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The first line states that at least one term must be true. The remaining 6 lines are the two-combinations of the four terms. Each combination forbids a pair of terms from being true simultaneously. Taken together the four terms are constrained such that one and only one must be true. Trying to think like this is absolutely brutal, and it is much easier to fall back on convenience functions operating over sparse arrays. (Designing these convenience functions from scratch is an immensely fun challenge, but thankfully only one person needs to be any good at it.)

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