TPTP Problem File: MSC028=1.p

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% File     : MSC028=1 : TPTP v7.5.0. Released v6.4.0.
% Domain   : Miscellaneous
% Problem  : 2 and 3 cents stamps
% Version  : Especial.
% English  : Suppose we have stamps of two different denominations, 3 cents and
%            5 cents. We want to show that it is possible to make up exactly 
%            any postage of 8 cents or more using stamps of these two 
%            denominations. The formula below asserts this, however "8" 
%            replaced by "some lower bound".

% Refs     : [Liu85] Liu (1985), Elements of Discrete Mathematics
%          : [Bau15] Baumgartner (2015), Email to Geoff Sutcliffe
% Source   : [Bau15]
% Names    : stamps.p [Bau15]

% Status   : Theorem
% Rating   : 0.62 v7.5.0, 0.70 v7.4.0, 0.62 v7.3.0, 0.50 v7.0.0, 0.57 v6.4.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type)
%            Number of atoms       :    4 (   1 equality)
%            Maximal formula depth :    8 (   8 average)
%            Number of connectives :    3 (   0   ~;   0   |;   2   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   1 propositional; 0-2 arity)
%            Number of functors    :    5 (   3 constant; 0-2 arity)
%            Number of variables   :    4 (   0 sgn;   1   !;   3   ?)
%                                         (   4   :;   0  !>;   0  ?*)
%            Maximal term depth    :    3 (   1 average)
%            Arithmetic symbols    :   11 (   2 prd;   2 fun;   3 num;   4 var)
% SPC      : TF0_THM_EQU_ARI

% Comments :
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tff(formula,conjecture,(
    ? [L: $int] :
    ! [K: $int] :
      ( $greater(K,L)
     => ? [S1: $int,S2: $int] :
          ( $greatereq(S1,0)
          & $greatereq(S2,0)
          & K = $sum($product(S1,3),$product(S2,5)) ) ) )).

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