Translate the following inference to logic notation: There is at least one x for which x_17 will not cook. For all x, if x_17 cooks, then x_17 is sleeping. For all x, if x_17 listens to a song, then x_17 is sleeping. For all x, if x_17 were happy, then x_17 is listening to a song. For all x, if x_17 sleeps, then x_17 is cooking. Therefore there is at least one x for which x_17 is not happy.
exists x: ~P(x). forall x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: S(x) -> R(x). forall x: Q(x) -> P(x). Therefore exists x: ~S(x).