Consider the following premises. p_3 -> ~t_4. r_1. r_1 -> q_23. ~q_23. Can we infer ~p_3 or q from them?
 From r_1 -> q_23, ~q_23 we can infer ~r_1. From ~r_1 we can infer ~r_1 or t_4. From ~r_1 or t_4, r_1 we can infer t_4. From p_3 -> ~t_4, t_4 we can infer ~p_3. Finally, from ~p_3 we can infer ~p_3 or q. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.