Translate the following inference to logic notation: There is at least one x for which x_7 is a sailor or x_7 is not excited. For all x, if x_7 were a sailor, then x_7 is bored. For all x, if x_7 were bored, then x_7 is working. Therefore there is at least one x for which if x_7 were excited, then x_7 is working.
exists x: P(x) or ~Q(x). forall x: P(x) -> R(x). forall x: R(x) -> S(x). Therefore exists x: Q(x) -> S(x).