The Google Script will automatically archive all the messages in your Gmail inbox that are older than 2 days. You can either use a Gmail search filter to find read messages or you can compare the message date with the current date through the script and archive messages accordingly.

function cleanInbox() {

  var delayDays = 2;

  var maxDate = new Date();
  maxDate.setDate(maxDate.getDate()-delayDays);

  var threads = GmailApp.getInboxThreads();

  for (var i = 0; i < threads.length; i++) {
    if (threads[i].getLastMessageDate() function archiveInbox() {
  var threads = GmailApp.search('label:inbox is:read older_than:2d');
  for (var i = 0; i < threads.length; i++) {
    threads[i].moveToArchive();
  }
}