Problem with database query

I have 2 tables in database. 
I need to get from database all rooms in which there is no reservation in the hours and date given by me.

rooms

id int(11)
name varchar(15)

reservations

id int(11)
room_id int(11)
date date
time_start time
time_finish time

My function: 

PHP Code:

public function get_free_rooms() {
    $date = $this->input->post('date', true);
    $time_start = $this->input->post('time_start', true);
    $time_finish = $this->input->post('time_finish', true);

    $query = $this->db->join('reservations','rooms.id = reservations.room_id','left')
        ->where('reservations.id IS NULL', null, false)
        ->where('reservations.date', $date)
        ->where('reservations.time_start<', $time_start)
        ->where('reservations.time_finish>', $time_finish)
        ->get('rooms');
    $query = $query->result();

    echo json_encode($query);
} 


My reservations table is empty now. When I give data:

$date = 2019-05-29, $time_start = 10:00:00, $time_finish = 13:00:00

result of query is an empty array and should return all rooms because there is no booking.