Consider the following premises. forall x_7: R_7(x_7) <-> S_7(x_7). ~R_7(f). p <-> S_7(f). Can we infer ~p from them?
 From forall x_7: R_7(x_7) <-> S_7(x_7) we can infer R_7(f) <-> S_7(f). From R_7(f) <-> S_7(f), ~R_7(f) we can infer ~S_7(f). Finally, from p <-> S_7(f), ~S_7(f) we can infer ~p. Therefore, the answer is yes.