Consider the following premises. p_3 -> U_4(j). u -> p_3. forall y: ~U_4(y). U_4(j) -> u. Can we infer p_3 from them?
 From forall y: ~U_4(y) we can infer ~U_4(j). From U_4(j) -> u, u -> p_3 we can infer U_4(j) -> p_3. From p_3 -> U_4(j), U_4(j) -> p_3 we can infer p_3 <-> U_4(j). Finally, from p_3 <-> U_4(j), ~U_4(j) we can infer ~p_3, which contradicts p_3. Therefore, the answer is no.