Translate the following inference to logic notation: For all x, x_18 is a scientist. For all x, if x_18 were fast, then x_18 is sleeping. For all x, x_18 will climb a mountain or x_18 is a lawyer. There is at least one x for which x_18 is a lawyer if and only if x_18 will sleep. For all x, x_18 will not climb a mountain or x_18 is fast. Therefore there is at least one x for which x_18 will sleep.
forall x: P(x). forall x: Q(x) -> R(x). forall x: S(x) or T(x). exists x: T(x) <-> R(x). forall x: ~S(x) or Q(x). Therefore exists x: R(x).