Consider the following premises. forall x_10: ~P_10(x_10) or R_10(x_10). forall x_10: P_10(x_10) or W_4(x_10). forall x_10: W_4(x_10) -> R_1(x_10). forall x_10: P_8(x_10) -> R_1(x_10). forall x_10: P_8(x_10) <-> R_10(x_10). Can we infer exists x_10: ~R_1(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) or W_4(x_10), forall x_10: ~P_10(x_10) or R_10(x_10) we can infer forall x_10: W_4(x_10) or R_10(x_10) via universal resolution. From forall x_10: P_8(x_10) <-> R_10(x_10) we can infer forall x_10: R_10(x_10) -> P_8(x_10) via universal biconditional elimination. From forall x_10: R_10(x_10) -> P_8(x_10), forall x_10: P_8(x_10) -> R_1(x_10) we can infer forall x_10: R_10(x_10) -> R_1(x_10) via universal transitivity. Finally, from forall x_10: W_4(x_10) -> R_1(x_10), forall x_10: R_10(x_10) -> R_1(x_10), forall x_10: W_4(x_10) or R_10(x_10) we can infer forall x_10: R_1(x_10) via universal disjunction elimination, which contradicts exists x_10: ~R_1(x_10). Therefore, the answer is no.