Consider the following premises. forall x_11: R_2(x_11) or S_3(x_11). P_1(a_1). forall x_11: ~R_2(x_11). Can we infer forall x_11: ~(P_1(x_11) and S_3(x_11)) from them? If possible, name the inference rules being used at each step.
 From forall x_11: R_2(x_11) or S_3(x_11), forall x_11: ~R_2(x_11) we can infer forall x_11: S_3(x_11) via universal disjunctive syllogism. From P_1(a_1) we can infer exists x_11: P_1(x_11) via existential generalization. Finally, from exists x_11: P_1(x_11), forall x_11: S_3(x_11) we can infer exists x_11: P_1(x_11) and S_3(x_11) via existential conjunction, which contradicts forall x_11: ~(P_1(x_11) and S_3(x_11)). Therefore, the answer is no.