Translate the following inference to logic notation: For all x, if x_6 cooks, then x_6 is a writer. There is at least one x for which if x_6 were a writer, then x_6 is a bartender. For all x, x_6 is happy if and only if x_6 will cook. Therefore there is at least one x for which if x_6 were happy, then x_6 is a bartender.
forall x: P(x) -> Q(x). exists x: Q(x) -> R(x). forall x: S(x) <-> P(x). Therefore exists x: S(x) -> R(x).