It seems natural to evaluate existential quantifiers using model-checking and any universally quantified statement can be transformed into an existentially quantified statement by applying double-negation and moving the inner negation through the quantifier.
Example:
forall x. p(x)
not (not (forall x. p(x)))
not (exists x. (not p(x)))
But I can’t think of how to apply this to Yudkowsky’s example so it’s probably useless for teaching :P
Exercise: Add as many qualifiers as you can that do not make your statement irrelevant or false.
For example:
Well, never mind, that didn’t work.