You are bounded by the fact that the statement is provable. Let a statement M be provable with a proof length K. By contradiction, if K is non finite, the statement must not be provable. Thus, there must be some positive integer K s.t. the proof length < K. Thus, it suffices to enumerate all proofs of length < K.
Insofar as we are given provability, we can solve halting.
Insofar as we are given provability, we can solve halting.