Bergoglio has an impediment to becoming pope as a Jesuit.

The false testimony and perjury, are crimes against public faith.

Bergoglio committed sin of perjury when he violated his priestly oath that all Jesuits make to God, to don't aspire or accept high ecclesiastical offices, which is an impediment keeping them from becoming pope. By breaking the oath he committed a mortal sin against the Second Commandment.

2016-10-18  The progressive Marxist Arturo Sosa, the new general, of the neo- Jesuits said:

"I think Mulemi is better suited for it. Regarding being called the 'black pope,' I don't like it.  Because the Jesuits, as probably many of you know we make a vow, a promise of neither aspire nor accept ecclesiastical offices ”  

Romereports edited the quote

“He’s a man that’s sick with power.”

Msgr. Adriano Bernardini, the then nuncio to Argentina
speaking about Cardinal Jorge Mario Bergoglio

In the New York Times article Laurie Goodsteinmarch wrote:

Men who join the Jesuits, the Roman Catholic Church’s largest religious order, take vows of poverty, chastity and obedience, and promise never to take any high office in the church.

The Jesuits are distinguished by their vow to obey the pope and to serve where he commands. The Rev. Antonio Spadaro, editor of La Civiltà Cattolica, a Jesuit journal in Rome, said in an interview that before the papal conclave, journalists were asking him whether Cardinal Bergoglio could be pope.

“And I said, ‘Not at all, because he’s a Jesuit,’ ” Father Spadaro said in an interview in his office on Friday. “We are used to serving a pope, not to be a pope.”
The Rev. Federico Lombardi, a Jesuit who serves as the Vatican spokesman, said that when he saw Cardinal Bergoglio emerge on the balcony of St. Peter’s Basilica as the new pope, “I was dumbfounded.”

The Jesuit Bartolomeo Sorge, about  Bergoglio's "election",  said:

"We, the Jesuits can be neither Monsignori, or bishops, indeed we vow to reject all ecclesiastical dignities. Much less, therefore, it was not foreseeable that a Jesuit would become pope. "

This means that Bergoglio  is not a pope because by oath he has an impediment by the same order of the Jesuits. 

In Mexican TV interview Bergoglio  talking about his invalid election said: "And next, I do not know what happened," he continues. "They made me stand up. They asked me if I agreed. I said yes.  I do not know if they made me swear something, I do not know do not remember."

Catechism of Saint Pius X

Q. What sin does he commit who swears falsely?
A. He who swears falsely commits a mortal sin, because he grievously dishonours God, the Infinite Truth, by calling Him to witness what is false.

 Q. What does the Second Commandment command us to do?
A. The Second Commandment commands us to honour the Holy Name of God as well as to keep our oaths and vows.