Consider the following premises. forall x_12: R(x_12) <-> P_3(x_12). exists x_12: R_4(x_12). forall x_12: P_8(x_12) -> P_3(x_12). forall x_12: P_8(x_12) or Q_8(x_12). forall x_12: Q_8(x_12) -> P_3(x_12). Can we infer exists x_12: R(x_12) and R_4(x_12) from them?
 From forall x_12: R(x_12) <-> P_3(x_12) we can infer forall x_12: P_3(x_12) -> R(x_12). From forall x_12: P_8(x_12) -> P_3(x_12), forall x_12: Q_8(x_12) -> P_3(x_12), forall x_12: P_8(x_12) or Q_8(x_12) we can infer forall x_12: P_3(x_12). From forall x_12: P_3(x_12) -> R(x_12), forall x_12: P_3(x_12) we can infer forall x_12: R(x_12). Finally, from forall x_12: R(x_12), exists x_12: R_4(x_12) we can infer exists x_12: R(x_12) and R_4(x_12). Therefore, the answer is yes.