Translate the following inference to logic notation: For all x, if x_12 were an artist, then x_12 is working. For all x, x_12 will sleep if and only if x_12 will work. For all x, x_12 will play squash. There is at least one x for which x_12 is an artist or x_12 will sleep. Therefore there is at least one x for which x_12 will play squash and x_12 will work.
forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). forall x: S(x). exists x: P(x) or R(x). Therefore exists x: S(x) and Q(x).