The list

Logic Level 2

You encounter an ancient Italian manuscript. Your hired historians discover that it is a list of sentences written by the Bellini and Cellini patriarchs. Just like with their caskets, Bellini writes only true sentences and Cellini writes only false ones.

Translated into English, the document reads as follows:
(1) None of these sentences was written by Cellini.
(2) One of these sentences was written by Cellini.
(3) Two of these sentences were written by Cellini.
(4) Three of these sentences were written by Cellini.
(5) Exactly one of these sentences was written by Bellini.

Your experts clearly detect two styles of handwriting, and tell you that is an absolute fact that both Bellini and Cellini wrote at least one sentence.

How many of the sentences were written by Cellini?

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