Translate the following inference to logic notation: For all x, if x_9 writes a letter, then x_9 is listening to a song. For all x, x_9 will write a letter or x_9 will make tea. There is at least one x for which if x_9 were bored, then x_9 is not listening to a song. For all x, if x_9 listens to a song, then x_9 is writing a letter. For all x, if x_9 makes tea, then x_9 is listening to a song. Therefore there is at least one x for which x_9 is not bored.
forall x: P(x) -> Q(x). forall x: P(x) or R(x). exists x: S(x) -> ~Q(x). forall x: Q(x) -> P(x). forall x: R(x) -> Q(x). Therefore exists x: ~S(x).