The Church has been headquarted in Rome since before you were born.  Those who reside in Rome as the pope and Cardinals are such, whether you want to accept reality or not.

I take that to mean you don't understand logic.

Your mistake is in assuming that Conciliar clerics are actually Catholic and that they possess jurisdiction.

Since they occupy the dioceses, we must assume they do, until is proven otherwise. 

He was also elected, don't forget.  Does that not matter?  If it doesn't, you must prove why.

Because he was a heretic before being elected. 

Ok, then get off and quit confusing this thread!  The topic is what to do with a pope AFTER his election, when he becomes a heretic.  Your view is completely different.  You can't "mix and match" papal problems with +Bellarmine's papal solutions.

You said that the Pope and his Cardinals are valid simply because they claim to be and live in Rome. That's nonsense logic and is what I was disputing. You also said that if there is a Pope, we must follow him, but that ignores the fact that there can and always have been false claimants to the Papacy. Location doesn't affect the validity of their claim, as much as you assert the contrary.

You said that the Pope and his Cardinals are valid simply because they claim to be and live in Rome. That's nonsense logic and is what I was disputing.

You are disputing the continous succession of Cardinals/Popes for over 2,000 years and assuming they must be "re-certified" to your own, personal satisfaction.  You are accusing the clergy of a crime, you must show the evidence (actually, you have no ability to accuse the clergy of a crime, but let's just pretend you did).  A prosecutor has to prove his case, not the other way around.

Only God knows whether or not Francis is an Antipope.
There is no doubt that he was elected a pope, but is he a pope or is he an antipope?
There is doubt that his election was both valid and licit, there is good reason to believe that it was either illicit but valid or licit and invalid.
 

Bishop Gracida, Bishop Emeritus of Corpus Christi and his blog . https://abyssum.org/about/

Let's see a little honesty and integrity on this thread. I personally make my confessions with a diocesan priest of whom both the Dominican Director-priest of Avrillé and the local CMRI (sedevacantist) priest have given moral approval and this diocesan priest (ordained in 1962) has expressed agreement with and reads Bishop Gracida. The assumptions being purported here as fact by Pax Vobis that no priests or bishops of the diocesan structure doubt the papacy and speak of the doubt of the papacy of Bergogio are just simply not truths.

6.  The Catholic Church teaches that a heretic would cease to be pope, and that a heretic couldn’t be validly elected pope
 
The Catholic Encyclopedia, “Heresy,” 1914, Vol. 7, p. 261: “The pope himself, if notoriously guilty of heresy, would cease to be pope because he would cease to be a member of the Church.”1
 
Heresy is the obstinate denial or doubt by a baptized person of an article of divine and Catholic Faith.  In other words, a baptized person who deliberately denies an authoritative teaching of the Catholic Church is a heretic. 
 
 
Martin Luther, perhaps the most notorious heretic in Church history, taught the heresy of Justification by faith alone, among many others
 
Besides antipopes reigning from Rome due to uncanonical elections, the Catholic Church teaches that if a pope were to become a heretic he would automatically lose his office and cease to be the pope.  This is the teaching of all the doctors and fathers of the Church who addressed the issue:
 
A heretic cannot be the pope 32
 
 
That a heretic cannot be a pope is rooted in the dogma that heretics are not members of the Catholic Church
 
It should be noted that the teaching from the saints and doctors of the Church, which is quoted above – that a pope who became a heretic would automatically cease to be pope – is rooted in the infallible dogma that a heretic is not a member of the Catholic Church.
 
Pope Eugene IV, Council of Florence, “Cantate Domino,” 1441: “The Holy Roman Church firmly believes, professes and preaches that all those who are outside the Catholic Church, not only pagans but also Jєωs or heretics and schismatics, cannot share in eternal life and will go into the everlasting fire which was prepared for the devil and his angels, unless they are joined to the Church before the end of their lives…”2
 
Pope Pius XII, Mystici Corporis Christi (# 23), June 29, 1943: “For not every sin, however grave it may be, is such as of its own nature to sever a man from the Body of the Church, as does schism or heresy or apostasy.”3
 
St. Robert Bellarmine, Cardinal and Doctor of the Church, De Romano Pontifice, II, 30:  "A pope who is a manifest heretic automatically (per se) ceases to be pope and head, just as he ceases automatically to be a Christian and a member of the Church.  Wherefore, he can be judged and punished by the Church.  This is the teaching of all the ancient Fathers who teach that manifest heretics immediately lose all jurisdiction."
 
St. Robert Bellarmine, De Romano Pontifice, II, 30:  "This principle is most certain.  The non-Christian cannot in any way be Pope, as Cajetan himself admits (ib. c. 26).  The reason for this is that he cannot be head of what he is not a member; now he who is not a Christian is not a member of the Church, and a manifest heretic is not a Christian, as is clearly taught by St. Cyprian (lib. 4, epist. 2), St. Athanasius (Scr. 2 cont. Arian.), St. Augustine (lib. De great. Christ. Cap. 20), St. Jerome (contra Lucifer.) and others; therefore the manifest heretic cannot be Pope."
 
St. Francis De Sales (17th century), Doctor of the Church, The Catholic Controversy, pp. 305-306:  "Now when he [the Pope] is explicitly a heretic, he falls ipso facto from his dignity and out of the Church..." 

St. Antoninus (1459): "In the case in which the pope would become a heretic, he would find himself, by that fact alone and without any other sentence, separated from the Church.  A head separated from a body cannot, as long as it remains separated, be head of the same body from which it was cut off.  A pope who would be separated from the Church by heresy, therefore, would by that very fact itself cease to be head of the Church.  He could not be a heretic and remain pope, because, since he is outside of the Church, he cannot possess the keys of the Church." (Summa Theologica, cited in Actes de Vatican

That a heretic cannot be a pope is rooted in the dogma that heretics are not members of the Catholic Church
 
It should be noted that the teaching from the saints and doctors of the Church, which is quoted above – that a pope who became a heretic would automatically cease to be pope – is rooted in the infallible dogma that a heretic is not a member of the Catholic Church.
 
Pope Eugene IV, Council of Florence, “Cantate Domino,” 1441: “The Holy Roman Church firmly believes, professes and preaches that all those who are outside the Catholic Church, not only pagans but also Jєωs or heretics and schismatics, cannot share in eternal life and will go into the everlasting fire which was prepared for the devil and his angels, unless they are joined to the Church before the end of their lives…”2
 
Pope Pius XII, Mystici Corporis Christi (# 23), June 29, 1943: “For not every sin, however grave it may be, is such as of its own nature to sever a man from the Body of the Church, as does schism or heresy or apostasy.”3
 
St. Robert Bellarmine, Cardinal and Doctor of the Church, De Romano Pontifice, II, 30:  "A pope who is a manifest heretic automatically (per se) ceases to be pope and head, just as he ceases automatically to be a Christian and a member of the Church.  Wherefore, he can be judged and punished by the Church.  This is the teaching of all the ancient Fathers who teach that manifest heretics immediately lose all jurisdiction."
 
St. Robert Bellarmine, De Romano Pontifice, II, 30:  "This principle is most certain.  The non-Christian cannot in any way be Pope, as Cajetan himself admits (ib. c. 26).  The reason for this is that he cannot be head of what he is not a member; now he who is not a Christian is not a member of the Church, and a manifest heretic is not a Christian, as is clearly taught by St. Cyprian (lib. 4, epist. 2), St. Athanasius (Scr. 2 cont. Arian.), St. Augustine (lib. De great. Christ. Cap. 20), St. Jerome (contra Lucifer.) and others; therefore the manifest heretic cannot be Pope."
 
St. Francis De Sales (17th century), Doctor of the Church, The Catholic Controversy, pp. 305-306:  "Now when he [the Pope] is explicitly a heretic, he falls ipso facto from his dignity and out of the Church..." 
St. Antoninus (1459): "In the case in which the pope would become a heretic, he would find himself, by that fact alone and without any other sentence, separated from the Church.  A head separated from a body cannot, as long as it remains separated, be head of the same body from which it was cut off.  A pope who would be separated from the Church by heresy, therefore, would by that very fact itself cease to be head of the Church.  He could not be a heretic and remain pope, because, since he is outside of the Church, he cannot possess the keys of the Church." (Summa Theologica, cited in Actes de Vatican I. V. Frond pub.) 
A heretic cannot be the pope 33
We can see that it’s the teaching of the Catholic Church that a man is severed from the Church by heresy, schism or apostasy.
 
Pope Leo XIII, Satis Cognitum (# 9), June 29, 1896: “The practice of the Church has always been the same, as is shown by the unanimous teaching of the Fathers, who were wont to hold as outside Catholic communion, and alien to the Church, whoever would recede in the least degree from any point of doctrine proposed by her authoritative Magisterium.”4
 
Pope Leo XIII, Satis Cognitum (# 9): “No one who merely disbelieves in all (these heresies) can for that reason regard himself as a Catholic or call himself one.  For there may be or arise some other heresies, which are not set out in this work of ours, and, if any one holds to a single one of these he is not a Catholic.”5
 
Pope Innocent III, Eius exemplo, Dec. 18, 1208: “By the heart we believe and by the mouth we confess the one Church, not of heretics, but the Holy Roman, Catholic, and Apostolic Church outside of which we believe that no one is saved.”6
 
Thus, it’s not merely the opinion of certain saints and doctors of the Church that a heretic would cease to be pope; it’s a fact inextricably bound up with a dogmatic teaching.  A truth inextricably bound up with a dogma is called a dogmatic fact.  It is, therefore, a dogmatic fact that a heretic cannot be the pope.  A heretic cannot be the pope, since one who is outside cannot head that of which he is not even a member.
 
Pope Leo XIII, Satis Cognitum (#15), June 29, 1896: “No one, therefore, unless in communion with Peter can share in his authority, since it is absurd to imagine that he who is outside can command in the Church.”7
 
 Pope Paul IV issued a Papal Bull solemnly declaring that the election of a heretic as pope is null and void
 
In 1559 Pope Paul IV issued an entire Papal Bull dealing with the subject and the possibility of a heretic being elected pope. 

At the time that Paul IV issued the Bull (quoted below) there were rumors that one of the cardinals was a secret Protestant.  In order to prevent the election of such a heretic to the Papacy, Pope Paul IV solemnly declared that a heretic cannot be validly elected pope.  Below are the pertinent portions of the Bull.  For the entire Bull, see our website.   Pope Paul IV, Bull cuм ex Apostolatus Officio, Feb. 15, 1559: “1… Remembering also that, where danger is greater, it must more fully and more diligently be counteracted, We have been concerned lest false prophets or others, even if they have only secular jurisdiction, should wretchedly ensnare the souls of the simple, and drag with them into perdition, destruction and damnation countless peoples committed to their care and rule, either in spiritual or in temporal matters; and We have been concerned also lest it may befall Us to see the abomination of desolation, which was spoken of by the prophet Daniel, in the holy place. In view of this, Our desire has been to fulfill our Pastoral duty, insofar as, with the help of God, We are able, so as to arrest the foxes who are occupying themselves in the destruction of the vineyard of the Lord and to keep the wolves from the sheepfolds, lest We seem to be dumb watchdogs that cannot bark and lest We perish with the wicked husbandman and be compared with the hireling…
 
6. In addition, [by this Our Constitution, which is to remain valid in perpetuity We enact, determine, decree and define:-] that if ever at any time it shall appear that any Bishop, even if he be acting as an Archbishop, Patriarch or Primate; or any Cardinal of the aforesaid Roman Church, or, as has already been mentioned, any legate, 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; (ii) it shall not be possible for it to acquire validity (nor for it to be said that it has thus acquired validity) through the acceptance of the office, of consecration, of subsequent authority, nor through possession of administration, nor through the putative enthronement of a Roman Pontiff, or Veneration, or obedience accorded to such by all, nor through the lapse of any period of time in the foregoing situation; (iii) it shall not be held as partially legitimate in any way… (vi) those thus promoted or elevated shall be deprived automatically, and without need for any further declaration, of all dignity, position, honour, title, authority, office and power…
 
10. No one at all, therefore, may infringe this docuмent of our approbation, reintroduction, sanction, statute and derogation of wills and decrees, or by rash presumption contradict it.  If anyone, however, should presume to attempt this, let him know that he is destined to incur the wrath of Almighty God and of the blessed Apostles, Peter and Paul.
 
Given in Rome at Saint Peter's in the year of the Incarnation of the Lord 1559, 15th February, in the fourth year of our Pontificate.
 
+ I, Paul, Bishop of the Catholic Church…” 
 
With the fullness of his papal authority, Pope Paul IV declared that the election of a heretic is invalid, even if it takes place with the unanimous consent of the cardinals and is accepted by all.
A heretic cannot be the pope 35
 
Pope Paul IV also declared that he was making this declaration in order to combat the arrival of the abomination of desolation, spoken of by Daniel, in the holy place.  This is astounding, and it seems to indicate that the Magisterium itself is connecting the eventual arrival of the abomination of desolation in the holy place (Matthew 24:15) with a heretic posing as the pope – perhaps because the heretic posing as the pope will give us the abomination of desolation in the holy place (the New Mass), as we believe is the case, or because the heretical antipope will himself constitute the abomination of desolation in the holy place.
 
The Catholic Encyclopedia repeats this truth declared by Pope Paul IV by asserting that the election of a heretic as pope would, of course, be completely null and void.
 The Catholic Encyclopedia, “Papal Elections,” 1914, Vol. 11, p. 456: "Of course, the election of a heretic, schismatic, or female [as Pope] would be null and void."8
 In line with the truth that a heretic cannot be the pope, the Church teaches that heretics cannot be prayed for in the canon of the Mass
 
A pope is prayed for in the Te Igitur prayer of the canon of the Mass.  But the Church also teaches that heretics cannot be prayed for in the canon of the Mass.  If a heretic could be a true pope, there would be an insoluble dilemma.  But it’s actually not a dilemma because a heretic cannot be a valid pope:
 
Libellus professionis fidei, April 2, 517, profession of faith prescribed under Pope St. Hormisdas: “And, therefore, I hope that I may merit to be in the one communion with you, which the Apostolic See proclaims, in which there is the whole and the true solidity of the Christian religion, promising that in the future the names of those separated from the communion of the Catholic Church, that is, those not agreeing with the Apostolic See, shall not be read during the sacred mysteries.  But if I shall attempt in any way to deviate from my profession, I confess that I am a confederate in my opinion with those whom I have condemned.  However, I have with my own hand signed this profession of mine, and to you, HORMISDAS, the holy and venerable Pope of the City of Rome, I have directed it.”9
 
Pope Benedict XIV, Ex Quo Primum (# 23), March 1, 1756: “Moreover heretics and schismatics are subject to the censure of major excommunication by the law of Can. de Ligu. 23, quest. 5, and Can. Nulli, 5, dist. 19.  But the sacred canons of the Church forbid public prayer for the excommunicated as can be seen in chap. A nobis, 2, and chap. Sacris on the sentence of excommunication.  Though this does not forbid prayer for their conversion, still such prayer must not take the form of proclaiming their names in the solemn prayer during the sacrifice of the Mass.”10
 
 
 
A heretic cannot be the pope 36
Pope Pius IX, Quartus Supra (# 9), January 6, 1873: “For this reason John, Bishop of Constantinople, solemnly declared – and the entire Eighth Ecuмenical Council did so later – ‘that the names of those who were separated from communion with the Catholic Church, that is of those who did not agree in all matters with the Apostolic See, are not to be read out during the sacred mysteries.’”11

http://www.mostholyfamilymonastery.com/6_noheretic_pope.pdf