TSTP Solution File: SET901+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET901+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 15:41:00 EDT 2009
% Result : Theorem 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 6 unt; 0 def)
% Number of atoms : 472 ( 0 equ)
% Maximal formula atoms : 400 ( 17 avg)
% Number of connectives : 694 ( 249 ~; 362 |; 83 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 85 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 4 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l46_zfmisc_1,plain,
! [A,B,C] :
( ( ~ subset(A,unordered_pair(B,C))
| $equal(empty_set,A)
| $equal(singleton(B),A)
| $equal(singleton(C),A)
| $equal(unordered_pair(B,C),A) )
& ( ~ $equal(singleton(B),A)
| subset(A,unordered_pair(B,C)) )
& ( ~ $equal(singleton(C),A)
| subset(A,unordered_pair(B,C)) )
& ( ~ $equal(unordered_pair(B,C),A)
| subset(A,unordered_pair(B,C)) )
& ( ~ $equal(empty_set,A)
| subset(A,unordered_pair(B,C)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET901+1.tptp',unknown),
[] ).
cnf(160741848,plain,
( ~ $equal(unordered_pair(B,C),A)
| subset(A,unordered_pair(B,C)) ),
inference(rewrite,[status(thm)],[l46_zfmisc_1]),
[] ).
fof(t42_zfmisc_1,plain,
( ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| subset(a,unordered_pair(b,c)) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| subset(a,unordered_pair(b,c)) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| subset(a,unordered_pair(b,c)) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| subset(a,unordered_pair(b,c)) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a)
| subset(a,unordered_pair(b,c)) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a)
| subset(a,unordered_pair(b,c)) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| subset(a,unordered_pair(b,c)) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| subset(a,unordered_pair(b,c)) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| subset(a,unordered_pair(b,c)) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| subset(a,unordered_pair(b,c)) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| subset(a,unordered_pair(b,c)) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| subset(a,unordered_pair(b,c)) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| subset(a,unordered_pair(b,c)) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| subset(a,unordered_pair(b,c)) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| subset(a,unordered_pair(b,c)) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| subset(a,unordered_pair(b,c)) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(empty_set,a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(empty_set,a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(empty_set,a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(empty_set,a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(empty_set,a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(empty_set,a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(empty_set,a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(empty_set,a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(empty_set,a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(empty_set,a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(empty_set,a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(empty_set,a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(empty_set,a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(empty_set,a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(empty_set,a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(empty_set,a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(singleton(b),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(singleton(b),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(singleton(b),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(singleton(b),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(singleton(b),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(singleton(b),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(singleton(b),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(singleton(b),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(b),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(b),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(b),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(b),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(b),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(b),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(b),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(b),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(singleton(c),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(singleton(c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(singleton(c),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(singleton(c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(singleton(c),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(singleton(c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(singleton(c),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(singleton(c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(c),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(c),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(c),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(c),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(unordered_pair(b,c),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(unordered_pair(b,c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(unordered_pair(b,c),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(empty_set,a)
| ~ $equal(unordered_pair(b,c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(unordered_pair(b,c),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(unordered_pair(b,c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(unordered_pair(b,c),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| ~ $equal(unordered_pair(b,c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(unordered_pair(b,c),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(unordered_pair(b,c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(unordered_pair(b,c),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(unordered_pair(b,c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(unordered_pair(b,c),a) )
& ( $equal(unordered_pair(b,c),a)
| ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(unordered_pair(b,c),a) )
& ( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(unordered_pair(b,c),a) )
& ( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| ~ subset(a,unordered_pair(b,c))
| ~ $equal(unordered_pair(b,c),a) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET901+1.tptp',unknown),
[] ).
cnf(160715864,plain,
( $equal(unordered_pair(b,c),a)
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a)
| subset(a,unordered_pair(b,c)) ),
inference(rewrite,[status(thm)],[t42_zfmisc_1]),
[] ).
cnf(190039352,plain,
( subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(singleton(b),a)
| $equal(empty_set,a) ),
inference(resolution,[status(thm)],[160741848,160715864]),
[] ).
cnf(160678392,plain,
( ~ subset(a,unordered_pair(b,c))
| ~ $equal(unordered_pair(b,c),a) ),
inference(rewrite,[status(thm)],[t42_zfmisc_1]),
[] ).
cnf(160691976,plain,
( ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(c),a) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t42_zfmisc_1,160678392]),
[] ).
cnf(160761280,plain,
( ~ $equal(singleton(C),A)
| subset(A,unordered_pair(B,C)) ),
inference(rewrite,[status(thm)],[l46_zfmisc_1]),
[] ).
cnf(189930080,plain,
~ $equal(singleton(c),a),
inference(resolution,[status(thm)],[160691976,160761280]),
[] ).
cnf(190632536,plain,
( subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| $equal(empty_set,a) ),
inference(resolution,[status(thm)],[190039352,189930080]),
[] ).
cnf(160673592,plain,
( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| ~ $equal(unordered_pair(b,c),a) ),
inference(rewrite,[status(thm)],[t42_zfmisc_1]),
[] ).
cnf(160697232,plain,
( ~ subset(a,unordered_pair(b,c))
| ~ $equal(singleton(b),a) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t42_zfmisc_1,160673592,160691976]),
[] ).
cnf(160765296,plain,
( ~ $equal(singleton(B),A)
| subset(A,unordered_pair(B,C)) ),
inference(rewrite,[status(thm)],[l46_zfmisc_1]),
[] ).
cnf(189989888,plain,
~ $equal(singleton(b),a),
inference(resolution,[status(thm)],[160697232,160765296]),
[] ).
cnf(190724176,plain,
( subset(a,unordered_pair(b,c))
| $equal(empty_set,a) ),
inference(resolution,[status(thm)],[190632536,189989888]),
[] ).
cnf(160687584,plain,
( ~ subset(a,unordered_pair(b,c))
| $equal(singleton(b),a)
| ~ $equal(singleton(c),a) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t42_zfmisc_1,160678392]),
[] ).
cnf(160702312,plain,
( ~ subset(a,unordered_pair(b,c))
| ~ $equal(empty_set,a) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t42_zfmisc_1,160687584,160697232,160678392]),
[] ).
cnf(160723072,plain,
( ~ $equal(empty_set,A)
| subset(A,unordered_pair(B,C)) ),
inference(rewrite,[status(thm)],[l46_zfmisc_1]),
[] ).
cnf(189721032,plain,
~ $equal(empty_set,a),
inference(resolution,[status(thm)],[160702312,160723072]),
[] ).
cnf(190833120,plain,
subset(a,unordered_pair(b,c)),
inference(resolution,[status(thm)],[190724176,189721032]),
[] ).
cnf(160775840,plain,
( ~ subset(A,unordered_pair(B,C))
| $equal(empty_set,A)
| $equal(singleton(B),A)
| $equal(singleton(C),A)
| $equal(unordered_pair(B,C),A) ),
inference(rewrite,[status(thm)],[l46_zfmisc_1]),
[] ).
cnf(190637120,plain,
( subset(a,unordered_pair(b,c))
| $equal(singleton(c),a)
| $equal(empty_set,a) ),
inference(resolution,[status(thm)],[190039352,189989888]),
[] ).
cnf(192139632,plain,
( $equal(empty_set,a)
| $equal(singleton(b),a)
| $equal(singleton(c),a)
| $equal(unordered_pair(b,c),a) ),
inference(resolution,[status(thm)],[160775840,190637120]),
[] ).
cnf(192217736,plain,
( $equal(empty_set,a)
| $equal(singleton(b),a)
| $equal(singleton(c),a) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[190039352,160678392,192139632]),
[] ).
cnf(192251104,plain,
( $equal(empty_set,a)
| $equal(singleton(b),a) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[190632536,160691976,192217736]),
[] ).
cnf(192279704,plain,
$equal(empty_set,a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[190724176,160697232,192251104]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[190833120,160702312,192279704]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l46_zfmisc_1,plain,(((~subset(A,unordered_pair(B,C))|$equal(empty_set,A)|$equal(singleton(B),A)|$equal(singleton(C),A)|$equal(unordered_pair(B,C),A))&(~$equal(singleton(B),A)|subset(A,unordered_pair(B,C)))&(~$equal(singleton(C),A)|subset(A,unordered_pair(B,C)))&(~$equal(unordered_pair(B,C),A)|subset(A,unordered_pair(B,C)))&(~$equal(empty_set,A)|subset(A,unordered_pair(B,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET901+1.tptp',unknown),[]).
%
% cnf(160741848,plain,(~$equal(unordered_pair(B,C),A)|subset(A,unordered_pair(B,C))),inference(rewrite,[status(thm)],[l46_zfmisc_1]),[]).
%
% fof(t42_zfmisc_1,plain,(((~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|subset(a,unordered_pair(b,c)))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|subset(a,unordered_pair(b,c)))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|subset(a,unordered_pair(b,c)))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|subset(a,unordered_pair(b,c)))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)|subset(a,unordered_pair(b,c)))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)|subset(a,unordered_pair(b,c)))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|subset(a,unordered_pair(b,c)))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|subset(a,unordered_pair(b,c)))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|subset(a,unordered_pair(b,c)))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|subset(a,unordered_pair(b,c)))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|subset(a,unordered_pair(b,c)))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|subset(a,unordered_pair(b,c)))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|subset(a,unordered_pair(b,c)))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|subset(a,unordered_pair(b,c)))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|subset(a,unordered_pair(b,c)))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|subset(a,unordered_pair(b,c)))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(empty_set,a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(empty_set,a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(empty_set,a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(empty_set,a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(empty_set,a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(empty_set,a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(empty_set,a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(empty_set,a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(empty_set,a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(empty_set,a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(empty_set,a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(empty_set,a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(empty_set,a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(empty_set,a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(empty_set,a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(empty_set,a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(singleton(b),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(singleton(b),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(singleton(b),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(singleton(b),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(singleton(b),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(singleton(b),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(singleton(b),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(singleton(b),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(singleton(b),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(singleton(b),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(singleton(b),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(singleton(b),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(singleton(b),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(singleton(b),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(singleton(b),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(singleton(b),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(singleton(c),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(singleton(c),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(singleton(c),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(singleton(c),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(singleton(c),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(singleton(c),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(singleton(c),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(singleton(c),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(singleton(c),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(singleton(c),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(singleton(c),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(singleton(c),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(singleton(c),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(singleton(c),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(singleton(c),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(singleton(c),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(unordered_pair(b,c),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(unordered_pair(b,c),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(unordered_pair(b,c),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|$equal(empty_set,a)|~$equal(unordered_pair(b,c),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(unordered_pair(b,c),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(unordered_pair(b,c),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(unordered_pair(b,c),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|~$equal(unordered_pair(b,c),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(unordered_pair(b,c),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(unordered_pair(b,c),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(unordered_pair(b,c),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|~$equal(unordered_pair(b,c),a))&(~subset(a,unordered_pair(b,c))|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(unordered_pair(b,c),a))&($equal(unordered_pair(b,c),a)|~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(unordered_pair(b,c),a))&(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(unordered_pair(b,c),a))&($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|~subset(a,unordered_pair(b,c))|~$equal(unordered_pair(b,c),a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET901+1.tptp',unknown),[]).
%
% cnf(160715864,plain,($equal(unordered_pair(b,c),a)|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)|subset(a,unordered_pair(b,c))),inference(rewrite,[status(thm)],[t42_zfmisc_1]),[]).
%
% cnf(190039352,plain,(subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(singleton(b),a)|$equal(empty_set,a)),inference(resolution,[status(thm)],[160741848,160715864]),[]).
%
% cnf(160678392,plain,(~subset(a,unordered_pair(b,c))|~$equal(unordered_pair(b,c),a)),inference(rewrite,[status(thm)],[t42_zfmisc_1]),[]).
%
% cnf(160691976,plain,(~subset(a,unordered_pair(b,c))|~$equal(singleton(c),a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t42_zfmisc_1,160678392]),[]).
%
% cnf(160761280,plain,(~$equal(singleton(C),A)|subset(A,unordered_pair(B,C))),inference(rewrite,[status(thm)],[l46_zfmisc_1]),[]).
%
% cnf(189930080,plain,(~$equal(singleton(c),a)),inference(resolution,[status(thm)],[160691976,160761280]),[]).
%
% cnf(190632536,plain,(subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|$equal(empty_set,a)),inference(resolution,[status(thm)],[190039352,189930080]),[]).
%
% cnf(160673592,plain,(~subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|~$equal(unordered_pair(b,c),a)),inference(rewrite,[status(thm)],[t42_zfmisc_1]),[]).
%
% cnf(160697232,plain,(~subset(a,unordered_pair(b,c))|~$equal(singleton(b),a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t42_zfmisc_1,160673592,160691976]),[]).
%
% cnf(160765296,plain,(~$equal(singleton(B),A)|subset(A,unordered_pair(B,C))),inference(rewrite,[status(thm)],[l46_zfmisc_1]),[]).
%
% cnf(189989888,plain,(~$equal(singleton(b),a)),inference(resolution,[status(thm)],[160697232,160765296]),[]).
%
% cnf(190724176,plain,(subset(a,unordered_pair(b,c))|$equal(empty_set,a)),inference(resolution,[status(thm)],[190632536,189989888]),[]).
%
% cnf(160687584,plain,(~subset(a,unordered_pair(b,c))|$equal(singleton(b),a)|~$equal(singleton(c),a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t42_zfmisc_1,160678392]),[]).
%
% cnf(160702312,plain,(~subset(a,unordered_pair(b,c))|~$equal(empty_set,a)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t42_zfmisc_1,160687584,160697232,160678392]),[]).
%
% cnf(160723072,plain,(~$equal(empty_set,A)|subset(A,unordered_pair(B,C))),inference(rewrite,[status(thm)],[l46_zfmisc_1]),[]).
%
% cnf(189721032,plain,(~$equal(empty_set,a)),inference(resolution,[status(thm)],[160702312,160723072]),[]).
%
% cnf(190833120,plain,(subset(a,unordered_pair(b,c))),inference(resolution,[status(thm)],[190724176,189721032]),[]).
%
% cnf(160775840,plain,(~subset(A,unordered_pair(B,C))|$equal(empty_set,A)|$equal(singleton(B),A)|$equal(singleton(C),A)|$equal(unordered_pair(B,C),A)),inference(rewrite,[status(thm)],[l46_zfmisc_1]),[]).
%
% cnf(190637120,plain,(subset(a,unordered_pair(b,c))|$equal(singleton(c),a)|$equal(empty_set,a)),inference(resolution,[status(thm)],[190039352,189989888]),[]).
%
% cnf(192139632,plain,($equal(empty_set,a)|$equal(singleton(b),a)|$equal(singleton(c),a)|$equal(unordered_pair(b,c),a)),inference(resolution,[status(thm)],[160775840,190637120]),[]).
%
% cnf(192217736,plain,($equal(empty_set,a)|$equal(singleton(b),a)|$equal(singleton(c),a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[190039352,160678392,192139632]),[]).
%
% cnf(192251104,plain,($equal(empty_set,a)|$equal(singleton(b),a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[190632536,160691976,192217736]),[]).
%
% cnf(192279704,plain,($equal(empty_set,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[190724176,160697232,192251104]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[190833120,160702312,192279704]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------