%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG118+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 : 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 08:25:56 AM UTC 2026
% Result : Theorem 36.05s 10.43s
% Output : CNFRefutation 36.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 9 unt; 1 def)
% Number of atoms : 169 ( 46 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 230 ( 108 ~; 95 |; 18 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 9 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ) ).
fof(mDefIdeal,definition,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ) ).
fof(mDivision,axiom,
! [X0,X1] :
( ( X1 != sz00
& aElement0(X1)
& aElement0(X0) )
=> ? [X2,X3] :
( ( X3 != sz00
=> iLess0(sbrdtbr0(X3),sbrdtbr0(X1)) )
& X0 = sdtpldt0(sdtasdt0(X2,X1),X3)
& aElement0(X3)
& aElement0(X2) ) ) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ) ).
fof(m__2273,hypothesis,
( ! [X0] :
( ( X0 != sz00
& aElementOf0(X0,xI) )
=> ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
& xu != sz00
& aElementOf0(xu,xI) ) ).
fof(m__,conjecture,
? [X0,X1] :
( ( iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
| X1 = sz00 )
& xb = sdtpldt0(sdtasdt0(X0,xu),X1)
& aElement0(X1)
& aElement0(X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1] :
( ( iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
| X1 = sz00 )
& xb = sdtpldt0(sdtasdt0(X0,xu),X1)
& aElement0(X1)
& aElement0(X0) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c23,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mEOfElem]) ).
cnf(c55,plain,
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(clausification,[status(esa)],[mDefIdeal]) ).
cnf(c75,plain,
( aElement0(sK81(X0,X1))
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mDivision]) ).
cnf(c76,plain,
( aElement0(sK82(X0,X1))
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mDivision]) ).
cnf(c77,plain,
( X0 = sdtpldt0(sdtasdt0(sK81(X0,X1),X1),sK82(X0,X1))
| X1 = sz00
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[mDivision]) ).
cnf(c78,plain,
( ~ aElement0(X1)
| X1 = sz00
| sK82(X0,X1) = sz00
| ~ aElement0(X0)
| iLess0(sbrdtbr0(sK82(X0,X1)),sbrdtbr0(X1)) ),
inference(clausification,[status(esa)],[mDivision]) ).
cnf(c109,plain,
aElement0(xb),
inference(clausification,[status(esa)],[m__2091]) ).
cnf(c112,plain,
aIdeal0(xI),
inference(clausification,[status(esa)],[m__2174]) ).
cnf(c120,plain,
aElementOf0(xu,xI),
inference(clausification,[status(esa)],[m__2273]) ).
cnf(c121,plain,
xu != sz00,
inference(clausification,[status(esa)],[m__2273]) ).
cnf(c129,plain,
( X1 != sz00
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c130,plain,
( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
| xb != sdtpldt0(sdtasdt0(X0,xu),X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aElement0(xu)
| ~ aElement0(X0)
| xu = sz00
| ~ aElement0(sK81(X0,xu))
| ~ aElement0(sK82(X0,xu))
| sK82(X0,xu) != sz00
| xb != X0 ),
inference(superposition,[status(thm)],[c77,c129]) ).
cnf(d1,plain,
( ~ aElement0(xu)
| ~ aElement0(sK82(X0,xu))
| ~ aElement0(sK81(X0,xu))
| ~ aElement0(X0)
| xb != X0
| sK82(X0,xu) != sz00 ),
inference(resolution,[status(thm)],[c121,d0]) ).
cnf(d2,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(resolution,[status(thm)],[c23,c120]) ).
cnf(d3,plain,
aSet0(xI),
inference(resolution,[status(thm)],[c55,c112]) ).
cnf(d4,plain,
aElement0(xu),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ aElement0(sK82(X0,xu))
| ~ aElement0(sK81(X0,xu))
| ~ aElement0(X0)
| xb != X0
| sK82(X0,xu) != sz00 ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ aElement0(xu)
| ~ aElement0(X0)
| xu = sz00
| ~ iLess0(sbrdtbr0(sK82(X0,xu)),sbrdtbr0(xu))
| ~ aElement0(sK81(X0,xu))
| ~ aElement0(sK82(X0,xu))
| xb != X0 ),
inference(superposition,[status(thm)],[c77,c130]) ).
cnf(d7,plain,
( ~ iLess0(sbrdtbr0(sK82(X0,xu)),sbrdtbr0(xu))
| ~ aElement0(xu)
| ~ aElement0(sK82(X0,xu))
| ~ aElement0(sK81(X0,xu))
| ~ aElement0(X0)
| xb != X0 ),
inference(resolution,[status(thm)],[c121,d6]) ).
cnf(d8,plain,
( ~ iLess0(sbrdtbr0(sK82(X0,xu)),sbrdtbr0(xu))
| ~ aElement0(sK82(X0,xu))
| ~ aElement0(sK81(X0,xu))
| ~ aElement0(X0)
| xb != X0 ),
inference(resolution,[status(thm)],[d4,d7]) ).
cnf(d9,plain,
( ~ iLess0(sbrdtbr0(sK82(xb,xu)),sbrdtbr0(xu))
| ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu))
| ~ aElement0(xb) ),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
( ~ iLess0(sbrdtbr0(sK82(xb,xu)),sbrdtbr0(xu))
| ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu)) ),
inference(resolution,[status(thm)],[c109,d9]) ).
cnf(d11,plain,
( ~ aElement0(xu)
| ~ aElement0(xb)
| sK82(xb,xu) = sz00
| xu = sz00
| ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu)) ),
inference(resolution,[status(thm)],[d10,c78]) ).
cnf(d12,plain,
( ~ aElement0(xu)
| ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu))
| xu = sz00
| sK82(xb,xu) = sz00 ),
inference(resolution,[status(thm)],[c109,d11]) ).
cnf(d13,plain,
( ~ aElement0(xu)
| ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu))
| sK82(xb,xu) = sz00 ),
inference(resolution,[status(thm)],[c121,d12]) ).
cnf(d14,plain,
( ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu))
| sK82(xb,xu) = sz00 ),
inference(resolution,[status(thm)],[d4,d13]) ).
cnf(d15,plain,
( ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu))
| ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu))
| ~ aElement0(xb)
| xb != xb
| sz00 != sz00 ),
inference(superposition,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
( ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu))
| xb != xb
| sz00 != sz00 ),
inference(resolution,[status(thm)],[c109,d15]) ).
cnf(d17,plain,
( ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu))
| sz00 != sz00 ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( ~ aElement0(sK82(xb,xu))
| ~ aElement0(sK81(xb,xu)) ),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
( ~ aElement0(xu)
| ~ aElement0(xb)
| xu = sz00
| ~ aElement0(sK81(xb,xu)) ),
inference(resolution,[status(thm)],[d18,c76]) ).
cnf(d20,plain,
( ~ aElement0(xu)
| ~ aElement0(sK81(xb,xu))
| xu = sz00 ),
inference(resolution,[status(thm)],[c109,d19]) ).
cnf(d21,plain,
( ~ aElement0(xu)
| ~ aElement0(sK81(xb,xu)) ),
inference(resolution,[status(thm)],[c121,d20]) ).
cnf(d22,plain,
~ aElement0(sK81(xb,xu)),
inference(resolution,[status(thm)],[d4,d21]) ).
cnf(d23,plain,
( ~ aElement0(xu)
| ~ aElement0(xb)
| xu = sz00 ),
inference(resolution,[status(thm)],[d22,c75]) ).
cnf(d24,plain,
( ~ aElement0(xu)
| xu = sz00 ),
inference(resolution,[status(thm)],[c109,d23]) ).
cnf(d25,plain,
~ aElement0(xu),
inference(resolution,[status(thm)],[c121,d24]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d4,d25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG118+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
% 0.09/5.38 % Computer : n010.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 26 06:10:24 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.05/10.43 % SZS status Theorem for theBenchmark.p
% 36.05/10.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------