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