A simple nonconstructive argument shows that most 3-CNF formulas with cn clauses (where c is a sufficiently large constant) are not satisfiable. It is an open question whether there is an efficient refutation algorithm that for most formulas with cn clauses proves that they are not satisfiable. We present a polynomial time algorithm that for most 3-CNF formulas with cn^3/2 clauses (where c is a sufficiently large constant) finds a subformula with Θ(c²n) clauses and then uses spectral methods to prove that this subformula is not satisfiable (and hence that the original formula is not satisfiable). Previously, it was only known how to efficiently certify the unsatisfiability of random 3-CNF formulas with at least   polylog(n)n^3/2 clauses. Our algorithm is simple enough to run in practice. We present some experimental results.