Translate the following inference to logic notation: For all x, x_7 is bored or x_7 will go running. For all x, if x_7 writes a letter, then x_7 is excited. For all x, x_7 is a sailor. For all x, if x_7 goes running, then x_7 is excited. For all x, x_7 is not bored or x_7 will write a letter. Therefore for all x, x_7 is excited.
forall x: P(x) or Q(x). forall x: R(x) -> S(x). forall x: T(x). forall x: Q(x) -> S(x). forall x: ~P(x) or R(x). Therefore forall x: S(x).