Consider the following premises. forall x_9: P_9(x_9). forall x_9: Q_9(x_9) -> R_8(x_9). forall x_9: R_8(x_9) -> S(x_9). forall x_9: P_9(x_9) -> R_8(x_9). exists x_9: W(x_9). Can we infer exists x_9: S(x_9) and W(x_9) from them?
 From forall x_9: P_9(x_9) we can infer forall x_9: P_9(x_9) or Q_9(x_9). From forall x_9: P_9(x_9) -> R_8(x_9), forall x_9: Q_9(x_9) -> R_8(x_9), forall x_9: P_9(x_9) or Q_9(x_9) we can infer forall x_9: R_8(x_9). From forall x_9: R_8(x_9) -> S(x_9), forall x_9: R_8(x_9) we can infer forall x_9: S(x_9). Finally, from forall x_9: S(x_9), exists x_9: W(x_9) we can infer exists x_9: S(x_9) and W(x_9). Therefore, the answer is yes.