Translate the following inference to logic notation: For all x, x_7 will not cook. There is at least one x for which if x_7 were a taxi driver, then x_7 is sleeping. For all x, x_7 will sleep if and only if x_7 will cook. Therefore there is at least one x for which x_7 is not a taxi driver.
forall x: ~P(x). exists x: Q(x) -> R(x). forall x: R(x) <-> P(x). Therefore exists x: ~Q(x).