Consider the following premises. forall x_7: U_3(x_7) <-> S_7(x_7). S_7(a_7) -> r. ~r. Can we infer ~U_3(a_7) from them? If possible, name the inference rules being used at each step.
 From forall x_7: U_3(x_7) <-> S_7(x_7) we can infer U_3(a_7) <-> S_7(a_7) via universal instantiation. From S_7(a_7) -> r, ~r we can infer ~S_7(a_7) via modus tollens. Finally, from U_3(a_7) <-> S_7(a_7), ~S_7(a_7) we can infer ~U_3(a_7) via biconditional elimination. Therefore, the answer is yes.