%------------------------------------------------------------------------------
% File     : NUM762_8 : TPTP v8.2.0. Released v8.0.0.
% Domain   : Number Theory
% Problem  : Landau theorem 65b
% Version  : Especial.
% English  : moref (pf x z) (pf y u)

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

% Status   : Theorem
% Rating   : 0.00 v8.1.0
% Syntax   : Number of formulae    :   17 (   3 unt;   8 typ;   0 def)
%            Number of atoms       :   17 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   13 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    2 (   0 fml;   2 var)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   2 usr;   0 prp; 2-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   17 (  17   !;   0   ?;  17   :)
% SPC      : TX0_THM_NEQ_NAR

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

tff(x,type,
    x: frac ).

tff(y,type,
    y: frac ).

tff(z,type,
    z: frac ).

tff(u,type,
    u: frac ).

tff(moref,type,
    moref: ( frac * frac ) > $o ).

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

tff(eq,type,
    eq: ( frac * frac ) > $o ).

tff(n,axiom,
    ( ~ moref(z,u)
   => eq(z,u) ) ).

tff(pf,type,
    pf: ( frac * frac ) > frac ).

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

tff(satz44,axiom,
    ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
      ( moref(Xx,Xy)
     => ( eq(Xx,Xz)
       => ( eq(Xy,Xu)
         => moref(Xz,Xu) ) ) ) ).

tff(satz61,axiom,
    ! [Xx: frac,Xy: frac,Xz: frac] :
      ( moref(Xx,Xy)
     => moref(pf(Xx,Xz),pf(Xy,Xz)) ) ).

tff(satz37,axiom,
    ! [Xx: frac] : eq(Xx,Xx) ).

tff(satz56,axiom,
    ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
      ( eq(Xx,Xy)
     => ( eq(Xz,Xu)
       => eq(pf(Xx,Xz),pf(Xy,Xu)) ) ) ).

tff(satz64,axiom,
    ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
      ( moref(Xx,Xy)
     => ( moref(Xz,Xu)
       => moref(pf(Xx,Xz),pf(Xy,Xu)) ) ) ).

tff(satz65b,conjecture,
    moref(pf(x,z),pf(y,u)) ).

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