grammaticality - "the witness that testifies for passing of time." Why *for* instead of *the*?

All of the potential answers are wrong. This is a famous quotation from Cicero. And it is invariably translated:

History is the witness that testifies to the passing of time.

(Or sometimes "history is the witness of the times", which may be closer to what Cicero meant.)

You testify for or against somebody, but you testify to a fact or event. So (b) and (c) are incorrect. And testify is generally an intransitive verb, so (a) is incorrect. And (d) is much worse than all of the other choices.