%------------------------------------------------------------------------------
% File     : RAL004^1 : TPTP v9.0.0. Released v7.0.0.
% Domain   : Real Algebra (Numbers and algebraic expressions)
% Problem  : Chart System Math I+A Blue Book, Problem 07CBAP118
% Version  : [Mat16] axioms : Especial.
% English  : 

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : Chart-1A-Blue-07CBAP118.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 ( 728 unt;1199 typ;   0 def)
%            Number of atoms       : 6405 (2208 equ;   0 cnn)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives : 39607 ( 104   ~; 233   |;1175   &;35968   @)
%                                         (1095 <=>;1032  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (   8 avg)
%            Number arithmetic     : 4466 ( 371 atm;1204 fun; 953 num;1938 var)
%            Number of types       :   40 (  36 usr;   3 ari)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1210 (1167 usr;  64 con; 0-9 aty)
%            Number of variables   : 8057 ( 405   ^;7087   !; 429   ?;8057   :)
%                                         ( 136  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: PA; Level: 1; Author: Munehiro Kobayashi;
%            Generated: 2015-01-07
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p1,conjecture,
    ! [V_a: $int,V_b: $int] :
      ( ( ( 'int.is-natural-number/1' @ V_a )
        & ( 'int.is-natural-number/1' @ V_b )
        & ( 'int.is-odd-number/1' @ V_a )
        & ( 'int.is-odd-number/1' @ V_b ) )
     => ( 'int.is-even-number/1' @ ( $sum @ ( 'int.^/2' @ V_a @ 2 ) @ ( 'int.^/2' @ V_b @ 2 ) ) ) ) ).

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