Consider the following premises. forall x_15: S(x_15) <-> Q_15(x_15). forall x_15: P_9(x_15) or Q_8(x_15). forall x_15: R_9(x_15) -> S(x_15). forall x_15: P_9(x_15) -> Q_9(x_15). forall x_15: Q_9(x_15) -> R_9(x_15). forall x_15: Q_8(x_15) -> R_9(x_15). Can we infer forall x_15: Q_15(x_15) from them?
 From forall x_15: S(x_15) <-> Q_15(x_15) we can infer forall x_15: S(x_15) -> Q_15(x_15). From forall x_15: P_9(x_15) -> Q_9(x_15), forall x_15: Q_9(x_15) -> R_9(x_15) we can infer forall x_15: P_9(x_15) -> R_9(x_15). From forall x_15: P_9(x_15) -> R_9(x_15), forall x_15: Q_8(x_15) -> R_9(x_15), forall x_15: P_9(x_15) or Q_8(x_15) we can infer forall x_15: R_9(x_15). From forall x_15: R_9(x_15) -> S(x_15), forall x_15: R_9(x_15) we can infer forall x_15: S(x_15). Finally, from forall x_15: S(x_15) -> Q_15(x_15), forall x_15: S(x_15) we can infer forall x_15: Q_15(x_15). Therefore, the answer is yes.