I’m looking for the best examples in the Pali canon where it can be conjectured that the Buddha uses a logical proof that relies upon the Law of the Excluded Middle to reach some conclusion.
Specifically, I’m looking for any/all examples in the canon where the Buddha draws some conclusion about the truth value of some proposition based on logically analyzing the proposition while employing LEM in the proof.
EDIT:
To clear up a misunderstanding I’m not looking for examples where the Buddha used Reductio Ad Absurdum (RAA) nor am I looking for examples where the Buddha made the proposition (P ^ ~P), but rather where the Buddha specifically used LEM as in classical logic as proof of some positive truth.
I’m looking for examples in the Pali canon where the Buddha is specifically using examples of classical logic (which uses LEM) in a way that would run afoul of constructivist logic which does not allow indirect proof, but does allow RAA.
Some terms:

Reductio Ad Absurdum (RAA): Involves assuming a proposition P, and from this assumption, deriving a contradiction (typically of the form Q∧¬Q). The presence of this contradiction allows us to conclude ¬P. This is RAA and does not rely upon LEM as an axiom.

Indirect Proof which implies LEM: This method starts by assuming ¬P and then deriving a contradiction (again, often of the form (Q∧¬Q). The contradiction leads to the conclusion that P must be true.
To make this very simple:
 Assume
P
, find a contradiction or absurdity and concludenot P
→ RAA  Assume
not P
, find a contradiction or absurdity and concludeP
→ LEM
I’m looking for cases of #2 and not for #1.
Thank you !