But the "computer" is magic, to you.
I could prove anything by claiming I completed a trivial-to-explain exhaustive search. The only support or refutation would be someone doing their own search. It's a very weak foundation.
We already had the ABC conjecture crisis: A theorem with a human-written proof so complex that no one besides the author can understand it. Some people claim to have refuted it. Most mathematicians are unqualified to decide.
If you prove that the theorem prover’s true and false determinations are correct—in the cases in which it can make them—then Bob’s your uncle.