Translate the following inference to logic notation: For all x, x_6 will not drink water. For all x, if x_6 goes running, then x_6 is taking a plane. For all x, if x_6 takes a plane, then x_6 is drinking water. For all x, if x_6 drinks water, then x_6 is running. There is at least one x for which x_6 will work if and only if x_6 will go running. Therefore there is at least one x for which x_6 will not work.
forall x: ~P(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). forall x: P(x) -> Q(x). exists x: S(x) <-> Q(x). Therefore exists x: ~S(x).