Translate the following inference to logic notation: For all x, x_6 will work or x_6 will sleep. There is at least one x for which x_6 will play a game. For all x, x_6 is a doctor. For all x, if x_6 works, then x_6 is not a doctor. Therefore there is at least one x for which x_6 will play a game and x_6 will sleep.
forall x: P(x) or Q(x). exists x: R(x). forall x: S(x). forall x: P(x) -> ~S(x). Therefore exists x: R(x) and Q(x).