Translate the following inference to logic notation: There is at least one x for which if x_6 sleeps, then x_6 is happy. For all x, x_6 will sleep. For all x, x_6 is happy if and only if x_6 will play a game. Therefore there is at least one x for which x_6 will play a game.
exists x: P(x) -> Q(x). forall x: P(x). forall x: Q(x) <-> R(x). Therefore exists x: R(x).