Translate the following inference to logic notation: There is at least one x for which if x_9 writes a letter, then x_9 is running. For all x, x_9 will not write a letter. For all x, if x_9 were a lawyer, then x_9 is running. For all x, if x_9 goes running, then x_9 is writing a letter. Therefore there is at least one x for which x_9 is not a lawyer.
exists x: P(x) -> Q(x). forall x: ~P(x). forall x: R(x) -> Q(x). forall x: Q(x) -> P(x). Therefore exists x: ~R(x).