Translate the following inference to logic notation: For all x, if x_6 goes running, then x_6 is climbing a mountain. For all x, x_6 is not a mechanic or x_6 is a lawyer. There is at least one x for which if x_6 were a lawyer, then x_6 is climbing a mountain. For all x, if x_6 were a soldier, then x_6 is running. For all x, x_6 is a mechanic or x_6 is a soldier. Therefore there is at least one x for which x_6 will climb a mountain.
forall x: P(x) -> Q(x). forall x: ~R(x) or S(x). exists x: S(x) -> Q(x). forall x: T(x) -> P(x). forall x: R(x) or T(x). Therefore exists x: Q(x).