Translate the following inference to logic notation: For all x, x_16 is a poet or x_16 is a doctor. For all x, x_16 will play a game if and only if x_16 is a poet. There is at least one x for which x_16 is not happy. For all x, x_16 will play a game if and only if x_16 is happy. Therefore there is at least one x for which x_16 is a doctor.
forall x: P(x) or Q(x). forall x: R(x) <-> P(x). exists x: ~S(x). forall x: R(x) <-> S(x). Therefore exists x: Q(x).