Translate the following inference to logic notation: For all x, if x_6 were a server, then x_6 is climbing a mountain. There is at least one x for which if x_6 goes running, then x_6 is a scientist. For all x, if x_6 climbs a mountain, then x_6 is running. For all x, if x_6 were a scientist, then x_6 is a server. Therefore there is at least one x for which x_6 will climb a mountain if and only if x_6 will go running.
forall x: P(x) -> Q(x). exists x: R(x) -> S(x). forall x: Q(x) -> R(x). forall x: S(x) -> P(x). Therefore exists x: Q(x) <-> R(x).