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