so here's the set-up: In a sentence like "Bill went to the store," several accepted constituency tests can produce "Bill went" as a constituent. These tests include the question test (What happened? Bill went.) and the ellipsis test (Bill went to the store, and to the docks, and to the playground, ... etc.). We also know that complete sentences are in themselves constituents, and "Bill went" is, technically, a complete sentence. It happens, in this case, to be contained within a larger sentence, but it is its own sentence nonetheless.
However, "Bill went" also fails certain constituency test, notably the clefting test (*It was Bill went that to the store).
So my question is: in this example, is "Bill went" a constituent or not? And, almost more importantly, if it is not a constituent, precisely why not?