TPTP Problem File: LIN003^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : LIN003^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Linear Algebra (Vectors)
% Problem : Chart System Math II+B Yellow Book, Problem 08CYBE053
% Version : [Mat16] axioms : Especial.
% English :
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : Chart-2B-Yellow-08CYBE053.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3485 ( 727 unt;1199 typ; 0 def)
% Number of atoms : 6581 (2214 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 39629 ( 104 ~; 233 |;1177 &;35989 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4486 ( 371 atm;1208 fun; 957 num;1950 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2416 (2416 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1210 (1167 usr; 64 con; 0-9 aty)
% Number of variables : 8072 ( 415 ^;7085 !; 436 ?;8072 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: RCF; Level: 4; Author: Munehiro Kobayashi;
% Generated: 2014-12-29
% : Answer
% ^ [V_max_dot_0: $real] :
% ( V_max_dot_0
% = ( 'sqrt/1' @ 2.0 ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p1_qustion,conjecture,
( 'find/1' @ $real
@ ^ [V_max: $real] :
? [V_C1: $real > $real > $o,V_C2: $real > $real > $o] :
( ( V_C1
= ( ^ [V_x_dot_1: $real,V_y_dot_1: $real] :
( 1.0
= ( $sum @ ( '^/2' @ V_x_dot_1 @ 2.0 ) @ ( '^/2' @ V_y_dot_1 @ 2.0 ) ) ) ) )
& ( V_C2
= ( ^ [V_a_dot_1: $real,V_b_dot_1: $real] :
( 2.0
= ( $sum @ ( '^/2' @ V_a_dot_1 @ 2.0 ) @ ( '^/2' @ V_b_dot_1 @ 2.0 ) ) ) ) )
& ( 'maximum/2'
@ ( 'set-by-def/1' @ $real
@ ^ [V_v: $real] :
? [V_x: $real,V_y: $real,V_a: $real,V_b: $real,V_f: $real > $real > $real > $real > $real] :
( ( V_f
= ( ^ [V_x_dot_0: $real,V_y_dot_0: $real,V_a_dot_0: $real,V_b_dot_0: $real] : ( $sum @ ( $product @ V_a_dot_0 @ V_x_dot_0 ) @ ( $product @ V_b_dot_0 @ V_y_dot_0 ) ) ) )
& ( V_C1 @ V_x @ V_y )
& ( V_C2 @ V_a @ V_b )
& ( V_v
= ( V_f @ V_x @ V_y @ V_a @ V_b ) ) ) )
@ V_max ) ) ) ).
%------------------------------------------------------------------------------