Translate the following inference to logic notation: There is at least one x for which x_7 is a sailor. For all x, if x_7 were a sailor, then x_7 is running. For all x, x_7 will go running if and only if x_7 is a soldier. Therefore there is at least one x for which x_7 is a soldier.
exists x: P(x). forall x: P(x) -> Q(x). forall x: Q(x) <-> R(x). Therefore exists x: R(x).