Exclude function from homepage only?

Question

Based on your pastes, i think what you’re going for is..

function cp_do_pagination() {   

    if( is_home() || is_singular() /* || is_front_page() */ )
        return;

    global $post; // <-- do you need this for something in particular?

    if( !function_exists('appthemes_pagination') )
        return;

    appthemes_pagination();
}

The is_singular() function covers is_page(), is_single() and is_attachment(), so no need for the additional conditionals.

Info on that function here, for reference.
http://codex.wordpress.org/Function_Reference/is_singular