No, that's a fallacy. A theorem prover in Prolog has a goal, which is contingent on it's continued existence. Yet, this doesn't make its existence into an instrumental goal. It could as well sacrifice itself (by I don't know, consuming all the memory and killing the process) in an attempt to accomplish said goal.
It literally does, this is by the definition of an "instrumental goal". The key word here being "contingent".
> It could as well sacrifice itself (by I don't know, consuming all the memory and killing the process) in an attempt to accomplish said goal.
True only for when self-sacrifice is orthogonal to accomplishing the terminal goal.
Your confusion might lie in that a prolog theorem solver is not a good example of a goal-driven agent.
Edit: The real clincher is if the AI has any goals that are contingent on it's continued existence (likely). Well then now it's existence is an instrumental goal.