%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM556+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 : n009.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 08:13:08 AM UTC 2026
% Result : Theorem 13.23s 3.01s
% Output : CNFRefutation 13.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 72 ( 23 unt; 0 def)
% Number of atoms : 188 ( 38 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 188 ( 72 ~; 70 |; 27 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ) ).
fof(mDiffCons,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aElement0(X0) )
=> ( ~ aElementOf0(X0,X1)
=> sdtmndt0(sdtpldt0(X1,X0),X0) = X1 ) ) ).
fof(mFConsSet,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> isFinite0(sdtpldt0(X1,X0)) ) ) ).
fof(mFDiffSet,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> isFinite0(sdtmndt0(X1,X0)) ) ) ).
fof(mCardCons,axiom,
! [X0] :
( ( isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ( ~ aElementOf0(X1,X0)
=> sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0)) ) ) ) ).
fof(mCardDiff,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( ( aElementOf0(X1,X0)
& isFinite0(X0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0) ) ) ).
fof(m__2202_02,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS) ).
fof(m__2270,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xS) )
& aSet0(xQ) ) ).
fof(m__2291,hypothesis,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ) ).
fof(m__2304,hypothesis,
( aElementOf0(xy,xQ)
& aElement0(xy) ) ).
fof(m__2357,hypothesis,
( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xQ,xy)) )
& aElement0(X0) ) )
& aSet0(xP)
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xQ,xy)) ) ).
fof(m__2411,hypothesis,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( X0 != xy
& aElementOf0(X0,xQ)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xQ,xy))
& ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ) ).
fof(m__,conjecture,
( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( sbrdtbr0(xP) = xk
& ( aSubsetOf0(xP,xS)
| ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mEOfElem]) ).
cnf(c47,plain,
( sdtmndt0(sdtpldt0(X1,X0),X0) = X1
| aElementOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mDiffCons]) ).
cnf(c50,plain,
( isFinite0(sdtpldt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mFConsSet]) ).
cnf(c51,plain,
( isFinite0(sdtmndt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mFDiffSet]) ).
cnf(c76,plain,
( ~ aSet0(X1)
| ~ isFinite0(X1)
| sbrdtbr0(sdtpldt0(X1,X0)) = szszuzczcdt0(sbrdtbr0(X1))
| aElementOf0(X0,X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mCardCons]) ).
cnf(c77,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X0,X1))) = sbrdtbr0(X0)
| ~ aElementOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mCardDiff]) ).
cnf(c128,plain,
aSet0(xS),
inference(clausification,[status(esa)],[m__2202_02]) ).
cnf(c158,plain,
aElementOf0(xx,xS),
inference(clausification,[status(esa)],[m__2256]) ).
cnf(c159,plain,
aSet0(xQ),
inference(clausification,[status(esa)],[m__2270]) ).
cnf(c160,plain,
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ),
inference(clausification,[status(esa)],[m__2270]) ).
cnf(c162,plain,
sbrdtbr0(xQ) = xk,
inference(clausification,[status(esa)],[m__2270]) ).
cnf(c165,plain,
isFinite0(xQ),
inference(clausification,[status(esa)],[m__2291]) ).
cnf(c167,plain,
aElement0(xy),
inference(clausification,[status(esa)],[m__2304]) ).
cnf(c168,plain,
aElementOf0(xy,xQ),
inference(clausification,[status(esa)],[m__2304]) ).
cnf(c171,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(clausification,[status(esa)],[m__2357]) ).
cnf(c173,plain,
( aElementOf0(X0,xQ)
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ),
inference(clausification,[status(esa)],[m__2357]) ).
cnf(c176,plain,
aSet0(xP),
inference(clausification,[status(esa)],[m__2357]) ).
cnf(c178,plain,
( X0 = xx
| aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElementOf0(X0,xP) ),
inference(clausification,[status(esa)],[m__2357]) ).
cnf(c181,plain,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(clausification,[status(esa)],[m__2357]) ).
cnf(c182,plain,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(clausification,[status(esa)],[m__2411]) ).
cnf(c188,plain,
( sbrdtbr0(xP) != xk
| aElementOf0(sK133,xP) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c189,plain,
( sbrdtbr0(xP) != xk
| ~ aElementOf0(sK133,xS) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( aElementOf0(X0,xQ)
| ~ aElementOf0(X0,xP)
| X0 = xx ),
inference(resolution,[status(thm)],[c178,c173]) ).
cnf(d1,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xQ) ),
inference(resolution,[status(thm)],[c77,c168]) ).
cnf(d2,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk ),
inference(demodulation,[status(thm)],[d1,c162]) ).
cnf(d3,plain,
( ~ isFinite0(xQ)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk ),
inference(resolution,[status(thm)],[c159,d2]) ).
cnf(d4,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = xk,
inference(resolution,[status(thm)],[c165,d3]) ).
cnf(d5,plain,
( ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| sbrdtbr0(sdtpldt0(sdtmndt0(xQ,xy),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) ),
inference(resolution,[status(thm)],[c76,c182]) ).
cnf(d6,plain,
( ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| sbrdtbr0(xP) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) ),
inference(demodulation,[status(thm)],[d5,c181]) ).
cnf(d7,plain,
( ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| sbrdtbr0(xP) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) ),
inference(resolution,[status(thm)],[c171,d6]) ).
cnf(d8,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c158,c0]) ).
cnf(d9,plain,
aElement0(xx),
inference(resolution,[status(thm)],[c128,d8]) ).
cnf(d10,plain,
( ~ isFinite0(sdtmndt0(xQ,xy))
| sbrdtbr0(xP) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ isFinite0(sdtmndt0(xQ,xy))
| sbrdtbr0(xP) = xk ),
inference(demodulation,[status(thm)],[d10,d4]) ).
cnf(d12,plain,
( ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| sdtmndt0(sdtpldt0(sdtmndt0(xQ,xy),xx),xx) = sdtmndt0(xQ,xy) ),
inference(resolution,[status(thm)],[c182,c47]) ).
cnf(d13,plain,
( ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| sdtmndt0(xP,xx) = sdtmndt0(xQ,xy) ),
inference(demodulation,[status(thm)],[d12,c181]) ).
cnf(d14,plain,
( ~ aElement0(xx)
| sdtmndt0(xP,xx) = sdtmndt0(xQ,xy) ),
inference(resolution,[status(thm)],[c171,d13]) ).
cnf(d15,plain,
sdtmndt0(xP,xx) = sdtmndt0(xQ,xy),
inference(resolution,[status(thm)],[d9,d14]) ).
cnf(d16,plain,
( ~ isFinite0(xP)
| ~ aElement0(xx)
| ~ aSet0(xP)
| isFinite0(sdtmndt0(xQ,xy)) ),
inference(superposition,[status(thm)],[d15,c51]) ).
cnf(d17,plain,
( ~ isFinite0(xP)
| isFinite0(sdtmndt0(xQ,xy))
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[c176,d16]) ).
cnf(d18,plain,
( ~ isFinite0(xP)
| isFinite0(sdtmndt0(xQ,xy)) ),
inference(resolution,[status(thm)],[d9,d17]) ).
cnf(d19,plain,
( ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xQ,xy))
| isFinite0(xP) ),
inference(superposition,[status(thm)],[c181,c50]) ).
cnf(d20,plain,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[c171,d19]) ).
cnf(d21,plain,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy)) ),
inference(resolution,[status(thm)],[d9,d20]) ).
cnf(d22,plain,
( ~ isFinite0(xQ)
| ~ aElement0(xy)
| ~ aSet0(xQ)
| isFinite0(xP) ),
inference(resolution,[status(thm)],[d21,c51]) ).
cnf(d23,plain,
( isFinite0(xP)
| ~ isFinite0(xQ)
| ~ aElement0(xy) ),
inference(resolution,[status(thm)],[c159,d22]) ).
cnf(d24,plain,
( isFinite0(xP)
| ~ aElement0(xy) ),
inference(resolution,[status(thm)],[c165,d23]) ).
cnf(d25,plain,
isFinite0(xP),
inference(resolution,[status(thm)],[c167,d24]) ).
cnf(d26,plain,
isFinite0(sdtmndt0(xQ,xy)),
inference(resolution,[status(thm)],[d25,d18]) ).
cnf(d27,plain,
sbrdtbr0(xP) = xk,
inference(resolution,[status(thm)],[d26,d11]) ).
cnf(d28,plain,
aElementOf0(sK133,xP),
inference(resolution,[status(thm)],[d27,c188]) ).
cnf(d29,plain,
( aElementOf0(sK133,xQ)
| sK133 = xx ),
inference(resolution,[status(thm)],[d28,d0]) ).
cnf(d30,plain,
( aElementOf0(sK133,xS)
| sK133 = xx ),
inference(resolution,[status(thm)],[d29,c160]) ).
cnf(d31,plain,
~ aElementOf0(sK133,xS),
inference(resolution,[status(thm)],[d27,c189]) ).
cnf(d32,plain,
sK133 = xx,
inference(resolution,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
~ aElementOf0(xx,xS),
inference(demodulation,[status(thm)],[d31,d32]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[c158,d33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM556+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.34 % Computer : n009.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Sat Sep 26 03:13:02 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.23/3.01 % SZS status Theorem for theBenchmark.p
% 13.23/3.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------