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Lecture Notes in Computer Science
For a reasonable sound and complete proof calculus for first-order logic consider the problem to decide, given a sentence ϕ of first-order logic and a natural number n, whether ϕ has no proof of length ≤ n. We show that there is a nondeterministic algorithm accepting this problem which, for fixed ϕ, has running time bounded by a polynomial in n if and only if there is an optimal proof system for the set TAUT of tautologies of propositional logic. This equivalence is an instance of a generaldoi:10.1007/978-3-642-15205-4_18 fatcat:4ge5ewg3graapmfn7fdqtvb5za