Translate the following inference to logic notation: For all x, x_12 will climb a mountain if and only if x_12 is a soldier. For all x, x_12 will climb a mountain or x_12 will listen to a song. For all x, if x_12 drinks water, then x_12 is a soldier. For all x, x_12 will drink water if and only if x_12 will listen to a song. Therefore for all x, x_12 is a soldier.
forall x: P(x) <-> Q(x). forall x: P(x) or R(x). forall x: S(x) -> Q(x). forall x: S(x) <-> R(x). Therefore forall x: Q(x).