Translate the following inference to logic notation: For all x, x_18 will cook. For all x, x_18 is not a carpenter or x_18 will play squash. For all x, x_18 is a carpenter or x_18 will work. There is at least one x for which x_18 will work if and only if x_18 will listen to a song. For all x, if x_18 plays squash, then x_18 is listening to a song. Therefore there is at least one x for which x_18 will listen to a song.
forall x: P(x). forall x: ~Q(x) or R(x). forall x: Q(x) or S(x). exists x: S(x) <-> T(x). forall x: R(x) -> T(x). Therefore exists x: T(x).