What are the legal proofs (evidences) over which the Usuliyyun (Juristic Theorists) differ, and what is their effect on juristic disagreement?

The differing opinions among jurists regarding the authority of disputed evidences—such as istishab (presumption of continuity), the saying of a Companion, the law of previous prophets, istihsan (juristic preference), and al-masalih al-mursalah (unrestricted public interests)—have led to their disagreements on many subsidiary jurisprudential issues.

For example, the disagreement over the authority of istishab led to their differing views on the inheritance of a missing person: Is he considered alive, and thus not inherited from, or dead, and therefore inherited from?

Similarly, the disagreement over the authority of a Companion's saying resulted in their differing views on the ruling of prostration of recitation (sujud al-tilawah): Is it obligatory or sunnah (recommended)?

Furthermore, the disagreement over the authority of the law of previous prophets led to their differing views on issues such as the permissibility of marriage with the wording of ijarah (leasing), the ruling on vowing to slaughter a child, and the obligation of udhiyah (sacrifice).

Their differing views on the authority of al-masalih al-mursalah impacted issues like the killing of a group for one person, and the imprisonment of a claimant of bankruptcy.