Translate the following inference to logic notation: For all x, x_14 is a sailor if and only if x_14 is a bartender. For all x, if x_14 climbs a mountain, then x_14 is a sailor. For all x, if x_14 were a sailor, then x_14 is climbing a mountain. There is at least one x for which if x_14 climbs a mountain, then x_14 is playing a game. Therefore there is at least one x for which if x_14 were a bartender, then x_14 is playing a game.
forall x: P(x) <-> Q(x). forall x: R(x) -> P(x). forall x: P(x) -> R(x). exists x: R(x) -> S(x). Therefore exists x: Q(x) -> S(x).