Translate the following inference to logic notation: For all x, if x_4 drinks water, then x_4 is a doctor. There is at least one x for which x_4 is not a doctor. For all x, if x_4 were excited, then x_4 is drinking water. For all x, if x_4 were a doctor, then x_4 is drinking water. For all x, if x_4 were bored, then x_4 is excited. Therefore there is at least one x for which x_4 is not bored.
forall x: P(x) -> Q(x). exists x: ~Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> P(x). forall x: S(x) -> R(x). Therefore exists x: ~S(x).