A mathematical theorem proved by one mathematician should not be accepted until each step in its proof has been independently verified  Computer-assisted proofs generally proceed by conducting a vast number of calculations -- surveying all the possible types of instances in which the theorem could apply and proving that the theorem holds for each type  In most computer-assisted proofs there are astronomically many types of instances to survey, and no human being could review every step in the proof
Hence, computer-assisted proofs involving astronomically many types of instances should not be accepted
The use of an independent computer program does not satisfy the requirement for independent verification of each step in a proof that is extended enough to be otherwise unverifiable.