CathInfo.com

Stubborn, don't ask sedevacantists, ask the infallible and extraordinary magisterium of the Church of Our Lord:
https://www.papalencyclicals.net/councils/ecuм20.htm

We are "bound to submit to" the Roman pontiff "by the duty of hierarchical subordination and true obedience, and this not only in matters concerning faith and morals, but also in those which regard the discipline and government of the church throughout the world."

Note that V1 states we owe the pope *true obedience*, yet this is impossible unless we always maintain the highest of all principles in the Church: "We are first of all under obedience to God, and only then under obedience to man". Leaving it at that, we come to a full stop, period. Sedes cannot stop there, they have some need to insist popes are not popes, as if that opinion is their religious obligation.

The Father and Christ are one. The Church and Christ are not one.

Christ is Christ. The Church is the Church. Christ is not the Church. The Church is not Christ.

The Church is in a mysterious way the Body of Christ, not actually, not literally but in a figurative sense.

Sorry but Christ and the Church are one and the same. So says St. Paul, many popes and saints etc,. You can look it up if you want. To say otherwise is to admit that Christ is not the Head of the Church. The Church is Christ's Mystical Body (head included) of which we (Catholics) are members. We are not the body of Christ, we are members of His Body (head included). Christ and the Church are one.

No one can believe in Christ, and at the same time not believe in His Church. As Pope Pius XII said referencing St. Paul, Christ and the Church are one: "The doctrine of the Mystical Body of Christ, which is the Church, was first taught us by the Redeemer Himself" and this has been repeated throughout many papal teachings, St. Augustine also taught that you can never separate Christ from the Church because the two are one.

At any rate, you can investigate on your own, the bottom line is, the indefectibility of the Church is not our concern, it is our foundation.

One arrives at a contradiction, if it is not possible to obey God and the Pope at the same time. Consequently, there is some error in the assumptions. One possibility: the Pope is not the Pope.

Do you know of any other possibility?

Yes, the popes have corrupted themselves, became modernist heretics and have lost the faith, while at the same time believing they're under the Holy Ghost's protection so whatever they teach can never harm the faithful or the Church, and they are always infallibly safe to follow.

I know, I know - Enter V1's teaching that quotes Our Lord praying that St. Peter not lose the faith....this divine revelation from Our Lord has not been in any way compromised or otherwise infringed upon, because it is a revelation from Our Lord Himself.     this is because Our Lord was referring to when the pope engages his papal infallibility. I cannot remember which if the Fathers taught this, but will look it up when I get the chance, or you can when you get the chance.  

At any rate, as regards the Church's infallibility and indefectibility, words of wisdom.....
"If these two Doctrines be true, then whatever the popes have said or done, whatever they ever say or do, will not be a violation of the Church' s attribute of infallibility. And no matter what anyone does, whether from within or without, he will not succeed in destroying the Church. The enemies of Christ's Church do not believe this, which explains why they will never cease to try". - Fr. Wathen, Who Shall Ascend?