Selecting only polygons that contain another polygon with Select by Location in QGIS

Question

In QGIS 3.16.11 on Windows 10 I have a layer with single polygons.

Given this polygon layer with, I'm trying to select only the polygons that that contain at least one other polygon (A & B)

1. My first thought was, gonna be easy just do:

   Research tools -> Select by Location

   INPUT: original_layer  
   INTERSECT: original_layer  
   PREDICATE: contain   
   

   But everything got selected. It's acting like contain select polygon that contain but also that are equal. same thing happens with are within.

2. Then I tried with intermediary layer of slightly inflated polygons and to do the contain on that layer

   Geoprocessing Tools -> Buffer

   INPUT: original_layer  
   DISTANCE: 0.00001
   OUPUT: inner_polygon_slighly_inflated  
   

   Research tools -> Select by Location

   INPUT: original_layer  
   INTERSECT: inner_polygon_slighly_inflated  
   PREDICATE: contain
   

   Then I got selected B, but not A.

Can't find a way to this and which seems quite simple. Is there a way to make a PREDICATE: contain but not equal?

Answer 1

Use "Select by expression" with this expression: overlay_contains(@layer).

Answer 2

This is an extension to @Babel's answer which I found absolutely efficient.

Hence the statement "selecting only polygons that contain another polygon" was not really clear to me, I think some users may find it also a bit obscure. So there must be a differentiation between (1) selecting only polygons that contain another polygon as filled holes and (2) selecting only polygons that contain another polygon that lay over.

Let's assume there is a polygon layer called 'poly_test', see image below.

Case 1. Selecting only polygons that contain another polygon as filled holes

selecting polygons like "id" = 5 but not "id" = 1

P.S. Here I moved the feature with "id" = 6 for visual purposes

In the "Select by expression" from the Selection Toolbar use the following expression

overlay_touches(@layer) and num_interior_rings($geometry)

and get the final output

Case 2. Selecting only polygons that contain another polygon that lay over, i.e.

selecting polygons like "id" = 2 but not "id" = 5

In the "Select by expression" from the Selection Toolbar use the following expression

overlay_contains(@layer) and num_interior_rings($geometry)

and get the final output

Case 3. Selecting both from Case 1 & 2

In the "Select by expression" from the Selection Toolbar use the following expression

(overlay_contains(@layer) or overlay_touches(@layer)) and num_interior_rings($geometry)

and get the final output