TPTP Problem File: GEO439^1.p
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% File : GEO439^1 : TPTP v9.1.0. Released v7.0.0.
% Domain : Geometry (Geometric figures and equations)
% Problem : The University of Tokyo, 2014, Science Course, Problem 6
% Version : [Mat16] axioms : Especial.
% English : Let O be the origin of the coordinate plane. The point P moves
% on the segment y = sqrt(3) x (0 =< x =< 2) and the point Q moves
% on the segment y = -sqrt(3)x (-2 =< x =< 0) so that the sum of
% the lengths of the segments OP and OQ is 6. Let D be the region
% that the segment PQ pass through. (1) Let s be a real number
% satisfying 0 =< s =< 2. Find the range of t such that the point
% (s, t) is in the region D. (2) Draw the region D.
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : Univ-Tokyo-2014-Ri-6.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3486 ( 708 unt;1200 typ; 0 def)
% Number of atoms : 8516 (2213 equ; 0 cnn)
% Maximal formula atoms : 41 ( 3 avg)
% Number of connectives : 39668 ( 104 ~; 233 |;1183 &;36022 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4482 ( 377 atm;1206 fun; 962 num;1937 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1221 (1178 usr; 75 con; 0-9 aty)
% Number of variables : 8065 ( 409 ^;7085 !; 435 ?;8065 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: RCF; Author: Hidenao Iwane; Generated: 2014-04-01
% : Answer
% ^ [V_t_dot_0: $real] :
% ( ( ( $lesseq @ ( $product @ ( '^/2' @ 3.0 @ ( $quotient @ 1.0 @ 2.0 ) ) @ 's/0' ) @ V_t_dot_0 )
% & ( $lesseq @ V_t_dot_0 @ ( $product @ ( $quotient @ ( '^/2' @ 3.0 @ ( $quotient @ 1.0 @ 2.0 ) ) @ 3.0 ) @ ( $sum @ 's/0' @ 4.0 ) ) )
% & ( $lesseq @ 1.0 @ 's/0' )
% & ( $lesseq @ 's/0' @ 2.0 ) )
% | ( ( $lesseq @ ( $product @ ( $quotient @ ( '^/2' @ 3.0 @ ( $quotient @ 1.0 @ 2.0 ) ) @ 3.0 ) @ ( $difference @ 4.0 @ 's/0' ) ) @ V_t_dot_0 )
% & ( $lesseq @ V_t_dot_0 @ ( $product @ ( $quotient @ ( '^/2' @ 3.0 @ ( $quotient @ 1.0 @ 2.0 ) ) @ 6.0 ) @ ( $sum @ ( '^/2' @ 's/0' @ 2.0 ) @ 9.0 ) ) )
% & ( $lesseq @ 0.0 @ 's/0' )
% & ( $lesseq @ 's/0' @ 1.0 ) ) ) )
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include('Axioms/MAT001^0.ax').
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thf('s/0_type',type,
's/0': $real ).
thf(p1_qustion,conjecture,
( 'find/1' @ $real
@ ^ [V_t: $real] :
? [V_P: '2d.Point',V_Q: '2d.Point',V_O: '2d.Point',V_D: '2d.Shape',V_Pf: '2d.Shape',V_Qf: '2d.Shape'] :
( ( V_D
= ( '2d.shape-of-cpfun/1'
@ ^ [V_d: '2d.Point'] :
( ( V_O = '2d.origin/0' )
& ( V_Pf
= ( '2d.intersection/2' @ ( '2d.graph-of/1' @ ( 'poly-fun/1' @ ( 'cons/2' @ $real @ 0.0 @ ( 'cons/2' @ $real @ ( 'sqrt/1' @ 3.0 ) @ ( 'nil/0' @ $real ) ) ) ) )
@ ( '2d.shape-of-cpfun/1'
@ ^ [V_q_dot_0: '2d.Point'] :
( ( $lesseq @ 0.0 @ ( '2d.x-coord/1' @ V_q_dot_0 ) )
& ( $lesseq @ ( '2d.x-coord/1' @ V_q_dot_0 ) @ 2.0 ) ) ) ) )
& ( '2d.on/2' @ V_P @ V_Pf )
& ( V_Qf
= ( '2d.intersection/2' @ ( '2d.graph-of/1' @ ( 'poly-fun/1' @ ( 'cons/2' @ $real @ 0.0 @ ( 'cons/2' @ $real @ ( $uminus @ ( 'sqrt/1' @ 3.0 ) ) @ ( 'nil/0' @ $real ) ) ) ) )
@ ( '2d.shape-of-cpfun/1'
@ ^ [V_q: '2d.Point'] :
( ( $lesseq @ ( $uminus @ 2.0 ) @ ( '2d.x-coord/1' @ V_q ) )
& ( $lesseq @ ( '2d.x-coord/1' @ V_q ) @ 0.0 ) ) ) ) )
& ( '2d.on/2' @ V_Q @ V_Qf )
& ( ( $sum @ ( '2d.distance/2' @ V_O @ V_P ) @ ( '2d.distance/2' @ V_O @ V_Q ) )
= 6.0 )
& ( '2d.on/2' @ V_d @ ( '2d.seg/2' @ V_P @ V_Q ) ) ) ) )
& ( $lesseq @ 0.0 @ 's/0' )
& ( $lesseq @ 's/0' @ 2.0 )
& ( '2d.on/2' @ ( '2d.point/2' @ 's/0' @ V_t ) @ V_D ) ) ) ).
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