k=6: sets S = basis + T, |T|=6: nodes at depth k-1: 3819246, sets with exactly k+1 = 7 triple points: 408445  [60.8s]
  of these: reducible 223275, irreducible and formal (class C_k) 137760, irreducible and not formal 47410  [74.5s]
  orbits under coordinate permutations: class 379, irreducible non-formal 199
  class representatives supersolvable: 379 of 379; violations: 0  [91.2s]
  irreducible non-formal representatives that are supersolvable: 0 of 199  [100.0s]
  freeness with exponents [1, 2, 2, 2, 2, 3] on a sample of class representatives: 40 of 40 free
  freeness on a sample of non-formal representatives: 0 of 40 free (expected 0)
  check_one (Lemmas 2-4, Lemma 3(d), free <=> class, supersolvable) on the same sample: violations 0
time 111.7s
