Consider the following premises. s_3 -> p_1. s_3 <-> q_11. p_1 -> s_3. Can we infer ~(q_11 -> p_1) from them? If possible, name the inference rules being used at each step.
 From s_3 <-> q_11 we can infer q_11 -> s_3 via biconditional elimination. From p_1 -> s_3, s_3 -> p_1 we can infer p_1 <-> s_3 via biconditional introduction. From p_1 <-> s_3 we can infer s_3 -> p_1 via biconditional elimination. Finally, from q_11 -> s_3, s_3 -> p_1 we can infer q_11 -> p_1 via transitivity, which contradicts ~(q_11 -> p_1). Therefore, the answer is no.