I may end up wishing I didn’t say this, but being that it was brought up, I think it’s only fair to quote the “Gentle Saint”
Thus we do not say that the Pope cannot err in his private opinions, as did John XXII (some details about the Beatific Vision, he admitted he was wrong after a great stir came up and theological inquiry was conducted); or be altogether a heretic, as Honorius was. Now when he is explicitly a heretic, he falls ipso facto from his dignity and out of the Church, and the Church must either deprive him, or, as some say, declare him deprived, of his Apostolic See, and must say as St. Peter did; Let another take his bishopric. - St. Francis de Sales, The Catholic Controversy, p. 306, Article 6, Ch. 14
It really is a necessary defense of the Primacy of the Roman See, and in turn, an integral part of Papal Infallibility. Note carefully, that no council, not even an ecumenical one can depose a Pope. Therefore, in order for him to be deposed, he cannot be a Pope, but rather a heretic, and since Canon Law (#1325 of the "old numbering system) states that a heretic is not part of the Church, as does Pope Leo XIII in Satis Cognitum, much less can a man who is not part of the Church be the head of it. He can’t be “deposed” since his loss of office is ipso facto, all that is necessary is to declare such a one deposed (deprived of office).
Yes, that seems to be a necessary result of Papal Infallibility, that a true Pope cannot be a formal heretic.
I hope this thread is not closed due to that, but I didn’t say the “s” word. The question was asked, and clearly, the answer is, a Pope will not say that. If he did, he’s not the Pope!