Consider the following premises. forall x_5: P_5(x_5) -> R_5(x_5). forall x_5: P_5(x_5) or Q_5(x_5). forall x_5: Q_5(x_5) -> R_5(x_5). Can we infer exists z: R_5(z) from them?
 From forall x_5: P_5(x_5) -> R_5(x_5), forall x_5: Q_5(x_5) -> R_5(x_5), forall x_5: P_5(x_5) or Q_5(x_5) we can infer forall x_5: R_5(x_5). From forall x_5: R_5(x_5) we can infer R_5(a_1). Finally, from R_5(a_1) we can infer exists z: R_5(z). Therefore, the answer is yes.