Translate the following inference to logic notation: For all x, if x_14 were a police officer, then x_14 is cooking. For all x, x_14 will write a letter or x_14 is not a musician. For all x, if x_14 writes a letter, then x_14 is not cooking. For all x, if x_14 goes running, then x_14 is cooking. There is at least one x for which if x_14 writes a letter, then x_14 is a musician. For all x, x_14 is a police officer or x_14 will go running. Therefore there is at least one x for which x_14 is not a musician.
forall x: P(x) -> Q(x). forall x: R(x) or ~S(x). forall x: R(x) -> ~Q(x). forall x: T(x) -> Q(x). exists x: R(x) -> S(x). forall x: P(x) or T(x). Therefore exists x: ~S(x).