Translate the following inference to logic notation: For all x, x_8 is not happy. For all x, if x_8 sleeps, then x_8 is happy. For all x, x_8 is happy if and only if x_8 will sleep. There is at least one x for which x_8 will sleep or x_8 is a poet. Therefore there is at least one x for which x_8 is a poet.
forall x: ~P(x). forall x: Q(x) -> P(x). forall x: P(x) <-> Q(x). exists x: Q(x) or R(x). Therefore exists x: R(x).