Exercise 12.3. Is the Check-Proof Problem described below computable?

Exercise 12.3. Is the Check-Proof Problem described below computable? Provide a convincing argument supporting your answer.

Check-Proof

Check-Proof

Input: A specification of an axiomatic system, a statement (the theorem), and a proof (a sequence of steps, each identifying the axiom that is applied).}

Output: Outputs True if the proof is a valid proof of the theorem in the system, or False if it is not a valid proof.