Translate the following inference to logic notation: There is at least one x for which y_1 will not go running. For all x, if y_1 cooks, then y_1 is sleeping. For all x, if y_1 goes running, then y_1 is cooking. For all x, if y_1 sleeps, then y_1 is running. Therefore there is at least one x for which y_1 will not cook.
exists x: ~P(x). forall x: Q(x) -> R(x). forall x: P(x) -> Q(x). forall x: R(x) -> P(x). Therefore exists x: ~Q(x).