Translate the following inference to logic notation: For all x, x_6 will work or x_6 is not an astronaut. For all x, x_6 will go running or x_6 is a cashier. There is at least one x for which if x_6 were a cashier, then x_6 is working. For all x, if x_6 goes running, then x_6 is an astronaut. Therefore there is at least one x for which x_6 will work.
forall x: P(x) or ~Q(x). forall x: R(x) or S(x). exists x: S(x) -> P(x). forall x: R(x) -> Q(x). Therefore exists x: P(x).