TPTP Problem File: GEO383^1.p
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% File : GEO383^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Geometry (Trigonometric functions)
% Problem : International Mathematical Olympiad, 1961, Problem 3
% Version : [Mat16] axioms : Especial.
% English : Solve the equation cos^n x - sin^n x = 1, where n is a natural
% number.
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : IMO-1961-3.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3486 ( 728 unt;1200 typ; 0 def)
% Number of atoms : 6694 (2209 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 39608 ( 104 ~; 233 |;1173 &;35972 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4469 ( 372 atm;1207 fun; 953 num;1937 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 : 8056 ( 406 ^;7085 !; 429 ?;8056 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: PA+trans; Score: 7; Author: Yiyang Zhan;
% Generated: 2015-01-29
% : Answer
% ^ [V_x_dot_0: $real] :
% ( ( ( 'int.is-odd-number/1' @ 'n/0' )
% & ? [V_m_dot_0: $int] :
% ( ( V_x_dot_0
% = ( $product @ 2.0 @ ( $product @ ( $to_real @ V_m_dot_0 ) @ 'Pi/0' ) ) )
% | ( V_x_dot_0
% = ( $sum @ ( $product @ 2.0 @ ( $product @ ( $to_real @ V_m_dot_0 ) @ 'Pi/0' ) ) @ ( $quotient @ ( $product @ 3.0 @ 'Pi/0' ) @ 2.0 ) ) ) ) )
% | ( ( 'int.is-even-number/1' @ 'n/0' )
% & ? [V_m: $int] :
% ( V_x_dot_0
% = ( $product @ ( $to_real @ V_m ) @ 'Pi/0' ) ) ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf('n/0_type',type,
'n/0': $int ).
thf(p_qustion,conjecture,
( 'find/1' @ $real
@ ^ [V_x: $real] :
( ( ( $difference @ ( '^/2' @ ( 'cos/1' @ V_x ) @ ( $to_real @ 'n/0' ) ) @ ( '^/2' @ ( 'sin/1' @ V_x ) @ ( $to_real @ 'n/0' ) ) )
= 1.0 )
& ( $greatereq @ ( $to_real @ 'n/0' ) @ 1.0 ) ) ) ).
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