Translate the following inference to logic notation: For all x, x_13 is a lawyer if and only if x_13 will climb a mountain. For all x, if x_13 climbs a mountain, then x_13 is a bartender. For all x, x_13 is not a lawyer. For all x, x_13 is a bartender or x_13 is a poet. There is at least one x for which if x_13 were a bartender, then x_13 is climbing a mountain. Therefore there is at least one x for which x_13 is a poet.
forall x: P(x) <-> Q(x). forall x: Q(x) -> R(x). forall x: ~P(x). forall x: R(x) or S(x). exists x: R(x) -> Q(x). Therefore exists x: S(x).