Translate the following inference to logic notation: For all x, x_15 is an electrician or x_15 is not a bartender. For all x, if x_15 sleeps, then x_15 is a bartender. There is at least one x for which x_15 is a carpenter if and only if x_15 is an electrician. For all x, x_15 will sleep. Therefore there is at least one x for which x_15 is a carpenter.
forall x: P(x) or ~Q(x). forall x: R(x) -> Q(x). exists x: S(x) <-> P(x). forall x: R(x). Therefore exists x: S(x).