所有Frankl完全（FC（6））集合族的全自动验证分类
Fully Automatic, Verified Classification of all Frankl-Complete (FC(6)) Set Families
摘要：
弗兰克尔猜想，1979年提出。并且仍然开放，指出在每个集合族中，对于并集是封闭的，至少有一半的集合中包含一个元素。一个族Fc称为Frankl-完全族（或FC-族），如果在每个包含Fc的并闭族F中，并Fc的一个元素至少出现在F的一半元素中（因此F满足Frankl条件）。FC-族在攻击Frankl猜想中起着重要的作用，因为它们能够实现显著的搜索空间修剪。通过定义和列举所有最小FC和最大nonFC-族，我们扩展了以前的工作，给出了一个6元宇宙上所有FC-族的总特征。我们使用一个完全自动化的，计算机辅助的方法，在证明助理伊莎贝尔/HOL正式验证。
英文摘要：
The Frankl's conjecture, formulated in 1979. and still open, states that in every family of sets closed for unions there is an element contained in at least half of the sets. A family Fc is called Frankl-complete (or FC-family) if in every union-closed family F containing Fc, one of the elements of union Fc occurs in at least half of the elements of F (so F satisfies the Frankl's condition). FC-families play an important role in attacking the Frankl's conjecture, since they enable significant search space pruning. We extend previous work by giving a total characterization of all FC-families over a 6-element universe, by defining and enumerating all minimal FC and maximal nonFC-families. We use a fully automated, computer assisted approach, formally verified within the proof-assistant Isabelle/HOL.
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