Consider the following premises. P_2(c) -> t. u -> t. forall x_2: P_2(x_2). Can we infer ~t from them?
 From forall x_2: P_2(x_2) we can infer P_2(c). From P_2(c) we can infer P_2(c) or u. Finally, from P_2(c) -> t, u -> t, P_2(c) or u we can infer t, which contradicts ~t. Therefore, the answer is no.