Translate the following inference to logic notation: For all x, if x_7 were an office clerk, then x_7 is playing tennis. For all x, x_7 will write a letter or x_7 is an office clerk. For all x, x_7 will not write a letter or x_7 is a doctor. For all x, x_7 will not play tennis. For all x, if x_7 plays tennis, then x_7 is an office clerk. Therefore for all x, x_7 is a doctor.
forall x: P(x) -> Q(x). forall x: R(x) or P(x). forall x: ~R(x) or S(x). forall x: ~Q(x). forall x: Q(x) -> P(x). Therefore forall x: S(x).