Consider the following premises. R_4(j_1) <-> s_4. forall z: P(z) -> R_4(z). forall z: ~P(z). forall z: R_4(z) -> P(z). Can we infer ~s_4 from them?
 From forall z: R_4(z) -> P(z), forall z: P(z) -> R_4(z) we can infer forall z: R_4(z) <-> P(z). From forall z: R_4(z) <-> P(z), forall z: ~P(z) we can infer forall z: ~R_4(z). From forall z: ~R_4(z) we can infer ~R_4(j_1). Finally, from R_4(j_1) <-> s_4, ~R_4(j_1) we can infer ~s_4. Therefore, the answer is yes.