%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% 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 08:33:34 AM UTC 2026
% Result : Theorem 10.09s 6.64s
% Output : CNFRefutation 10.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 26 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 6 |; 4 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l4_zfmisc_1,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = singleton(X1)
| X0 = 'empty$uset' ) ) ).
fof(t37_xboole_1,axiom,
! [X0,X1] :
( 'set$udifference'(X0,X1) = 'empty$uset'
<=> subset(X0,X1) ) ).
fof(t66_zfmisc_1,conjecture,
! [X0,X1] :
~ ( X0 != singleton(X1)
& X0 != 'empty$uset'
& 'set$udifference'(X0,singleton(X1)) = 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
~ ( X0 != singleton(X1)
& X0 != 'empty$uset'
& 'set$udifference'(X0,singleton(X1)) = 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[t66_zfmisc_1]) ).
cnf(c1,plain,
( X0 = singleton(X1)
| X0 = 'empty$uset'
| ~ subset(X0,singleton(X1)) ),
inference(clausification,[status(esa)],[l4_zfmisc_1]) ).
cnf(c7,plain,
( subset(X0,X1)
| 'set$udifference'(X0,X1) != 'empty$uset' ),
inference(clausification,[status(esa)],[t37_xboole_1]) ).
cnf(c9,plain,
'set$udifference'(sK8,singleton(sK9)) = 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10,plain,
sK8 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c11,plain,
sK8 != singleton(sK9),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset(sK8,singleton(sK9))
| 'empty$uset' != 'empty$uset' ),
inference(superposition,[status(thm)],[c9,c7]) ).
cnf(d1,plain,
subset(sK8,singleton(sK9)),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
( sK8 = singleton(sK9)
| sK8 = 'empty$uset' ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
sK8 = singleton(sK9),
inference(resolution,[status(thm)],[c10,d2]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c11,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET923+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n002.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 08:28:26 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.09/6.64 % SZS status Theorem for theBenchmark.p
% 10.09/6.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------