TPTP Problem File: RAL026^1.p
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% File : RAL026^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Real Algebra (Number sequences)
% Problem : International Mathematical Olympiad, 1967, Problem 6
% Version : [Mat16] axioms : Especial.
% English : In a sports contest, there were m medals awarded on n successive
% days (n > 1). On the first day, one medal and 1/7 of the
% remaining m - 1 medals were awarded. On the second day, two
% medals and 1/7 of the now remaining medals were awarded; and so
% on. On the n-th and last day, the remaining n medals were awarded.
% How many days did the contest last, and how many medals were
% awarded altogether?
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : IMO-1967-6.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3487 ( 711 unt;1201 typ; 0 def)
% Number of atoms : 7891 (2212 equ; 0 cnn)
% Maximal formula atoms : 40 ( 3 avg)
% Number of connectives : 39636 ( 104 ~; 233 |;1177 &;35995 @)
% (1095 <=>;1032 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4471 ( 373 atm;1206 fun; 955 num;1937 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1217 (1174 usr; 71 con; 0-9 aty)
% Number of variables : 8058 ( 406 ^;7086 !; 430 ?;8058 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: PA(comb); Score: 8; Author: Takuya Matsuzaki;
% Generated: 2015-01-24
% : Answer
% ^ [V_nm_dot_0: ( 'ListOf' @ $int )] :
% ( V_nm_dot_0
% = ( 'cons/2' @ $int @ 6 @ ( 'cons/2' @ $int @ 36 @ ( 'nil/0' @ $int ) ) ) ) )
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include('Axioms/MAT001^0.ax').
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thf('m/0_type',type,
'm/0': $int ).
thf('n/0_type',type,
'n/0': $int ).
thf(p_qustion,conjecture,
( 'find/1' @ ( 'ListOf' @ $int )
@ ^ [V_nm: 'ListOf' @ $int] :
? [V_medals: 'ListOf' @ $int] :
( ( 'n/0'
= ( 'list-len/1' @ $int @ V_medals ) )
& ! [V_k: $int] :
( ( ( $lesseq @ 1 @ V_k )
& ( $lesseq @ V_k @ 'n/0' ) )
=> ( ( ( 'nth/2' @ $int @ ( $difference @ V_k @ 1 ) @ V_medals )
= ( $sum @ V_k @ ( $quotient_f @ ( 'int.sum/1' @ ( 'nthcdr/2' @ $int @ V_k @ V_medals ) ) @ 7 ) ) )
& ( 'int.is-divisible-by/2' @ ( 'int.sum/1' @ ( 'nthcdr/2' @ $int @ V_k @ V_medals ) ) @ 7 ) ) )
& ( 'm/0'
= ( 'int.sum/1' @ V_medals ) )
& ( V_nm
= ( 'cons/2' @ $int @ 'n/0' @ ( 'cons/2' @ $int @ 'm/0' @ ( 'nil/0' @ $int ) ) ) ) ) ) ).
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