PHP script not running when I submit form

Question

This is my HTML form:

<div class="container">
            <div class="panel panel-default">
                <div class="panel heading">
                    <h1 style="text-align: center;">Choose your difficulty level </h1>
                </div>
                <div class="panel-body">
                    <div class="form-group">
                        <fieldset>
                            <form action="backup.php" method="POST">
                                <h4>What is your difficulty level?</h4>
                                <select name="startdiff" class="form-control">
                                    <option value="5">5</option>
                                    <option value="10">10</option>
                                    <option value="15">15</option>
                                </select>
                                <br />
                                <input type="button" name="subdiff" class="btn-primary btn-lg btn-success" value="Let's go!">
                            </form>
                        </fieldset>
                    </div>
                </div>
            </div>
        </div>

And this is what "backup.php" looks like:

<?php
include('connect.php');
include('my_class.php');

$admin = new User();

if (isset($_POST['subdiff']))
{

    $difficulty = $_POST['startdiff'];

    $admin->set_difficulty($difficulty);

    header('Location: getstarted.php');

}


?>

Note that I named it backup.php because my POST methods were all contained in one huge switch method but this specific form is the only one giving me problems, so please don't advise me on conventional naming methods.

What could be the problem?