Consider the following premises. forall x_8: Q_6(x_8) -> W(x_8). forall x_8: W(x_8) or ~Q_8(x_8). exists x_8: ~W(x_8) or R(x_8). forall x_8: Q_8(x_8) or Q_6(x_8). Can we infer exists x_8: Q_1(x_8) or R(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: W(x_8) or ~Q_8(x_8) we can infer forall x_8: Q_8(x_8) -> W(x_8) via universal rewriting. From forall x_8: Q_8(x_8) -> W(x_8), forall x_8: Q_6(x_8) -> W(x_8), forall x_8: Q_8(x_8) or Q_6(x_8) we can infer forall x_8: W(x_8) via universal disjunction elimination. From forall x_8: W(x_8) we can infer forall x_8: W(x_8) or Q_1(x_8) via universal addition. Finally, from forall x_8: W(x_8) or Q_1(x_8), exists x_8: ~W(x_8) or R(x_8) we can infer exists x_8: Q_1(x_8) or R(x_8) via existential resolution. Therefore, the answer is yes.