Well, not exactly. You think I am using Papal Infallibility to maintain the "mystery" of Church's Indefectibility. But for me that is not the case.
What I think is that sedes are judging the pope, something we are not permitted to do per canon law, cuм ex and every other Church teaching out there since the first Pentecost Sunday.
Per cuм ex we *are* permitted to do what we are doing, i.e. "contradict" him by persevering in the true faith and condemning the NO. R&R do this without concern of the status of popes because the conciliar popes have met the criteria of cuм ex by deviating from the faith. Whether they were or never were popes is irrelevant, everyone on earth (except sedes) knows them all as popes, and as long as we persevere in the faith, his status does not matter. Our salvation depends on us keeping the faith no matter what scandals that "must needs be" cometh.
This is how I got to this point:
1) If one is a public heretic = proof one is not a member of the Catholic Church
2) If he is not member of the Church = not the pope
3) If not the pope = false pope
You have to remember here that heresy is a sin, a Catholic who has fallen into the sin of heresy is a sinner, in the case of the pope (and to not lose sight of what heresy is), lets say the pope is a mortal sinner. Should the heretic pope decide to repent, all he has to do is go to confession same as you and I and every other Catholic and his sin of heresy can be forgiven.
Now obviously you know that this sacrament is for Catholics only, for members of the Church only, and that one who is not a member of the Church cannot use it, but the pope can use it same as only Catholics can. And in danger of death, Trent says repentant heretics can also receive the sacrament of Extreme Unction, which is another sacrament only members of the Church can receive. Ergo, the pope is a member of the Church.
And before you go there, yes, I agree that he should first publicly abjure his heresies, but regardless, that's up to him, the remedy for forgiveness of his sin of heresy is the same for all members of the Church in the state of sin, the sacrament of Penance.
All of this is to say a heretic who was a Catholic is still a member of the Church in virtue of the sacrament of penance, which is to say that relying on the above formula as part of your reasoning, doesn't work.