Consider the following premises. q. u_2 -> q. u_2 or ~q. Can we infer ~u_2 from them?
 From u_2 or ~q we can infer q -> u_2. From u_2 -> q, q -> u_2 we can infer u_2 <-> q. From u_2 <-> q we can infer q -> u_2. Finally, from q -> u_2, q we can infer u_2, which contradicts ~u_2. Therefore, the answer is no.