Consider the following premises. forall x_9: ~Q_9(x_9) or R_7(x_9). forall x_9: R_9(x_9) -> R_5(x_9). forall x_9: R_7(x_9) -> R_5(x_9). forall x_9: P_9(x_9) or Q_9(x_9). forall x_9: ~P_9(x_9) or R_9(x_9). Can we infer exists z: R_5(z) from them?
 From forall x_9: P_9(x_9) or Q_9(x_9), forall x_9: ~P_9(x_9) or R_9(x_9) we can infer forall x_9: Q_9(x_9) or R_9(x_9). From forall x_9: Q_9(x_9) or R_9(x_9), forall x_9: ~Q_9(x_9) or R_7(x_9) we can infer forall x_9: R_9(x_9) or R_7(x_9). From forall x_9: R_9(x_9) -> R_5(x_9), forall x_9: R_7(x_9) -> R_5(x_9), forall x_9: R_9(x_9) or R_7(x_9) we can infer forall x_9: R_5(x_9). From forall x_9: R_5(x_9) we can infer R_5(i). Finally, from R_5(i) we can infer exists z: R_5(z). Therefore, the answer is yes.