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This is the great debate in the theology of this question, a question which is unsettled, but which the Sedevacantists pontificate on. That is the problem, setting oneself up as Pope to decide upon a matter which is not settled by the Church. That is not Catholic. Cardinal Journet, however, can help with the logic:

Many and good theologians of the XVIth and XVIIth Century have admitted that it was possible that a Pope could fall, as a private person, into the sin of heresy, not only occult, but also manifest. The ones like Bellarmine and Suarez, have then thought that the Pope, by cutting himself off from the Church, was ipso facto deposed; Papa haereticus est depositus. It appears that heresy is seen by these theologians as a sort of moral 'ѕυιcιdє' suppressing the subject of the papacy. We return thus easily to the first way we said the Pontificate is lost.

"The others, as Cajetan and John of St Thomas, whose analysis seems to me more penetrating, have considered that even after a manifest sin of heresy, the Pope is not yet deposed, but should be deposed by the Church; Papa haereticus non est depositus sed deponendus. Nevertheless they added the Church is not on that account above the Pope. They had recourse to the same explanation we used in the excursus IV1. They remarked that on the one hand, by divine right, the Church must be united to the Pope as a body to its head; and on the other hand, that, by divine right, he who is a manifest heretic must be avoided after one or two monitions (Tit III,10). There is thus an absolute antimony between the fact of being a Pope and persevering into heresy after one or two warnings. The action of the Church is simply declarative; it manifests that there is an incorrigible sin of heresy; then the Power of Authority of God exercises itself to disjoin the papacy from a subject who, persisting into heresy after admonition, becomes, by divine right, incapable to hold it any longer. In virtue of Scripture, the Church designates and God deposes. God works with the Church, says John of St Thomas, a little like a Pope would decide to attach indugences to certain pilgrimage places, but would leave to a minister the care to specify the places, II-II, Q1, disp2, a3, n29, tVII, p264. The explanation of Cajetan and John of St Thomas... leads us, in its turn, to the case of a subject who, from a certain moment, begins to become, by Divine Right, incapable to hold the privilege of the Papacy. It is reductible to the loss of pontificate by loss of subject. It is indeed the fundamental case, of which others will only be variants - L'Eglise du Verbe Incarne, vol I, p 625

It looks to me like Journet is confirming Lad's view of Bellarmine, which is distinguished from "the others," Cajetan and St. Thomas, who say the Church must depose.

Quote from: DecemRationis
It looks to me like Journet is confirming Lad's view of Bellarmine, which is distinguished from "the others," Cajetan and St. Thomas, who say the Church must depose.

Whoops; concedo.

But the JST quote stands, with him asserting that Bellarmine’s position still requires a declaration from the Church that Christ has deposed the heretical pope:


Of these two [intermediate] explanations, Azorius (2, tom. 2, cap. 7) adopts the first, which holds that the Church is superior to the Pope in the case of heresy; while Cajetan adopts the latter and treats of it at length.  Bellarmine, however, reports his opinion and attacks it in his work de Romano pontifice, bk. 2, ch. 30, objecting especially to these two points: namely, that Cajetan says that the Pope who is a manifest heretic [according to the Church's human judgment] is not ipso facto deposed; and also that the Church deposes the Pope in a real and authoritative manner.  Suarez also, in the disputation that we have frequently cited, sect. 6, num. 7, attacks Cajetan for saying that, in the case of heresy, the Church is superior to the Pope, not insofar as he is Pope, but insofar as he is a private individual.  Cajetan, however, did not say this; he only said that, even in the case of heresy, the Church is not absolutely superior to the Pope, but instead is superior to the bond between the papacy and the person, dissolving it in the same way that she forged it at his election; and this power of the Church is ministerial, for only Christ our Lord is superior to the Pope without qualification.  Hence, Bellarmine and Suarez are of the opinion that, by the very fact that the Pope is a manifest heretic and declared to be incorrigible, he is deposed [ipso facto] by Christ our Lord without any intermediary, and not by any authority of the Church.