A genuine pope can never be judged or deposed since he has no superior on earth.
HOWEVER, if a genuine pope were as a private individual to embrace, heresy, apostasy or schism from the Church, then BY HIS OWN ACT, he would cease to be a Catholic and therefore he would fall from the Office of the Papacy without any declaration being necessary.
With the post 1958 crop, ALL were heretics before their election and as non-Catholics were thus inelegible for the office, and the elections completely null and void.
So Bergoglio is merely a non-pope.
Confer Sections 6 & 7:
"6. ...or even the Roman Pontiff, prior to his promotion or his elevation as Cardinal or Roman Pontiff, has deviated from the Catholic Faith or fallen into some heresy:
(i) the promotion or elevation, even if it shall have been uncontested and by the unanimous assent of all the Cardinals, shall be null, void and worthless;"
A friend advised me to first spend a year reading The Wanderer for a year and then decide. I did as he said and by the the time the year was up, Albino Cardinal Luciani had been elected and murdered and Karol Cardinal Wojtlya had been elected. Those historical facts, beyond my control, seemed to have ratified in my life my decision to stay. Our long international nightmare was over.
I have not regretted my decision to stay. I am not a sedevacantist and never was. Nor shall I ever be. I am quite aware of the theories of fellow disappointed Catholics that Guisseppe Cardinal Siri had REALLY been elected to succeed Pope Pius XII and/or elected again to succeed Pope John XXIII but somehow cheated out of his election by dark forces bent on the destruction of the Church. Siri would have made a fine pope but I simply don't believe these elaborate conspiracy theories necessary to such beliefs.
Not that conspiracies do not occur even in the Church as evidenced by the apparent murder of Luciani. If you imagine that Luciani was a heretic you badly misjudge the man. He was a lifelong disciple of Alfredo Cardinal Ottaviani who had a falling out with him over submission to papal authority.
On the occasion of the election of Cardinal Luciani as John Paul I, I drove to Westbury, Long Island with a carful of Catholic Yalies to attend an afternoon weekday Tridentine Mass at the chapel of the Traditional priest, Fr. Gomar DePauw. In his homily, he told us that he had spoken to Cardinal Ottaviani about the election of Cardinal Luciani and that Cardinal Ottaviani was delighted. Surely you are aware that Cardinal Ottaviani was the prefect of the Holy Office under Pius XII for many years. Was even Pius XII (generally conceded even by sede vacantists to be a valid pope (see your reference to "post-1958 popes" that being the year of his death). Was Pope Pius XII a fool or a heretic to retain Cardinal Ottaviani as prefect of the Holy Office for many years? If either, then this becomes a conspiracy soooooo vast as to.....
At some point, in the face of the available evidence, we must give due regard to questioning our own respective judgments when they conflict with the evidence.
The first and most relevant evidence is that Jesus Christ founded the Church as we know it and promised to be with it all days even unto the end of the Earth. He is coming back, maybe in our lifetimes, maybe not in our lifetimes, at a time known only to God the Father. If I cannot trust the promises of Jesus Christ and of God the Father (he who hears Jesus Christ hears the Father as well) and trust the Paraclete, just whom should I trust (as Peter himself once asked)? Schismatics? Sedevacantists? Skeptics? The professionally disgruntled and unsatisfiable? I am going with God in all three of His Persons on this one. Your experience may vary but only at your own eternal peril.
I clearly distinguished in my post those who are regarded as anti-popes from the legitimate ones. I simply disagree with the remarkable notion that Popes John XXIII, Paul VI, John Paul I, St. John Paul II, Benedict XVI and Francis were all (or any of them) disqualified by heresy from the papacy.
Some of the times of up to three "popes" at a time having to be resolved by councils or, far worse, by monarchs, were disgraceful episodes. Even valid popes have been disgraces such as Alexander VI and Benedict IX and they are not alone. OTOH, it is a proof of Jesus Christ being with the Church that it has survived even such miscreants as these in the papacy. No mere human institution could possibly have survived all that Catholicism has survived over nearly two thousand years of shovelling dirt on the coffins of His enemies.
Secondly, there is the matter of Apostolic Succession, distinguishing our priests from mere ministers or pastors, and guaranteeing the validity of our sacraments, particularly the Real Presence in the Holy Eucharist and the forgiveness of sins via the Sacrament of Penance (or Reconciliation as known to more modern Catholics than I). We and the Orthodox enjoy Apostolic Succession as other churches do not. Pope Pius XII died in 1958. That was 58 long years ago. If the Church lasts another 50 years, certainly all of his bishops and priests will be dead. If Jesus Christ has not returned by then, what will you make of His promise to be with the Church all days, etc.?
Will the Church that Jesus Christ founded then be confined to some small priestless remnant, unable to consecrate the Holy Eucharist or to be able to hear confessions and be unable to transmit the forgiveness of God because the power of the Keys will have lapsed without any earthly way of re-establishing it? Are mere humans THAT capable of thwarting the will of Almighty God? Humans are quite capable of sin and we prove that every day of our lives, even the most saintly of humans. God is still in charge and is far more capable of thwarting the fallen will of mere men.
Just as medieval monarchs or even councils had no authority (power coupled with morality) to depose popes, neither do sedevacantists who merely issue erroneous opinions enticing their fellow men to their own sedevacantist errors (grounded in the spiritual quicksand of their own wounded feelings if they are as I was in the mid-1970s). The modern sedevacantist does not risk even a forceful "inquiry" by the Holy Office much less rack and ruin, being drawn and quartered or burning at the stake. Those who went before us, wrong or right, were made of sterner stuff.
Bergoglio is a foolish man of all too many air-headed opinions, few of them useful for the task of shepherding the flock. He is about 78 years old already and will be gone soon enough and is quite unlikely to do damage on the level of John XXIII or Paul VI. The mistake of his election is unlikely to be repeated by the next conclave.
Pope Paul IV, back there in 1559, apparently failed to express an opinion as to just who was authorized to determine just which pope(s) election(s) were null and void and worthless because the elected one(s) had fallen into some heresy. If he had specified, you would have told us. Surely the long dead Pope Paul IV did not specify thee or me.
It seems impossible for any human to commit any sin that does not involve the sin of pride in that sins are instances of us placing our own individual priorities over those of our Creator. He gave us free will but it is breathtaking how many are, out of pride, willing to abuse free will and, as one prominent non-Catholic American, even older than I, has said that he has never seen fit to ask forgiveness for a single sin. I have sinned. Have you? On many occasions, I have been forgiven. Have you?
Why are we arguing over the claims of sedevacantism? Do as you will but I ask you to reflect on the foregoing and respond as you see fit but not merely for the sake of responding.
May God bless you and yours!