Translate the following inference to logic notation: There is at least one x for which x_13 will not cook. For all x, if x_13 were fast, then x_13 is happy. For all x, x_13 is a nurse or x_13 is fast. For all x, x_13 will cook or x_13 will go running. For all x, if x_13 were a nurse, then x_13 is happy. Therefore there is at least one x for which x_13 is happy and x_13 will go running.
exists x: ~P(x). forall x: Q(x) -> R(x). forall x: S(x) or Q(x). forall x: P(x) or T(x). forall x: S(x) -> R(x). Therefore exists x: R(x) and T(x).