## TPTP Problem File: RAL022^1.p

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%------------------------------------------------------------------------------
% File     : RAL022^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Basics of equation/inequality)
% Problem  : International Mathematical Olympiad, 1963, Problem 1
% Version  : [Mat16] axioms : Especial.
% English  : Find all real roots of the equation sqrt(x^2 - p) +
%            2 sqrt(x^2 - 1) = x, where p is a real parameter.

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : IMO-1963-1.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3486 (   0 unit;1200 type;   0 defn)
%            Number of atoms       : 45313 (2209 equality;22702 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39608 ( 104   ~; 233   |;1172   &;35973   @)
%                                         (1095 <=>;1031  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1247 (1200   :;   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: 6; Author: Jumma Kudo;
%            Generated: 2014-12-16
%            ^ [V_x_dot_0: \$real] :
%              ( ( \$lesseq @ 'p/0' @ ( \$quotient @ 4.0 @ 3.0 ) )
%              & ( \$lesseq @ 0.0 @ 'p/0' )
%              & ( V_x_dot_0
%                = ( \$quotient @ ( \$difference @ 4.0 @ 'p/0' ) @ ( 'sqrt/1' @ ( \$product @ 8.0 @ ( \$difference @ 2.0 @ 'p/0' ) ) ) ) ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf('p/0_type',type,(
'p/0': \$real )).

thf(p_qustion,conjecture,
( 'find/1' @ \$real
@ ^ [V_x: \$real] :
( ( \$sum @ ( 'sqrt/1' @ ( \$difference @ ( '^/2' @ V_x @ 2.0 ) @ 'p/0' ) ) @ ( \$product @ 2.0 @ ( 'sqrt/1' @ ( \$difference @ ( '^/2' @ V_x @ 2.0 ) @ 1.0 ) ) ) )
= V_x ) )).

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