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Francis fits the definition of an anti-pope.  He's technically still vying for the Seat, since Benedict claims to still hold partial office.

The precedence is Antacletus II, anti-pope of 1130.    So you can say he's the "Pope"... and pray for him.  Mother Mary described him as "worm ridden".

St. Francis of Assisi described him as a "non canonically elected destroyer". 

He will go down in history with the name of "Pope" and with the prefix, "anti" for eternity.

Agreed. The bolded part is the reason that Cardinal Bergoglio is not and has never been the authentic Pope.

1. Benedict's "resignation" was not valid according to Canon Law, so whether Benedict intended it or not, he is still the Pope in the eyes of God and by Church law.

2. A new Pope cannot be elected until the See is vacated. So the March 2013 Conclave, even if legitimate in every way, cannot produce a new sitting Pope until Benedict properly resigns.

3. So what we have is the equivalent of Sede Privationism, except that Benedict (not Bergoglio) is the actual Pope and has had his power removed by his enemies (Bergoglio and the C9, aka the 10 horns of the Beast). Benedict is a prisoner, while his putative replacement illegitimately claims the See. All legitimate acts of "the Pope" have ended unless and until Benedict resumes his Papacy or Benedict dies.

4. Everything Bergoglio does is canonically irrelevant, but those who believe the deception that he is the legitimate Pope will be scandalized and fall away from the Catholic faith. So what Bergoglio has done and is doing is practically relevant in the arena of trying to save souls of scandalized Catholics. 

5. If Benedict dies before Bergoglio (which is unlikely), then the questions surrounding illegal vote-trading in Bergoglio's election would come into play. Because of those shenanigans, Bergoglio would still be an illegitimate pope according to Canon Law.

6. The Antichrist will soon be revealed (in less than 3 years). He is either Bergoglio himself or someone close to him in the nascent Counterfeit Church. A new "religion of woke" with the God of the Abrahamic House (Father) and the Mother Pachamama (Mother) will give birth to Brotherhood of Man/Satan (Son). This new Unholy Trinity will be fully-formed Counterfeit Church, the Beast ridden by the Whore of Babylon.

Agreed. The bolded part is the reason that Cardinal Bergoglio is not and has never been the authentic Pope.

1. Benedict's "resignation" was not valid according to Canon Law, so whether Benedict intended it or not, he is still the Pope in the eyes of God and by Church law.

2. A new Pope cannot be elected until the See is vacated. So the March 2013 Conclave, even if legitimate in every way, cannot produce a new sitting Pope until Benedict properly resigns.

3. So what we have is the equivalent of Sede Privationism, except that Benedict (not Bergoglio) is the actual Pope and has had his power removed by his enemies (Bergoglio and the C9, aka the 10 horns of the Beast). Benedict is a prisoner, while his putative replacement illegitimately claims the See. All legitimate acts of "the Pope" have ended unless and until Benedict resumes his Papacy or Benedict dies.

4. Everything Bergoglio does is canonically irrelevant, but those who believe the deception that he is the legitimate Pope will be scandalized and fall away from the Catholic faith. So what Bergoglio has done and is doing is practically relevant in the arena of trying to save souls of scandalized Catholics.

5. If Benedict dies before Bergoglio (which is unlikely), then the questions surrounding illegal vote-trading in Bergoglio's election would come into play. Because of those shenanigans, Bergoglio would still be an illegitimate pope according to Canon Law.

6. The Antichrist will soon be revealed (in less than 3 years). He is either Bergoglio himself or someone close to him in the nascent Counterfeit Church. A new "religion of woke" with the God of the Abrahamic House (Father) and the Mother Pachamama (Mother) will give birth to Brotherhood of Man/Satan (Son). This new Unholy Trinity will be fully-formed Counterfeit Church, the Beast ridden by the Whore of Babylon.

The fact that Benedict is still alive is somewhat providential. He "resigned" (whether or not one believes it) in 2013 and is still alive and, last I checked, quite well. That's very strange given all that's been going on.

Whether or not he's the Pope is beyond me. I doubt it. But know that Bergoglio simply cannot be because A: he is a manifest heretic; and B: he is most likely not even a real priest since he was ordained in the new rite, Benedict is at least a legitimate priest yet (not that that helps the Pope question anyway)