okay you cannot do it like that… you copied the class-fire-resources.php file into the child theme… but it wont be used… not how child themes work…
wp knows nothing about that file – its included by the parent theme… so you have to make all your changes to the parent theme…
now if it was called or included by a standard wp theme file, ie a template file such as page.php, wp would use it instead… but it getting included is all in the parent theme, so it will still include it…
did you make your edits to the child or the parent? without ftp, I cannot make changes to the parent… so if you made the changes to the child, please make to parent theme instead…