## TPTP Problem File: RAL038^1.p

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```%------------------------------------------------------------------------------
% File     : RAL038^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra
% Problem  : International Mathematical Olympiad, 2000, Problem 2
% Version  : [Mat16] axioms : Especial.
% English  : A, B, C are positive reals with product 1. Prove that (A - 1 +
%            1/B)(B - 1 + 1/C)(C - 1 + 1/A) <= 1.

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : IMO-2000-2.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45335 (2209 equality;22711 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39630 ( 104   ~; 233   |;1175   &;35991   @)
%                                         (1095 <=>;1032  =>;   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   : 8058 (  66 sgn;7088   !; 429   ?; 405   ^)
%                                         (8058   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1977 (   6 prd;   9 fun;  23 num;1939 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: RCF; Score: 7; Author: Munehiro Kobayashi;
%            Generated: 2014-11-13
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p,conjecture,(
! [V_A: \$real,V_B: \$real,V_C: \$real] :
( ( ( 1.0
= ( \$product @ V_A @ ( \$product @ V_B @ V_C ) ) )
& ( \$less @ 0.0 @ V_A )
& ( \$less @ 0.0 @ V_B )
& ( \$less @ 0.0 @ V_C ) )
=> ( \$lesseq @ ( \$product @ ( \$sum @ ( \$difference @ V_A @ 1.0 ) @ ( \$quotient @ 1.0 @ V_B ) ) @ ( \$product @ ( \$sum @ ( \$difference @ V_B @ 1.0 ) @ ( \$quotient @ 1.0 @ V_C ) ) @ ( \$sum @ ( \$difference @ V_C @ 1.0 ) @ ( \$quotient @ 1.0 @ V_A ) ) ) ) @ 1.0 ) ) )).

%------------------------------------------------------------------------------
```