Translate the following inference to logic notation: For all x, if x_12 were a poet, then x_12 is not a musician. For all x, if x_12 listens to a song, then x_12 is a poet. There is at least one x for which x_12 is a musician. For all x, if x_12 were fast, then x_12 is listening to a song. Therefore there is at least one x for which x_12 is not fast.
forall x: P(x) -> ~Q(x). forall x: R(x) -> P(x). exists x: Q(x). forall x: S(x) -> R(x). Therefore exists x: ~S(x).