## TPTP Problem File: RAL007^1.p

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```%------------------------------------------------------------------------------
% File     : RAL007^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Numbers and algebraic expressions)
% Problem  : Chart System Math I+A Red Book, Problem 07CRAE040
% 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-Red-07CRAE040.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3486 (   0 unit;1200 type;   0 defn)
%            Number of atoms       : 45322 (2209 equality;22711 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39617 ( 104   ~; 233   |;1177   &;35977   @)
%                                         (1095 <=>;1031  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1248 (1200   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8061 (  66 sgn;7085   !; 431   ?; 409   ^)
%                                         (8061   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1981 (   6 prd;   9 fun;  24 num;1942 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: PA; Level: 4; Author: Munehiro Kobayashi;
%            Generated: 2015-01-07
%            ^ [V_min_dot_0: \$int] : ( V_min_dot_0 = 8 ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf('min/0_type',type,(
'min/0': \$int )).

thf(p1_qustion,conjecture,
( 'find/1' @ \$int
@ ( ^ [V_min: \$int] :
( 'minimum/3' @ \$int
@ ( 'set-by-def/1' @ \$int
@ ( ^ [V_v: \$int] :
? [V_a: \$int,V_b: \$int] :
( ( \$is_int @ V_a )
& ( \$is_int @ V_b )
& ( \$less @ 0 @ V_a )
& ( \$lesseq @ V_a @ V_b )
& ( \$lesseq @ 50 @ ( \$product @ V_a @ V_b ) )
& ( V_v = V_b ) ) ) )
@ ( ^ [V_lhs: \$int,V_rhs: \$int] :
( \$less @ V_lhs @ V_rhs ) ) @ V_min ) ) )).
%------------------------------------------------------------------------------
```