Translate the following inference to logic notation: For all x, x_7 is fast if and only if x_7 is bored. For all x, x_7 will climb a mountain if and only if x_7 is bored. For all x, x_7 will not climb a mountain. There is at least one x for which if x_7 drinks water, then x_7 is fast. Therefore there is at least one x for which x_7 will not drink water.
forall x: P(x) <-> Q(x). forall x: R(x) <-> Q(x). forall x: ~R(x). exists x: S(x) -> P(x). Therefore exists x: ~S(x).