%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM538+2 : 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 : n010.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 08:13:04 AM UTC 2026
% Result : Theorem 15.97s 2.46s
% Output : CNFRefutation 15.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 15 unt; 1 def)
% Number of atoms : 182 ( 31 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 200 ( 79 ~; 95 |; 10 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ) ).
fof(mDefSub,definition,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ) ).
fof(mSubFSet,axiom,
! [X0] :
( ( isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> isFinite0(X1) ) ) ).
fof(mConsDiff,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ) ).
fof(mCardCons,axiom,
! [X0] :
( ( isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ( ~ aElementOf0(X1,X0)
=> sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0)) ) ) ) ).
fof(m__1522,hypothesis,
aSet0(xS) ).
fof(m__1522_02,hypothesis,
( aElementOf0(xx,xS)
& isFinite0(xS) ) ).
fof(m__,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mEOfElem]) ).
cnf(c8,plain,
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mDefSub]) ).
cnf(c9,plain,
( aElementOf0(sK14(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mDefSub]) ).
cnf(c10,plain,
( ~ aElementOf0(sK14(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mDefSub]) ).
cnf(c11,plain,
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mSubFSet]) ).
cnf(c46,plain,
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mConsDiff]) ).
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,
aSet0(xS),
inference(clausification,[status(esa)],[m__1522]) ).
cnf(c78,plain,
isFinite0(xS),
inference(clausification,[status(esa)],[m__1522_02]) ).
cnf(c79,plain,
aElementOf0(xx,xS),
inference(clausification,[status(esa)],[m__1522_02]) ).
cnf(c80,plain,
aSet0(sdtmndt0(xS,xx)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c82,plain,
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c83,plain,
( X0 != xx
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c84,plain,
( X0 = xx
| ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c85,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aSet0(xS)
| sdtpldt0(sdtmndt0(xS,xx),xx) = xS ),
inference(resolution,[status(thm)],[c79,c46]) ).
cnf(d1,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) = xS,
inference(resolution,[status(thm)],[c77,d0]) ).
cnf(d2,plain,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(equality_resolution,[status(thm)],[c83]) ).
cnf(d3,plain,
( ~ isFinite0(sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aSet0(sdtmndt0(xS,xx))
| sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ),
inference(resolution,[status(thm)],[c76,d2]) ).
cnf(d4,plain,
( ~ isFinite0(sdtmndt0(xS,xx))
| ~ aElement0(xx)
| sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ),
inference(resolution,[status(thm)],[c80,d3]) ).
cnf(d5,plain,
( aElementOf0(sK14(X0,sdtmndt0(xS,xx)),xS)
| aSubsetOf0(sdtmndt0(xS,xx),X0)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c9,c82]) ).
cnf(d6,plain,
( aSubsetOf0(sdtmndt0(xS,xx),X0)
| aElementOf0(sK14(X0,sdtmndt0(xS,xx)),xS)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c80,d5]) ).
cnf(d7,plain,
( aSubsetOf0(sdtmndt0(xS,xx),xS)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(xS)
| aSubsetOf0(sdtmndt0(xS,xx),xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[d6,c10]) ).
cnf(d8,plain,
( aSubsetOf0(sdtmndt0(xS,xx),xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c80,d7]) ).
cnf(d9,plain,
( ~ isFinite0(xS)
| isFinite0(sdtmndt0(xS,xx))
| ~ aSet0(xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[d8,c11]) ).
cnf(d10,plain,
( ~ isFinite0(xS)
| isFinite0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[c77,d9]) ).
cnf(d11,plain,
isFinite0(sdtmndt0(xS,xx)),
inference(resolution,[status(thm)],[c78,d10]) ).
cnf(d12,plain,
( ~ aElement0(xx)
| sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ),
inference(resolution,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
( aElement0(sK14(X0,X1))
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d14,plain,
( ~ aElement0(sK14(sdtmndt0(xS,xx),X0))
| ~ aElementOf0(sK14(sdtmndt0(xS,xx),X0),xS)
| sK14(sdtmndt0(xS,xx),X0) = xx
| aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(X0)
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[c10,c84]) ).
cnf(d15,plain,
( aSubsetOf0(X0,sdtmndt0(xS,xx))
| ~ aElement0(sK14(sdtmndt0(xS,xx),X0))
| ~ aElementOf0(sK14(sdtmndt0(xS,xx),X0),xS)
| ~ aSet0(X0)
| sK14(sdtmndt0(xS,xx),X0) = xx ),
inference(resolution,[status(thm)],[c80,d14]) ).
cnf(d16,plain,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| ~ aSet0(xS)
| ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(xS,sdtmndt0(xS,xx))
| ~ aElement0(sK14(sdtmndt0(xS,xx),xS))
| ~ aSet0(xS)
| sK14(sdtmndt0(xS,xx),xS) = xx ),
inference(resolution,[status(thm)],[d15,c9]) ).
cnf(d17,plain,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| ~ aElement0(sK14(sdtmndt0(xS,xx),xS))
| ~ aSet0(xS)
| sK14(sdtmndt0(xS,xx),xS) = xx ),
inference(resolution,[status(thm)],[c80,d16]) ).
cnf(d18,plain,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| ~ aElement0(sK14(sdtmndt0(xS,xx),xS))
| sK14(sdtmndt0(xS,xx),xS) = xx ),
inference(resolution,[status(thm)],[c77,d17]) ).
cnf(d19,plain,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtmndt0(xS,xx))
| sK14(sdtmndt0(xS,xx),xS) = xx ),
inference(resolution,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| ~ aSet0(xS)
| sK14(sdtmndt0(xS,xx),xS) = xx ),
inference(resolution,[status(thm)],[c80,d19]) ).
cnf(d21,plain,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| sK14(sdtmndt0(xS,xx),xS) = xx ),
inference(resolution,[status(thm)],[c77,d20]) ).
cnf(d22,plain,
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| sK14(sdtmndt0(xS,xx),xS) = xx ),
inference(resolution,[status(thm)],[d21,c8]) ).
cnf(d23,plain,
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,sdtmndt0(xS,xx))
| sK14(sdtmndt0(xS,xx),xS) = xx ),
inference(resolution,[status(thm)],[c80,d22]) ).
cnf(d24,plain,
( ~ aElementOf0(xx,xS)
| sK14(sdtmndt0(xS,xx),xS) = xx ),
inference(resolution,[status(thm)],[d23,d2]) ).
cnf(d25,plain,
sK14(sdtmndt0(xS,xx),xS) = xx,
inference(resolution,[status(thm)],[c79,d24]) ).
cnf(d26,plain,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(xS)
| aElement0(xx) ),
inference(superposition,[status(thm)],[d25,d13]) ).
cnf(d27,plain,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c80,d26]) ).
cnf(d28,plain,
( aSubsetOf0(xS,sdtmndt0(xS,xx))
| aElement0(xx) ),
inference(resolution,[status(thm)],[c77,d27]) ).
cnf(d29,plain,
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| aElement0(xx) ),
inference(resolution,[status(thm)],[d28,c8]) ).
cnf(d30,plain,
( aElement0(xx)
| ~ aElementOf0(X0,xS)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(resolution,[status(thm)],[c80,d29]) ).
cnf(d31,plain,
( aElement0(xx)
| ~ aElementOf0(xx,xS) ),
inference(resolution,[status(thm)],[d30,d2]) ).
cnf(d32,plain,
aElement0(xx),
inference(resolution,[status(thm)],[c79,d31]) ).
cnf(d33,plain,
sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))),
inference(resolution,[status(thm)],[d32,d12]) ).
cnf(d34,plain,
sbrdtbr0(xS) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))),
inference(demodulation,[status(thm)],[d33,d1]) ).
cnf(d35,plain,
sbrdtbr0(xS) != sbrdtbr0(xS),
inference(demodulation,[status(thm)],[c85,d34]) ).
cnf(d36,plain,
$false,
inference(equality_resolution,[status(thm)],[d35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM538+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 03:09:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.97/2.46 % SZS status Theorem for theBenchmark.p
% 15.97/2.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------