%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET061-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art04.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 15:26:14 EDT 2009

% Result   : Unsatisfiable 0.4s
% Output   : Refutation 0.4s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   12 (   6 unt;   0 def)
%            Number of atoms       :   18 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   14 (   8   ~;   6   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   13 (   2 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_existence_of_null_class_1,plain,
    member(z,null_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-6.tptp',unknown),
    [] ).

cnf(156437192,plain,
    member(z,null_class),
    inference(rewrite,[status(thm)],[prove_existence_of_null_class_1]),
    [] ).

fof(complement1,plain,
    ! [A,B] :
      ( ~ member(A,complement(B))
      | ~ member(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-6.tptp',unknown),
    [] ).

cnf(156645616,plain,
    ( ~ member(A,complement(B))
    | ~ member(A,B) ),
    inference(rewrite,[status(thm)],[complement1]),
    [] ).

cnf(166053128,plain,
    ~ member(z,complement(null_class)),
    inference(resolution,[status(thm)],[156645616,156437192]),
    [] ).

fof(intersection1,plain,
    ! [A,B,C] :
      ( ~ member(A,intersection(B,C))
      | member(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-6.tptp',unknown),
    [] ).

cnf(156631000,plain,
    ( ~ member(A,intersection(B,C))
    | member(A,B) ),
    inference(rewrite,[status(thm)],[intersection1]),
    [] ).

cnf(177990880,plain,
    ~ member(z,intersection(complement(null_class),A)),
    inference(resolution,[status(thm)],[166053128,156631000]),
    [] ).

fof(regularity2,plain,
    ! [A] :
      ( $equal(null_class,A)
      | $equal(intersection(A,regular(A)),null_class) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-6.tptp',unknown),
    [] ).

cnf(157010888,plain,
    ( $equal(null_class,A)
    | $equal(intersection(A,regular(A)),null_class) ),
    inference(rewrite,[status(thm)],[regularity2]),
    [] ).

cnf(185105472,plain,
    $equal(null_class,complement(null_class)),
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[156437192,177990880,157010888,theory(equality)]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[156437192,185105472,166053128,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_existence_of_null_class_1,plain,(member(z,null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-6.tptp',unknown),[]).
% 
% cnf(156437192,plain,(member(z,null_class)),inference(rewrite,[status(thm)],[prove_existence_of_null_class_1]),[]).
% 
% fof(complement1,plain,(~member(A,complement(B))|~member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-6.tptp',unknown),[]).
% 
% cnf(156645616,plain,(~member(A,complement(B))|~member(A,B)),inference(rewrite,[status(thm)],[complement1]),[]).
% 
% cnf(166053128,plain,(~member(z,complement(null_class))),inference(resolution,[status(thm)],[156645616,156437192]),[]).
% 
% fof(intersection1,plain,(~member(A,intersection(B,C))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-6.tptp',unknown),[]).
% 
% cnf(156631000,plain,(~member(A,intersection(B,C))|member(A,B)),inference(rewrite,[status(thm)],[intersection1]),[]).
% 
% cnf(177990880,plain,(~member(z,intersection(complement(null_class),A))),inference(resolution,[status(thm)],[166053128,156631000]),[]).
% 
% fof(regularity2,plain,($equal(null_class,A)|$equal(intersection(A,regular(A)),null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET061-6.tptp',unknown),[]).
% 
% cnf(157010888,plain,($equal(null_class,A)|$equal(intersection(A,regular(A)),null_class)),inference(rewrite,[status(thm)],[regularity2]),[]).
% 
% cnf(185105472,plain,($equal(null_class,complement(null_class))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[156437192,177990880,157010888,theory(equality)]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[156437192,185105472,166053128,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------