Translate the following inference to logic notation: For all x, if x_17 were a carpenter, then x_17 is a lawyer. For all x, if x_17 goes running, then x_17 is playing a game. For all x, if x_17 were a carpenter, then x_17 is running. For all x, if x_17 were a lawyer, then x_17 is a carpenter. There is at least one x for which x_17 will not play a game. Therefore there is at least one x for which x_17 is not a lawyer.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: P(x) -> R(x). forall x: Q(x) -> P(x). exists x: ~S(x). Therefore exists x: ~Q(x).