Translate the following inference to logic notation: There is at least one x for which x_16 is a scientist if and only if x_16 is an astronaut. For all x, if x_16 were a scientist, then x_16 is a poet. For all x, if x_16 were a poet, then x_16 is an astronaut. For all x, if x_16 were a scientist, then x_16 is playing a game. Therefore there is at least one x for which if x_16 were an astronaut, then x_16 is playing a game.
exists x: P(x) <-> Q(x). forall x: P(x) -> R(x). forall x: R(x) -> Q(x). forall x: P(x) -> S(x). Therefore exists x: Q(x) -> S(x).