Translate the following inference to logic notation: For all x, x_12 is not an artist. For all x, if x_12 plays tennis, then x_12 is sleeping. For all x, if x_12 were a writer, then x_12 is playing tennis. For all x, if x_12 were an artist, then x_12 is playing tennis. There is at least one x for which if x_12 sleeps, then x_12 is a writer. For all x, if x_12 plays tennis, then x_12 is an artist. Therefore there is at least one x for which x_12 is not a writer.
forall x: ~P(x). forall x: Q(x) -> R(x). forall x: S(x) -> Q(x). forall x: P(x) -> Q(x). exists x: R(x) -> S(x). forall x: Q(x) -> P(x). Therefore exists x: ~S(x).