Translate the following inference to logic notation: For all x, if x_13 writes a letter, then x_13 is running. There is at least one x for which x_13 is bored if and only if x_13 will go running. For all x, x_13 is not bored. Therefore there is at least one x for which x_13 will not write a letter.
forall x: P(x) -> Q(x). exists x: R(x) <-> Q(x). forall x: ~R(x). Therefore exists x: ~P(x).