Translate the following inference to logic notation: For all x, x_12 is not a writer. There is at least one x for which x_12 will sleep or x_12 will not work. For all x, if x_12 were happy, then x_12 is sleeping. For all x, if x_12 sleeps, then x_12 is a writer. For all x, if x_12 were a writer, then x_12 is happy. Therefore there is at least one x for which x_12 will not work.
forall x: ~P(x). exists x: Q(x) or ~R(x). forall x: S(x) -> Q(x). forall x: Q(x) -> P(x). forall x: P(x) -> S(x). Therefore exists x: ~R(x).