11. Algorithms for Computing Minimal Unsatisfiable Subsets. 12. This sentence is unsatisfiable ( a contradiction ) because of the universal quantifier ( \ forall ). 13. If the formula is unsatisfiable , the algorithm will always output YES with probability 1 / 2. 14. If a tableau calculus is complete, every unsatisfiable set of formulae has an associated closed tableau. 15. If the constraint store is unsatisfiable , this simplification may detect this unsatisfiability sometimes, but not always. 16. Therefore, the algorithm either correctly finds a satisfying assignment or it correctly determines that the input is unsatisfiable . 17. Such a set is easily recognizable as satisfiable or unsatisfiable with respect to the semantics of the logic in question. 18. A tableau calculus is called complete if it allows building a tableau proof for every given unsatisfiable set of formulae. 19. The interpreter has proved the goal when the current goal is empty and the constraint store is not detected unsatisfiable . 20. A constraint satisfaction problem may be relationally consistent, have no empty domain or unsatisfiable constraint, and yet be unsatisfiable.
