Consider the following premises. forall y: P_3(y). exists y: S_3(y) and P(y). Can we infer forall y: ~(S_3(y) and P_3(y)) from them? If possible, name the inference rules being used at each step.
 From exists y: S_3(y) and P(y) we can infer exists y: S_3(y) via existential simplification. Finally, from exists y: S_3(y), forall y: P_3(y) we can infer exists y: S_3(y) and P_3(y) via existential conjunction, which contradicts forall y: ~(S_3(y) and P_3(y)). Therefore, the answer is no.