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