Translate the following inference to logic notation: For all x, x_6 is curious. There is at least one x for which if x_6 were curious, then x_6 is working. For all x, x_6 will work if and only if x_6 will go running. Therefore there is at least one x for which x_6 will work.
forall x: P(x). exists x: P(x) -> Q(x). forall x: Q(x) <-> R(x). Therefore exists x: Q(x).