%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET006-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art07.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 15:22:46 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   15 (   8 unt;   0 def)
%            Number of atoms       :   24 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   19 (  10   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   17 (   1 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(member_of_intersection_is_member_of_set2,plain,
    ! [A,B,C,D] :
      ( ~ intersection(A,B,C)
      | ~ member(D,C)
      | member(D,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET006-1.tptp',unknown),
    [] ).

cnf(146660488,plain,
    ( ~ intersection(A,B,C)
    | ~ member(D,C)
    | member(D,B) ),
    inference(rewrite,[status(thm)],[member_of_intersection_is_member_of_set2]),
    [] ).

fof(d_intersection_a_is_d,plain,
    intersection(d,a,d),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET006-1.tptp',unknown),
    [] ).

cnf(146696424,plain,
    intersection(d,a,d),
    inference(rewrite,[status(thm)],[d_intersection_a_is_d]),
    [] ).

cnf(154507248,plain,
    ( ~ member(A,d)
    | member(A,a) ),
    inference(resolution,[status(thm)],[146660488,146696424]),
    [] ).

fof(subsets_axiom1,plain,
    ! [A,B] :
      ( subset(A,B)
      | member(member_of_1_not_of_2(A,B),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET006-1.tptp',unknown),
    [] ).

cnf(146616000,plain,
    ( subset(A,B)
    | member(member_of_1_not_of_2(A,B),A) ),
    inference(rewrite,[status(thm)],[subsets_axiom1]),
    [] ).

fof(prove_d_is_a_subset_of_a,plain,
    ~ subset(d,a),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET006-1.tptp',unknown),
    [] ).

cnf(146700376,plain,
    ~ subset(d,a),
    inference(rewrite,[status(thm)],[prove_d_is_a_subset_of_a]),
    [] ).

cnf(154548864,plain,
    member(member_of_1_not_of_2(d,a),d),
    inference(resolution,[status(thm)],[146616000,146700376]),
    [] ).

cnf(154593368,plain,
    member(member_of_1_not_of_2(d,a),a),
    inference(resolution,[status(thm)],[154507248,154548864]),
    [] ).

fof(subsets_axiom2,plain,
    ! [A,B] :
      ( ~ member(member_of_1_not_of_2(A,B),B)
      | subset(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET006-1.tptp',unknown),
    [] ).

cnf(146621824,plain,
    ( ~ member(member_of_1_not_of_2(A,B),B)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[subsets_axiom2]),
    [] ).

cnf(154562552,plain,
    ~ member(member_of_1_not_of_2(d,a),a),
    inference(resolution,[status(thm)],[146621824,146700376]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[154593368,154562552]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(member_of_intersection_is_member_of_set2,plain,(~intersection(A,B,C)|~member(D,C)|member(D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET006-1.tptp',unknown),[]).
% 
% cnf(146660488,plain,(~intersection(A,B,C)|~member(D,C)|member(D,B)),inference(rewrite,[status(thm)],[member_of_intersection_is_member_of_set2]),[]).
% 
% fof(d_intersection_a_is_d,plain,(intersection(d,a,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET006-1.tptp',unknown),[]).
% 
% cnf(146696424,plain,(intersection(d,a,d)),inference(rewrite,[status(thm)],[d_intersection_a_is_d]),[]).
% 
% cnf(154507248,plain,(~member(A,d)|member(A,a)),inference(resolution,[status(thm)],[146660488,146696424]),[]).
% 
% fof(subsets_axiom1,plain,(subset(A,B)|member(member_of_1_not_of_2(A,B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET006-1.tptp',unknown),[]).
% 
% cnf(146616000,plain,(subset(A,B)|member(member_of_1_not_of_2(A,B),A)),inference(rewrite,[status(thm)],[subsets_axiom1]),[]).
% 
% fof(prove_d_is_a_subset_of_a,plain,(~subset(d,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET006-1.tptp',unknown),[]).
% 
% cnf(146700376,plain,(~subset(d,a)),inference(rewrite,[status(thm)],[prove_d_is_a_subset_of_a]),[]).
% 
% cnf(154548864,plain,(member(member_of_1_not_of_2(d,a),d)),inference(resolution,[status(thm)],[146616000,146700376]),[]).
% 
% cnf(154593368,plain,(member(member_of_1_not_of_2(d,a),a)),inference(resolution,[status(thm)],[154507248,154548864]),[]).
% 
% fof(subsets_axiom2,plain,(~member(member_of_1_not_of_2(A,B),B)|subset(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET006-1.tptp',unknown),[]).
% 
% cnf(146621824,plain,(~member(member_of_1_not_of_2(A,B),B)|subset(A,B)),inference(rewrite,[status(thm)],[subsets_axiom2]),[]).
% 
% cnf(154562552,plain,(~member(member_of_1_not_of_2(d,a),a)),inference(resolution,[status(thm)],[146621824,146700376]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[154593368,154562552]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------