Yes, this formula appears to be correct. It represents the principle of inclusion-exclusion for four sets (A), (B), (C), and (D). The formula calculates the union of these four sets. Here is the formula written out more clearly:

[ |A \cup B \cup C \cup D| = |A| + |B| + |C| + |D| - |A \cap B| - |A \cap C| - |A \cap D| - |B \cap C| - |B \cap D| - |C \cap D| + |A \cap B \cap C| + |A \cap B \cap D| + |A \cap C \cap D| + |B \cap C \cap D| - |A \cap B \cap C \cap D| ]

Here is a breakdown of the inclusion-exclusion principle for four sets:

1. Add the sizes of the individual sets.
2. Subtract the sizes of all possible intersections of two sets (since they are counted twice in the first step).
3. Add the sizes of all possible intersections of three sets (since they were subtracted too many times in the previous step).
4. Subtract the size of the intersection of all four sets (since it was added too many times in the previous steps).