Translate the following inference to logic notation: For all x, x_8 will climb a mountain if and only if x_8 will sleep. For all x, if x_8 drinks water, then x_8 is climbing a mountain. For all x, x_8 will drink water or x_8 will listen to a song. For all x, x_8 will not sleep. Therefore for all x, x_8 will listen to a song.
forall x: P(x) <-> Q(x). forall x: R(x) -> P(x). forall x: R(x) or S(x). forall x: ~Q(x). Therefore forall x: S(x).