Translate the following inference to logic notation: For all x, if x_4 were a mechanic, then x_4 is playing a game. For all x, if x_4 were a poet, then x_4 is a mechanic. There is at least one x for which x_4 is excited or x_4 is not a poet. For all x, if x_4 plays a game, then x_4 is a poet. Therefore there is at least one x for which if x_4 were a mechanic, then x_4 is excited.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: S(x) or ~R(x). forall x: Q(x) -> R(x). Therefore exists x: P(x) -> S(x).