%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU150+3 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 15:49:18 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 9 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 2 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 1 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t8_zfmisc_1,plain,
! [B,C,A] :
( ~ $equal(unordered_pair(B,C),singleton(A))
| $equal(B,A) ),
file('/tmp/SystemOnTPTP10825/SEU150+3.p',unknown),
[] ).
cnf(151965808,plain,
( ~ $equal(unordered_pair(B,C),singleton(A))
| $equal(B,A) ),
inference(rewrite,[status(thm)],[t8_zfmisc_1]),
[] ).
fof(t9_zfmisc_1,plain,
( $equal(unordered_pair(b,c),singleton(a))
& ~ $equal(c,b) ),
file('/tmp/SystemOnTPTP10825/SEU150+3.p',unknown),
[] ).
cnf(152033128,plain,
$equal(unordered_pair(b,c),singleton(a)),
inference(rewrite,[status(thm)],[t9_zfmisc_1]),
[] ).
cnf(162504976,plain,
$equal(b,a),
inference(resolution,[status(thm)],[151965808,152033128]),
[] ).
cnf(162594976,plain,
$equal(unordered_pair(b,c),singleton(b)),
inference(paramodulation,[status(thm)],[162504976,152033128,theory(equality)]),
[] ).
fof(commutativity_k2_tarski,plain,
! [B,A] : $equal(unordered_pair(B,A),unordered_pair(A,B)),
file('/tmp/SystemOnTPTP10825/SEU150+3.p',unknown),
[] ).
cnf(151933560,plain,
$equal(unordered_pair(B,A),unordered_pair(A,B)),
inference(rewrite,[status(thm)],[commutativity_k2_tarski]),
[] ).
cnf(162625752,plain,
$equal(unordered_pair(c,b),singleton(b)),
inference(paramodulation,[status(thm)],[162594976,151933560,theory(equality)]),
[] ).
cnf(162748192,plain,
$equal(c,b),
inference(resolution,[status(thm)],[162625752,151965808]),
[] ).
cnf(152021672,plain,
~ $equal(c,b),
inference(rewrite,[status(thm)],[t9_zfmisc_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[162748192,152021672]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t8_zfmisc_1,plain,(~$equal(unordered_pair(B,C),singleton(A))|$equal(B,A)),file('/tmp/SystemOnTPTP10825/SEU150+3.p',unknown),[]).
%
% cnf(151965808,plain,(~$equal(unordered_pair(B,C),singleton(A))|$equal(B,A)),inference(rewrite,[status(thm)],[t8_zfmisc_1]),[]).
%
% fof(t9_zfmisc_1,plain,(($equal(unordered_pair(b,c),singleton(a))&~$equal(c,b))),file('/tmp/SystemOnTPTP10825/SEU150+3.p',unknown),[]).
%
% cnf(152033128,plain,($equal(unordered_pair(b,c),singleton(a))),inference(rewrite,[status(thm)],[t9_zfmisc_1]),[]).
%
% cnf(162504976,plain,($equal(b,a)),inference(resolution,[status(thm)],[151965808,152033128]),[]).
%
% cnf(162594976,plain,($equal(unordered_pair(b,c),singleton(b))),inference(paramodulation,[status(thm)],[162504976,152033128,theory(equality)]),[]).
%
% fof(commutativity_k2_tarski,plain,($equal(unordered_pair(B,A),unordered_pair(A,B))),file('/tmp/SystemOnTPTP10825/SEU150+3.p',unknown),[]).
%
% cnf(151933560,plain,($equal(unordered_pair(B,A),unordered_pair(A,B))),inference(rewrite,[status(thm)],[commutativity_k2_tarski]),[]).
%
% cnf(162625752,plain,($equal(unordered_pair(c,b),singleton(b))),inference(paramodulation,[status(thm)],[162594976,151933560,theory(equality)]),[]).
%
% cnf(162748192,plain,($equal(c,b)),inference(resolution,[status(thm)],[162625752,151965808]),[]).
%
% cnf(152021672,plain,(~$equal(c,b)),inference(rewrite,[status(thm)],[t9_zfmisc_1]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[162748192,152021672]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------