Select the grammatically correct option to complete the rival's statement.

"He claims to understand the complex rules of 4D quantum chess, but I highly doubt he actually _____."

The correct answer is does.

This question tests the restriction on the substitution phrase do so. We use "do so" (or "do it") to replace an action (dynamic verb). However, we cannot use "do so" or "do it" to substitute for a state (stative verbs like understand, know, like, or own).

Instead, we must use standard ellipsis, leaving only the auxiliary verb does to stand in for "understands the complex rules."