Read Abbe de Nantes on the subject of Sedevacantism.  He has dealt with it thoroughly.

Note Bellarmine's language: "To my judgment..."

 All of these approaches are open.

"Therefore, the true opinion is the fifth, according to which the Pope who is manifestly a heretic ceases by himself to be Pope and head, in the same way as he ceases to be a Christian and a member of the body of the Church; and for this reason he can be judged and punished by the Church. This is the opinion of all the ancient Fathers, who teach that manifest heretics immediately lose all jurisdiction, and outstandingly that of St. Cyprian (lib. 4, epist. 2) who speaks as follows of Novatian, who was Pope [i.e. antipope] in the schism which occurred during the pontificate of St. Cornelius: 'He would not be able to retain the episcopate [i.e. of Rome], and, if he was made bishop before, he separated himself from the body of those who were, like him, bishops, and from the unity of the Church.'

According to what St. Cyprian affirms in this passage, even had Novatian been the true and legitimate Pope, he would have automatically fallen from the pontificate, if he separated himself from the Church.

"This is the opinion of great recent doctors, as John Driedo (lib. 4 de Script. et dogmat. Eccles., cap. 2, par. 2, sent. 2), who teaches that only they separate themselves from the Church who are expelled, like the excommunicated, and those who depart by themselves from her or oppose her, as heretics and schismatics. And in his seventh affirmation, he maintains that in those who turn away from the Church, there remains absolutely no spiritual power over those who are in the Church. Melchior Cano says the same (lib. 4 de loc., cap. 2), teaching that heretics are neither parts nor members of the Church, and that it cannot even be conceived that anyone could be head and Pope, without being member and part (cap. ult. ad argument. 12). And he teaches in the same place, in plain words, that occult heretics are still of the Church, they are parts and members, and that therefore the Pope who is an occult heretic is still Pope. This is also the opinion of the other authors whom we cite in book I De Ecclesia.

"The foundation of this argument is that the manifest heretic is not in any way a member of the Church, that is, neither spiritually nor corporally, which signifies that he is not such by internal union nor by external union. For even bad Catholics [i.e. who are not heretics] are united and are members, spiritually by faith, corporally by confession of faith and by participation in the visible sacraments; the occult heretics are united and are members although only by external union; on the contrary, the good catechumens belong to the Church only by an internal union, not by the external; but manifest heretics do not pertain in any manner, as we have already proved."

But Bellarmine leaves the Church at St. Gertudes in Ohio....he didn't clearly foresee the consequences of his thinking and neglected the juridical aspects that Cajeatan and Suarez and others saw.

"The fourth opinion is that of Cajetan, for whom (de auctor. papae et con., cap. 20 et 21) the manifestly heretical Pope is not "ipso facto" deposed, but can and must be deposed by the Church. To my judgment, this opinion cannot be defended. For, in the first place, it is proven with arguments from authority and from reason that the manifest heretic is "ipso facto" deposed. The argument from authority is based on St. Paul (Titus, c. 3), who orders that the heretic be avoided after two warnings, that is, after showing himself to be manifestly obstinate - which means before any excommunication or judicial sentence. And this is what St. Jerome writes, adding that the other sinners are excluded from the Church by sentence of excommunication, but the heretics exile themselves and separate themselves by their own act from the body of Christ. Now, a Pope who remains Pope cannot be avoided, for how could we be required to avoid our own head? How can we separate ourselves from a member united to us?

"Besides that, the second affirmation of Cajetan, that the Pope heretic can be truly and authoritatively deposed by the Church, is no less false than the first. For if the Church deposes the Pope against his will it is certainly above the Pope; however, Cajetan himself defends, in the same treatise, the contrary of this. Cajetan responds that the Church, in deposing the Pope, does not have authority over the Pope, but only over the link that unites the person to the pontificate. In the same way that the Church in uniting the pontificate to such a person, is not, because of this, above the Pontiff, so also the Church can separate the pontificate from such a person in case of heresy, without saying that it is above the Pope.

The Church is a juridical body, not only one with ontological consequences for heresy. Bellarmine also said a heretic pope "can be judged by the Church..." a declaratory sentence.

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No, they are not. The true opinion is the fifth.

 SJB locuta, causa finita. Presto.

]"Therefore, the true opinion is the fifth, according to which the Pope who is manifestly a heretic ceases by himself to be Pope and head, in the same way as he ceases to be a Christian and a member of the body of the Church; and for this reason he can be judged and punished by the Church. This is the opinion of all the ancient Fathers, who teach that manifest heretics immediately lose all jurisdiction, and outstandingly that of St. Cyprian (lib. 4, epist. 2) who speaks as follows of Novatian, who was Pope [i.e. antipope] in the schism which occurred during the pontificate of St. Cornelius: 'He would not be able to retain the episcopate [i.e. of Rome], and, if he was made bishop before, he separated himself from the body of those who were, like him, bishops, and from the unity of the Church.

A doubtful sacrament is no sacrament. How many then must doubt for it to be so?

If I doubt that your priest was ordained validly doth it become so? What if five, ten, 20 of us doubt?

But 99%  of all Catholics (including traditionalists) doubt your conclusions.

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Numbers do not matter.

Huh? Then what does? Your doubt alone? One priest alone? (Let me preempt you and remind you that Athanasius had not shown the Pope to be a heretic, so the ship tipped to the side of the Pope)

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No, just a real positive reason to doubt. Go look it up. It has nothing to do with the quantity of "doubters

Ah, so any crank (or tiny group of cranks) can posit sincere doubt and a Pope ceases to be Pope, presto eh?