The present pope of the Catholic Church is Pope Benedict. HE STILL BELIEVES HE HAS THE CHARISMS OF THE PAPACY. Therefore, there are limited possibilities:
1) Pope Benedict is wrong; he does not have charisms of the papacy. But if this is true, then he has mistakenly (not willingly) renounced the papacy. Since a pope must WILLINGLY renounces the papacy, this is a self-contradicting notion.
2) Pope Benedict has expressed himself poorly; he intended to relinquish the charisms of the papacy despite his later statements.
3) Both Pope Benedict and Pope Francis are popes. This seems impossible.
4) Pope Francis was invalidly elevated. This has happened before, and therefore seems imminently possible.
Since only #2 and #4 are likely possible, and the truthfulness of #2 is unclear, #4 must be regarded as possible. In that case, we must look to the fruits, wherein we find that Pope Francis has sown utterly astounding moral confusion. While he has not directly invoked his infallibility to unambiguously proclaim heresy, he has plainly and unmistakably led anyone who follow him as a sheep follows a shepherd into heresy.
To use the technical term from Catholic theology: BINGO!