%------------------------------------------------------------------------------
% File     : NUM713_8 : TPTP v8.2.0. Released v8.0.0.
% Domain   : Number Theory
% Problem  : Landau theorem 32a
% Version  : Especial.
% English  : ~(forall x_0:nat.~(ts x z = pl (ts y z) x_0))

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

% Status   : Theorem
% Rating   : 0.00 v8.1.0
% Syntax   : Number of formulae    :   11 (   4 unt;   6 typ;   0 def)
%            Number of atoms       :    4 (   4 equ)
%            Maximal formula atoms :    1 (   0 avg)
%            Number of connectives :    7 (   6   ~;   0   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Maximal term depth    :    3 (   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  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    8 (   8   !;   0   ?;   8   :)
% 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(z,type,
    z: nat ).

tff(pl,type,
    pl: ( nat * nat ) > nat ).

tff(m,axiom,
    ~ ! [Xx_0: nat] : x != pl(y,Xx_0) ).

tff(ts,type,
    ts: ( nat * nat ) > nat ).

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

tff(satz29,axiom,
    ! [Xx: nat,Xy: nat] : ts(Xx,Xy) = ts(Xy,Xx) ).

tff(satz30,axiom,
    ! [Xx: nat,Xy: nat,Xz: nat] : ts(Xx,pl(Xy,Xz)) = pl(ts(Xx,Xy),ts(Xx,Xz)) ).

tff(satz32a,conjecture,
    ~ ! [Xx_0: nat] : ts(x,z) != pl(ts(y,z),Xx_0) ).

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