Consider the following premises. forall x_15: P_12(x_15) -> Q(x_15). forall x_15: P_12(x_15) or P_15(x_15). forall x_15: P_15(x_15) <-> Q(x_15). forall x_15: P_8(x_15) <-> Q(x_15). forall x_15: P_8(x_15) -> R_1(x_15). Can we infer forall x_15: R_1(x_15) from them?
 From forall x_15: P_15(x_15) <-> Q(x_15) we can infer forall x_15: P_15(x_15) -> Q(x_15). From forall x_15: P_12(x_15) -> Q(x_15), forall x_15: P_15(x_15) -> Q(x_15), forall x_15: P_12(x_15) or P_15(x_15) we can infer forall x_15: Q(x_15). From forall x_15: P_8(x_15) <-> Q(x_15) we can infer forall x_15: Q(x_15) -> P_8(x_15). From forall x_15: Q(x_15) -> P_8(x_15), forall x_15: P_8(x_15) -> R_1(x_15) we can infer forall x_15: Q(x_15) -> R_1(x_15). Finally, from forall x_15: Q(x_15) -> R_1(x_15), forall x_15: Q(x_15) we can infer forall x_15: R_1(x_15). Therefore, the answer is yes.