TPTP Problem File: GEO368^1.p
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% File : GEO368^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Geometry (Geometric quantities)
% Problem : Chart System Math I+A Yellow Book, Problem 07CY1E217
% 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-1A-Yellow-07CY1E217.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3486 ( 727 unt;1200 typ; 0 def)
% Number of atoms : 7686 (2217 equ; 0 cnn)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 39727 ( 104 ~; 233 |;1192 &;36072 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 8 avg)
% Number arithmetic : 4469 ( 373 atm;1203 fun; 956 num;1937 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1222 (1179 usr; 76 con; 0-9 aty)
% Number of variables : 8069 ( 407 ^;7085 !; 441 ?;8069 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: RCF; Level: 4; Author: Jumma Kudo;
% Generated: 2014-12-25
% : Answer
% ^ [V_St_dot_0: $real] :
% ( V_St_dot_0
% = ( $difference @ ( $difference @ ( $product @ 3.0 @ ( $product @ ( 'sqrt/1' @ 3.0 ) @ 't/0' ) ) @ ( $product @ ( 'sqrt/1' @ 3.0 ) @ ( '^/2' @ 't/0' @ 2.0 ) ) ) @ ( $product @ 3.0 @ ( $quotient @ ( 'sqrt/1' @ 3.0 ) @ 2.0 ) ) ) ) )
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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' @ $real
@ ^ [V_St: $real] :
? [V_O: '3d.Point',V_X: '3d.Point',V_Y: '3d.Point',V_Z: '3d.Point',V_A: '3d.Point',V_P: '3d.Point',V_B: '3d.Point',V_Q: '3d.Point',V_C: '3d.Point',V_R: '3d.Point',V_F: '3d.Shape',V_G: '3d.Shape'] :
( ( '3d.perpendicular/2' @ ( '3d.line/2' @ V_O @ V_X ) @ ( '3d.line/2' @ V_O @ V_Y ) )
& ( '3d.perpendicular/2' @ ( '3d.line/2' @ V_O @ V_X ) @ ( '3d.line/2' @ V_O @ V_Z ) )
& ( '3d.perpendicular/2' @ ( '3d.line/2' @ V_O @ V_Y ) @ ( '3d.line/2' @ V_O @ V_Z ) )
& ( '3d.on/2' @ V_A @ ( '3d.half-line/2' @ V_O @ V_X ) )
& ( '3d.on/2' @ V_P @ ( '3d.half-line/2' @ V_O @ V_X ) )
& ( '3d.on/2' @ V_B @ ( '3d.half-line/2' @ V_O @ V_Y ) )
& ( '3d.on/2' @ V_Q @ ( '3d.half-line/2' @ V_O @ V_Y ) )
& ( '3d.on/2' @ V_C @ ( '3d.half-line/2' @ V_O @ V_Z ) )
& ( '3d.on/2' @ V_R @ ( '3d.half-line/2' @ V_O @ V_Z ) )
& ( ( '3d.length-of/1' @ ( '3d.seg/2' @ V_O @ V_A ) )
= 1.0 )
& ( ( '3d.length-of/1' @ ( '3d.seg/2' @ V_O @ V_B ) )
= 1.0 )
& ( ( '3d.length-of/1' @ ( '3d.seg/2' @ V_O @ V_C ) )
= 1.0 )
& ( $lesseq @ 1.0 @ 't/0' )
& ( $lesseq @ 't/0' @ 2.0 )
& ( ( '3d.length-of/1' @ ( '3d.seg/2' @ V_O @ V_P ) )
= 't/0' )
& ( ( '3d.length-of/1' @ ( '3d.seg/2' @ V_O @ V_Q ) )
= 't/0' )
& ( ( '3d.length-of/1' @ ( '3d.seg/2' @ V_O @ V_R ) )
= 't/0' )
& ( V_F
= ( '3d.cube/8' @ V_O @ V_A @ V_B @ ( '3d.vec->point/1' @ ( '3d.v+/2' @ ( '3d.vec/2' @ '3d.origin/0' @ V_A ) @ ( '3d.vec/2' @ '3d.origin/0' @ V_B ) ) ) @ V_C @ ( '3d.vec->point/1' @ ( '3d.v+/2' @ ( '3d.vec/2' @ '3d.origin/0' @ V_A ) @ ( '3d.vec/2' @ '3d.origin/0' @ V_C ) ) ) @ ( '3d.vec->point/1' @ ( '3d.v+/2' @ ( '3d.vec/2' @ '3d.origin/0' @ V_C ) @ ( '3d.vec/2' @ '3d.origin/0' @ V_B ) ) ) @ ( '3d.vec->point/1' @ ( '3d.v+/2' @ ( '3d.v+/2' @ ( '3d.vec/2' @ '3d.origin/0' @ V_A ) @ ( '3d.vec/2' @ '3d.origin/0' @ V_B ) ) @ ( '3d.vec/2' @ '3d.origin/0' @ V_C ) ) ) ) )
& ( V_G
= ( '3d.triangle/3' @ V_P @ V_Q @ V_R ) )
& ( V_St
= ( '3d.area-of/1'
@ ( '3d.shape-of-cpfun/1'
@ ^ [V_T: '3d.Point'] :
( ( '3d.on/2' @ V_T @ V_G )
& ( '3d.on/2' @ V_T @ V_F ) ) ) ) ) ) ) ).
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