Consider the following premises. p or ~q. t -> q. p_11 -> q_1. t or p_11. q_1 -> p. Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From p_11 -> q_1, q_1 -> p we can infer p_11 -> p via transitivity. From p or ~q we can infer q -> p via rewriting. From t -> q, q -> p we can infer t -> p via transitivity. Finally, from t -> p, p_11 -> p, t or p_11 we can infer p via disjunction elimination, which contradicts ~p. Therefore, the answer is no.