%------------------------------------------------------------------------------
% File     : NUM398+1 : TPTP v9.0.0. Released v3.2.0.
% Domain   : Number Theory (Ordinals)
% Problem  : Ordinal numbers, theorem 31
% Version  : [Urb06] axioms : Especial.
% English  :

% Refs     : [Ban90] Bancerek (1990), The Ordinal Numbers
%            [Urb06] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb06]
% Names    : ordinal1__t31_ordinal1 [Urb06]

% Status   : Theorem
% Rating   : 0.21 v3.2.0
% Syntax   : Number of formulae    :   39 (   5 unit)
%            Number of atoms       :  115 (   4 equality)
%            Maximal formula depth :   11 (   5 average)
%            Number of connectives :   92 (  16 ~  ;   1  |;  55  &)
%                                         (   4 <=>;  16 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   13 (   0 propositional; 1-2 arity)
%            Number of functors    :    2 (   1 constant; 0-1 arity)
%            Number of variables   :   52 (   1 singleton;  38 !;  14 ?)
%            Maximal term depth    :    2 (   1 average)

% Comments : Translated by MPTP 0.2 from the original problem in the Mizar
%            library, www.mizar.org
% Bugfixes : v3.4.0 - Renamed to SEU234+3
%------------------------------------------------------------------------------