Translate the following inference to logic notation: For all x, x_13 is not a doctor. For all x, x_13 is a soldier or x_13 will sleep. There is at least one x for which x_13 is a doctor if and only if x_13 is a poet. For all x, if x_13 were a soldier, then x_13 is a poet. Therefore there is at least one x for which x_13 will sleep.
forall x: ~P(x). forall x: Q(x) or R(x). exists x: P(x) <-> S(x). forall x: Q(x) -> S(x). Therefore exists x: R(x).