Translate the following inference to logic notation: There is at least one x for which if x_6 cooks, then x_6 is climbing a mountain. For all x, x_6 will climb a mountain if and only if x_6 will take a plane. For all x, x_6 will take a plane or x_6 is a bartender. For all x, if x_6 were a bartender, then x_6 is cooking. Therefore there is at least one x for which x_6 will climb a mountain.
exists x: P(x) -> Q(x). forall x: Q(x) <-> R(x). forall x: R(x) or S(x). forall x: S(x) -> P(x). Therefore exists x: Q(x).