Translate the following inference to logic notation: For all x, if y_2 climbs a mountain, then y_2 is poor. For all x, if y_2 were poor, then y_2 is a soldier. There is at least one x for which y_2 will not climb a mountain. For all x, if y_2 were a soldier, then y_2 is climbing a mountain. Therefore there is at least one x for which y_2 is not a soldier.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: ~P(x). forall x: R(x) -> P(x). Therefore exists x: ~R(x).