Consider the following premises. t_3 or ~p. p_1 or p. t_3 <-> p_1. Can we infer ~t_3 from them? If possible, name the inference rules being used at each step.
 From t_3 or ~p we can infer p -> t_3 via rewriting. From t_3 <-> p_1 we can infer p_1 -> t_3 via biconditional elimination. Finally, from p_1 -> t_3, p -> t_3, p_1 or p we can infer t_3 via disjunction elimination, which contradicts ~t_3. Therefore, the answer is no.