== statement (i): 2k-1 vertices, k-1 triples
  k=2: 1 classes, violations of the conclusion: 0  [0.0s]
  k=3: 1 classes, violations of the conclusion: 0  [0.0s]
  k=4: 2 classes, violations of the conclusion: 0  [0.0s]
  k=5: 5 classes, violations of the conclusion: 0  [0.0s]
  k=6: 12 classes, violations of the conclusion: 0  [0.3s]
== statement (ii), v=1: 2k vertices, one 4-edge + (k-2) triples
  k=3: 1 classes, connected 1, violations among connected: 0; disconnected classes without a good triple: 0  [0.0s]
  k=4: 3 classes, connected 3, violations among connected: 0; disconnected classes without a good triple: 0  [0.0s]
  k=5: 10 classes, connected 8, violations among connected: 0; disconnected classes without a good triple: 1  [0.1s]
      e.g. disconnected, no good triple: [(0, 1, 2, 3), (4, 5, 6), (4, 7, 8), (5, 7, 9)]
== statement (ii), v=0: 2k vertices, k+1 triples
  k=3: 1 classes, connected 1, with an admissible T: 1, violations of the conclusion among those: 1; inequality failures: 0; cases (t,c)=(4,0): 1; connected classes with no admissible T and no good triple: 0  [0.0s]
      VIOLATION: [(0, 1, 2), (0, 3, 4), (1, 3, 5), (2, 4, 5)]
  k=4: 5 classes, connected 5, with an admissible T: 1, violations of the conclusion among those: 0; inequality failures: 0; cases (t,c)=(4,0): 0; connected classes with no admissible T and no good triple: 4  [0.0s]
      e.g. no admissible T, no good triple (relations independent, so rank < k): [(0, 1, 2), (0, 3, 4), (1, 3, 5), (0, 5, 6), (1, 4, 7)]
      e.g. no admissible T, no good triple (relations independent, so rank < k): [(0, 1, 2), (0, 3, 4), (1, 3, 5), (0, 5, 6), (2, 4, 7)]
  k=5: 56 classes, connected 54, with an admissible T: 4, violations of the conclusion among those: 0; inequality failures: 0; cases (t,c)=(4,0): 0; connected classes with no admissible T and no good triple: 30  [0.6s]
      e.g. no admissible T, no good triple (relations independent, so rank < k): [(0, 1, 2), (0, 3, 4), (1, 3, 5), (0, 5, 6), (0, 7, 8), (1, 7, 9)]
      e.g. no admissible T, no good triple (relations independent, so rank < k): [(0, 1, 2), (0, 3, 4), (1, 3, 5), (0, 5, 6), (0, 7, 8), (2, 7, 9)]
