Consider the following premises. forall x_7: P_7(x_7) or Q_7(x_7). forall x_7: ~P_7(x_7) or R_7(x_7). forall x_7: Q_7(x_7) -> R_5(x_7). forall x_7: R_7(x_7) -> R_5(x_7). Can we infer exists z: R_5(z) from them?
 From forall x_7: P_7(x_7) or Q_7(x_7), forall x_7: ~P_7(x_7) or R_7(x_7) we can infer forall x_7: Q_7(x_7) or R_7(x_7). From forall x_7: Q_7(x_7) -> R_5(x_7), forall x_7: R_7(x_7) -> R_5(x_7), forall x_7: Q_7(x_7) or R_7(x_7) we can infer forall x_7: R_5(x_7). From forall x_7: R_5(x_7) we can infer R_5(f). Finally, from R_5(f) we can infer exists z: R_5(z). Therefore, the answer is yes.