Consider the following premises. forall x_8: P_8(x_8) -> Q_8(x_8). forall x_8: Q_8(x_8) -> R_8(x_8). ~P_8(e_4). R_8(e_4) -> P_8(e_4). Can we infer R_8(e_4) from them?
 From forall x_8: P_8(x_8) -> Q_8(x_8), forall x_8: Q_8(x_8) -> R_8(x_8) we can infer forall x_8: P_8(x_8) -> R_8(x_8). From forall x_8: P_8(x_8) -> R_8(x_8) we can infer P_8(e_4) -> R_8(e_4). From R_8(e_4) -> P_8(e_4), P_8(e_4) -> R_8(e_4) we can infer R_8(e_4) <-> P_8(e_4). Finally, from R_8(e_4) <-> P_8(e_4), ~P_8(e_4) we can infer ~R_8(e_4), which contradicts R_8(e_4). Therefore, the answer is no.