%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM558+3 : 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 : n016.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 08:13:09 AM UTC 2026
% Result : Theorem 29.35s 5.25s
% Output : CNFRefutation 29.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 14 unt; 1 def)
% Number of atoms : 107 ( 13 equ)
% Maximal formula atoms : 43 ( 3 avg)
% Number of connectives : 98 ( 20 ~; 19 |; 37 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 18 !; 1 ?)
% 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(m__2202_02,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ) ).
fof(m__2227,hypothesis,
( ~ ( ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> ( slbdtsldtrb0(xS,xk) = slcrc0
| ~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
& ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xT)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xT,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xT)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( ( sbrdtbr0(X0) = xk
& ( aSubsetOf0(X0,xS)
| ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( sbrdtbr0(X0) = xk
& aSubsetOf0(X0,xS)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSet0(X0) ) ) )
& aSet0(slbdtsldtrb0(xS,xk)) ) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS) ).
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__2378,hypothesis,
( aElementOf0(xP,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xP) = xk
& aSubsetOf0(xP,xS)
& ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) ) ) ).
fof(m__,conjecture,
aElementOf0(xx,xT) ).
fof(negated_conjecture,negated_conjecture,
~ aElementOf0(xx,xT),
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(c128,plain,
aSet0(xS),
inference(clausification,[status(esa)],[m__2202_02]) ).
cnf(c129,plain,
aSet0(xT),
inference(clausification,[status(esa)],[m__2202_02]) ).
cnf(c142,plain,
( aSubsetOf0(X0,xT)
| ~ aElementOf0(X0,slbdtsldtrb0(xT,xk)) ),
inference(clausification,[status(esa)],[m__2227]) ).
cnf(c147,plain,
( aElementOf0(X0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ),
inference(clausification,[status(esa)],[m__2227]) ).
cnf(c158,plain,
aElementOf0(xx,xS),
inference(clausification,[status(esa)],[m__2256]) ).
cnf(c180,plain,
( X0 != xx
| ~ aElement0(X0)
| aElementOf0(X0,xP) ),
inference(clausification,[status(esa)],[m__2357]) ).
cnf(c185,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(clausification,[status(esa)],[m__2378]) ).
cnf(c186,plain,
~ aElementOf0(xx,xT),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aElement0(xx)
| aElementOf0(xx,xP) ),
inference(equality_resolution,[status(thm)],[c180]) ).
cnf(d1,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c158,c0]) ).
cnf(d2,plain,
aElement0(xx),
inference(resolution,[status(thm)],[c128,d1]) ).
cnf(d3,plain,
aElementOf0(xx,xP),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
aElementOf0(xP,slbdtsldtrb0(xT,xk)),
inference(resolution,[status(thm)],[c147,c185]) ).
cnf(d5,plain,
aSubsetOf0(xP,xT),
inference(resolution,[status(thm)],[d4,c142]) ).
cnf(d6,plain,
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[status(thm)],[d5,c8]) ).
cnf(d7,plain,
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xT) ),
inference(resolution,[status(thm)],[c129,d6]) ).
cnf(d8,plain,
aElementOf0(xx,xT),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c186,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM558+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.77 % Computer : n016.cluster.edu
% 0.10/0.77 % Model : x86_64 x86_64
% 0.10/0.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.77 % Memory : 8046.5625MB
% 0.10/0.77 % OS : Linux 6.8.0-71-generic
% 0.10/0.77 % CPULimit : 300
% 0.10/0.77 % WCLimit : 300
% 0.10/0.77 % DateTime : Sat Sep 26 03:18:32 UTC 2026
% 0.10/0.78 % CPUTime :
% 0.10/0.78 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.35/5.25 % SZS status Theorem for theBenchmark.p
% 29.35/5.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------