Translate the following inference to logic notation: For all x, x_11 is bored. For all x, if x_11 works, then x_11 is listening to a song. For all x, x_11 is excited or x_11 will work. There is at least one x for which if x_11 were a bartender, then x_11 is listening to a song. For all x, x_11 is not excited or x_11 is a bartender. Therefore there is at least one x for which x_11 will listen to a song and x_11 is bored.
forall x: P(x). forall x: Q(x) -> R(x). forall x: S(x) or Q(x). exists x: T(x) -> R(x). forall x: ~S(x) or T(x). Therefore exists x: R(x) and P(x).