%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET592+3 : TPTP v3.4.2. Released v2.2.0.
% 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 15:32:11 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    :   13 (   7 unt;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   20 (  10   ~;   7   |;   3   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    9 (   0 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(intersection_of_subsets,plain,
    ! [A,B,C] :
      ( ~ subset(A,B)
      | ~ subset(A,C)
      | subset(A,intersection(B,C)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET592+3.tptp',unknown),
    [] ).

cnf(152910592,plain,
    ( ~ subset(A,B)
    | ~ subset(A,C)
    | subset(A,intersection(B,C)) ),
    inference(rewrite,[status(thm)],[intersection_of_subsets]),
    [] ).

fof(prove_th51,plain,
    ( subset(b,c)
    & subset(b,d)
    & $equal(intersection(c,d),empty_set)
    & ~ $equal(empty_set,b) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET592+3.tptp',unknown),
    [] ).

cnf(153144616,plain,
    subset(b,d),
    inference(rewrite,[status(thm)],[prove_th51]),
    [] ).

cnf(168995560,plain,
    ( ~ subset(b,A)
    | subset(b,intersection(A,d)) ),
    inference(resolution,[status(thm)],[152910592,153144616]),
    [] ).

cnf(153151608,plain,
    subset(b,c),
    inference(rewrite,[status(thm)],[prove_th51]),
    [] ).

cnf(169053328,plain,
    subset(b,intersection(c,d)),
    inference(resolution,[status(thm)],[168995560,153151608]),
    [] ).

fof(subset_of_empty_set_is_empty_set,plain,
    ! [A] :
      ( ~ subset(A,empty_set)
      | $equal(empty_set,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET592+3.tptp',unknown),
    [] ).

cnf(152902960,plain,
    ( ~ subset(A,empty_set)
    | $equal(empty_set,A) ),
    inference(rewrite,[status(thm)],[subset_of_empty_set_is_empty_set]),
    [] ).

cnf(153129888,plain,
    ~ $equal(empty_set,b),
    inference(rewrite,[status(thm)],[prove_th51]),
    [] ).

cnf(169197440,plain,
    ~ subset(b,empty_set),
    inference(resolution,[status(thm)],[152902960,153129888]),
    [] ).

cnf(153137288,plain,
    $equal(intersection(c,d),empty_set),
    inference(rewrite,[status(thm)],[prove_th51]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[169053328,169197440,153137288,theory(equality)]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(intersection_of_subsets,plain,(~subset(A,B)|~subset(A,C)|subset(A,intersection(B,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET592+3.tptp',unknown),[]).
% 
% cnf(152910592,plain,(~subset(A,B)|~subset(A,C)|subset(A,intersection(B,C))),inference(rewrite,[status(thm)],[intersection_of_subsets]),[]).
% 
% fof(prove_th51,plain,((subset(b,c)&subset(b,d)&$equal(intersection(c,d),empty_set)&~$equal(empty_set,b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET592+3.tptp',unknown),[]).
% 
% cnf(153144616,plain,(subset(b,d)),inference(rewrite,[status(thm)],[prove_th51]),[]).
% 
% cnf(168995560,plain,(~subset(b,A)|subset(b,intersection(A,d))),inference(resolution,[status(thm)],[152910592,153144616]),[]).
% 
% cnf(153151608,plain,(subset(b,c)),inference(rewrite,[status(thm)],[prove_th51]),[]).
% 
% cnf(169053328,plain,(subset(b,intersection(c,d))),inference(resolution,[status(thm)],[168995560,153151608]),[]).
% 
% fof(subset_of_empty_set_is_empty_set,plain,(~subset(A,empty_set)|$equal(empty_set,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET592+3.tptp',unknown),[]).
% 
% cnf(152902960,plain,(~subset(A,empty_set)|$equal(empty_set,A)),inference(rewrite,[status(thm)],[subset_of_empty_set_is_empty_set]),[]).
% 
% cnf(153129888,plain,(~$equal(empty_set,b)),inference(rewrite,[status(thm)],[prove_th51]),[]).
% 
% cnf(169197440,plain,(~subset(b,empty_set)),inference(resolution,[status(thm)],[152902960,153129888]),[]).
% 
% cnf(153137288,plain,($equal(intersection(c,d),empty_set)),inference(rewrite,[status(thm)],[prove_th51]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[169053328,169197440,153137288,theory(equality)]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------