Exclude function from homepage only?

Question

There is a function in a theme that I am using that does some pagination stuff. I do NOT want that function to show up on my home page (only), so I'm trying to set up an if/else statement but can't for the life of me can't get it to work right. Using the following code, the function shows up not only on the homepage but also on the category pages. I am using this code in my index.php file and my site is setup to show posts from a custom post type.

<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
    <div>My Loop Stuff Here</div>
<?php endwhile; ?>

<?php if (!( is_home() || is_front_page() )) : function_to_NOT_show_on_homepage(); endif; ?>

<?php else: ?>
    [else stuffs]
<?php endif; ?>

<?php wp_reset_query(); ?>