Consider the following premises. forall x_16: ~P_16(x_16) or Q_1(x_16). R_14(e) -> s_4. forall x_16: ~Q_16(x_16) or R_14(x_16). Q_1(e) -> s_4. forall x_16: P_16(x_16) or Q_16(x_16). Can we infer ~s_4 from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) or Q_16(x_16), forall x_16: ~P_16(x_16) or Q_1(x_16) we can infer forall x_16: Q_16(x_16) or Q_1(x_16) via universal resolution. From forall x_16: Q_16(x_16) or Q_1(x_16), forall x_16: ~Q_16(x_16) or R_14(x_16) we can infer forall x_16: Q_1(x_16) or R_14(x_16) via universal resolution. From forall x_16: Q_1(x_16) or R_14(x_16) we can infer Q_1(e) or R_14(e) via universal instantiation. Finally, from Q_1(e) -> s_4, R_14(e) -> s_4, Q_1(e) or R_14(e) we can infer s_4 via disjunction elimination, which contradicts ~s_4. Therefore, the answer is no.