Write a PBT which generates arbitrary predicates, documents and indexes. Then runs find(pred) and find(Not(pred)) and verifies the following properties:

1. find(pred) and find(Not(pred)) should be disjoint sets
2. The union of the two sets should contain the entire collection

Because MQL does not have a top-level $not operator, we can achieve the desired behavior by using a top-level $nor with a single child.

The alternative (or in addition) approach could be to restrict this to generate $not for children of path match expression. For example, {foo: pred} and {foo: {$not: pred}}. In this case, we'd need to be careful that we are only generate a single top-level predicate.