Consider the following premises. w_4. w -> w_4. t_4 -> u_1. w -> u_1. w_4 -> w. Can we infer ~u_1 from them? If possible, name the inference rules being used at each step.
 From w -> w_4, w_4 -> w we can infer w <-> w_4 via biconditional introduction. From w <-> w_4 we can infer w_4 -> w via biconditional elimination. From w_4 -> w, w -> u_1 we can infer w_4 -> u_1 via transitivity. From w_4 we can infer w_4 or t_4 via addition. Finally, from w_4 -> u_1, t_4 -> u_1, w_4 or t_4 we can infer u_1 via disjunction elimination, which contradicts ~u_1. Therefore, the answer is no.