Translate the following inference to logic notation: For all x, x_7 is not excited. There is at least one x for which if x_7 were a writer, then x_7 is a carpenter. For all x, if x_7 were a writer, then x_7 is excited. For all x, if x_7 were a carpenter, then x_7 is listening to a song. For all x, if x_7 listens to a song, then x_7 is a writer. Therefore there is at least one x for which x_7 is not a carpenter.
forall x: ~P(x). exists x: Q(x) -> R(x). forall x: Q(x) -> P(x). forall x: R(x) -> S(x). forall x: S(x) -> Q(x). Therefore exists x: ~R(x).