%------------------------------------------------------------------------------
% File     : NUM656_8 : TPTP v8.2.0. Released v8.0.0.
% Domain   : Number Theory
% Problem  : Landau theorem 10g
% Version  : Especial.
% English  : ~(~(less x y) -> x = y)

% Refs     :
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : 0.00 v8.1.0
% Syntax   : Number of formulae    :    9 (   1 unt;   5 typ;   0 def)
%            Number of atoms       :    9 (   3 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   18 (  11   ~;   0   |;   0   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    2 (   0 fml;   2 var)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   0 prp; 2-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :    3 (   3   !;   0   ?;   3   :)
% SPC      : TX0_THM_EQU_NAR

% Comments : Translated to TXF from the THF version.
%------------------------------------------------------------------------------
tff(nat_type,type,
    nat: $tType ).

tff(x,type,
    x: nat ).

tff(y,type,
    y: nat ).

tff(more,type,
    more: ( nat * nat ) > $o ).

tff(m,axiom,
    more(x,y) ).

tff(less,type,
    less: ( nat * nat ) > $o ).

tff(et,axiom,
    ! [Xa: $o] :
      ( ~ ~ (Xa)
     => (Xa) ) ).

tff(satz10b,axiom,
    ! [Xx: nat,Xy: nat] :
      ~ ( ( ( Xx = Xy )
         => ~ more(Xx,Xy) )
       => ~ ~ ( ( more(Xx,Xy)
               => ~ less(Xx,Xy) )
             => ~ ( less(Xx,Xy)
                 => ( Xx != Xy ) ) ) ) ).

tff(satz10g,conjecture,
    ~ ( ~ less(x,y)
     => ( x = y ) ) ).

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