%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET001-1 : TPTP v3.4.2. Released v1.0.0.
% 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 15:22:27 EDT 2009

% Result   : Unsatisfiable 0.0s
% Output   : Refutation 0.0s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   14 (   9 unt;   0 def)
%            Number of atoms       :   21 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   16 (   9   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   11 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(membership_in_subsets,plain,
    ! [A,B,C] :
      ( ~ member(A,B)
      | ~ subset(B,C)
      | member(A,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET001-1.tptp',unknown),
    [] ).

cnf(144883304,plain,
    ( ~ member(A,B)
    | ~ subset(B,C)
    | member(A,C) ),
    inference(rewrite,[status(thm)],[membership_in_subsets]),
    [] ).

fof(set_equal_sets_are_subsets1,plain,
    ! [A,B] :
      ( ~ equal_sets(A,B)
      | subset(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET001-1.tptp',unknown),
    [] ).

cnf(144901896,plain,
    ( ~ equal_sets(A,B)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[set_equal_sets_are_subsets1]),
    [] ).

fof(b_equals_bb,plain,
    equal_sets(b,bb),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET001-1.tptp',unknown),
    [] ).

cnf(144922328,plain,
    equal_sets(b,bb),
    inference(rewrite,[status(thm)],[b_equals_bb]),
    [] ).

cnf(152714416,plain,
    subset(b,bb),
    inference(resolution,[status(thm)],[144901896,144922328]),
    [] ).

cnf(152766616,plain,
    ( ~ member(A,b)
    | member(A,bb) ),
    inference(resolution,[status(thm)],[144883304,152714416]),
    [] ).

fof(element_of_b,plain,
    member(element_of_b,b),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET001-1.tptp',unknown),
    [] ).

cnf(144927064,plain,
    member(element_of_b,b),
    inference(rewrite,[status(thm)],[element_of_b]),
    [] ).

cnf(152771384,plain,
    member(element_of_b,bb),
    inference(resolution,[status(thm)],[152766616,144927064]),
    [] ).

fof(prove_element_of_bb,plain,
    ~ member(element_of_b,bb),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET001-1.tptp',unknown),
    [] ).

cnf(144930952,plain,
    ~ member(element_of_b,bb),
    inference(rewrite,[status(thm)],[prove_element_of_bb]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[152771384,144930952]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(membership_in_subsets,plain,(~member(A,B)|~subset(B,C)|member(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET001-1.tptp',unknown),[]).
% 
% cnf(144883304,plain,(~member(A,B)|~subset(B,C)|member(A,C)),inference(rewrite,[status(thm)],[membership_in_subsets]),[]).
% 
% fof(set_equal_sets_are_subsets1,plain,(~equal_sets(A,B)|subset(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET001-1.tptp',unknown),[]).
% 
% cnf(144901896,plain,(~equal_sets(A,B)|subset(A,B)),inference(rewrite,[status(thm)],[set_equal_sets_are_subsets1]),[]).
% 
% fof(b_equals_bb,plain,(equal_sets(b,bb)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET001-1.tptp',unknown),[]).
% 
% cnf(144922328,plain,(equal_sets(b,bb)),inference(rewrite,[status(thm)],[b_equals_bb]),[]).
% 
% cnf(152714416,plain,(subset(b,bb)),inference(resolution,[status(thm)],[144901896,144922328]),[]).
% 
% cnf(152766616,plain,(~member(A,b)|member(A,bb)),inference(resolution,[status(thm)],[144883304,152714416]),[]).
% 
% fof(element_of_b,plain,(member(element_of_b,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET001-1.tptp',unknown),[]).
% 
% cnf(144927064,plain,(member(element_of_b,b)),inference(rewrite,[status(thm)],[element_of_b]),[]).
% 
% cnf(152771384,plain,(member(element_of_b,bb)),inference(resolution,[status(thm)],[152766616,144927064]),[]).
% 
% fof(prove_element_of_bb,plain,(~member(element_of_b,bb)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET001-1.tptp',unknown),[]).
% 
% cnf(144930952,plain,(~member(element_of_b,bb)),inference(rewrite,[status(thm)],[prove_element_of_bb]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[152771384,144930952]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------