%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET003-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art05.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 15:22:35 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            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   :   18 (   2 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(member_of_set1_is_member_of_union,plain,
    ! [A,B,C,D] :
      ( ~ union(A,B,C)
      | ~ member(D,A)
      | member(D,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET003-1.tptp',unknown),
    [] ).

cnf(154318560,plain,
    ( ~ union(A,B,C)
    | ~ member(D,A)
    | member(D,C) ),
    inference(rewrite,[status(thm)],[member_of_set1_is_member_of_union]),
    [] ).

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/SET003-1.tptp',unknown),
    [] ).

cnf(154272248,plain,
    ( subset(A,B)
    | member(member_of_1_not_of_2(A,B),A) ),
    inference(rewrite,[status(thm)],[subsets_axiom1]),
    [] ).

fof(prove_a_is_a_subset_of_aUa,plain,
    ~ subset(a,aua),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET003-1.tptp',unknown),
    [] ).

cnf(154358336,plain,
    ~ subset(a,aua),
    inference(rewrite,[status(thm)],[prove_a_is_a_subset_of_aUa]),
    [] ).

cnf(162217096,plain,
    member(member_of_1_not_of_2(a,aua),a),
    inference(resolution,[status(thm)],[154272248,154358336]),
    [] ).

cnf(162273808,plain,
    ( ~ union(a,A,B)
    | member(member_of_1_not_of_2(a,aua),B) ),
    inference(resolution,[status(thm)],[154318560,162217096]),
    [] ).

fof(a_union_a_is_aUa,plain,
    union(a,a,aua),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET003-1.tptp',unknown),
    [] ).

cnf(154354368,plain,
    union(a,a,aua),
    inference(rewrite,[status(thm)],[a_union_a_is_aUa]),
    [] ).

cnf(162278760,plain,
    member(member_of_1_not_of_2(a,aua),aua),
    inference(resolution,[status(thm)],[162273808,154354368]),
    [] ).

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/SET003-1.tptp',unknown),
    [] ).

cnf(154278104,plain,
    ( ~ member(member_of_1_not_of_2(A,B),B)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[subsets_axiom2]),
    [] ).

cnf(162234912,plain,
    ~ member(member_of_1_not_of_2(a,aua),aua),
    inference(resolution,[status(thm)],[154278104,154358336]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[162278760,162234912]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(member_of_set1_is_member_of_union,plain,(~union(A,B,C)|~member(D,A)|member(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET003-1.tptp',unknown),[]).
% 
% cnf(154318560,plain,(~union(A,B,C)|~member(D,A)|member(D,C)),inference(rewrite,[status(thm)],[member_of_set1_is_member_of_union]),[]).
% 
% 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/SET003-1.tptp',unknown),[]).
% 
% cnf(154272248,plain,(subset(A,B)|member(member_of_1_not_of_2(A,B),A)),inference(rewrite,[status(thm)],[subsets_axiom1]),[]).
% 
% fof(prove_a_is_a_subset_of_aUa,plain,(~subset(a,aua)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET003-1.tptp',unknown),[]).
% 
% cnf(154358336,plain,(~subset(a,aua)),inference(rewrite,[status(thm)],[prove_a_is_a_subset_of_aUa]),[]).
% 
% cnf(162217096,plain,(member(member_of_1_not_of_2(a,aua),a)),inference(resolution,[status(thm)],[154272248,154358336]),[]).
% 
% cnf(162273808,plain,(~union(a,A,B)|member(member_of_1_not_of_2(a,aua),B)),inference(resolution,[status(thm)],[154318560,162217096]),[]).
% 
% fof(a_union_a_is_aUa,plain,(union(a,a,aua)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET003-1.tptp',unknown),[]).
% 
% cnf(154354368,plain,(union(a,a,aua)),inference(rewrite,[status(thm)],[a_union_a_is_aUa]),[]).
% 
% cnf(162278760,plain,(member(member_of_1_not_of_2(a,aua),aua)),inference(resolution,[status(thm)],[162273808,154354368]),[]).
% 
% 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/SET003-1.tptp',unknown),[]).
% 
% cnf(154278104,plain,(~member(member_of_1_not_of_2(A,B),B)|subset(A,B)),inference(rewrite,[status(thm)],[subsets_axiom2]),[]).
% 
% cnf(162234912,plain,(~member(member_of_1_not_of_2(a,aua),aua)),inference(resolution,[status(thm)],[154278104,154358336]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[162278760,162234912]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------