%------------------------------------------------------------------------------
% File     : SET810+4 : TPTP v9.0.0. Released v3.2.0.
% Domain   : Set Theory (Order relations)
% Problem  : Ordinal numbers do not contain each other
% Version  : [Pas05] axioms.
% English  : If a and b are ordinal numbers, it is not possible that a belongs
%            to b and b belongs to a

% Refs     : [Pas05] Pastre (2005), Email to G. Sutcliffe
% Source   : [Pas05]
% Names    :

% Status   : Theorem
% Rating   : 0.21 v9.0.0, 0.19 v8.2.0, 0.14 v8.1.0, 0.19 v7.4.0, 0.17 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.13 v6.4.0, 0.12 v6.3.0, 0.21 v6.2.0, 0.24 v6.1.0, 0.27 v6.0.0, 0.30 v5.4.0, 0.32 v5.3.0, 0.33 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.25 v3.7.0, 0.30 v3.5.0, 0.32 v3.4.0, 0.26 v3.3.0, 0.07 v3.2.0
% Syntax   : Number of formulae    :   20 (   1 unt;   0 def)
%            Number of atoms       :   69 (   4 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :   53 (   4   ~;   3   |;  18   &)
%                                         (  17 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   0 prp; 1-3 aty)
%            Number of functors    :   13 (  13 usr;   3 con; 0-3 aty)
%            Number of variables   :   58 (  55   !;   3   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%------------------------------------------------------------------------------
%----Include set theory definitions
include('Axioms/SET006+0.ax').
%----Include ordinal numbers axioms
include('Axioms/SET006+4.ax').
%------------------------------------------------------------------------------
fof(thV3,conjecture,
    ! [A,B] :
      ( ( member(A,on)
        & member(B,on) )
     => ~ ( member(A,B)
          & member(B,A) ) ) ).

%------------------------------------------------------------------------------