We show that any language in nondeterministic time \exp(\exp(\cdots\exp(n))), where the number of iterated exponentials is an arbitrary function R(n), can be decided by a multiprover interactive proof system with a classical polynomial-time verifier and a constant number of quantum entangled provers, with completeness 1 and soundness 1 - \exp(-C\exp(\cdots\exp(n))), ... more >>>