What is the ruling on deposing the Caliph in the four schools of thought?

Scholars have unanimously agreed on the obligation to obey a just Muslim ruler (Caliph) and the prohibition of rebelling against him, based on the Almighty's saying: {O YOU WHO HAVE BELIEVED, OBEY ALLAH AND OBEY THE MESSENGER AND THOSE IN AUTHORITY AMONG YOU} (4:59), and on prophetic traditions that emphasize listening to and obeying the ruler as long as clear disbelief is not apparent, or as long as he does not prevent prayer.

If the Caliph's disbelief or tyranny is proven, then the ruling on rebelling against him and deposing him is contingent upon the presence of benefit and the absence of a greater harm. A tyrannical Imam (ruler) is not to be deposed due to his injustice or فسق (transgression/immorality) after his imamate has been established. It is preferable to admonish him and not rebel against him to avoid greater harms. However, if a just Imam arises, then it is permissible at that point to rebel against the tyrannical Imam and assist the just one who has risen.

According to the four schools of thought, it is not permissible to depose a Caliph if he is just. And even if he commits disbelief or tyranny, his deposition is not permissible if it results in a greater harm, for averting harm takes precedence over attaining benefits.