Consider the following premises. forall x: P_2(x) <-> T_4(x). T_4(i_1) and u_2. Can we infer ~P_2(i_1) from them?
 From forall x: P_2(x) <-> T_4(x) we can infer P_2(i_1) <-> T_4(i_1). From P_2(i_1) <-> T_4(i_1) we can infer T_4(i_1) -> P_2(i_1). From T_4(i_1) and u_2 we can infer T_4(i_1). Finally, from T_4(i_1) -> P_2(i_1), T_4(i_1) we can infer P_2(i_1), which contradicts ~P_2(i_1). Therefore, the answer is no.