Translate the following inference to logic notation: For all x, x_8 is a carpenter if and only if x_8 will sleep. For all x, x_8 is not happy or x_8 is a cashier. For all x, x_8 will not drink water. For all x, if x_8 sleeps, then x_8 is drinking water. There is at least one x for which x_8 is happy or x_8 is a carpenter. Therefore there is at least one x for which x_8 is a cashier.
forall x: P(x) <-> Q(x). forall x: ~R(x) or S(x). forall x: ~T(x). forall x: Q(x) -> T(x). exists x: R(x) or P(x). Therefore exists x: S(x).