TPTP Problem File: NUM762^1.p

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```%------------------------------------------------------------------------------
% File     : NUM762^1 : TPTP v7.1.0. Released v3.7.0.
% Domain   : Number Theory
% Problem  : Landau theorem 65b
% Version  : Especial.
% English  : moref (pf x z) (pf y u)

% Refs     : [Lan30] Landau (1930), Grundlagen der Analysis
%          : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : satz65b [Lan30]

% Status   : Theorem
%          : Without extensionality : Theorem
% Rating   : 0.38 v7.1.0, 0.43 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.50 v6.2.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.33 v4.0.1, 1.00 v4.0.0, 0.67 v3.7.0
% Syntax   : Number of formulae    :   17 (   0 unit;   8 type;   0 defn)
%            Number of atoms       :   69 (   0 equality;  34 variable)
%            Maximal formula depth :   11 (   5 average)
%            Number of connectives :   63 (   3   ~;   0   |;   0   &;  50   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8   :;   0   =)
%            Number of variables   :   17 (   0 sgn;  17   !;   0   ?;   0   ^)
%                                         (  17   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_NEQ_NAR

%------------------------------------------------------------------------------
thf(frac_type,type,(
frac: \$tType )).

thf(x,type,(
x: frac )).

thf(y,type,(
y: frac )).

thf(z,type,(
z: frac )).

thf(u,type,(
u: frac )).

thf(moref,type,(
moref: frac > frac > \$o )).

thf(m,axiom,
( moref @ x @ y )).

thf(eq,type,(
eq: frac > frac > \$o )).

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

thf(pf,type,(
pf: frac > frac > frac )).

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

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

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

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

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

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

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

%------------------------------------------------------------------------------
```