Consider the following premises. p_11 <-> p. q_3 -> p. p_11 -> q_3. Can we infer ~(p_11 -> p) from them? If possible, name the inference rules being used at each step.
 From p_11 <-> p we can infer p -> p_11 via biconditional elimination. Finally, from p_11 -> q_3, q_3 -> p we can infer p_11 -> p via transitivity, which contradicts ~(p_11 -> p). Therefore, the answer is no.