## TPTP Problem File: RAL011^1.p

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```%------------------------------------------------------------------------------
% File     : RAL011^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Numbers and algebraic expressions)
% Problem  : Chart System Math I+A Yellow Book, Problem 07CY1R037
% 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-Yellow-07CY1R037.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45330 (2211 equality;22708 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39623 ( 104   ~; 233   |;1176   &;35984   @)
%                                         (1095 <=>;1031  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1247 (1199   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8059 (  66 sgn;7085   !; 431   ?; 407   ^)
%                                         (8059   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1978 (   6 prd;   9 fun;  24 num;1939 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: PA; Level: 4; Author: Munehiro Kobayashi;
%            Generated: 2015-01-08
%            ^ [V_n_dot_0: \$int] : ( V_n_dot_0 = 5 ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p1_qustion,conjecture,
( 'find/1' @ \$int
@ ( ^ [V_n: \$int] :
( 'is-cardinality-of/2' @ ( 'Pair' @ \$int @ \$int ) @ V_n
@ ( 'set-by-def/1' @ ( 'Pair' @ \$int @ \$int )
@ ( ^ [V_pair: ( 'Pair' @ \$int @ \$int )] :
? [V_x: \$int,V_y: \$int] :
( ( V_x
= ( 'fst/1' @ \$int @ \$int @ V_pair ) )
& ( V_y
= ( 'snd/1' @ \$int @ \$int @ V_pair ) )
& ( 'int.is-natural-number/1' @ V_x )
& ( 'int.is-natural-number/1' @ V_y )
& ( 33
= ( \$sum @ ( \$product @ 2 @ V_x ) @ ( \$product @ 3 @ V_y ) ) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------
```