%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SEU150+1 : TPTP v3.4.2. Released v3.3.0.
% 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 15:49:13 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/SystemOnTPTP12203/SEU150+1.p',unknown),
    [] ).

cnf(171197288,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/SystemOnTPTP12203/SEU150+1.p',unknown),
    [] ).

cnf(171260416,plain,
    $equal(unordered_pair(b,c),singleton(a)),
    inference(rewrite,[status(thm)],[t9_zfmisc_1]),
    [] ).

cnf(181692336,plain,
    $equal(b,a),
    inference(resolution,[status(thm)],[171197288,171260416]),
    [] ).

cnf(181788064,plain,
    $equal(unordered_pair(b,c),singleton(b)),
    inference(paramodulation,[status(thm)],[181692336,171260416,theory(equality)]),
    [] ).

fof(commutativity_k2_tarski,plain,
    ! [B,A] : $equal(unordered_pair(B,A),unordered_pair(A,B)),
    file('/tmp/SystemOnTPTP12203/SEU150+1.p',unknown),
    [] ).

cnf(171169752,plain,
    $equal(unordered_pair(B,A),unordered_pair(A,B)),
    inference(rewrite,[status(thm)],[commutativity_k2_tarski]),
    [] ).

cnf(181814760,plain,
    $equal(unordered_pair(c,b),singleton(b)),
    inference(paramodulation,[status(thm)],[181788064,171169752,theory(equality)]),
    [] ).

cnf(181941224,plain,
    $equal(c,b),
    inference(resolution,[status(thm)],[181814760,171197288]),
    [] ).

cnf(171253096,plain,
    ~ $equal(c,b),
    inference(rewrite,[status(thm)],[t9_zfmisc_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[181941224,171253096]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(t8_zfmisc_1,plain,(~$equal(unordered_pair(B,C),singleton(A))|$equal(B,A)),file('/tmp/SystemOnTPTP12203/SEU150+1.p',unknown),[]).
% 
% cnf(171197288,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/SystemOnTPTP12203/SEU150+1.p',unknown),[]).
% 
% cnf(171260416,plain,($equal(unordered_pair(b,c),singleton(a))),inference(rewrite,[status(thm)],[t9_zfmisc_1]),[]).
% 
% cnf(181692336,plain,($equal(b,a)),inference(resolution,[status(thm)],[171197288,171260416]),[]).
% 
% cnf(181788064,plain,($equal(unordered_pair(b,c),singleton(b))),inference(paramodulation,[status(thm)],[181692336,171260416,theory(equality)]),[]).
% 
% fof(commutativity_k2_tarski,plain,($equal(unordered_pair(B,A),unordered_pair(A,B))),file('/tmp/SystemOnTPTP12203/SEU150+1.p',unknown),[]).
% 
% cnf(171169752,plain,($equal(unordered_pair(B,A),unordered_pair(A,B))),inference(rewrite,[status(thm)],[commutativity_k2_tarski]),[]).
% 
% cnf(181814760,plain,($equal(unordered_pair(c,b),singleton(b))),inference(paramodulation,[status(thm)],[181788064,171169752,theory(equality)]),[]).
% 
% cnf(181941224,plain,($equal(c,b)),inference(resolution,[status(thm)],[181814760,171197288]),[]).
% 
% cnf(171253096,plain,(~$equal(c,b)),inference(rewrite,[status(thm)],[t9_zfmisc_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[181941224,171253096]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------