Consider the following premises. u -> p_1. ~s. w -> p_1. u or w. u_3 <-> s. Can we infer u_3 from them? If possible, name the inference rules being used at each step.
 From u -> p_1, w -> p_1, u or w we can infer p_1 via disjunction elimination. Finally, from u_3 <-> s, ~s we can infer ~u_3 via biconditional elimination, which contradicts u_3. Therefore, the answer is no.