Consider the following premises. S_1(a_18) -> p_2. forall z_4: S_1(z_4). Can we infer ~p_2 from them?
 From forall z_4: S_1(z_4) we can infer S_1(a_18). Finally, from S_1(a_18) -> p_2, S_1(a_18) we can infer p_2, which contradicts ~p_2. Therefore, the answer is no.