Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is.

Cheryl gave them a list of ten possible dates:
      May 15,     May 16,     May 19
      June 17,    June 18
      July 14,    July 16
      August 14,  August 15,  August 17

Cheryl then tells Albert the &nbsp; ''month'' &nbsp; of birth, &nbsp; and Bernard the &nbsp; ''day'' &nbsp; (of the month) &nbsp; of birth.
  1)  Albert:   I don't know when Cheryl's birthday is, but I know that Bernard does not know too.
  2)  Bernard:  At first I don't know when Cheryl's birthday is, but I know now.
  3)  Albert:   Then I also know when Cheryl's birthday is.


;Task
Write a computer program to deduce, by successive elimination, Cheryl's birthday.


;Related task:
* [[Sum and Product Puzzle]]


;References
* [https://en.wikipedia.org/wiki/Cheryl%27s_Birthday Wikipedia article] of the same name.
* [https://en.wikipedia.org/wiki/Tuple_relational_calculus, Tuple Relational Calculus]
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