St Robert uses the term manifest heretic.
He explains it here:
The fourth opinion is of Cajetan. There, he teaches, that a manifestly heretical Pope is not ipso facto deposed; but can and ought to be deposed by the Church. Now in my judgement, such an opinion cannot be defended. For in the first place, that a manifest heretic would be ipso facto deposed, is proven from authority and reason. The Authority is of St Paul, who commands Titus, that after two censures, that is, after he appears manifestly perinacious, an heretic is to be shunned: and he understands this before excommunication and sentence of a judge. (On The Roman Pontiff, Bk II, Ch XXX)
So, for him, a manifest heretic is a public formal heretic, not just a material heretic; one whose pertinacity has been demonstrated after admonitions. I think it is likely, given the other quotes of St Robert provided in this thread, that he believed those admonitions should come from a Council, which would judge the heresy and convict the Pope of same. Then would come the declaration from the authority (the Council) of his heresy so that it would be manifest to the Church. Then we have a manifest heretic in the sense that St Robert Bellarmine is referring to:
"The second, whether or not it is lawful for a Council to be summoned by anyone other than the Pope when the Pope should not summon it, for the reason that he is a heretic or schismatic... To the second and third, I respond... in those two cases an imperfect Council could be gathered which would suffice to provide for the Church from the head. For the Church, without a doubt, has the authority to provide for itself from the head... Hence, that imperfect Council can happen, if either it is summoned by the college of Cardinals, or the bishops themselves come together in a place of themselves."
"...the Roman Pontiff cannot be deprived of his right to summon Councils and preside over them... unless he were first convicted by the legitimate judgement of a Council and is not the Supreme Pontiff. Moreover... the supreme prince, as long as he is not declared or judged to have legitimately been deprived of his rule, is always the supreme judge..."
"...inferiors ought not be free from the obedience to superiors, unless first he were legitimately deposed or declared not to be a superior... they do not swear that they are not going to say what they think in the Council, or that they are not going to depose him if they were to clearly prove that he is a heretic."
"...the Supreme Pontiff, does not lose jurisdiction, nor dignity, or the name of the head in the Church, until either he separates himself publicly from the Church, or being convicted of heresy is separated against his will."
There is no need to depose anyone.
They never even became consecrated popes.
They were well known heretics before they were elected.
They had already left the Church.
They were no longer Catholic.
Somebody outside the Church cannot become pope.
Can a Muslim or a Protestant or Hindu become pope? No.
They are outside the Church.
You can elect them, dress them up, say the prayers, but no consecration can take place.
Well, it's the same with a heretic. They are not Catholic just like a Muslim or Hindu is not Catholic.
A priest could put a twinkie on the altar and say the prayers but it can't be consecrated because it is invalid matter.
In the same way, a heretic who is outside the Church can be dressed up, and they say the prayers, but it is invalid matter and no papal consecration takes place.
The Holy Fathers teach unanimously not only that heretics are outside of the Church, but also that they are “ipso facto” deprived of all ecclesiastical jurisdiction and dignity. St. Cyprian (lib. 2, epist. 6) says: “We affirm that absolutely no heretic or schismatic has any power or right”; and he also teaches (lib. 2, epist. 1) that the heretics who return to the Church must be received as laymen, even though they have been formerly priests or bishops in the Church. St. Optatus (lib. 1 cont. Parmen.) teaches that heretics and schismatics cannot have the keys of the kingdom of heaven, nor bind nor loose. St. Ambrose (lib. 1 de poenit., ca. 2), St. Augustine (in Enchir., cap 65), St. Jerome (lib. cont. Lucifer.) teach the same.
https://cmri.org/articles-on-the-traditional-catholic-faith/on-the-roman-pontiff/If a heretic, somebody outside the Church, was to somehow magically be consecrated as pope
and teach heresy and guide souls to worship false gods
sending souls to eternal damnation
then the Gates of Hell have prevailed against the Church.
Is that possible?
Our Lord Jesus Christ said NO.
He said that is not possible.
So what happened then?
These men were never consecrated popes in the first place.
The Gates of Hell have not prevailed.
The Church is still here holding fast to the Apostolic Traditions of the
One True Religion
yet without a pope.