Translate the following inference to logic notation: For all x, if x_8 goes running, then x_8 is sleeping. For all x, if x_8 were fast, then x_8 is a lawyer. There is at least one x for which x_8 will go running or x_8 is fast. For all x, x_8 is a lawyer if and only if x_8 will sleep. Therefore there is at least one x for which x_8 is a lawyer.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). exists x: P(x) or R(x). forall x: S(x) <-> Q(x). Therefore exists x: S(x).