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Is there a place I can find a list of known unsatisfiable cores for X variables [no more then 10] in CNF format?

Or is there an 'easy' way to find out, say I have 7 variables how many clauses [of the 7 variables] do I need for an unsatisfiable cores.

[I calculated 2-5 by hand, I am just trying to figure out 6+].

Thanks

Staque

FTNomad
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  • I think the tag of this question is improper. Please change the tag of this question. – Hanul Jeon Sep 15 '14 at 02:28
  • What is a core? – DanielV Sep 15 '14 at 02:54
  • @DanielV: a subset of clauses whose conjunction is still unsatisfiable is called an unsatisfiable core of the original formula. – Axel Kemper Sep 15 '14 at 19:18
  • @AxelKemper Does that also require that a core doesn't have a subset of unsatisfiable clauses? Is everyone saying CNF when they mean 3-CNF? – DanielV Sep 16 '14 at 04:16
  • @DanielV: An unsatisfiable core is called "minimal", if none of its clauses can be removed without making it satisfiable. In other words: Not all unsatisfiable cores have this property. See http://en.wikipedia.org/wiki/Unsatisfiable_core – Axel Kemper Sep 16 '14 at 07:16
  • @AxelKemper Thank you Axel. – DanielV Sep 16 '14 at 07:17
  • @DanielV: CNF is not restricted to clauses with three literals. See http://en.wikipedia.org/wiki/Conjunctive_normal_form – Axel Kemper Sep 16 '14 at 07:18

2 Answers2

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The question you are asking has been dealt with in the literature, and there is even a system that does it. Here is an example: https://sun.iwu.edu/~mliffito/publications/jar_liffiton_CAMUS.pdf

user362500
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The potential number of pairwise different clauses with $n$ variables and the number of sorted sets of clauses:

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Your proposed list of unsatisfiable cores is intractable long for any meaningful number of variables.

A brute-force way to find such unsatisfiable cores would be to enumerate the sets with a given number of variables and clauses. To be an unsatisfiable core, the set of clauses has to be unsatisfiable as a whole. This can be checked by using a SAT solver or enumerating up to $2^n$ variable assignments.

Unsatisfiable cores are usually created or extracted with respect to a given Boolean formula rather than compiling a complete list of all conceivable cores.

Axel Kemper
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