Consider the following premises. forall x: R_2(x). exists x: W(x) and Q_4(x). Can we infer forall x: ~W(x) from them? If possible, name the inference rules being used at each step.
 From exists x: W(x) and Q_4(x) we can infer exists x: W(x) via existential simplification. From exists x: W(x), forall x: R_2(x) we can infer exists x: W(x) and R_2(x) via existential conjunction. Finally, from exists x: W(x) and R_2(x) we can infer exists x: W(x) via existential simplification, which contradicts forall x: ~W(x). Therefore, the answer is no.