Translate the following inference to logic notation: For all x, x_8 will sleep if and only if x_8 is happy. For all x, x_8 is not happy. For all x, x_8 will go running if and only if x_8 will sleep. For all x, x_8 will go running if and only if x_8 is sad. Therefore for all x, x_8 is not sad.
forall x: P(x) <-> Q(x). forall x: ~Q(x). forall x: R(x) <-> P(x). forall x: R(x) <-> S(x). Therefore forall x: ~S(x).