Translate the following inference to logic notation: For all x, x_8 will sleep. For all x, if x_8 were happy, then x_8 is not sleeping. For all x, if x_8 were happy, then x_8 is making tea. For all x, x_8 will make tea if and only if x_8 is happy. Therefore for all x, x_8 will not make tea.
forall x: P(x). forall x: Q(x) -> ~P(x). forall x: Q(x) -> R(x). forall x: R(x) <-> Q(x). Therefore forall x: ~R(x).