If QGROUP-ISO is many-one complete for NP(log2 n) under polynomial time reductions then CLIQUE is in coNTIME[nO(1), 2O( √n log n) ]/poly. I.e. for inputs of length n, CLIQUE has polynomial-size proofs which can be verified in 2O( √n log n) time with the help of a polynomial-size advice.

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