## TPTP Problem File: RAL004^1.p

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```%------------------------------------------------------------------------------
% File     : RAL004^1 : TPTP v7.5.0. 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 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45310 (2208 equality;22705 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39607 ( 104   ~; 233   |;1175   &;35968   @)
%                                         (1095 <=>;1032  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1246 (1199   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8057 (  66 sgn;7087   !; 429   ?; 405   ^)
%                                         (8057   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1976 (   6 prd;   9 fun;  23 num;1938 var)
% 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 ) ) ) ) )).
%------------------------------------------------------------------------------
```