TPTP Problem File: RAL026^1.p

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% File     : RAL026^1 : TPTP v7.5.0. 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 (   0 unit;1201 type;   0 defn)
%            Number of atoms       : 45345 (2212 equality;22711 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39636 ( 104   ~; 233   |;1177   &;35995   @)
%                                         (1095 <=>;1032  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1248 (1201   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8058 (  66 sgn;7086   !; 430   ?; 406   ^)
%                                         (8058   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1975 (   6 prd;   9 fun;  23 num;1937 var)
% 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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