Consider the following premises. forall x_11: S(x_11) or ~Q(x_11). forall x_11: S_1(x_11). exists x_11: Q(x_11). Can we infer forall x_11: ~(S_1(x_11) and S(x_11)) from them? If possible, name the inference rules being used at each step.
 From forall x_11: S(x_11) or ~Q(x_11) we can infer forall x_11: Q(x_11) -> S(x_11) via universal rewriting. From forall x_11: Q(x_11) -> S(x_11), exists x_11: Q(x_11) we can infer exists x_11: S(x_11) via existential modus ponens. Finally, from forall x_11: S_1(x_11), exists x_11: S(x_11) we can infer exists x_11: S_1(x_11) and S(x_11) via existential conjunction, which contradicts forall x_11: ~(S_1(x_11) and S(x_11)). Therefore, the answer is no.