Translate the following inference to logic notation: For all x, if x_8 were fast, then x_8 is a server. There is at least one x for which x_8 is happy or x_8 is not a server. For all x, x_8 is bored or x_8 is fast. For all x, if x_8 were bored, then x_8 is happy. Therefore there is at least one x for which x_8 is happy.
forall x: P(x) -> Q(x). exists x: R(x) or ~Q(x). forall x: S(x) or P(x). forall x: S(x) -> R(x). Therefore exists x: R(x).