What is the required proof to see the clear disbelief in disputing the matter with its people?

Scholars have differed on the meaning of "kufr" (disbelief) mentioned in the Hadith. Some interpret it as major sins, and they believe that challenging the ruler should be through denunciation and clarification of the truth, not through rebellion. Others take "kufr" literally, and they believe that challenging the ruler means to rebel against them.

In both interpretations, "proof" (burhan) refers to a decisive text and clear evidence that the act constitutes manifest kufr. If kufr means major sins, then challenging the ruler is through denunciation, not rebellion. If kufr is taken literally, then challenging the ruler might escalate to fighting, but this is only permissible if there is manifest kufr for which there is a decisive text and clear evidence.

Sheikh Ibn Uthaymeen set conditions for rebellion against a ruler if he commits manifest kufr: that the kufr be known with certainty, not mere suspicion; that it be actual kufr and not mere transgression (fisq); that the kufr be manifest and explicit, not open to interpretation; and that there be proof and decisive evidence from Allah that it is indeed kufr.

In general, scholars have agreed on the obligation to denounce evil according to one's ability, and that it is not permissible to rebel against rulers due to their transgression. They also agreed that rebellion against them through fighting is not permissible unless there is manifest kufr for which there is a decisive text not open to interpretation.