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Let Ω be a set of unsatisfiable clauses, an implicit resolution refutation of Ω is a circuit β with a resolution proof α of the statement " β describes a correct tree-like resolution refutation of Ω ". We show that such a system is p-equivalent to Extended Frege. More generally, let τ be a tautology, a [P, Q]-proof of τ is a pair (α, β) s.t. α is a P-proof… (More)

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