Evaluate whether an expression is tautology or not

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I am looking for an algorithm to find whether an expression is a tautology or not ? I tried using truth table (brute force) but this is not feasible in my case.

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David Eisenstat On BEST ANSWER

A formula is a tautology if and only if its negation is satisfiable. Satisfiability is an NP-hard problem, but there are many solvers that do better than brute force.