## TPTP Problem File: RAL018^1.p

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```%------------------------------------------------------------------------------
% File     : RAL018^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Basics of equation/inequality)
% Problem  : International Mathematical Olympiad, 1959, Problem 2
% Version  : [Mat16] axioms : Especial.
% English  : For what real values of x is sqrt(x + sqrt(2x - 1)) +
%            sqrt(x - sqrt(2x - 1)) = A, given (a) A = sqrt(2), (b) A = 1,
%            (c) A = 2, where only non-negative real numbers are admitted
%            for square roots?

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : IMO-1959-2.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45321 (2209 equality;22704 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39616 ( 104   ~; 233   |;1173   &;35980   @)
%                                         (1095 <=>;1031  =>;   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   : 8056 (  66 sgn;7085   !; 429   ?; 406   ^)
%                                         (8056   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1975 (   6 prd;   9 fun;  23 num;1937 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: RCF; Score: 8; Author: Jumma Kudo;
%            Generated: 2014-12-09
%            ^ [V_x_dot_0: \$real] :
%              ( ( \$lesseq @ ( \$quotient @ 1.0 @ 2.0 ) @ V_x_dot_0 )
%              & ( \$lesseq @ V_x_dot_0 @ 1.0 ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p1_qustion,conjecture,
( 'find/1' @ \$real
@ ( ^ [V_x: \$real] :
( ( \$lesseq @ 0.0 @ V_x )
& ( ( \$sum @ ( 'sqrt/1' @ ( \$sum @ V_x @ ( 'sqrt/1' @ ( \$difference @ ( \$product @ 2.0 @ V_x ) @ 1.0 ) ) ) ) @ ( 'sqrt/1' @ ( \$difference @ V_x @ ( 'sqrt/1' @ ( \$difference @ ( \$product @ 2.0 @ V_x ) @ 1.0 ) ) ) ) )
= ( 'sqrt/1' @ 2.0 ) ) ) ) )).
%------------------------------------------------------------------------------
```