TSTP Solution File: SEU152+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU152+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:49:26 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 5 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 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; 2 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t12_xboole_1,plain,
! [A,B] :
( ~ subset(A,B)
| $equal(set_union2(A,B),B) ),
file('/tmp/SystemOnTPTP12365/SEU152+1.p',unknown),
[] ).
cnf(173246672,plain,
( ~ subset(A,B)
| $equal(set_union2(A,B),B) ),
inference(rewrite,[status(thm)],[t12_xboole_1]),
[] ).
fof(l2_zfmisc_1,plain,
! [A,B] :
( ( ~ subset(singleton(A),B)
| in(A,B) )
& ( subset(singleton(A),B)
| ~ in(A,B) ) ),
file('/tmp/SystemOnTPTP12365/SEU152+1.p',unknown),
[] ).
cnf(173230840,plain,
( subset(singleton(A),B)
| ~ in(A,B) ),
inference(rewrite,[status(thm)],[l2_zfmisc_1]),
[] ).
fof(l23_zfmisc_1,plain,
( in(a,b)
& ~ $equal(set_union2(singleton(a),b),b) ),
file('/tmp/SystemOnTPTP12365/SEU152+1.p',unknown),
[] ).
cnf(173224408,plain,
in(a,b),
inference(rewrite,[status(thm)],[l23_zfmisc_1]),
[] ).
cnf(183681744,plain,
subset(singleton(a),b),
inference(resolution,[status(thm)],[173230840,173224408]),
[] ).
cnf(183698832,plain,
$equal(set_union2(singleton(a),b),b),
inference(resolution,[status(thm)],[173246672,183681744]),
[] ).
cnf(173211344,plain,
~ $equal(set_union2(singleton(a),b),b),
inference(rewrite,[status(thm)],[l23_zfmisc_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[183698832,173211344]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t12_xboole_1,plain,(~subset(A,B)|$equal(set_union2(A,B),B)),file('/tmp/SystemOnTPTP12365/SEU152+1.p',unknown),[]).
%
% cnf(173246672,plain,(~subset(A,B)|$equal(set_union2(A,B),B)),inference(rewrite,[status(thm)],[t12_xboole_1]),[]).
%
% fof(l2_zfmisc_1,plain,(((~subset(singleton(A),B)|in(A,B))&(subset(singleton(A),B)|~in(A,B)))),file('/tmp/SystemOnTPTP12365/SEU152+1.p',unknown),[]).
%
% cnf(173230840,plain,(subset(singleton(A),B)|~in(A,B)),inference(rewrite,[status(thm)],[l2_zfmisc_1]),[]).
%
% fof(l23_zfmisc_1,plain,((in(a,b)&~$equal(set_union2(singleton(a),b),b))),file('/tmp/SystemOnTPTP12365/SEU152+1.p',unknown),[]).
%
% cnf(173224408,plain,(in(a,b)),inference(rewrite,[status(thm)],[l23_zfmisc_1]),[]).
%
% cnf(183681744,plain,(subset(singleton(a),b)),inference(resolution,[status(thm)],[173230840,173224408]),[]).
%
% cnf(183698832,plain,($equal(set_union2(singleton(a),b),b)),inference(resolution,[status(thm)],[173246672,183681744]),[]).
%
% cnf(173211344,plain,(~$equal(set_union2(singleton(a),b),b)),inference(rewrite,[status(thm)],[l23_zfmisc_1]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[183698832,173211344]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------