Translate the following inference to logic notation: For all x, if x_12 were a scientist, then x_12 is a lawyer. For all x, x_12 is not an office clerk. There is at least one x for which x_12 is a poet if and only if x_12 will work. For all x, x_12 will work if and only if x_12 is a scientist. For all x, x_12 is a lawyer if and only if x_12 is an office clerk. Therefore there is at least one x for which x_12 is not a poet.
forall x: P(x) -> Q(x). forall x: ~R(x). exists x: S(x) <-> T(x). forall x: T(x) <-> P(x). forall x: Q(x) <-> R(x). Therefore exists x: ~S(x).