Consider the following premises. forall x_7: U(x_7) <-> S_7(x_7). ~U(a). S_7(a) <-> r_3. Can we infer r_3 from them? If possible, name the inference rules being used at each step.
 From forall x_7: U(x_7) <-> S_7(x_7) we can infer U(a) <-> S_7(a) via universal instantiation. From U(a) <-> S_7(a), ~U(a) we can infer ~S_7(a) via biconditional elimination. Finally, from S_7(a) <-> r_3, ~S_7(a) we can infer ~r_3 via biconditional elimination, which contradicts r_3. Therefore, the answer is no.