Translate the following inference to logic notation: For all x, x_16 is a scientist if and only if x_16 will go running. For all x, x_16 is a scientist. There is at least one x for which x_16 will cook. For all x, if x_16 cooks, then x_16 is sleeping. Therefore there is at least one x for which x_16 will go running and x_16 will sleep.
forall x: P(x) <-> Q(x). forall x: P(x). exists x: R(x). forall x: R(x) -> S(x). Therefore exists x: Q(x) and S(x).