TSTP Solution File: SET927+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET927+1 : TPTP v3.4.2. Released v3.2.0.
% 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 15:41:53 EDT 2009
% Result : Theorem 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 266 ( 0 equ)
% Maximal formula atoms : 216 ( 12 avg)
% Number of connectives : 372 ( 127 ~; 189 |; 56 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 57 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 2 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l39_zfmisc_1,plain,
! [B,C,A] :
( ( in(B,C)
| $equal(B,A)
| ~ $equal(set_difference(unordered_pair(A,B),C),singleton(A)) )
& ( ~ in(A,C)
| ~ $equal(set_difference(unordered_pair(A,B),C),singleton(A)) )
& ( ~ in(B,C)
| in(A,C)
| $equal(set_difference(unordered_pair(A,B),C),singleton(A)) )
& ( ~ $equal(B,A)
| in(A,C)
| $equal(set_difference(unordered_pair(A,B),C),singleton(A)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET927+1.tptp',unknown),
[] ).
cnf(141920056,plain,
( ~ in(A,C)
| ~ $equal(set_difference(unordered_pair(A,B),C),singleton(A)) ),
inference(rewrite,[status(thm)],[l39_zfmisc_1]),
[] ).
fof(t70_zfmisc_1,plain,
( ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(b,c) )
& ( $equal(b,a)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(b,c) )
& ( ~ in(a,c)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(b,c) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(b,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(b,c) )
& ( $equal(b,a)
| in(b,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(b,c) )
& ( ~ in(a,c)
| in(b,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(b,c) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(b,c) )
& ( $equal(b,a)
| ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(b,c) )
& ( ~ in(a,c)
| ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(b,c) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| ~ in(b,c) )
& ( $equal(b,a)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| ~ in(b,c) )
& ( ~ in(a,c)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| ~ in(b,c) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(b,c)
| in(a,c)
| ~ in(b,c) )
& ( $equal(b,a)
| in(b,c)
| in(a,c)
| ~ in(b,c) )
& ( ~ in(a,c)
| in(b,c)
| in(a,c)
| ~ in(b,c) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(a,c)
| in(a,c)
| ~ in(b,c) )
& ( $equal(b,a)
| ~ in(a,c)
| in(a,c)
| ~ in(b,c) )
& ( ~ in(a,c)
| ~ in(a,c)
| in(a,c)
| ~ in(b,c) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(b,a) )
& ( $equal(b,a)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(b,a) )
& ( ~ in(a,c)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(b,a) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(b,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(b,a) )
& ( $equal(b,a)
| in(b,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(b,a) )
& ( ~ in(a,c)
| in(b,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(b,a) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(b,a) )
& ( $equal(b,a)
| ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(b,a) )
& ( ~ in(a,c)
| ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(b,a) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| ~ $equal(b,a) )
& ( $equal(b,a)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| ~ $equal(b,a) )
& ( ~ in(a,c)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| ~ $equal(b,a) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(b,c)
| in(a,c)
| ~ $equal(b,a) )
& ( $equal(b,a)
| in(b,c)
| in(a,c)
| ~ $equal(b,a) )
& ( ~ in(a,c)
| in(b,c)
| in(a,c)
| ~ $equal(b,a) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(a,c)
| in(a,c)
| ~ $equal(b,a) )
& ( $equal(b,a)
| ~ in(a,c)
| in(a,c)
| ~ $equal(b,a) )
& ( ~ in(a,c)
| ~ in(a,c)
| in(a,c)
| ~ $equal(b,a) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( $equal(b,a)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ in(a,c)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(b,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( $equal(b,a)
| in(b,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ in(a,c)
| in(b,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( $equal(b,a)
| ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ in(a,c)
| ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( $equal(b,a)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ in(a,c)
| ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(b,c)
| in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( $equal(b,a)
| in(b,c)
| in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ in(a,c)
| in(b,c)
| in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| ~ in(a,c)
| in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( $equal(b,a)
| ~ in(a,c)
| in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) )
& ( ~ in(a,c)
| ~ in(a,c)
| in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET927+1.tptp',unknown),
[] ).
cnf(141848352,plain,
( ~ in(a,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) ),
inference(rewrite,[status(thm)],[t70_zfmisc_1]),
[] ).
cnf(165597680,plain,
~ in(a,c),
inference(resolution,[status(thm)],[141920056,141848352]),
[] ).
cnf(141915304,plain,
( ~ in(B,C)
| in(A,C)
| $equal(set_difference(unordered_pair(A,B),C),singleton(A)) ),
inference(rewrite,[status(thm)],[l39_zfmisc_1]),
[] ).
cnf(141928216,plain,
( in(B,C)
| $equal(B,A)
| ~ $equal(set_difference(unordered_pair(A,B),C),singleton(A)) ),
inference(rewrite,[status(thm)],[l39_zfmisc_1]),
[] ).
cnf(141904512,plain,
( ~ $equal(B,A)
| in(A,C)
| $equal(set_difference(unordered_pair(A,B),C),singleton(A)) ),
inference(rewrite,[status(thm)],[l39_zfmisc_1]),
[] ).
cnf(165786832,plain,
( in(A,B)
| $equal(set_difference(unordered_pair(A,A),B),singleton(A)) ),
inference(equality_resolution,[status(thm)],[141904512]),
[] ).
cnf(166074560,plain,
$equal(set_difference(unordered_pair(a,a),c),singleton(a)),
inference(resolution,[status(thm)],[165786832,165597680]),
[] ).
cnf(141853768,plain,
( $equal(b,a)
| in(b,c)
| $equal(set_difference(unordered_pair(a,b),c),singleton(a)) ),
inference(rewrite,[status(thm)],[t70_zfmisc_1]),
[] ).
cnf(166347128,plain,
( $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(b,c) ),
inference(paramodulation,[status(thm)],[166074560,141853768,theory(equality)]),
[] ).
cnf(169553512,plain,
( in(b,c)
| $equal(b,a) ),
inference(resolution,[status(thm)],[141928216,166347128]),
[] ).
cnf(165811120,plain,
( ~ $equal(A,a)
| $equal(set_difference(unordered_pair(a,A),c),singleton(a)) ),
inference(resolution,[status(thm)],[141904512,165597680]),
[] ).
cnf(141874496,plain,
( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| ~ $equal(b,a) ),
inference(rewrite,[status(thm)],[t70_zfmisc_1]),
[] ).
cnf(172257400,plain,
( ~ $equal(set_difference(unordered_pair(a,A),c),singleton(a))
| ~ $equal(b,a) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165811120,141920056,141874496]),
[] ).
cnf(172325184,plain,
in(b,c),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169553512,166347128,172257400]),
[] ).
cnf(172354376,plain,
( in(A,c)
| $equal(set_difference(unordered_pair(A,b),c),singleton(A)) ),
inference(resolution,[status(thm)],[141915304,172325184]),
[] ).
cnf(141888960,plain,
( ~ $equal(set_difference(unordered_pair(a,b),c),singleton(a))
| in(a,c)
| ~ in(b,c) ),
inference(rewrite,[status(thm)],[t70_zfmisc_1]),
[] ).
cnf(172358416,plain,
in(a,c),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172354376,141888960,172325184]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[165597680,172358416]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l39_zfmisc_1,plain,(((in(B,C)|$equal(B,A)|~$equal(set_difference(unordered_pair(A,B),C),singleton(A)))&(~in(A,C)|~$equal(set_difference(unordered_pair(A,B),C),singleton(A)))&(~in(B,C)|in(A,C)|$equal(set_difference(unordered_pair(A,B),C),singleton(A)))&(~$equal(B,A)|in(A,C)|$equal(set_difference(unordered_pair(A,B),C),singleton(A))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET927+1.tptp',unknown),[]).
%
% cnf(141920056,plain,(~in(A,C)|~$equal(set_difference(unordered_pair(A,B),C),singleton(A))),inference(rewrite,[status(thm)],[l39_zfmisc_1]),[]).
%
% fof(t70_zfmisc_1,plain,(((~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(b,c))&($equal(b,a)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(b,c))&(~in(a,c)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(b,c))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(b,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(b,c))&($equal(b,a)|in(b,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(b,c))&(~in(a,c)|in(b,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(b,c))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(b,c))&($equal(b,a)|~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(b,c))&(~in(a,c)|~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(b,c))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|~in(b,c))&($equal(b,a)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|~in(b,c))&(~in(a,c)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|~in(b,c))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(b,c)|in(a,c)|~in(b,c))&($equal(b,a)|in(b,c)|in(a,c)|~in(b,c))&(~in(a,c)|in(b,c)|in(a,c)|~in(b,c))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(a,c)|in(a,c)|~in(b,c))&($equal(b,a)|~in(a,c)|in(a,c)|~in(b,c))&(~in(a,c)|~in(a,c)|in(a,c)|~in(b,c))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(b,a))&($equal(b,a)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(b,a))&(~in(a,c)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(b,a))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(b,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(b,a))&($equal(b,a)|in(b,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(b,a))&(~in(a,c)|in(b,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(b,a))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(b,a))&($equal(b,a)|~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(b,a))&(~in(a,c)|~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(b,a))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|~$equal(b,a))&($equal(b,a)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|~$equal(b,a))&(~in(a,c)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|~$equal(b,a))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(b,c)|in(a,c)|~$equal(b,a))&($equal(b,a)|in(b,c)|in(a,c)|~$equal(b,a))&(~in(a,c)|in(b,c)|in(a,c)|~$equal(b,a))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(a,c)|in(a,c)|~$equal(b,a))&($equal(b,a)|~in(a,c)|in(a,c)|~$equal(b,a))&(~in(a,c)|~in(a,c)|in(a,c)|~$equal(b,a))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&($equal(b,a)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~in(a,c)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(b,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&($equal(b,a)|in(b,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~in(a,c)|in(b,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&($equal(b,a)|~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~in(a,c)|~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&($equal(b,a)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~in(a,c)|~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(b,c)|in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&($equal(b,a)|in(b,c)|in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~in(a,c)|in(b,c)|in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|~in(a,c)|in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&($equal(b,a)|~in(a,c)|in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a)))&(~in(a,c)|~in(a,c)|in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET927+1.tptp',unknown),[]).
%
% cnf(141848352,plain,(~in(a,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))),inference(rewrite,[status(thm)],[t70_zfmisc_1]),[]).
%
% cnf(165597680,plain,(~in(a,c)),inference(resolution,[status(thm)],[141920056,141848352]),[]).
%
% cnf(141915304,plain,(~in(B,C)|in(A,C)|$equal(set_difference(unordered_pair(A,B),C),singleton(A))),inference(rewrite,[status(thm)],[l39_zfmisc_1]),[]).
%
% cnf(141928216,plain,(in(B,C)|$equal(B,A)|~$equal(set_difference(unordered_pair(A,B),C),singleton(A))),inference(rewrite,[status(thm)],[l39_zfmisc_1]),[]).
%
% cnf(141904512,plain,(~$equal(B,A)|in(A,C)|$equal(set_difference(unordered_pair(A,B),C),singleton(A))),inference(rewrite,[status(thm)],[l39_zfmisc_1]),[]).
%
% cnf(165786832,plain,(in(A,B)|$equal(set_difference(unordered_pair(A,A),B),singleton(A))),inference(equality_resolution,[status(thm)],[141904512]),[]).
%
% cnf(166074560,plain,($equal(set_difference(unordered_pair(a,a),c),singleton(a))),inference(resolution,[status(thm)],[165786832,165597680]),[]).
%
% cnf(141853768,plain,($equal(b,a)|in(b,c)|$equal(set_difference(unordered_pair(a,b),c),singleton(a))),inference(rewrite,[status(thm)],[t70_zfmisc_1]),[]).
%
% cnf(166347128,plain,($equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(b,c)),inference(paramodulation,[status(thm)],[166074560,141853768,theory(equality)]),[]).
%
% cnf(169553512,plain,(in(b,c)|$equal(b,a)),inference(resolution,[status(thm)],[141928216,166347128]),[]).
%
% cnf(165811120,plain,(~$equal(A,a)|$equal(set_difference(unordered_pair(a,A),c),singleton(a))),inference(resolution,[status(thm)],[141904512,165597680]),[]).
%
% cnf(141874496,plain,(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|~$equal(b,a)),inference(rewrite,[status(thm)],[t70_zfmisc_1]),[]).
%
% cnf(172257400,plain,(~$equal(set_difference(unordered_pair(a,A),c),singleton(a))|~$equal(b,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165811120,141920056,141874496]),[]).
%
% cnf(172325184,plain,(in(b,c)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169553512,166347128,172257400]),[]).
%
% cnf(172354376,plain,(in(A,c)|$equal(set_difference(unordered_pair(A,b),c),singleton(A))),inference(resolution,[status(thm)],[141915304,172325184]),[]).
%
% cnf(141888960,plain,(~$equal(set_difference(unordered_pair(a,b),c),singleton(a))|in(a,c)|~in(b,c)),inference(rewrite,[status(thm)],[t70_zfmisc_1]),[]).
%
% cnf(172358416,plain,(in(a,c)),inference(forward_subsumption_resolution__resolution,[status(thm)],[172354376,141888960,172325184]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[165597680,172358416]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------