Translate the following inference to logic notation: There is at least one x for which x_13 will go running if and only if x_13 will work. For all x, x_13 will work if and only if x_13 will sleep. For all x, x_13 is a lawyer if and only if x_13 will sleep. For all x, x_13 will not go running. Therefore there is at least one x for which x_13 is not a lawyer.
exists x: P(x) <-> Q(x). forall x: Q(x) <-> R(x). forall x: S(x) <-> R(x). forall x: ~P(x). Therefore exists x: ~S(x).