Consider the following premises. p_14 <-> q_14. q_14 or ~q_7. p_14 -> s. Can we infer ~(q_7 -> s) from them? If possible, name the inference rules being used at each step.
 From p_14 <-> q_14 we can infer q_14 -> p_14 via biconditional elimination. From q_14 or ~q_7 we can infer q_7 -> q_14 via rewriting. From q_14 -> p_14, p_14 -> s we can infer q_14 -> s via transitivity. Finally, from q_7 -> q_14, q_14 -> s we can infer q_7 -> s via transitivity, which contradicts ~(q_7 -> s). Therefore, the answer is no.