Translate the following inference to logic notation: For all x, x_8 will not take a plane. For all x, if x_8 sleeps, then x_8 is a janitor. For all x, x_8 will take a plane if and only if x_8 is a janitor. There is at least one x for which if x_8 were a musician, then x_8 is sleeping. Therefore there is at least one x for which x_8 is not a musician.
forall x: ~P(x). forall x: Q(x) -> R(x). forall x: P(x) <-> R(x). exists x: S(x) -> Q(x). Therefore exists x: ~S(x).