Open problems on the combinatorics of conflicts between clauses

Status of open problems from the first report on the subject ("On the conflict matrix of clause-sets", University of Wales Swansea, Computer Science Report Series, CSR 7-2003)

1. Open.
2. Open.
3. Open.
4. Counterexample for Conjecture 5.2 found by Xishun Zhao.
5. Xishun Zhao proved, that in fact every non-saturated minimally unsatisfiable clause-set with deficiency one is not exact.
   There are non-saturated minimally unsatisfiable clause-set with deficiency one which are not eigensharp.
6. Xishun Zhao found a counterexample for Conjecture 5.3, an example for an eigensharp and unsatisfiable clause-set which is not linearly lean.
7. The counterexample for Point 6 is also a counterexample for Conjecture 5.4.
8. Open.
9. Counterexample found by Xishun Zhao.
10. Obviously, there are symmetric distance matrices with more positive than negative eigenvalues, and also with non-integral eigenvalues.
11. Open.
12. Open.