TPTP Problem File: RAL025^1.p
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% File : RAL025^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Real Algebra (Simultaneous equations)
% Problem : International Mathematical Olympiad, 1966, Problem 5
% Version : [Mat16] axioms : Especial.
% English : Solve the system of equations
% |a_1 - a_2| x_2 + |a_1 - a_3| x_3 + |a_1 - a_4| x_4 = 1
% |a_2 - a_1| x_1 + |a_2 - a_3| x_3 + |a_2 - a_4| x_4 = 1
% |a_3 - a_1| x_1 + |a_3 - a_2| x_2 + |a_3 - a_4| x_4 = 1
% |a_4 - a_1| x_1 + |a_4 - a_2| x_2 + |a_4 - a_3| x_3 = 1
% where a_1, a_2, a_3, a_4 are four different 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-1966-5.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3489 ( 711 unt;1203 typ; 0 def)
% Number of atoms : 7896 (2213 equ; 0 cnn)
% Maximal formula atoms : 40 ( 3 avg)
% Number of connectives : 39705 ( 104 ~; 233 |;1177 &;36065 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4501 ( 371 atm;1235 fun; 955 num;1940 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1216 (1173 usr; 70 con; 0-9 aty)
% Number of variables : 8060 ( 406 ^;7085 !; 433 ?;8060 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: RCF; Score: 7; Author: Jumma Kudo;
% Generated: 2014-12-03
% : Answer
% ^ [V_xs_dot_0: ( 'ListOf' @ $real )] :
% ( ( 'pairwise-distinct/1' @ $real @ ( 'cons/2' @ $real @ 'A1/0' @ ( 'cons/2' @ $real @ 'A2/0' @ ( 'cons/2' @ $real @ 'A3/0' @ ( 'cons/2' @ $real @ 'A4/0' @ ( 'nil/0' @ $real ) ) ) ) ) )
% & ( V_xs_dot_0
% = ( 'cons/2' @ $real @ ( $quotient @ 1.0 @ ( $difference @ 'A1/0' @ 'A4/0' ) ) @ ( 'cons/2' @ $real @ 0.0 @ ( 'cons/2' @ $real @ 0.0 @ ( 'cons/2' @ $real @ ( $quotient @ 1.0 @ ( $difference @ 'A1/0' @ 'A4/0' ) ) @ ( 'nil/0' @ $real ) ) ) ) ) ) ) )
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include('Axioms/MAT001^0.ax').
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thf('A1/0_type',type,
'A1/0': $real ).
thf('A2/0_type',type,
'A2/0': $real ).
thf('A3/0_type',type,
'A3/0': $real ).
thf('A4/0_type',type,
'A4/0': $real ).
thf(p_qustion,conjecture,
( 'find/1' @ ( 'ListOf' @ $real )
@ ^ [V_xs: 'ListOf' @ $real] :
( ( 'pairwise-distinct/1' @ $real @ ( 'cons/2' @ $real @ 'A1/0' @ ( 'cons/2' @ $real @ 'A2/0' @ ( 'cons/2' @ $real @ 'A3/0' @ ( 'cons/2' @ $real @ 'A4/0' @ ( 'nil/0' @ $real ) ) ) ) ) )
& ? [V_X1: $real,V_X2: $real,V_X3: $real,V_X4: $real] :
( ( V_xs
= ( 'cons/2' @ $real @ V_X1 @ ( 'cons/2' @ $real @ V_X2 @ ( 'cons/2' @ $real @ V_X3 @ ( 'cons/2' @ $real @ V_X4 @ ( 'nil/0' @ $real ) ) ) ) ) )
& ( ( $sum @ ( $product @ ( 'abs/1' @ ( $difference @ 'A1/0' @ 'A2/0' ) ) @ V_X2 ) @ ( $sum @ ( $product @ ( 'abs/1' @ ( $difference @ 'A1/0' @ 'A3/0' ) ) @ V_X3 ) @ ( $product @ ( 'abs/1' @ ( $difference @ 'A1/0' @ 'A4/0' ) ) @ V_X4 ) ) )
= 1.0 )
& ( ( $sum @ ( $product @ ( 'abs/1' @ ( $difference @ 'A2/0' @ 'A1/0' ) ) @ V_X1 ) @ ( $sum @ ( $product @ ( 'abs/1' @ ( $difference @ 'A2/0' @ 'A3/0' ) ) @ V_X3 ) @ ( $product @ ( 'abs/1' @ ( $difference @ 'A2/0' @ 'A4/0' ) ) @ V_X4 ) ) )
= 1.0 )
& ( ( $sum @ ( $product @ ( 'abs/1' @ ( $difference @ 'A3/0' @ 'A2/0' ) ) @ V_X2 ) @ ( $sum @ ( $product @ ( 'abs/1' @ ( $difference @ 'A3/0' @ 'A1/0' ) ) @ V_X1 ) @ ( $product @ ( 'abs/1' @ ( $difference @ 'A3/0' @ 'A4/0' ) ) @ V_X4 ) ) )
= 1.0 )
& ( ( $sum @ ( $product @ ( 'abs/1' @ ( $difference @ 'A4/0' @ 'A2/0' ) ) @ V_X2 ) @ ( $sum @ ( $product @ ( 'abs/1' @ ( $difference @ 'A4/0' @ 'A3/0' ) ) @ V_X3 ) @ ( $product @ ( 'abs/1' @ ( $difference @ 'A4/0' @ 'A1/0' ) ) @ V_X1 ) ) )
= 1.0 ) ) ) ) ).
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