Consider the following premises. U_1(d_1) or ~u. forall z: U_1(z) <-> R_1(z). ~R_1(d_1). Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From forall z: U_1(z) <-> R_1(z) we can infer U_1(d_1) <-> R_1(d_1) via universal instantiation. From U_1(d_1) or ~u we can infer u -> U_1(d_1) via rewriting. From U_1(d_1) <-> R_1(d_1), ~R_1(d_1) we can infer ~U_1(d_1) via biconditional elimination. Finally, from u -> U_1(d_1), ~U_1(d_1) we can infer ~u via modus tollens. Therefore, the answer is yes.