Translate the following inference to logic notation: For all x, x_13 is a lawyer. For all x, if x_13 were a lawyer, then x_13 is a police officer. For all x, x_13 will take a plane if and only if x_13 will cook. For all x, if x_13 works, then x_13 is cooking. For all x, if x_13 were a police officer, then x_13 is working. Therefore for all x, x_13 will cook.
forall x: P(x). forall x: P(x) -> Q(x). forall x: R(x) <-> S(x). forall x: T(x) -> S(x). forall x: Q(x) -> T(x). Therefore forall x: S(x).