The perfectly rational agent considers all possible different world-states, determines the utility of each of them, and states "X", where X is the utility of the perfect world.

For the number "X+epsilon" to have been a legal response, the agent would have had to been mistaken about their utility function or what the possible worlds were.

Therefore X is the largest real number.

Note that this is a constructive proof, and any attempt at counterexample should attempt to prove that the specific X discovered by a perfectly rational omniscient abstract agent with a genie. If the general solution is true, it will be trivially true for one number.