%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM536+2 : 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 : n002.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 25.49s 4.46s
% Output : CNFRefutation 25.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 11 unt; 1 def)
% Number of atoms : 176 ( 27 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 201 ( 76 ~; 96 |; 14 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 11 !; 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(mSubASymm,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X0)
& aSubsetOf0(X0,X1) )
=> X0 = X1 ) ) ).
fof(m__679,hypothesis,
( aSet0(xS)
& aElement0(xx) ) ).
fof(m__679_02,hypothesis,
~ aElementOf0(xx,xS) ).
fof(m__,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( X0 != xx
& aElementOf0(X0,sdtpldt0(xS,xx))
& aElement0(X0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> sdtmndt0(sdtpldt0(xS,xx),xx) = xS ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(xS,xx))
<=> ( ( X0 = xx
| aElementOf0(X0,xS) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
<=> ( X0 != xx
& aElementOf0(X0,sdtpldt0(xS,xx))
& aElement0(X0) ) )
& aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
=> sdtmndt0(sdtpldt0(xS,xx),xx) = xS ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mEOfElem]) ).
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(c13,plain,
( ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0)
| X1 = X0
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(clausification,[status(esa)],[mSubASymm]) ).
cnf(c48,plain,
aSet0(xS),
inference(clausification,[status(esa)],[m__679]) ).
cnf(c49,plain,
~ aElementOf0(xx,xS),
inference(clausification,[status(esa)],[m__679_02]) ).
cnf(c52,plain,
( X0 = xx
| aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c53,plain,
( ~ aElementOf0(X0,xS)
| ~ aElement0(X0)
| aElementOf0(X0,sdtpldt0(xS,xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c55,plain,
aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c57,plain,
( aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c58,plain,
( X0 != xx
| ~ aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c59,plain,
( X0 = xx
| ~ aElementOf0(X0,sdtpldt0(xS,xx))
| ~ aElement0(X0)
| aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c60,plain,
sdtmndt0(sdtpldt0(xS,xx),xx) != xS,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( aElementOf0(sK14(X0,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtpldt0(xS,xx))
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X0)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c9,c57]) ).
cnf(d1,plain,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X0)
| aElementOf0(sK14(X0,sdtmndt0(sdtpldt0(xS,xx),xx)),sdtpldt0(xS,xx))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c55,d0]) ).
cnf(d2,plain,
( aElementOf0(sK14(X0,sdtmndt0(sdtpldt0(xS,xx),xx)),xS)
| sK14(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),X0)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[d1,c52]) ).
cnf(d3,plain,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS)
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| sK14(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[d2,c10]) ).
cnf(d4,plain,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| sK14(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[c55,d3]) ).
cnf(d5,plain,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| sK14(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[c48,d4]) ).
cnf(d6,plain,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS)
| aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(superposition,[status(thm)],[d5,c9]) ).
cnf(d7,plain,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c55,d6]) ).
cnf(d8,plain,
~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(equality_resolution,[status(thm)],[c58]) ).
cnf(d9,plain,
( aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS),
inference(resolution,[status(thm)],[c48,d9]) ).
cnf(d11,plain,
( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[d10,c13]) ).
cnf(d12,plain,
( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS)
| xS = sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[c55,d11]) ).
cnf(d13,plain,
( ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| xS = sdtmndt0(sdtpldt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[c48,d12]) ).
cnf(d14,plain,
( ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),X0))
| ~ aElementOf0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),X0),sdtpldt0(xS,xx))
| sK14(sdtmndt0(sdtpldt0(xS,xx),xx),X0) = xx
| aSubsetOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(X0)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[c10,c59]) ).
cnf(d15,plain,
( aSubsetOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),X0))
| ~ aElementOf0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),X0),sdtpldt0(xS,xx))
| ~ aSet0(X0)
| sK14(sdtmndt0(sdtpldt0(xS,xx),xx),X0) = xx ),
inference(resolution,[status(thm)],[c55,d14]) ).
cnf(d16,plain,
( ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),X0))
| ~ aElementOf0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),X0),xS)
| aSubsetOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),X0))
| ~ aSet0(X0)
| sK14(sdtmndt0(sdtpldt0(xS,xx),xx),X0) = xx ),
inference(resolution,[status(thm)],[d15,c53]) ).
cnf(d17,plain,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),xS))
| ~ aSet0(xS)
| sK14(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[d16,c9]) ).
cnf(d18,plain,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),xS))
| ~ aSet0(xS)
| sK14(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[c55,d17]) ).
cnf(d19,plain,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),xS))
| sK14(sdtmndt0(sdtpldt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[c48,d18]) ).
cnf(d20,plain,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),xS))
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS)
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| aElementOf0(xx,xS) ),
inference(superposition,[status(thm)],[d19,c9]) ).
cnf(d21,plain,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),xS))
| aElementOf0(xx,xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c55,d20]) ).
cnf(d22,plain,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),xS))
| aElementOf0(xx,xS) ),
inference(resolution,[status(thm)],[c48,d21]) ).
cnf(d23,plain,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aElement0(sK14(sdtmndt0(sdtpldt0(xS,xx),xx),xS)) ),
inference(resolution,[status(thm)],[c49,d22]) ).
cnf(d24,plain,
( aElement0(sK14(X0,X1))
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d25,plain,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c55,d25]) ).
cnf(d27,plain,
aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)),
inference(resolution,[status(thm)],[c48,d26]) ).
cnf(d28,plain,
xS = sdtmndt0(sdtpldt0(xS,xx),xx),
inference(resolution,[status(thm)],[d27,d13]) ).
cnf(d29,plain,
xS != xS,
inference(demodulation,[status(thm)],[c60,d28]) ).
cnf(d30,plain,
$false,
inference(equality_resolution,[status(thm)],[d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM536+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n002.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sat Sep 26 03:11:20 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.49/4.46 % SZS status Theorem for theBenchmark.p
% 25.49/4.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------