Translate the following inference to logic notation: For all x, x will not drink water. For all x, if x sleeps, then x is drinking water. There is at least one x for which x will go running if and only if x will sleep. Therefore there is at least one x for which x will not go running.
forall x: ~P(x). forall x: Q(x) -> P(x). exists x: R(x) <-> Q(x). Therefore exists x: ~R(x).