Translate the following inference to logic notation: There is at least one x for which x_14 will not work. For all x, x_14 is a cashier. For all x, x_14 will work or x_14 will cook. For all x, if x_14 cooks, then x_14 is excited. Therefore there is at least one x for which x_14 is a cashier and x_14 is excited.
exists x: ~P(x). forall x: Q(x). forall x: P(x) or R(x). forall x: R(x) -> S(x). Therefore exists x: Q(x) and S(x).