How to inverse query using Artifactory Query Language?

In Artfactory, I have a list of "repo" properties, some of which come with a "path" property. I need to find all items that do not match these properties. I was wondering if there was a way to structure my logic so that this could be done in one query.

Here's my current, broken logic:

curl -u $credentials \
-X POST https://my-artifactory-server.com/artifactory/api/search/aql \
-H content-type:text/plain -d 'items.find({ 
    "$and": [
        {"repo" : {"$neq" : "top_level_directory"}},
        { 
            "$and": [ 
                {"repo" : {"$neq" : "other_top_level_directory"}},
                {"path" : {"$nmatch" : "sub_directory/*"}}
            ]
        }
    ]
}).include("repo","path","name","size","modified")'

The issue with this is that while the "repo" property is unique, the "path" property is not. All subdirectories would thus be excluded from the query result.

Yes. AQL is like a logical clause and therefore we can structurize it. I'm assuming the following is the original query:

{
  "$or": [
    { "repo": { "$eq": "top_level_directory" } },
    {
      "$and": [
        { "repo": { "$eq": "other_top_level_directory" } },
        { "path": { "$match": "sub_directory/*" } }
      ]
    }
  ]
}

A - repo == top_level_directory
B - repo == other_top_level_directory
C - path =~ sub_directory/*

Original query:
A ∨ (B ∧ C)

Inversion:
¬(A ∨ (B ∧ C))
<=> (De Morgan)
¬A ∧ ¬(B ∧ C))
<=> (De Morgan)
¬A ∧ (¬B ∨ ¬C)) 

And the following query deduced:

{
  "$and": [
    { "repo": { "$neq": "top_level_directory" } },
    {
      "$or": [
        { "repo": { "$neq": "other_top_level_directory" } },
        { "path": { "$nmatch": "sub_directory/*" } }
      ]
    }
  ]
}