Base tables that have a unique constraint but not the primary key

SELECT A.table_schema, A.table_name 
FROM INFORMATION_SCHEMA.tables A
INNER JOIN INFORMATION_SCHEMA.schemata B
  ON A.table_schema = B.schema_name
WHERE (A.table_schema, A.table_name) NOT IN 
  (SELECT table_schema, table_name FROM INFORMATION_SCHEMA.table_constraints
   WHERE constraint_type IN ('PRIMARY KEY'))
AND (A.table_schema, A.table_name) IN 
  (SELECT table_schema, table_name FROM INFORMATION_SCHEMA.table_constraints
   WHERE constraint_type IN ('UNIQUE'))
AND A.table_type = 'BASE TABLE'
AND (A.table_schema = 'public' OR B.schema_owner <> 'postgres')


AND NOT EXISTS (
    SELECT 1
    FROM pg_inherits i
    INNER JOIN pg_class c ON c.oid = i.inhparent
    INNER JOIN pg_namespace n ON n.oid = c.relnamespace
    WHERE n.nspname = A.table_schema 
      AND c.relname = A.table_name
)

ORDER BY A.table_schema, A.table_name;