TSTP Solution File: SEU160+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU160+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 15:50:01 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 82 ( 32 ~; 37 |; 13 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 8 ( 1 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l4_zfmisc_1,plain,
! [A,B] :
( ( ~ subset(A,singleton(B))
| $equal(empty_set,A)
| $equal(singleton(B),A) )
& ( ~ $equal(singleton(B),A)
| subset(A,singleton(B)) )
& ( ~ $equal(empty_set,A)
| subset(A,singleton(B)) ) ),
file('/tmp/SystemOnTPTP3896/SEU160+1.p',unknown),
[] ).
cnf(146869000,plain,
( ~ $equal(singleton(B),A)
| subset(A,singleton(B)) ),
inference(rewrite,[status(thm)],[l4_zfmisc_1]),
[] ).
fof(t39_zfmisc_1,plain,
( ( ~ subset(a,singleton(b))
| ~ subset(a,singleton(b))
| subset(a,singleton(b)) )
& ( $equal(empty_set,a)
| ~ subset(a,singleton(b))
| subset(a,singleton(b)) )
& ( ~ subset(a,singleton(b))
| $equal(singleton(b),a)
| subset(a,singleton(b)) )
& ( $equal(empty_set,a)
| $equal(singleton(b),a)
| subset(a,singleton(b)) )
& ( ~ subset(a,singleton(b))
| ~ subset(a,singleton(b))
| ~ $equal(empty_set,a) )
& ( $equal(empty_set,a)
| ~ subset(a,singleton(b))
| ~ $equal(empty_set,a) )
& ( ~ subset(a,singleton(b))
| $equal(singleton(b),a)
| ~ $equal(empty_set,a) )
& ( $equal(empty_set,a)
| $equal(singleton(b),a)
| ~ $equal(empty_set,a) )
& ( ~ subset(a,singleton(b))
| ~ subset(a,singleton(b))
| ~ $equal(singleton(b),a) )
& ( $equal(empty_set,a)
| ~ subset(a,singleton(b))
| ~ $equal(singleton(b),a) )
& ( ~ subset(a,singleton(b))
| $equal(singleton(b),a)
| ~ $equal(singleton(b),a) )
& ( $equal(empty_set,a)
| $equal(singleton(b),a)
| ~ $equal(singleton(b),a) ) ),
file('/tmp/SystemOnTPTP3896/SEU160+1.p',unknown),
[] ).
cnf(146828384,plain,
( ~ subset(a,singleton(b))
| ~ $equal(singleton(b),a) ),
inference(rewrite,[status(thm)],[t39_zfmisc_1]),
[] ).
cnf(146832504,plain,
( ~ subset(a,singleton(b))
| ~ $equal(empty_set,a) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t39_zfmisc_1,146828384]),
[] ).
cnf(146845352,plain,
( ~ $equal(empty_set,A)
| subset(A,singleton(B)) ),
inference(rewrite,[status(thm)],[l4_zfmisc_1]),
[] ).
cnf(162620664,plain,
~ $equal(empty_set,a),
inference(resolution,[status(thm)],[146832504,146845352]),
[] ).
cnf(146838824,plain,
( $equal(empty_set,a)
| $equal(singleton(b),a)
| subset(a,singleton(b)) ),
inference(rewrite,[status(thm)],[t39_zfmisc_1]),
[] ).
cnf(162629336,plain,
( $equal(singleton(b),a)
| subset(a,singleton(b)) ),
inference(resolution,[status(thm)],[162620664,146838824]),
[] ).
cnf(162672504,plain,
subset(a,singleton(b)),
inference(resolution,[status(thm)],[146869000,162629336]),
[] ).
cnf(146876304,plain,
( ~ subset(A,singleton(B))
| $equal(empty_set,A)
| $equal(singleton(B),A) ),
inference(rewrite,[status(thm)],[l4_zfmisc_1]),
[] ).
cnf(162691440,plain,
~ $equal(singleton(b),a),
inference(resolution,[status(thm)],[146828384,162672504]),
[] ).
cnf(162733432,plain,
$equal(empty_set,a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162672504,146876304,162691440]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[162733432,162620664]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l4_zfmisc_1,plain,(((~subset(A,singleton(B))|$equal(empty_set,A)|$equal(singleton(B),A))&(~$equal(singleton(B),A)|subset(A,singleton(B)))&(~$equal(empty_set,A)|subset(A,singleton(B))))),file('/tmp/SystemOnTPTP3896/SEU160+1.p',unknown),[]).
%
% cnf(146869000,plain,(~$equal(singleton(B),A)|subset(A,singleton(B))),inference(rewrite,[status(thm)],[l4_zfmisc_1]),[]).
%
% fof(t39_zfmisc_1,plain,(((~subset(a,singleton(b))|~subset(a,singleton(b))|subset(a,singleton(b)))&($equal(empty_set,a)|~subset(a,singleton(b))|subset(a,singleton(b)))&(~subset(a,singleton(b))|$equal(singleton(b),a)|subset(a,singleton(b)))&($equal(empty_set,a)|$equal(singleton(b),a)|subset(a,singleton(b)))&(~subset(a,singleton(b))|~subset(a,singleton(b))|~$equal(empty_set,a))&($equal(empty_set,a)|~subset(a,singleton(b))|~$equal(empty_set,a))&(~subset(a,singleton(b))|$equal(singleton(b),a)|~$equal(empty_set,a))&($equal(empty_set,a)|$equal(singleton(b),a)|~$equal(empty_set,a))&(~subset(a,singleton(b))|~subset(a,singleton(b))|~$equal(singleton(b),a))&($equal(empty_set,a)|~subset(a,singleton(b))|~$equal(singleton(b),a))&(~subset(a,singleton(b))|$equal(singleton(b),a)|~$equal(singleton(b),a))&($equal(empty_set,a)|$equal(singleton(b),a)|~$equal(singleton(b),a)))),file('/tmp/SystemOnTPTP3896/SEU160+1.p',unknown),[]).
%
% cnf(146828384,plain,(~subset(a,singleton(b))|~$equal(singleton(b),a)),inference(rewrite,[status(thm)],[t39_zfmisc_1]),[]).
%
% cnf(146832504,plain,(~subset(a,singleton(b))|~$equal(empty_set,a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t39_zfmisc_1,146828384]),[]).
%
% cnf(146845352,plain,(~$equal(empty_set,A)|subset(A,singleton(B))),inference(rewrite,[status(thm)],[l4_zfmisc_1]),[]).
%
% cnf(162620664,plain,(~$equal(empty_set,a)),inference(resolution,[status(thm)],[146832504,146845352]),[]).
%
% cnf(146838824,plain,($equal(empty_set,a)|$equal(singleton(b),a)|subset(a,singleton(b))),inference(rewrite,[status(thm)],[t39_zfmisc_1]),[]).
%
% cnf(162629336,plain,($equal(singleton(b),a)|subset(a,singleton(b))),inference(resolution,[status(thm)],[162620664,146838824]),[]).
%
% cnf(162672504,plain,(subset(a,singleton(b))),inference(resolution,[status(thm)],[146869000,162629336]),[]).
%
% cnf(146876304,plain,(~subset(A,singleton(B))|$equal(empty_set,A)|$equal(singleton(B),A)),inference(rewrite,[status(thm)],[l4_zfmisc_1]),[]).
%
% cnf(162691440,plain,(~$equal(singleton(b),a)),inference(resolution,[status(thm)],[146828384,162672504]),[]).
%
% cnf(162733432,plain,($equal(empty_set,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162672504,146876304,162691440]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[162733432,162620664]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------