Translate the following inference to logic notation: For all x, x_12 will not drink water or x_12 will cook. For all x, x_12 is not an astronaut or x_12 will write a letter. For all x, x_12 will drink water or x_12 is an astronaut. For all x, x_12 will go running. There is at least one x for which if x_12 cooks, then x_12 is not running. Therefore there is at least one x for which x_12 will write a letter.
forall x: ~P(x) or Q(x). forall x: ~R(x) or S(x). forall x: P(x) or R(x). forall x: T(x). exists x: Q(x) -> ~T(x). Therefore exists x: S(x).