Consider the following premises. p <-> u. s_2 or q_20. ~u. s_2 -> r_4. s_1 -> p. q_20 -> r_4. Can we infer s_1 from them? If possible, name the inference rules being used at each step.
 From s_2 -> r_4, q_20 -> r_4, s_2 or q_20 we can infer r_4 via disjunction elimination. From p <-> u, ~u we can infer ~p via biconditional elimination. Finally, from s_1 -> p, ~p we can infer ~s_1 via modus tollens, which contradicts s_1. Therefore, the answer is no.