Postgis select polygons that are inside and not touching

select_polys_inside.sql

SELECT c.cadaster_id, r.name
 , CASE 
   WHEN ST_CoveredBy(c.geom, r.geom) 
   THEN c.geom 
   ELSE 
    ST_Multi(
      ST_Intersection(c.geom,r.geom)
      ) END AS geom 
 FROM cadaster AS c 
   INNER JOIN roads_ply AS r 
    ON (ST_Intersects(c.geom, r.geom) 
      AND NOT ST_Touches(c.geom, r.geom) );