TPTP Problem File: GEO395^1.p
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% File : GEO395^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Geometry (Triangles)
% Problem : International Mathematical Olympiad, 1968, Problem 1
% Version : [Mat16] axioms : Especial.
% English : Prove that there is one and only one triangle whose side lengths
% are consecutive integers, and one of whose angles is twice as
% large as another.
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : IMO-1968-1.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3485 ( 728 unt;1199 typ; 0 def)
% Number of atoms : 6816 (2229 equ; 0 cnn)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 39696 ( 104 ~; 241 |;1185 &;36039 @)
% (1095 <=>;1032 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4481 ( 371 atm;1215 fun; 957 num;1938 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1211 (1168 usr; 65 con; 0-9 aty)
% Number of variables : 8067 ( 405 ^;7089 !; 437 ?;8067 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: RCF+PA; Score: 6; Author: Jumma Kudo;
% Generated: 2014-11-28
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include('Axioms/MAT001^0.ax').
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thf(p,conjecture,
? [V_a: $int,V_A: '2d.Point',V_B: '2d.Point',V_C: '2d.Point'] :
( ( ( '2d.length-of/1' @ ( '2d.seg/2' @ V_A @ V_B ) )
= ( $to_real @ V_a ) )
& ( ( '2d.length-of/1' @ ( '2d.seg/2' @ V_B @ V_C ) )
= ( $sum @ ( $to_real @ V_a ) @ 1.0 ) )
& ( ( '2d.length-of/1' @ ( '2d.seg/2' @ V_A @ V_C ) )
= ( $sum @ ( $to_real @ V_a ) @ 2.0 ) )
& ( '2d.is-triangle/3' @ V_A @ V_B @ V_C )
& ? [V_Ang1_dot_0: '2d.Angle',V_Ang2_dot_0: '2d.Angle'] :
( ( ( V_Ang1_dot_0
= ( '2d.angle/3' @ V_A @ V_B @ V_C ) )
| ( V_Ang1_dot_0
= ( '2d.angle/3' @ V_B @ V_C @ V_A ) )
| ( V_Ang1_dot_0
= ( '2d.angle/3' @ V_C @ V_A @ V_B ) ) )
& ( ( V_Ang2_dot_0
= ( '2d.angle/3' @ V_A @ V_B @ V_C ) )
| ( V_Ang2_dot_0
= ( '2d.angle/3' @ V_B @ V_C @ V_A ) )
| ( V_Ang2_dot_0
= ( '2d.angle/3' @ V_C @ V_A @ V_B ) ) )
& ( ( '2d.rad-of-angle/1' @ V_Ang1_dot_0 )
= ( $product @ 2.0 @ ( '2d.rad-of-angle/1' @ V_Ang2_dot_0 ) ) ) )
& ! [V_b: $int,V_A1: '2d.Point',V_B1: '2d.Point',V_C1: '2d.Point'] :
( ( ( ( '2d.length-of/1' @ ( '2d.seg/2' @ V_A1 @ V_B1 ) )
= ( $to_real @ V_b ) )
& ( ( '2d.length-of/1' @ ( '2d.seg/2' @ V_B1 @ V_C1 ) )
= ( $sum @ ( $to_real @ V_b ) @ 1.0 ) )
& ( ( '2d.length-of/1' @ ( '2d.seg/2' @ V_A1 @ V_C1 ) )
= ( $sum @ ( $to_real @ V_b ) @ 2.0 ) )
& ( '2d.is-triangle/3' @ V_A1 @ V_B1 @ V_C1 )
& ? [V_Ang1: '2d.Angle',V_Ang2: '2d.Angle'] :
( ( ( V_Ang1
= ( '2d.angle/3' @ V_A1 @ V_B1 @ V_C1 ) )
| ( V_Ang1
= ( '2d.angle/3' @ V_B1 @ V_C1 @ V_A1 ) )
| ( V_Ang1
= ( '2d.angle/3' @ V_C1 @ V_A1 @ V_B1 ) ) )
& ( ( V_Ang2
= ( '2d.angle/3' @ V_A1 @ V_B1 @ V_C1 ) )
| ( V_Ang2
= ( '2d.angle/3' @ V_B1 @ V_C1 @ V_A1 ) )
| ( V_Ang2
= ( '2d.angle/3' @ V_C1 @ V_A1 @ V_B1 ) ) )
& ( ( '2d.rad-of-angle/1' @ V_Ang1 )
= ( $product @ 2.0 @ ( '2d.rad-of-angle/1' @ V_Ang2 ) ) ) ) )
=> ( V_b = V_a ) ) ) ).
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