Translate the following inference to logic notation: For all x, x_16 is not rich. For all x, x_16 is a mechanic if and only if x_16 is rich. For all x, x_16 is a carpenter if and only if x_16 is excited. There is at least one x for which x_16 will go running if and only if x_16 is excited. For all x, x_16 is a mechanic if and only if x_16 is a carpenter. Therefore there is at least one x for which x_16 will not go running.
forall x: ~P(x). forall x: Q(x) <-> P(x). forall x: R(x) <-> S(x). exists x: T(x) <-> S(x). forall x: Q(x) <-> R(x). Therefore exists x: ~T(x).