To use shortcode in a PHP file (outside the post editor) you have the handy little function
do_shortcode();
so in your case you use:
<?php
do_shortcode('[mingleforum]');
?>
Update:
following the first comment,
I figured its publicly known for some reason,
if you are expecting output from the shortcode then echo it out.
<?php
echo do_shortcode('[mingleforum]');
?>