Consider the following premises. forall x_16: R_16(x_16) <-> S_16(x_16). p_2 <-> ~S_16(d). ~R_16(d). Can we infer ~p_2 from them?
 From forall x_16: R_16(x_16) <-> S_16(x_16) we can infer R_16(d) <-> S_16(d). From R_16(d) <-> S_16(d), ~R_16(d) we can infer ~S_16(d). From p_2 <-> ~S_16(d) we can infer ~S_16(d) -> p_2. Finally, from ~S_16(d) -> p_2, ~S_16(d) we can infer p_2, which contradicts ~p_2. Therefore, the answer is no.