The case type pronoun that is required to complete the sentence would be A) nominative. It is the subject case, and since we need a subject here, nominative is the option we have to use. For example:
They and the other vaulters have been training for months.
They is a nominative personal pronoun.
Possessive would be theirs, and as you can see, it doesn't fit.
Objective would be them, and it is also incorrect.
Antecedent just means a pronoun.
