Consider the following premises. ~r_1. r_1 <-> q_15. r_1 -> q_15. s_4 -> q_15. Can we infer s_4 from them? If possible, name the inference rules being used at each step.
 From r_1 <-> q_15 we can infer q_15 -> r_1 via biconditional elimination. From q_15 -> r_1, r_1 -> q_15 we can infer q_15 <-> r_1 via biconditional introduction. From q_15 <-> r_1, ~r_1 we can infer ~q_15 via biconditional elimination. Finally, from s_4 -> q_15, ~q_15 we can infer ~s_4 via modus tollens, which contradicts s_4. Therefore, the answer is no.