TPTP Problem File: RAL023^1.p
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% File : RAL023^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Real Algebra (Simultaneous equations)
% Problem : International Mathematical Olympiad, 1963, Problem 4
% Version : [Mat16] axioms : Especial.
% English : Find all solutions x_1, x_2, x_3, x_4, x_5 of the system
% x_5 + x_2 = y x_1; x_1 + x_3 = y x_2; x_2 + x_4 = y x_3;
% x_3 + x_5 = y x_4; x_4 + x_1 = y x_5, where y is a parameter.
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : IMO-1963-4.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3486 ( 711 unt;1200 typ; 0 def)
% Number of atoms : 7867 (2214 equ; 0 cnn)
% Maximal formula atoms : 40 ( 3 avg)
% Number of connectives : 39637 ( 104 ~; 233 |;1177 &;35997 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4476 ( 371 atm;1213 fun; 951 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: 6; Author: Jumma Kudo;
% Generated: 2014-12-16
% : Answer
% ^ [V_x1x2x3x4x5_dot_0: ( 'ListOf' @ $real )] :
% ( ( ( ( $difference @ ( $sum @ ( '^/2' @ 'y/0' @ 2.0 ) @ 'y/0' ) @ 1.0 )
% = 0.0 )
% & ? [V_s_dot_0: $real,V_t: $real] :
% ( V_x1x2x3x4x5_dot_0
% = ( 'cons/2' @ $real @ V_s_dot_0 @ ( 'cons/2' @ $real @ V_t @ ( 'cons/2' @ $real @ ( $sum @ ( $uminus @ V_s_dot_0 ) @ ( $product @ 'y/0' @ V_t ) ) @ ( 'cons/2' @ $real @ ( $uminus @ ( $sum @ ( $product @ ( $difference @ ( '^/2' @ 'y/0' @ 2.0 ) @ 1.0 ) @ V_s_dot_0 ) @ ( $product @ 'y/0' @ V_t ) ) ) @ ( 'cons/2' @ $real @ ( $difference @ ( $product @ 'y/0' @ V_s_dot_0 ) @ V_t ) @ ( 'nil/0' @ $real ) ) ) ) ) ) ) )
% | ( ( 'y/0' = 2.0 )
% & ? [V_s: $real] :
% ( V_x1x2x3x4x5_dot_0
% = ( 'cons/2' @ $real @ V_s @ ( 'cons/2' @ $real @ V_s @ ( 'cons/2' @ $real @ V_s @ ( 'cons/2' @ $real @ V_s @ ( 'cons/2' @ $real @ V_s @ ( 'nil/0' @ $real ) ) ) ) ) ) ) )
% | ( V_x1x2x3x4x5_dot_0
% = ( 'cons/2' @ $real @ 0.0 @ ( 'cons/2' @ $real @ 0.0 @ ( 'cons/2' @ $real @ 0.0 @ ( 'cons/2' @ $real @ 0.0 @ ( 'cons/2' @ $real @ 0.0 @ ( 'nil/0' @ $real ) ) ) ) ) ) ) ) )
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include('Axioms/MAT001^0.ax').
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thf('y/0_type',type,
'y/0': $real ).
thf(p_qustion,conjecture,
( 'find/1' @ ( 'ListOf' @ $real )
@ ^ [V_x1x2x3x4x5: 'ListOf' @ $real] :
? [V_x1: $real,V_x2: $real,V_x3: $real,V_x4: $real,V_x5: $real] :
( ( V_x1x2x3x4x5
= ( '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 ) ) ) ) ) ) )
& ( ( $sum @ V_x2 @ V_x5 )
= ( $product @ 'y/0' @ V_x1 ) )
& ( ( $sum @ V_x1 @ V_x3 )
= ( $product @ 'y/0' @ V_x2 ) )
& ( ( $sum @ V_x2 @ V_x4 )
= ( $product @ 'y/0' @ V_x3 ) )
& ( ( $sum @ V_x3 @ V_x5 )
= ( $product @ 'y/0' @ V_x4 ) )
& ( ( $sum @ V_x4 @ V_x1 )
= ( $product @ 'y/0' @ V_x5 ) ) ) ) ).
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