http://strobertbellarmine.net/books/Concerning_A_SSPX_Dossier_on_Sedevacantism.pdf

15.  Fr. Boulet has now completed his explanation of the principles which he believes govern judgements of heresy and the loss of papal office attendant upon public (or notorious) heresy.  Now he highlights difficulties inherent in the sedevacantist theories he has seen.

4.  Problems with the Sedevacantist thesis:  After the study of the theological and canonical possibility for a Pope to fall into heresy, let me go to the subject that concerns us, namely what we can think about the sedevacantist theories which are being promoted around us.

Before reviewing these difficulties, please recall that the theory of the bulk of sedevacantists is rather dull in comparison with some explanations of the crisis.  As already explained, it consists simply in denying that Paul VI was Pope when he promulgated the docuмents of Vatican II and the Novus Ordo Missae, and denying that John Paul II was Pope when he promulgated his numerous erroneous and even heretical encyclicals, as well as the 1983 Code, and consequent upon these twin denials, that Benedict XVI as the open and unrepentant follower and successor of these two anti-Popes has made his own the acts of these two revolutionaries, and thus involves his "papacy" in their common condemnation.  The root and cause of this theory is that the infallibility and indefectibility of the Church demands it.  The "Pope heretic" thesis is a solution resorted to as a result of the difficulties inherent in considering that the Vatican II revolution was prosecuted by legitimate ecclesiastical authority.  In other words, we look to the classical discussions of the "Pope heretic" thesis by the great theologians as a solution to the otherwise-insoluble problems of ecclesiology posed by the revolution of Vatican II.  

It will immediately be recognised that this is a minimalist position.  That we do not seek to assert things we do not know with certitude.  That were there is insoluble mystery we leave it aside, rather than pose a rash and false solution.  In other words, our sedevacantism is the least we can honestly assert, not the most.  We only hold these claimants to be false claimants because we cannot avoid doing so.