TPTP Problem File: LIN014^1.p
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% File : LIN014^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Linear Algebra (Vectors)
% Problem : The University of Tokyo, 1985, Humanities Course, Problem 4
% Version : [Mat16] axioms : Especial.
% English : Let t be a positive number. In the x y z space, let P be the
% point (t, t, 0), let Q be the point symmetric to P about the
% plane containing the x axis and the point (t, t, 1), and let R
% be the point symmetric to P about the plane containing the y
% axis and the point (t, t, 1). Let O be the origin. (1) Find the
% coordinates of Q and R. (2) Find the volume of the tetrahedron
% whose vertices are the points O, P, Q, and R.
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : Univ-Tokyo-1985-Bun-4.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3486 ( 710 unt;1200 typ; 0 def)
% Number of atoms : 7927 (2212 equ; 0 cnn)
% Maximal formula atoms : 40 ( 3 avg)
% Number of connectives : 39660 ( 104 ~; 233 |;1184 &;36013 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4472 ( 372 atm;1203 fun; 955 num;1942 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1218 (1175 usr; 72 con; 0-9 aty)
% Number of variables : 8067 ( 406 ^;7085 !; 440 ?;8067 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: RCF; Author: Yiyang Zhan; Generated: 2014-03-17
% : Answer
% ^ [V_QR_dot_0: ( ''ListOf'' @ $real )] :
% ( ( $less @ 0.0 @ 't/0' )
% & ( V_QR_dot_0
% = ( 'cons/2' @ $real @ 't/0' @ ( 'cons/2' @ $real @ ( $quotient @ ( $difference @ ( '^/2' @ 't/0' @ 3.0 ) @ 't/0' ) @ ( $sum @ ( '^/2' @ 't/0' @ 2.0 ) @ 1.0 ) ) @ ( 'cons/2' @ $real @ ( $quotient @ ( $product @ 2.0 @ ( '^/2' @ 't/0' @ 2.0 ) ) @ ( $sum @ ( '^/2' @ 't/0' @ 2.0 ) @ 1.0 ) ) @ ( 'cons/2' @ $real @ ( $quotient @ ( $difference @ ( '^/2' @ 't/0' @ 3.0 ) @ 't/0' ) @ ( $sum @ ( '^/2' @ 't/0' @ 2.0 ) @ 1.0 ) ) @ ( 'cons/2' @ $real @ 't/0' @ ( 'cons/2' @ $real @ ( $quotient @ ( $product @ 2.0 @ ( '^/2' @ 't/0' @ 2.0 ) ) @ ( $sum @ ( '^/2' @ 't/0' @ 2.0 ) @ 1.0 ) ) @ ( 'nil/0' @ $real ) ) ) ) ) ) ) ) ) )
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include('Axioms/MAT001^0.ax').
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thf('t/0_type',type,
't/0': $real ).
thf(p1_qustion,conjecture,
( 'find/1' @ ( 'ListOf' @ $real )
@ ^ [V_QR: 'ListOf' @ $real] :
? [V_P: '3d.Point',V_H: '3d.Shape',V_K: '3d.Shape',V_Q: '3d.Point',V_R: '3d.Point',V_Qx: $real,V_Qy: $real,V_Qz: $real,V_Rx: $real,V_Ry: $real,V_Rz: $real] :
( ( $less @ 0.0 @ 't/0' )
& ( V_P
= ( '3d.point/3' @ 't/0' @ 't/0' @ 0.0 ) )
& ( '3d.plane-type/1' @ V_H )
& ( '3d.on/2' @ ( '3d.point/3' @ 't/0' @ 't/0' @ 1.0 ) @ V_H )
& ( '3d.inside-of/2' @ '3d.x-axis/0' @ V_H )
& ( '3d.plane-symmetry/3' @ V_P @ V_Q @ V_H )
& ( '3d.plane-type/1' @ V_K )
& ( '3d.on/2' @ ( '3d.point/3' @ 't/0' @ 't/0' @ 1.0 ) @ V_K )
& ( '3d.inside-of/2' @ '3d.y-axis/0' @ V_K )
& ( '3d.plane-symmetry/3' @ V_P @ V_R @ V_K )
& ( V_Q
= ( '3d.point/3' @ V_Qx @ V_Qy @ V_Qz ) )
& ( V_R
= ( '3d.point/3' @ V_Rx @ V_Ry @ V_Rz ) )
& ( V_QR
= ( 'cons/2' @ $real @ V_Qx @ ( 'cons/2' @ $real @ V_Qy @ ( 'cons/2' @ $real @ V_Qz @ ( 'cons/2' @ $real @ V_Rx @ ( 'cons/2' @ $real @ V_Ry @ ( 'cons/2' @ $real @ V_Rz @ ( 'nil/0' @ $real ) ) ) ) ) ) ) ) ) ) ).
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