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Question: Function on sets.

What Maple function answers the following:

Produce (a minimal set of) sets that generate, by union, every intersection of sets given.

Examples:
F({1, 2, 3}, {1, 4, 5}, {2, 3, 4});

{}, {1}, {4}, {5}, {2, 3};


F({1, 2, 3, 6}, {1, 4, 5, 6}, {2, 3, 4, 6});
{1}, {4}, {5}, {6}, {2, 3};


Correction:
Produce (a minimal set of) disjoint sets that generate, by union, every intersection of sets given.

Intersection and union here are n-ary operators and every combination of sets is considered for intersection.

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