Translate the following inference to logic notation: For all x, x_14 is a carpenter. For all x, if x_14 takes a plane, then x_14 is a carpenter. There is at least one x for which x_14 will not take a plane. For all x, x_14 is a carpenter if and only if x_14 will take a plane. Therefore there is at least one x for which x_14 will sleep.
forall x: P(x). forall x: Q(x) -> P(x). exists x: ~Q(x). forall x: P(x) <-> Q(x). Therefore exists x: R(x).