%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU147+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 08:41:01 AM UTC 2026
% Result : Theorem 9.93s 1.86s
% Output : CNFRefutation 9.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 55 ( 33 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 46 ( 17 ~; 24 |; 0 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ) ).
fof(d1_zfmisc_1,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [X0,X1] : subset(X0,X0) ).
fof(t3_xboole_1,axiom,
! [X0] :
( subset(X0,'empty$uset')
=> X0 = 'empty$uset' ) ).
fof(t1_zfmisc_1,conjecture,
powerset('empty$uset') = singleton('empty$uset') ).
fof(negated_conjecture,negated_conjecture,
powerset('empty$uset') != singleton('empty$uset'),
inference(negate_conjecture,[status(cth)],[t1_zfmisc_1]) ).
cnf(c1,plain,
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c2,plain,
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(clausification,[status(esa)],[d1_tarski]) ).
cnf(c10,plain,
( subset(sK9(X1,X0),X1)
| in(sK9(X1,X0),X0)
| X0 = powerset(X1) ),
inference(clausification,[status(esa)],[d1_zfmisc_1]) ).
cnf(c11,plain,
( ~ in(sK9(X1,X0),X0)
| ~ subset(sK9(X1,X0),X1)
| X0 = powerset(X1) ),
inference(clausification,[status(esa)],[d1_zfmisc_1]) ).
cnf(c16,plain,
subset(X0,X0),
inference(clausification,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(c21,plain,
( X0 = 'empty$uset'
| ~ subset(X0,'empty$uset') ),
inference(clausification,[status(esa)],[t3_xboole_1]) ).
cnf(c22,plain,
powerset('empty$uset') != singleton('empty$uset'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(d1,plain,
( sK9(X1,singleton(X0)) = X0
| subset(sK9(X1,singleton(X0)),X1)
| singleton(X0) = powerset(X1) ),
inference(resolution,[status(thm)],[c10,d0]) ).
cnf(d2,plain,
( sK9('empty$uset',singleton(X0)) = 'empty$uset'
| sK9('empty$uset',singleton(X0)) = X0
| singleton(X0) = powerset('empty$uset') ),
inference(resolution,[status(thm)],[d1,c21]) ).
cnf(d3,plain,
( sK9('empty$uset',singleton(X0)) = 'empty$uset'
| singleton(X0) = powerset('empty$uset')
| X0 != 'empty$uset' ),
inference(equality_factoring,[status(thm)],[d2]) ).
cnf(d4,plain,
( sK9('empty$uset',singleton('empty$uset')) = 'empty$uset'
| singleton('empty$uset') = powerset('empty$uset') ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( singleton('empty$uset') = powerset('empty$uset')
| ~ in(sK9('empty$uset',singleton('empty$uset')),singleton('empty$uset'))
| singleton('empty$uset') = powerset('empty$uset')
| ~ subset('empty$uset','empty$uset') ),
inference(superposition,[status(thm)],[d4,c11]) ).
cnf(d6,plain,
( ~ in(sK9('empty$uset',singleton('empty$uset')),singleton('empty$uset'))
| singleton('empty$uset') = powerset('empty$uset') ),
inference(resolution,[status(thm)],[c16,d5]) ).
cnf(d7,plain,
( singleton('empty$uset') = powerset('empty$uset')
| singleton('empty$uset') = powerset('empty$uset')
| ~ in('empty$uset',singleton('empty$uset')) ),
inference(superposition,[status(thm)],[d4,d6]) ).
cnf(d8,plain,
( in(X0,singleton(X1))
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d9,plain,
in(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
singleton('empty$uset') = powerset('empty$uset'),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
singleton('empty$uset') != singleton('empty$uset'),
inference(demodulation,[status(thm)],[c22,d10]) ).
cnf(d12,plain,
$false,
inference(equality_resolution,[status(thm)],[d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU147+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n017.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 08:35:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.93/1.86 % SZS status Theorem for theBenchmark.p
% 9.93/1.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------