Translate the following inference to logic notation: For all x, if x_6 were a mechanic, then x_6 is excited. For all x, if x_6 were excited, then x_6 is climbing a mountain. There is at least one x for which if x_6 were a poet, then x_6 is a mechanic. For all x, if x_6 climbs a mountain, then x_6 is a poet. Therefore there is at least one x for which x_6 will climb a mountain if and only if x_6 is a poet.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: S(x) -> P(x). forall x: R(x) -> S(x). Therefore exists x: R(x) <-> S(x).