%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : NUM405+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art02.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 15:03:47 EDT 2009

% Result   : Theorem 14.9s
% Output   : Refutation 14.9s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   12 (   4 unt;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   35 (  15   ~;  15   |;   5   &)
%                                         (   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    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   14 (   4 sgn   4   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(s1_xboole_0__e2_43__ordinal1,plain,
    ! [C,A] :
      ( ( ordinal(C)
        | ~ in(C,b(A)) )
      & ( in(C,A)
        | ~ in(C,b(A)) )
      & ( in(C,b(A))
        | ~ in(C,A)
        | ~ ordinal(C) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM405+1.tptp',unknown),
    [] ).

cnf(161998808,plain,
    ( ordinal(C)
    | ~ in(C,b(A)) ),
    inference(rewrite,[status(thm)],[s1_xboole_0__e2_43__ordinal1]),
    [] ).

fof(t37_ordinal1,plain,
    ! [A] :
      ( ( ordinal(b(A))
        | in(b(A),A) )
      & ( ~ in(b(A),A)
        | in(b(A),A) )
      & ( ordinal(b(A))
        | ~ ordinal(b(A)) )
      & ( ~ in(b(A),A)
        | ~ ordinal(b(A)) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM405+1.tptp',unknown),
    [] ).

cnf(162030256,plain,
    ( ordinal(b(A))
    | in(b(A),A) ),
    inference(rewrite,[status(thm)],[t37_ordinal1]),
    [] ).

cnf(171425400,plain,
    ordinal(b(b(A))),
    inference(resolution,[status(thm)],[161998808,162030256]),
    [] ).

cnf(161978848,plain,
    ( in(C,b(A))
    | ~ in(C,A)
    | ~ ordinal(C) ),
    inference(rewrite,[status(thm)],[s1_xboole_0__e2_43__ordinal1]),
    [] ).

fof(t38_ordinal1,plain,
    ! [B] :
      ( ~ ordinal(B)
      | in(B,a) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM405+1.tptp',unknown),
    [] ).

cnf(162067560,plain,
    ( ~ ordinal(B)
    | in(B,a) ),
    inference(rewrite,[status(thm)],[t38_ordinal1]),
    [] ).

cnf(171452248,plain,
    in(b(b(A)),a),
    inference(resolution,[status(thm)],[171425400,162067560]),
    [] ).

cnf(442920168,plain,
    in(b(b(B)),b(a)),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[171425400,161978848,171452248]),
    [] ).

cnf(162023944,plain,
    ( ~ in(b(A),A)
    | ~ ordinal(b(A)) ),
    inference(rewrite,[status(thm)],[t37_ordinal1]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[171425400,442920168,162023944]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 15 seconds
% START OF PROOF SEQUENCE
% fof(s1_xboole_0__e2_43__ordinal1,plain,(((ordinal(C)|~in(C,b(A)))&(in(C,A)|~in(C,b(A)))&(in(C,b(A))|~in(C,A)|~ordinal(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM405+1.tptp',unknown),[]).
% 
% cnf(161998808,plain,(ordinal(C)|~in(C,b(A))),inference(rewrite,[status(thm)],[s1_xboole_0__e2_43__ordinal1]),[]).
% 
% fof(t37_ordinal1,plain,(((ordinal(b(A))|in(b(A),A))&(~in(b(A),A)|in(b(A),A))&(ordinal(b(A))|~ordinal(b(A)))&(~in(b(A),A)|~ordinal(b(A))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM405+1.tptp',unknown),[]).
% 
% cnf(162030256,plain,(ordinal(b(A))|in(b(A),A)),inference(rewrite,[status(thm)],[t37_ordinal1]),[]).
% 
% cnf(171425400,plain,(ordinal(b(b(A)))),inference(resolution,[status(thm)],[161998808,162030256]),[]).
% 
% cnf(161978848,plain,(in(C,b(A))|~in(C,A)|~ordinal(C)),inference(rewrite,[status(thm)],[s1_xboole_0__e2_43__ordinal1]),[]).
% 
% fof(t38_ordinal1,plain,(~ordinal(B)|in(B,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM405+1.tptp',unknown),[]).
% 
% cnf(162067560,plain,(~ordinal(B)|in(B,a)),inference(rewrite,[status(thm)],[t38_ordinal1]),[]).
% 
% cnf(171452248,plain,(in(b(b(A)),a)),inference(resolution,[status(thm)],[171425400,162067560]),[]).
% 
% cnf(442920168,plain,(in(b(b(B)),b(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[171425400,161978848,171452248]),[]).
% 
% cnf(162023944,plain,(~in(b(A),A)|~ordinal(b(A))),inference(rewrite,[status(thm)],[t37_ordinal1]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[171425400,442920168,162023944]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------