Many Sedevacantists quote the papal bull
Cum Ex Apostolatus, of Paul IV, as a
legal basis for their position that the Popes after Pius XII were not
legitimate Popes.
In the following quotation, the
Sedevacantist Bishop, Donald Sanborn, rector of Most Holy Trinity Seminary, explains the two reasons this argument, which is used by his fellow Sedevacantists, is false: First, Cum ex
Apostolatus was derogated by the 1917 Code, and hence no longer has legal
force. Second, even if it were in force, it would only not apply to the recent Popes, since they are not legally recognized as heretics by the Church. Sanborn only mentions Benedict/Ratzinger by name (since it was written prior to his abdication), but the same applies to Francis and the other recent Popes.
The following is taken from Bp. Sanborn’s
explanation of the Sedeprivationist Thesis of Guérard des Lauriers:
Q. Does not Cum ex apostolatus of Pope
Paul IV contradict the thesis?
A. Cum ex apostolatus is an apostolic
constitution, a law, made by Pope Paul IV, which says that if a pope should be
a heretic, his elevation to this dignity would be null. It was made in order to
ensure that no Protestant could ever become the Pope. It does not apply to
the present case for two reasons. The first is that it is no longer the law.
It was derogated (made obsolete) by the 1917 Code of Canon Law. The
second reason, and the more important, is that even if it should for some cause
still have force, it could only apply to Ratzinger if he were legally
recognized as a public heretic. But, as we have seen, there is no legal
condemnation of Ratzinger. Before the law of the Church he does not have the
status of heretic because (1) he himself does not hold himself guilty of
heresy, and (2) no legitimate superior holds him guilty of heresy. Cum ex
apostolatus certainly expresses the mind of the Church with regard to heretics
holding office. It makes an excellent theological argument, but it does not
make a legal argument.” http://mostholytrinityseminary.org/wp-content/uploads/2019/01/Explanation-of-the-Thesis.pdf
One final point is that Bishop
Sanborn’s admission that Cum ex
Apostolatus is “no longer law” shows that he's well aware that it does not
retain legal force simply because it is referenced in a footnote to Canon
188.4, which is another argument used by his fellow Sedevacantists. Canon Gregory Hesse teaches the same in this video.
* Fr. Coronata also explains that Cum ex Apostaolatus is
null in Institutiones Iuris Canonici.