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