The author is trying to partially discredit the use of computers to prove mathematical theorems, so making positive assumptions about them is not necessary to his argument.

The proportion of successful attempts is irrelevant: the author is concerned with the process for verifying attempts.

The author’s argument is about verifying theorems that have many steps. So he doesn’t need to make any assumptions about proofs with only a few steps.

This would suggest a limitation of non-computer math proofs. Since the author’s aim is to partially discredit computer-assisted math proofs, this assumption is not necessary to his argument.

Negated, this is: the use of an independent computer program does satisfy the requirement for independent verification. If so, the author’s argument that computer-assisted proofs shouldn’t be accepted because they can’t be verified collapses. Consequently, he must assume that (E) is true.