%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET194+3 : TPTP v3.4.2. Released v2.2.0.
% 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 15:29:58 EDT 2009

% Result   : Theorem 0.0s
% Output   : Refutation 0.0s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   11 (   6 unt;   0 def)
%            Number of atoms       :   26 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   26 (  11   ~;  11   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-3 aty)
%            Number of variables   :   19 (   7 sgn   6   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(subset_defn,plain,
    ! [A,B,C] :
      ( ( ~ subset(A,B)
        | ~ member(C,A)
        | member(C,B) )
      & ( ~ member(d(A,B,C),B)
        | subset(A,B) )
      & ( member(d(A,B,C),A)
        | subset(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET194+3.tptp',unknown),
    [] ).

cnf(166668168,plain,
    ( ~ member(d(A,B,C),B)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[subset_defn]),
    [] ).

fof(prove_subset_of_union,plain,
    ~ subset(b,union(b,c)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET194+3.tptp',unknown),
    [] ).

cnf(166764552,plain,
    ~ subset(b,union(b,c)),
    inference(rewrite,[status(thm)],[prove_subset_of_union]),
    [] ).

cnf(174576728,plain,
    ~ member(d(b,union(b,c),A),union(b,c)),
    inference(resolution,[status(thm)],[166668168,166764552]),
    [] ).

fof(union_defn,plain,
    ! [C,A,B] :
      ( ( ~ member(C,union(A,B))
        | member(C,A)
        | member(C,B) )
      & ( ~ member(C,B)
        | member(C,union(A,B)) )
      & ( ~ member(C,A)
        | member(C,union(A,B)) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET194+3.tptp',unknown),
    [] ).

cnf(166636632,plain,
    ( ~ member(C,A)
    | member(C,union(A,B)) ),
    inference(rewrite,[status(thm)],[union_defn]),
    [] ).

cnf(166662400,plain,
    ( member(d(A,B,C),A)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[subset_defn]),
    [] ).

cnf(174563024,plain,
    member(d(b,union(b,c),A),b),
    inference(resolution,[status(thm)],[166662400,166764552]),
    [] ).

cnf(174595744,plain,
    member(d(b,union(b,c),B),union(b,A)),
    inference(resolution,[status(thm)],[166636632,174563024]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[174576728,174595744]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(subset_defn,plain,(((~subset(A,B)|~member(C,A)|member(C,B))&(~member(d(A,B,C),B)|subset(A,B))&(member(d(A,B,C),A)|subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET194+3.tptp',unknown),[]).
% 
% cnf(166668168,plain,(~member(d(A,B,C),B)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
% 
% fof(prove_subset_of_union,plain,(~subset(b,union(b,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET194+3.tptp',unknown),[]).
% 
% cnf(166764552,plain,(~subset(b,union(b,c))),inference(rewrite,[status(thm)],[prove_subset_of_union]),[]).
% 
% cnf(174576728,plain,(~member(d(b,union(b,c),A),union(b,c))),inference(resolution,[status(thm)],[166668168,166764552]),[]).
% 
% fof(union_defn,plain,(((~member(C,union(A,B))|member(C,A)|member(C,B))&(~member(C,B)|member(C,union(A,B)))&(~member(C,A)|member(C,union(A,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET194+3.tptp',unknown),[]).
% 
% cnf(166636632,plain,(~member(C,A)|member(C,union(A,B))),inference(rewrite,[status(thm)],[union_defn]),[]).
% 
% cnf(166662400,plain,(member(d(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
% 
% cnf(174563024,plain,(member(d(b,union(b,c),A),b)),inference(resolution,[status(thm)],[166662400,166764552]),[]).
% 
% cnf(174595744,plain,(member(d(b,union(b,c),B),union(b,A))),inference(resolution,[status(thm)],[166636632,174563024]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[174576728,174595744]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------