Translate the following inference to logic notation: There is at least one x for which x_9 is a doctor if and only if x_9 is a taxi driver. For all x, if x_9 climbs a mountain, then x_9 is a soldier. For all x, if x_9 were a taxi driver, then x_9 is climbing a mountain. Therefore there is at least one x for which if x_9 were a doctor, then x_9 is a soldier.
exists x: P(x) <-> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). Therefore exists x: P(x) -> S(x).