You're doing it wrong.
A working honeypot
HTML
<form>
<input type="text" name="mail" id="mail">
<input type="submit">
</form>
<style>
#mail{display:none;}
</style>
PHP
if($_POST && $_POST["mail"] != ""){
die("Sorry, no robots");
}
How does it work
You have a hidden field inside your form. Typically, a robot will attempt to fill any form field available with data in the hope that it will not get rejected. Once it submits that form, your script will detect the input and die. If a human was filling it out, they would not see the hidden input (type=text style=display:none) and leave it empty. Thus the php would allow the submit to go ahead.
If you PHP script dies as soon as it detects the honeypot field, then you are saving yourself cpu cycles (because there is no need to reply reasonably to a robot).
For more information on honeypot, see this question:
How do I add Honey pot fields to my forms?