nebuloushomosapien on "Is this code right?"

<?php

/* POST TYPE */

add_action('init','create_product_post_type');
function create_product_post_type() {
	// Labels
	$labels = array(
		'name' => __('Products','framework'),
		'singular_name' => __('Product','framework'),
		'add_new' => __('Add new','framework'),
		'add_new_item' => __('Add new product','framework'),
		'edit_item' => __('Edit','framework'),
		'new_item' => __('New product','framework'),
		'view_item' => __('View product','framework'),
		'search_items' => __('Search product','framework'),
		'not_found' =>  __('No product found','framework'),
		'not_found_in_trash' => __('No product found in trash','framework'),
		'parent_item_colon' => '',
		'menu_name' => __('Products','framework')
	);

	$short_url = (get_option('tz_products_short_url') != '') ? get_option('tz_products_short_url') : 0;
	$slug_first_part = ((get_option('tz_custom_products_slug') != '') ? get_option('tz_custom_products_slug') : 'product');
	if($short_url == 1) {
		$slug = $slug_first_part;
	} else {
		$slug = $slug_first_part."/%product_category%/%product_brand%";
	}

Could this be a reason for having a vanilla ice creams URL on my site as

http://www.mysite.com/product/vanilla-ice-cream

when I desperately want it to be

http://www.mysite.com/vanilla-ice-cream

?? if yes what needs to be changed??