Translate the following inference to logic notation: For all x, x_8 is sad or x_8 is fast. For all x, x_8 is not sad or x_8 is a scientist. There is at least one x for which if x_8 were a soldier, then x_8 is a scientist. For all x, if x_8 were a scientist, then x_8 is a soldier. For all x, if x_8 were fast, then x_8 is a soldier. Therefore there is at least one x for which x_8 is a soldier.
forall x: P(x) or Q(x). forall x: ~P(x) or R(x). exists x: S(x) -> R(x). forall x: R(x) -> S(x). forall x: Q(x) -> S(x). Therefore exists x: S(x).