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