Let's read Vatican I chapter two called "the permanence of the primacy of blessed Peter in the Roman Pontiffs." My comments are in italics
On the permanence of the primacy of blessed Peter in the Roman pontiffs1. That which our Lord Jesus Christ, the prince of shepherds and great shepherd of the sheep, established in the blessed apostle Peter, for the continual salvation and permanent benefit of the Church, must of necessity remain for ever, by Christ's authority, in the Church which, founded as it is upon a rock, will stand firm until the end of time .This alone put the nail in the coffin of sedevacantism that says or implies there never will be another pope. It states the Papacy is for the "CONTINUAL SALVATION" and "PERMANENT benefit of the Church" a sedevacantism might make an aburd argument that this might refer to the benefit of the past, long dead popes, however, the next statement destroys this notion by saying the papacy must "of necessity REMAIN FOR EVER." How in any sense can the papacy "remain forever" and have no occupant for 50 years? Especially, after all the Cardinals have long died?! Since, there are no procedures in Church Law for electing Popes by non Cardinals it must be conceded that there never will be another pope! This heretical, sedevacantist position logically means the papacy's "remaining forever" is not actually a "NECESSITY" for the Church!Furthermore, the words about the Chuch being founded on the Rock, which is Peter and the Popes (St Peter's successors), show that the Church stands firm because Christ established the papacy to last "until the end of time."
2. For no one can be in doubt, indeed it was known in every age that the holy and most blessed Peter, prince and head of the apostles, the pillar of faith and the foundation of the Catholic Church, received the keys of the kingdom from our lord Jesus Christ, the savior and redeemer of the human race, and that to this day and for ever he lives and presides and exercises judgment in his successors the bishops of the Holy Roman See, which he founded and consecrated with his blood .This quotes the words of a Papal Legate at the Ecumenical Council of Chalcedon. Even back then it was recognized St Peter would have perpetual successors! Notice it says ST Peter "FOR EVER" "lives and presides....in his successors." Taking a position that there can be no more pope denies these very words! The sedevacantist position would mean that St Peter NO LONGER "lives and presides and excercises judgement in his successors"! Sedevantists when they read this have to ignore the word successors!
I do not expect a serious answer from a Sedevacantist. Since, in my experience 9/10 of them are just "Demon Bros" clones that get the vast majority of their misinformation from those heretics. And yes, they are heretics for their denial of Catholic dogma such as "baptism of desire." They are major proponents of "Extra Ecclesia Nulla Salis." They will be judge by this doctrine on Judgement Day when they are proved to be OUTSIDE the Church (should they die in their sinful error) for their denial of Christian dogma, being authors of schism, and for rejecting the Rock on which the Lord built His Church! Below are two videos I recently made on Sedevacantism.5. Therefore, if anyone says that it is not by the institution of Christ the lord himself (that is to say, by divine law) that blessed Peter should have perpetual successors in the primacy over the whole Church; or that the Roman Pontiff is not the successor of blessed Peter in this primacy: let him be anathema.It says St Peter would have "perpetual successors." Sedevacantists try to say this is qualified by the following phraise "in the primacy," the pretend this means "as long as there is a pope he will be in the primacy." However, read the rest of the canon and it specifically condemns the idea that maybe the Roman Pontiff is not the successor of St Peter in the primacy. The sedevancantists might have a point if the word "perpetual" were ommited, and the canon said instead "that blessed Peter should have successrs in the primacy"! However, the word PERPETUAL is there. They can try all the want to make this word superfluous.