TPTP Problem File: RAL029^1.p
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% File : RAL029^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Real Algebra (Basics of equation/inequality)
% Problem : International Mathematical Olympiad, 1972, Problem 4
% Version : [Mat16] axioms : Especial.
% English : Find all solutions (x_1, x_2, x_3, x_4, x_5) of the system of
% inequalities
% (x_1^2 - x_3 x_5)(x_2^2 - x_3 x_5) =< 0
% (x_2^2 - x_4 x_1)(x_3^2 - x_4 x_1) =< 0
% (x_3^2 - x_5 x_2)(x_4^2 - x_5 x_2) =< 0
% (x_4^2 - x_1 x_3)(x_5^2 - x_1 x_3) =< 0
% (x_5^2 - x_2 x_4)(x_1^2 - x_2 x_4) =< 0
% where x_1, x_2, x_3, x_4, x_5 are positive real numbers.
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : IMO-1972-4.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3485 ( 711 unt;1199 typ; 0 def)
% Number of atoms : 8039 (2209 equ; 0 cnn)
% Maximal formula atoms : 40 ( 3 avg)
% Number of connectives : 39712 ( 104 ~; 233 |;1182 &;36067 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4521 ( 381 atm;1228 fun; 971 num;1941 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1211 (1168 usr; 65 con; 0-9 aty)
% Number of variables : 8061 ( 406 ^;7085 !; 434 ?;8061 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: RCF; Score: 7; Author: Jumma Kudo;
% Generated: 2014-11-27
% : Answer
% ^ [V_XL_dot_0: ( 'ListOf' @ $real )] :
% ? [V_X1_dot_0: $real,V_X2_dot_0: $real,V_X3_dot_0: $real,V_X4_dot_0: $real,V_X5_dot_0: $real] :
% ( ( V_XL_dot_0
% = ( 'cons/2' @ $real @ V_X1_dot_0 @ ( 'cons/2' @ $real @ V_X2_dot_0 @ ( 'cons/2' @ $real @ V_X3_dot_0 @ ( 'cons/2' @ $real @ V_X4_dot_0 @ ( 'cons/2' @ $real @ V_X5_dot_0 @ ( 'nil/0' @ $real ) ) ) ) ) ) )
% & ( V_X1_dot_0 = V_X2_dot_0 )
% & ( $less @ 0.0 @ V_X1_dot_0 )
% & ( $less @ 0.0 @ V_X2_dot_0 )
% & ( $less @ 0.0 @ V_X3_dot_0 )
% & ( $less @ 0.0 @ V_X4_dot_0 )
% & ( $less @ 0.0 @ V_X5_dot_0 )
% & ( V_X2_dot_0 = V_X3_dot_0 )
% & ( V_X3_dot_0 = V_X4_dot_0 )
% & ( V_X4_dot_0 = V_X5_dot_0 ) ) )
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include('Axioms/MAT001^0.ax').
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thf(p_qustion,conjecture,
( 'find/1' @ ( 'ListOf' @ $real )
@ ^ [V_XL: 'ListOf' @ $real] :
? [V_X1: $real,V_X2: $real,V_X3: $real,V_X4: $real,V_X5: $real] :
( ( $lesseq @ ( $product @ ( $difference @ ( '^/2' @ V_X1 @ 2.0 ) @ ( $product @ V_X3 @ V_X5 ) ) @ ( $difference @ ( '^/2' @ V_X2 @ 2.0 ) @ ( $product @ V_X3 @ V_X5 ) ) ) @ 0.0 )
& ( $lesseq @ ( $product @ ( $difference @ ( '^/2' @ V_X2 @ 2.0 ) @ ( $product @ V_X1 @ V_X4 ) ) @ ( $difference @ ( '^/2' @ V_X3 @ 2.0 ) @ ( $product @ V_X4 @ V_X1 ) ) ) @ 0.0 )
& ( $lesseq @ ( $product @ ( $difference @ ( '^/2' @ V_X3 @ 2.0 ) @ ( $product @ V_X2 @ V_X5 ) ) @ ( $difference @ ( '^/2' @ V_X4 @ 2.0 ) @ ( $product @ V_X2 @ V_X5 ) ) ) @ 0.0 )
& ( $lesseq @ ( $product @ ( $difference @ ( '^/2' @ V_X4 @ 2.0 ) @ ( $product @ V_X1 @ V_X3 ) ) @ ( $difference @ ( '^/2' @ V_X5 @ 2.0 ) @ ( $product @ V_X1 @ V_X3 ) ) ) @ 0.0 )
& ( $lesseq @ ( $product @ ( $difference @ ( '^/2' @ V_X5 @ 2.0 ) @ ( $product @ V_X2 @ V_X4 ) ) @ ( $difference @ ( '^/2' @ V_X1 @ 2.0 ) @ ( $product @ V_X2 @ V_X4 ) ) ) @ 0.0 )
& ( $less @ 0.0 @ V_X1 )
& ( $less @ 0.0 @ V_X2 )
& ( $less @ 0.0 @ V_X3 )
& ( $less @ 0.0 @ V_X4 )
& ( $less @ 0.0 @ V_X5 )
& ( V_XL
= ( 'cons/2' @ $real @ V_X1 @ ( 'cons/2' @ $real @ V_X2 @ ( 'cons/2' @ $real @ V_X3 @ ( 'cons/2' @ $real @ V_X4 @ ( 'cons/2' @ $real @ V_X5 @ ( 'nil/0' @ $real ) ) ) ) ) ) ) ) ) ).
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