Translate the following inference to logic notation: For all x, x_5 is fast or x_5 will climb a mountain. For all x, x_5 is a police officer if and only if x_5 will climb a mountain. For all x, if x_5 were fast, then x_5 is sleeping. For all x, if x_5 sleeps, then x_5 is a police officer. Therefore for all x, x_5 is a police officer.
forall x: P(x) or Q(x). forall x: R(x) <-> Q(x). forall x: P(x) -> S(x). forall x: S(x) -> R(x). Therefore forall x: R(x).