Ancient tradition credited the Athenian Thespis as having

dushyanta , when credit as a verb followed by another verb (an action), credit takes with.

Correct: She is credited with saving the company.
Correct: If the whistleblower is treated as the law requires, he will be credited with having restored at least some degree of force to the rule of law.

Credit as a verb takes to only if a noun (and not an action) follows the verb credit:
Correct: The song was credited to the wrong composer.
Correct: The refund will be credited to your account.

In options D and E, credited is followed by two different verbs: to have invented and to be the inventor for.
I doubt that credited to be is ever correct, but in any case, to be is a verb and thus cannot be paired with the verb credit.
Credited to have invented is also wrong because to have invented is a verb phrase.

Credit with followed by action/verb is correct.

To give credit to someone for something is common and idiomatic, but in that case, credit is a noun.
See earlier posts in the thread; they address noun usage.