Consider the following premises. u_1 <-> t. w -> r_1. u_1 -> w. Can we infer ~(t -> r_1) from them? If possible, name the inference rules being used at each step.
 From u_1 <-> t we can infer t -> u_1 via biconditional elimination. From u_1 -> w, w -> r_1 we can infer u_1 -> r_1 via transitivity. Finally, from t -> u_1, u_1 -> r_1 we can infer t -> r_1 via transitivity, which contradicts ~(t -> r_1). Therefore, the answer is no.