One witness from Group A and one witness from Group B (which contradict each other) want to jointly testify about a new matter. Is this permitted?
Since we know certainly that one of them lied (the groups contradict each other), combining a witness from each group means certainly one of the two is a liar. Their joint testimony has no validity.
Question 2
Reuven has two notes against Shimon — one for 100 zuz signed by Group A and one for 200 signed by Group B (which contradict each other). How much must Shimon pay?
The bearer of notes with uncertain witnesses holds the weaker hand (yad ba'al ha-shtar al ha-tachtonah). Shimon pays the lesser amount — 100 zuz — and takes an oath about the additional 100.
Question 3
Reuven sues Levi with a note from Group A, and Shimon also sues Levi with a note from Group B (which contradicts Group A). What is the outcome?
Since certainly one of the two claimants (Reuven or Shimon) has a valid claim, both take a Rabbinic oath and collect. This is treated like a storekeeper who takes an oath based on his ledger.
Question 4
A plaintiff brings witnesses who are disqualified through hazamah. He brings another group — also disqualified. He then brings a third group whose testimony is found valid. Is judgment rendered on the basis of the third group?
Although the plaintiff is presumed to bring false witnesses, the third group has not themselves been presumed liars. Their testimony is evaluated independently and, if valid, the court adjudicates on its basis.
Question 5
Two witnesses testify that a plaintiff asked them to forge a specific document. The document's signatures are later validated. Can the document be used to collect?
A document about which a forger-protest has been raised is permanently tainted — it can never be used to collect, even if the signatures are authenticated. The Rambam notes one possible exception: if the witnesses to the document themselves testify about their own signatures.