Attempts to produce minimal Resolution refutations
Résumé
We address the challenge of searching minimal refutations proofs of inconsistent CNF formulae using the Resolution rule. We propose two algorithms which can only afford formulae of at most 5 variables with a desktop computer. A faster but incomplete algorithm is used to produce "hard" 5 variables 3CNF formulae though a stochastic greedy search. It allowed us to find formulae that can be refuted by producing clauses of at most 3 literals, but whose all minimal refutations contain at least one clause of 4 literals.
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