Consider the following premises. R_1(h) -> P_3(h). forall z_1: P_3(z_1) -> R_1(z_1). ~P_3(h). Can we infer R_1(h) from them?
 From forall z_1: P_3(z_1) -> R_1(z_1) we can infer P_3(h) -> R_1(h). From P_3(h) -> R_1(h), R_1(h) -> P_3(h) we can infer P_3(h) <-> R_1(h). Finally, from P_3(h) <-> R_1(h), ~P_3(h) we can infer ~R_1(h), which contradicts R_1(h). Therefore, the answer is no.