Specifically, the sequences involving intersections among three sets, denoted as $S_1$, $S_2$, and $S_3$, do not yield productive outcomes. The identified non-functional orderings include the intersections of $S_1$ and $S_2$, $S_1$ and $S_3$, as well as $S_2$ and $S_3$. Moreover, individual references to $S_2$ and $S_3$, followed by the intersection of all three sets ($S_1 \cap S_2 \cap S_3$), and concluding with $S_1$, are also listed as unsuccessful. This observation underscores the complexity and specificity required in determining effective sequences for these set operations. The commitment to updating this list upon discovering more ineffectual arrangements emphasizes an ongoing investigation into the matter.