Consider the following premises. q_3 -> u_3. u_3 -> R_12(a_12). R_12(a_12) -> q_3. forall x_12: ~R_12(x_12). Can we infer u_3 from them? If possible, name the inference rules being used at each step.
 From forall x_12: ~R_12(x_12) we can infer ~R_12(a_12) via universal instantiation. From R_12(a_12) -> q_3, q_3 -> u_3 we can infer R_12(a_12) -> u_3 via transitivity. From u_3 -> R_12(a_12), R_12(a_12) -> u_3 we can infer u_3 <-> R_12(a_12) via biconditional introduction. Finally, from u_3 <-> R_12(a_12), ~R_12(a_12) we can infer ~u_3 via biconditional elimination, which contradicts u_3. Therefore, the answer is no.