Hmmm...well I am not a huge fan of the encyclical either, but I believe he is the valid Pope.
Previous Popes have written horrible encyclicals too, including some supporting slavery. But none have required Catholics to believe in slavery, and likewise Francis cannot bind Catholics on matters of economics or science anyway, so I do not see how this means he is not Pope.
The encyclical is awful. It is trash. It may be heresy. It certainly enshrined certain gnostic concepts. But going back to the start. I have questions about Benedict’s abdication. If his abdication is not on the up and up, then Bergoglio is an anti-pope.
As it is, based on the encyclical one, I have questions.