Translate the following inference to logic notation: For all x, x_8 is a carpenter or x_8 will climb a mountain. For all x, x_8 is not a carpenter or x_8 is happy. For all x, x_8 will drink water if and only if x_8 is happy. For all x, x_8 will not drink water. For all x, x_8 will not climb a mountain or x_8 is a soldier. Therefore for all x, x_8 is a soldier.
forall x: P(x) or Q(x). forall x: ~P(x) or R(x). forall x: S(x) <-> R(x). forall x: ~S(x). forall x: ~Q(x) or T(x). Therefore forall x: T(x).