Translate the following inference to logic notation: For all x, if x_17 were an astronaut, then x_17 is running. For all x, x_17 will play squash. For all x, x_17 will go running if and only if x_17 is bored. For all x, if x_17 takes a plane, then x_17 is an astronaut. There is at least one x for which x_17 will take a plane or x_17 is bored. Therefore there is at least one x for which x_17 will play squash and x_17 will go running.
forall x: P(x) -> Q(x). forall x: R(x). forall x: Q(x) <-> S(x). forall x: T(x) -> P(x). exists x: T(x) or S(x). Therefore exists x: R(x) and Q(x).