Bergoglio is not Catholic, therefore he is not the pope.
CUM EX APOSTOLATUS OFFICIO - APOSTOLIC CONSTITUTION OF HIS HOLINESS POPE PAUL IV, 15TH FEBUARY 1559 - (ROMAN BULLARIUM VOL. IV. SEC. I, PP. 354-357)
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;
And, like ALL automatic penalties in Canon Law, absolutely meaningless and without effect.