Herbrand's theorem


Herbrand's theorem is one of the most important theorems of constructive first order logic: Formula is a tautology if and only if the tautology is some development of Herbrand's formula.

Since each development is a finite formula of the propositional calculus, so it can be settled in finite (exponential) time, the number of Herbrand expansions for the formula is a countable set, which proves each tautology of the first order logic, though it may take an unlimited amount time. Algorithm n = 0; proven = false; while (proven == false) { Y = nre_surfing_Herbrand (X, n); Y '= convert_function_form (Y); if (is_auto (Y ')) proven = true; else n = n + 1; } generate evidence based on Y;

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