  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.
