%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET633+3 : TPTP v3.4.2. Released v2.2.0.
% 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 15:33:53 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   11 (   7 unt;   0 def)
%            Number of atoms       :   18 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   14 (   7   ~;   5   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   11 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(union_subset,plain,
    ! [A,B,C] :
      ( ~ subset(A,B)
      | ~ subset(C,B)
      | subset(union(A,C),B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET633+3.tptp',unknown),
    [] ).

cnf(142906816,plain,
    ( ~ subset(A,B)
    | ~ subset(C,B)
    | subset(union(A,C),B) ),
    inference(rewrite,[status(thm)],[union_subset]),
    [] ).

fof(prove_th115,plain,
    ( subset(difference(b,c),d)
    & subset(difference(c,b),d)
    & ~ subset(symmetric_difference(b,c),d) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET633+3.tptp',unknown),
    [] ).

cnf(143108808,plain,
    subset(difference(c,b),d),
    inference(rewrite,[status(thm)],[prove_th115]),
    [] ).

cnf(156287544,plain,
    ( ~ subset(A,d)
    | subset(union(A,difference(c,b)),d) ),
    inference(resolution,[status(thm)],[142906816,143108808]),
    [] ).

cnf(143116056,plain,
    subset(difference(b,c),d),
    inference(rewrite,[status(thm)],[prove_th115]),
    [] ).

cnf(156358544,plain,
    subset(union(difference(b,c),difference(c,b)),d),
    inference(resolution,[status(thm)],[156287544,143116056]),
    [] ).

cnf(143101448,plain,
    ~ subset(symmetric_difference(b,c),d),
    inference(rewrite,[status(thm)],[prove_th115]),
    [] ).

fof(symmetric_difference_defn,plain,
    ! [A,B] : $equal(union(difference(A,B),difference(B,A)),symmetric_difference(A,B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET633+3.tptp',unknown),
    [] ).

cnf(142892680,plain,
    $equal(union(difference(A,B),difference(B,A)),symmetric_difference(A,B)),
    inference(rewrite,[status(thm)],[symmetric_difference_defn]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[156358544,143101448,142892680,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(union_subset,plain,(~subset(A,B)|~subset(C,B)|subset(union(A,C),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET633+3.tptp',unknown),[]).
% 
% cnf(142906816,plain,(~subset(A,B)|~subset(C,B)|subset(union(A,C),B)),inference(rewrite,[status(thm)],[union_subset]),[]).
% 
% fof(prove_th115,plain,((subset(difference(b,c),d)&subset(difference(c,b),d)&~subset(symmetric_difference(b,c),d))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET633+3.tptp',unknown),[]).
% 
% cnf(143108808,plain,(subset(difference(c,b),d)),inference(rewrite,[status(thm)],[prove_th115]),[]).
% 
% cnf(156287544,plain,(~subset(A,d)|subset(union(A,difference(c,b)),d)),inference(resolution,[status(thm)],[142906816,143108808]),[]).
% 
% cnf(143116056,plain,(subset(difference(b,c),d)),inference(rewrite,[status(thm)],[prove_th115]),[]).
% 
% cnf(156358544,plain,(subset(union(difference(b,c),difference(c,b)),d)),inference(resolution,[status(thm)],[156287544,143116056]),[]).
% 
% cnf(143101448,plain,(~subset(symmetric_difference(b,c),d)),inference(rewrite,[status(thm)],[prove_th115]),[]).
% 
% fof(symmetric_difference_defn,plain,($equal(union(difference(A,B),difference(B,A)),symmetric_difference(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET633+3.tptp',unknown),[]).
% 
% cnf(142892680,plain,($equal(union(difference(A,B),difference(B,A)),symmetric_difference(A,B))),inference(rewrite,[status(thm)],[symmetric_difference_defn]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[156358544,143101448,142892680,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------