Consider the following premises. forall z: R_4(z) <-> P(z). r -> u. r or R_4(b). u -> P(b). Can we infer ~P(b) from them?
 From forall z: R_4(z) <-> P(z) we can infer R_4(b) <-> P(b). From r -> u, u -> P(b) we can infer r -> P(b). From R_4(b) <-> P(b) we can infer R_4(b) -> P(b). Finally, from r -> P(b), R_4(b) -> P(b), r or R_4(b) we can infer P(b), which contradicts ~P(b). Therefore, the answer is no.