Consider the following premises. forall y_2: P_3(y_2) <-> U_4(y_2). forall z_3: U_4(z_3). Can we infer ~P_3(a_6) from them? If possible, name the inference rules being used at each step.
 From forall y_2: P_3(y_2) <-> U_4(y_2) we can infer forall y_2: U_4(y_2) -> P_3(y_2) via universal biconditional elimination. From forall z_3: U_4(z_3) we can infer U_4(a_6) via universal instantiation. From forall y_2: U_4(y_2) -> P_3(y_2) we can infer U_4(a_6) -> P_3(a_6) via universal instantiation. Finally, from U_4(a_6) -> P_3(a_6), U_4(a_6) we can infer P_3(a_6) via modus ponens, which contradicts ~P_3(a_6). Therefore, the answer is no.