5.39 % Computer : n013.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Sat Sep 26 03:26:43 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.56/10.46 % SZS status Theorem for theBenchmark.p
% 30.56/10.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------