## TPTP Problem File: RAL030^1.p

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%------------------------------------------------------------------------------
% File     : RAL030^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Inequalities)
% Problem  : International Mathematical Olympiad, 1974, Problem 5
% Version  : [Mat16] axioms : Especial.
% English  : Determine all possible values of S = a/a+b+d + b/a+b+c + c/b+c+d +
%            d/a+c+d where a, b, c, d are arbitrary positive numbers.

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : IMO-1974-5.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45341 (2209 equality;22720 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39636 ( 104   ~; 233   |;1176   &;35997   @)
%                                         (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   : 8060 (  66 sgn;7085   !; 433   ?; 406   ^)
%                                         (8060   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1979 (   6 prd;   9 fun;  23 num;1941 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: RCF; Score: 7; Author: Jumma Kudo;
%            Generated: 2014-11-26
%            ^ [V_S_dot_0: \$real] :
%              ( ( \$less @ 1.0 @ V_S_dot_0 )
%              & ( \$less @ V_S_dot_0 @ 2.0 ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p_qustion,conjecture,
( 'find/1' @ \$real
@ ^ [V_S: \$real] :
? [V_a: \$real,V_b: \$real,V_c: \$real,V_d: \$real] :
( ( \$greater @ V_a @ 0.0 )
& ( \$greater @ V_b @ 0.0 )
& ( \$greater @ V_c @ 0.0 )
& ( \$greater @ V_d @ 0.0 )
& ( V_S
= ( \$sum @ ( \$quotient @ V_a @ ( \$sum @ V_a @ ( \$sum @ V_b @ V_d ) ) ) @ ( \$sum @ ( \$quotient @ V_b @ ( \$sum @ V_a @ ( \$sum @ V_b @ V_c ) ) ) @ ( \$sum @ ( \$quotient @ V_c @ ( \$sum @ V_b @ ( \$sum @ V_c @ V_d ) ) ) @ ( \$quotient @ V_d @ ( \$sum @ V_a @ ( \$sum @ V_c @ V_d ) ) ) ) ) ) ) ) )).

%------------------------------------------------------------------------------