Consider the following premises. u_4 -> ~u_1. u_1. s_2 <-> u_4. s_2 <-> r. Can we infer r from them? If possible, name the inference rules being used at each step.
 From u_4 -> ~u_1, u_1 we can infer ~u_4 via modus tollens. From s_2 <-> u_4, ~u_4 we can infer ~s_2 via biconditional elimination. Finally, from s_2 <-> r, ~s_2 we can infer ~r via biconditional elimination, which contradicts r. Therefore, the answer is no.