%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG099+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 : n004.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 08:25:52 AM UTC 2026
% Result : Theorem 17.35s 17.67s
% Output : CNFRefutation 17.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 18 unt; 0 def)
% Number of atoms : 86 ( 3 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 76 ( 28 ~; 22 |; 16 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtpldt0(X0,X1)) ) ).
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtasdt0(X0,X1)) ) ).
fof(mEOfElem,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ) ).
fof(m__1205,hypothesis,
( aIdeal0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) )
& ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ) ).
fof(m__1217,hypothesis,
( aElement0(xy)
& aElement0(xx) ) ).
fof(m__1294,hypothesis,
( sdtpldt0(xa,xb) = sz10
& aElementOf0(xb,xJ)
& aElementOf0(xa,xI) ) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) ).
fof(m__1332,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI) ).
fof(m__1409,hypothesis,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ) ).
fof(m__,conjecture,
? [X0] :
( ( sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(X0,xx,xI)
| aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) )
& aElement0(X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( ( sdteqdtlpzmzozddtrp0(X0,xy,xJ)
| aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ) )
& ( sdteqdtlpzmzozddtrp0(X0,xx,xI)
| aElementOf0(sdtpldt0(X0,smndt0(xx)),xI) )
& aElement0(X0) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c3,plain,
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mSortsB]) ).
cnf(c4,plain,
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
cnf(c23,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mEOfElem]) ).
cnf(c69,plain,
aSet0(xI),
inference(clausification,[status(esa)],[m__1205]) ).
cnf(c73,plain,
aSet0(xJ),
inference(clausification,[status(esa)],[m__1205]) ).
cnf(c81,plain,
aElement0(xx),
inference(clausification,[status(esa)],[m__1217]) ).
cnf(c82,plain,
aElement0(xy),
inference(clausification,[status(esa)],[m__1217]) ).
cnf(c83,plain,
aElementOf0(xa,xI),
inference(clausification,[status(esa)],[m__1294]) ).
cnf(c84,plain,
aElementOf0(xb,xJ),
inference(clausification,[status(esa)],[m__1294]) ).
cnf(c86,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(clausification,[status(esa)],[m__1319]) ).
cnf(c87,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(clausification,[status(esa)],[m__1332]) ).
cnf(c88,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(clausification,[status(esa)],[m__1409]) ).
cnf(c89,plain,
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb))
| aElement0(xw) ),
inference(superposition,[status(thm)],[c86,c3]) ).
cnf(d1,plain,
( ~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
| ~ aElement0(xw) ),
inference(resolution,[status(thm)],[c88,c89]) ).
cnf(d2,plain,
~ aElement0(xw),
inference(resolution,[status(thm)],[c87,d1]) ).
cnf(d3,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ aElement0(xy)
| ~ aElement0(xa)
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( ~ aElement0(xa)
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(resolution,[status(thm)],[c82,d4]) ).
cnf(d6,plain,
( ~ aSet0(xI)
| aElement0(xa) ),
inference(resolution,[status(thm)],[c23,c83]) ).
cnf(d7,plain,
aElement0(xa),
inference(resolution,[status(thm)],[c69,d6]) ).
cnf(d8,plain,
~ aElement0(sdtasdt0(xx,xb)),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ aElement0(xx)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[d8,c4]) ).
cnf(d10,plain,
~ aElement0(xb),
inference(resolution,[status(thm)],[c81,d9]) ).
cnf(d11,plain,
( ~ aSet0(xJ)
| aElement0(xb) ),
inference(resolution,[status(thm)],[c23,c84]) ).
cnf(d12,plain,
aElement0(xb),
inference(resolution,[status(thm)],[c73,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG099+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
% 0.10/15.40 % Computer : n004.cluster.edu
% 0.10/15.40 % Model : x86_64 x86_64
% 0.10/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.40 % Memory : 8046.5625MB
% 0.10/15.40 % OS : Linux 6.8.0-71-generic
% 0.02/15.40 % CPULimit : 300
% 0.02/15.40 % WCLimit : 300
% 0.02/15.40 % DateTime : Sat Sep 26 06:05:23 UTC 2026
% 0.02/15.40 % CPUTime :
% 0.02/15.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.35/17.67 % SZS status Theorem for theBenchmark.p
% 17.35/17.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------