Translate the following inference to logic notation: For all x, x_7 will go running if and only if x_7 is a carpenter. For all x, x_7 will not go running. For all x, if x_7 were an astronaut, then x_7 is sleeping. For all x, x_7 is a carpenter or x_7 is an astronaut. Therefore for all x, x_7 will sleep.
forall x: P(x) <-> Q(x). forall x: ~P(x). forall x: R(x) -> S(x). forall x: Q(x) or R(x). Therefore forall x: S(x).