Translate the following inference to logic notation: For all x, if x_14 were an electrician, then x_14 is cooking. For all x, x_14 will not cook. For all x, if x_14 were an artist, then x_14 is sleeping. There is at least one x for which x_14 will sleep if and only if x_14 is an electrician. For all x, if x_14 sleeps, then x_14 is an artist. For all x, if x_14 cooks, then x_14 is an electrician. Therefore there is at least one x for which x_14 is not an artist.
forall x: P(x) -> Q(x). forall x: ~Q(x). forall x: R(x) -> S(x). exists x: S(x) <-> P(x). forall x: S(x) -> R(x). forall x: Q(x) -> P(x). Therefore exists x: ~R(x).