TPTP Problem File: GEO380^1.p
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% File : GEO380^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Geometry (Hexahedrons)
% Problem : International Mathematical Olympiad, 1960, Problem 5
% Version : [Mat16] axioms : Especial.
% English : Consider the cube ABCDA'B'C'D'(with face ABCD directly above
% face A'B'C'D'). (a) Find the locus of the midpoints of segments
% XY, where X is any point of AC and Y is any point of B'D'. (b)
% Find the locus of points Z which lie on the segments XY of part
% (a) with ZY = 2XZ.
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : IMO-1960-5.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3486 ( 726 unt;1200 typ; 0 def)
% Number of atoms : 6682 (2218 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 39642 ( 104 ~; 233 |;1183 &;35996 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4475 ( 372 atm;1203 fun; 964 num;1936 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1213 (1170 usr; 67 con; 0-9 aty)
% Number of variables : 8067 ( 407 ^;7085 !; 439 ?;8067 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: RCF; Score: 7; Author: Jumma Kudo;
% Generated: 2014-12-04
% : Answer
% ^ [V_M_dot_0: '3d.Shape'] :
% ( ( $less @ 0.0 @ 'a/0' )
% & ( V_M_dot_0
% = ( '3d.set-of-cfun/1'
% @ ^ [V_x: $real,V_y: $real,V_z: $real] :
% ( ( V_z
% = ( $quotient @ 'a/0' @ 2.0 ) )
% & ( $lesseq @ ( $product @ ( $quotient @ 1.0 @ 2.0 ) @ 'a/0' ) @ ( $sum @ V_x @ V_y ) )
% & ( $lesseq @ ( $sum @ V_x @ V_y ) @ ( $product @ ( $quotient @ 3.0 @ 2.0 ) @ 'a/0' ) )
% & ( $lesseq @ ( $product @ ( $uminus @ ( $quotient @ 1.0 @ 2.0 ) ) @ 'a/0' ) @ ( $difference @ V_x @ V_y ) )
% & ( $lesseq @ ( $difference @ V_x @ V_y ) @ ( $product @ ( $quotient @ 1.0 @ 2.0 ) @ 'a/0' ) ) ) ) ) ) )
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include('Axioms/MAT001^0.ax').
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thf('a/0_type',type,
'a/0': $real ).
thf(p1_qustion,conjecture,
( 'find/1' @ '3d.Shape'
@ ^ [V_M: '3d.Shape'] :
( ( $less @ 0.0 @ 'a/0' )
& ? [V_A1: '3d.Point',V_B1: '3d.Point',V_C1: '3d.Point',V_D1: '3d.Point',V_A2: '3d.Point',V_B2: '3d.Point',V_C2: '3d.Point',V_D2: '3d.Point'] :
( ( V_A1
= ( '3d.point/3' @ 'a/0' @ 0.0 @ 0.0 ) )
& ( V_B1
= ( '3d.point/3' @ 'a/0' @ 'a/0' @ 0.0 ) )
& ( V_C1
= ( '3d.point/3' @ 0.0 @ 'a/0' @ 0.0 ) )
& ( V_D1
= ( '3d.point/3' @ 0.0 @ 0.0 @ 0.0 ) )
& ( V_A2
= ( '3d.point/3' @ 'a/0' @ 0.0 @ 'a/0' ) )
& ( V_B2
= ( '3d.point/3' @ 'a/0' @ 'a/0' @ 'a/0' ) )
& ( V_C2
= ( '3d.point/3' @ 0.0 @ 'a/0' @ 'a/0' ) )
& ( V_D2
= ( '3d.point/3' @ 0.0 @ 0.0 @ 'a/0' ) )
& ( V_M
= ( '3d.shape-of-cpfun/1'
@ ^ [V_p: '3d.Point'] :
? [V_X: '3d.Point',V_Y: '3d.Point'] :
( ( '3d.on/2' @ V_X @ ( '3d.seg/2' @ V_A1 @ V_C1 ) )
& ( '3d.on/2' @ V_Y @ ( '3d.seg/2' @ V_B2 @ V_D2 ) )
& ( V_p
= ( '3d.midpoint-of/2' @ V_X @ V_Y ) ) ) ) ) ) ) ) ).
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