TSTP Solution File: SET886+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET886+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 15:40:41 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 16 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 3 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 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 : 16 ( 1 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(reflexivity_r1_tarski,plain,
! [A] : subset(A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET886+1.tptp',unknown),
[] ).
cnf(164915232,plain,
subset(A,A),
inference(rewrite,[status(thm)],[reflexivity_r1_tarski]),
[] ).
fof(t26_zfmisc_1,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),singleton(C))
| $equal(C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET886+1.tptp',unknown),
[] ).
cnf(164925040,plain,
( ~ subset(unordered_pair(A,B),singleton(C))
| $equal(C,A) ),
inference(rewrite,[status(thm)],[t26_zfmisc_1]),
[] ).
fof(t69_enumset1,plain,
! [A] : $equal(singleton(A),unordered_pair(A,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET886+1.tptp',unknown),
[] ).
cnf(164995368,plain,
$equal(singleton(A),unordered_pair(A,A)),
inference(rewrite,[status(thm)],[t69_enumset1]),
[] ).
cnf(175618104,plain,
( ~ subset(singleton(A),singleton(B))
| $equal(B,A) ),
inference(paramodulation,[status(thm)],[164925040,164995368,theory(equality)]),
[] ).
fof(t27_zfmisc_1,plain,
( subset(unordered_pair(a,b),singleton(c))
& ~ $equal(unordered_pair(a,b),singleton(c)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET886+1.tptp',unknown),
[] ).
cnf(164991600,plain,
subset(unordered_pair(a,b),singleton(c)),
inference(rewrite,[status(thm)],[t27_zfmisc_1]),
[] ).
cnf(175493888,plain,
$equal(c,a),
inference(resolution,[status(thm)],[164925040,164991600]),
[] ).
cnf(164984008,plain,
~ $equal(unordered_pair(a,b),singleton(c)),
inference(rewrite,[status(thm)],[t27_zfmisc_1]),
[] ).
cnf(175653064,plain,
~ $equal(unordered_pair(c,b),singleton(c)),
inference(paramodulation,[status(thm)],[175493888,164984008,theory(equality)]),
[] ).
cnf(175637240,plain,
subset(unordered_pair(c,b),singleton(c)),
inference(paramodulation,[status(thm)],[175493888,164991600,theory(equality)]),
[] ).
fof(commutativity_k2_tarski,plain,
! [B,A] : $equal(unordered_pair(B,A),unordered_pair(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET886+1.tptp',unknown),
[] ).
cnf(164900936,plain,
$equal(unordered_pair(B,A),unordered_pair(A,B)),
inference(rewrite,[status(thm)],[commutativity_k2_tarski]),
[] ).
cnf(175713320,plain,
subset(unordered_pair(b,c),singleton(c)),
inference(paramodulation,[status(thm)],[175637240,164900936,theory(equality)]),
[] ).
cnf(175729624,plain,
$equal(c,b),
inference(resolution,[status(thm)],[175713320,164925040]),
[] ).
cnf(175909800,plain,
~ $equal(unordered_pair(c,c),singleton(c)),
inference(paramodulation,[status(thm)],[175653064,175729624,theory(equality)]),
[] ).
cnf(176261520,plain,
~ subset(singleton(singleton(c)),singleton(unordered_pair(c,c))),
inference(resolution,[status(thm)],[175618104,175909800]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164915232,176261520,164995368,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(reflexivity_r1_tarski,plain,(subset(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET886+1.tptp',unknown),[]).
%
% cnf(164915232,plain,(subset(A,A)),inference(rewrite,[status(thm)],[reflexivity_r1_tarski]),[]).
%
% fof(t26_zfmisc_1,plain,(~subset(unordered_pair(A,B),singleton(C))|$equal(C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET886+1.tptp',unknown),[]).
%
% cnf(164925040,plain,(~subset(unordered_pair(A,B),singleton(C))|$equal(C,A)),inference(rewrite,[status(thm)],[t26_zfmisc_1]),[]).
%
% fof(t69_enumset1,plain,($equal(singleton(A),unordered_pair(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET886+1.tptp',unknown),[]).
%
% cnf(164995368,plain,($equal(singleton(A),unordered_pair(A,A))),inference(rewrite,[status(thm)],[t69_enumset1]),[]).
%
% cnf(175618104,plain,(~subset(singleton(A),singleton(B))|$equal(B,A)),inference(paramodulation,[status(thm)],[164925040,164995368,theory(equality)]),[]).
%
% fof(t27_zfmisc_1,plain,((subset(unordered_pair(a,b),singleton(c))&~$equal(unordered_pair(a,b),singleton(c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET886+1.tptp',unknown),[]).
%
% cnf(164991600,plain,(subset(unordered_pair(a,b),singleton(c))),inference(rewrite,[status(thm)],[t27_zfmisc_1]),[]).
%
% cnf(175493888,plain,($equal(c,a)),inference(resolution,[status(thm)],[164925040,164991600]),[]).
%
% cnf(164984008,plain,(~$equal(unordered_pair(a,b),singleton(c))),inference(rewrite,[status(thm)],[t27_zfmisc_1]),[]).
%
% cnf(175653064,plain,(~$equal(unordered_pair(c,b),singleton(c))),inference(paramodulation,[status(thm)],[175493888,164984008,theory(equality)]),[]).
%
% cnf(175637240,plain,(subset(unordered_pair(c,b),singleton(c))),inference(paramodulation,[status(thm)],[175493888,164991600,theory(equality)]),[]).
%
% fof(commutativity_k2_tarski,plain,($equal(unordered_pair(B,A),unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET886+1.tptp',unknown),[]).
%
% cnf(164900936,plain,($equal(unordered_pair(B,A),unordered_pair(A,B))),inference(rewrite,[status(thm)],[commutativity_k2_tarski]),[]).
%
% cnf(175713320,plain,(subset(unordered_pair(b,c),singleton(c))),inference(paramodulation,[status(thm)],[175637240,164900936,theory(equality)]),[]).
%
% cnf(175729624,plain,($equal(c,b)),inference(resolution,[status(thm)],[175713320,164925040]),[]).
%
% cnf(175909800,plain,(~$equal(unordered_pair(c,c),singleton(c))),inference(paramodulation,[status(thm)],[175653064,175729624,theory(equality)]),[]).
%
% cnf(176261520,plain,(~subset(singleton(singleton(c)),singleton(unordered_pair(c,c)))),inference(resolution,[status(thm)],[175618104,175909800]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[164915232,176261520,164995368,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------