Translate the following inference to logic notation: For all x, if x_12 were a bartender, then x_12 is climbing a mountain. There is at least one x for which if x_12 were a bartender, then x_12 is not cooking. For all x, x_12 will cook. For all x, x_12 will climb a mountain if and only if x_12 is a bartender. Therefore there is at least one x for which x_12 will not climb a mountain.
forall x: P(x) -> Q(x). exists x: P(x) -> ~R(x). forall x: R(x). forall x: Q(x) <-> P(x). Therefore exists x: ~Q(x).