%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET926+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 : n020.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 08:33:35 AM UTC 2026
% Result : Theorem 10.16s 1.63s
% Output : CNFRefutation 10.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 20 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 6 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 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 : 14 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l34_zfmisc_1,axiom,
! [X0,X1] :
( 'set$udifference'(singleton(X0),X1) = singleton(X0)
<=> ~ in(X0,X1) ) ).
fof(l36_zfmisc_1,axiom,
! [X0,X1] :
( 'set$udifference'(singleton(X0),X1) = 'empty$uset'
<=> in(X0,X1) ) ).
fof(t69_zfmisc_1,conjecture,
! [X0,X1] :
( 'set$udifference'(singleton(X0),X1) = singleton(X0)
| 'set$udifference'(singleton(X0),X1) = 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'set$udifference'(singleton(X0),X1) = singleton(X0)
| 'set$udifference'(singleton(X0),X1) = 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[t69_zfmisc_1]) ).
cnf(c3,plain,
( in(X0,X1)
| 'set$udifference'(singleton(X0),X1) = singleton(X0) ),
inference(clausification,[status(esa)],[l34_zfmisc_1]) ).
cnf(c5,plain,
( ~ in(X0,X1)
| 'set$udifference'(singleton(X0),X1) = 'empty$uset' ),
inference(clausification,[status(esa)],[l36_zfmisc_1]) ).
cnf(c8,plain,
'set$udifference'(singleton(sK8),sK9) != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c9,plain,
'set$udifference'(singleton(sK8),sK9) != singleton(sK8),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'set$udifference'(singleton(X0),X1) = singleton(X0)
| 'set$udifference'(singleton(X0),X1) = 'empty$uset' ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d1,plain,
( 'set$udifference'(singleton(sK8),sK9) = 'empty$uset'
| singleton(sK8) != singleton(sK8) ),
inference(superposition,[status(thm)],[d0,c9]) ).
cnf(d2,plain,
singleton(sK8) != singleton(sK8),
inference(resolution,[status(thm)],[c8,d1]) ).
cnf(d3,plain,
$false,
inference(equality_resolution,[status(thm)],[d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET926+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
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 08:27:03 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.16/1.63 % SZS status Theorem for theBenchmark.p
% 10.16/1.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------