Consider the following premises. forall x_8: R_1(x_8) <-> Q_8(x_8). R_1(a_5) or w. w -> Q_8(a_5). Can we infer ~Q_8(a_5) from them? If possible, name the inference rules being used at each step.
 From forall x_8: R_1(x_8) <-> Q_8(x_8) we can infer forall x_8: R_1(x_8) -> Q_8(x_8) via universal biconditional elimination. From forall x_8: R_1(x_8) -> Q_8(x_8) we can infer R_1(a_5) -> Q_8(a_5) via universal instantiation. Finally, from R_1(a_5) -> Q_8(a_5), w -> Q_8(a_5), R_1(a_5) or w we can infer Q_8(a_5) via disjunction elimination, which contradicts ~Q_8(a_5). Therefore, the answer is no.