Translate the following inference to logic notation: There is at least one x for which x_9 will not sleep. For all x, x_9 will cook if and only if x_9 will sleep. For all x, x_9 will cook. Therefore there is at least one x for which x_9 will climb a mountain.
exists x: ~P(x). forall x: Q(x) <-> P(x). forall x: Q(x). Therefore exists x: R(x).