%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SEU161+1 : TPTP v3.4.2. Released v3.3.0.
% 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 15:50:07 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    7 (   4 unt;   0 def)
%            Number of atoms       :   10 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   4   ~;   2   |;   1   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    4 (   0 sgn   2   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l23_zfmisc_1,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | $equal(set_union2(singleton(A),B),B) ),
    file('/tmp/SystemOnTPTP13296/SEU161+1.p',unknown),
    [] ).

cnf(155982944,plain,
    ( ~ in(A,B)
    | $equal(set_union2(singleton(A),B),B) ),
    inference(rewrite,[status(thm)],[l23_zfmisc_1]),
    [] ).

fof(t46_zfmisc_1,plain,
    ( in(a,b)
    & ~ $equal(set_union2(singleton(a),b),b) ),
    file('/tmp/SystemOnTPTP13296/SEU161+1.p',unknown),
    [] ).

cnf(155978152,plain,
    in(a,b),
    inference(rewrite,[status(thm)],[t46_zfmisc_1]),
    [] ).

cnf(166401904,plain,
    $equal(set_union2(singleton(a),b),b),
    inference(resolution,[status(thm)],[155982944,155978152]),
    [] ).

cnf(155965112,plain,
    ~ $equal(set_union2(singleton(a),b),b),
    inference(rewrite,[status(thm)],[t46_zfmisc_1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[166401904,155965112]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l23_zfmisc_1,plain,(~in(A,B)|$equal(set_union2(singleton(A),B),B)),file('/tmp/SystemOnTPTP13296/SEU161+1.p',unknown),[]).
% 
% cnf(155982944,plain,(~in(A,B)|$equal(set_union2(singleton(A),B),B)),inference(rewrite,[status(thm)],[l23_zfmisc_1]),[]).
% 
% fof(t46_zfmisc_1,plain,((in(a,b)&~$equal(set_union2(singleton(a),b),b))),file('/tmp/SystemOnTPTP13296/SEU161+1.p',unknown),[]).
% 
% cnf(155978152,plain,(in(a,b)),inference(rewrite,[status(thm)],[t46_zfmisc_1]),[]).
% 
% cnf(166401904,plain,($equal(set_union2(singleton(a),b),b)),inference(resolution,[status(thm)],[155982944,155978152]),[]).
% 
% cnf(155965112,plain,(~$equal(set_union2(singleton(a),b),b)),inference(rewrite,[status(thm)],[t46_zfmisc_1]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[166401904,155965112]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------