Translate the following inference to logic notation: For all x, if x_12 climbs a mountain, then x_12 is a soldier. Elisabeth is not a soldier. If Elisabeth doesn't climb a mountain, then it is raining. For all x, if x_12 were a soldier, then x_12 is climbing a mountain. Therefore it is raining.
forall x: P(x) -> Q(x). ~Q(a). ~P(a) -> p. forall x: Q(x) -> P(x). Therefore p.