Translate the following inference to logic notation: For all x, x_11 will sleep. For all x, if x_11 were a doctor, then x_11 is cooking. For all x, if x_11 climbs a mountain, then x_11 is a doctor. There is at least one x for which if x_11 drinks water, then x_11 is climbing a mountain. For all x, if x_11 cooks, then x_11 is not sleeping. Therefore there is at least one x for which x_11 will not drink water.
forall x: P(x). forall x: Q(x) -> R(x). forall x: S(x) -> Q(x). exists x: T(x) -> S(x). forall x: R(x) -> ~P(x). Therefore exists x: ~T(x).