Translate the following inference to logic notation: For all x, if x_6 sleeps, then x_6 is writing a letter. For all x, x_6 will sleep or x_6 is not a scientist. For all x, if x_6 writes a letter, then x_6 is a scientist. Therefore for all x, if x_6 were a scientist, then x_6 is sleeping.
forall x: P(x) -> Q(x). forall x: P(x) or ~R(x). forall x: Q(x) -> R(x). Therefore forall x: R(x) -> P(x).