Atheists think that all theism is irrational.
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Theism is then at its most basic the belief in at least one god. There are, however, many different types of theists. Monotheists and polytheists are well known, but there are a variety of others as well. There terms describe types of religious thought rather than specific religions. Here are some of the more commonly discussed ones.
The second version of this definition seems to match Definition 1 above.