Just wanted to note, in light of the latest posts about formal / material heresy, that the Cassisiacuм Thesis does not rely upon determining the heresy (formal, manifest, public, occult, material, etc) of the pope - something that it is very problematic for a variety of reasons -; but simply on his loss of Authority given his public and persistent opposition to the Church timeless teachings. The contradiction is sufficient proof that Divine Assistance is lacking and thus, their supreme power of jurisdiction. This is what Pontifical Authority formally consists of. St. Bellarmine calls it the "form of the pontificate" which is immediately communicated by God Himself. Because the conciliar popes lack the "form" of the Pontificate, they are not formally popes.
Every Catholic can and should conclude that presently there is an absence of Authority in the Church. And that this is the case without appealing to the possible personal heresy of the pope (or bishops). The conclusion is based solely on the contradiction that exists between the teachings of these false prophets and that of the true Church. This alone suffices, as St. Bellarmine teaches, to enable the faithful to protect themselves from being led astray.
In order for our souls not to perish (because this is all what is about, right?) and save ourselves from these false teachers, it is sufficient that we are able to recognize that these teachers no longer have any Authority. According to the Thesis, it is not necessary for the faithful to accuse them of the sin of heresy... "Nor is it necessary for them to affirm that these teachers are definitively and juridically deposed, and as a result no longer hold their sees even materially".