Session timeout

Hey guys if the user exits the browser will this code still run the user_logout.php ? 

Thanks

session_cache_expire( 20 );

session_start(); // NEVER FORGET TO START THE SESSION!!!

$inactive = 1200; //20 minutes *60

if(isset($_SESSION['start']) ) {

$session_life = time() - $_SESSION['start'];

if($session_life > $inactive){

header("Location: user_logout.php");

}

}

$_SESSION['start'] = time();



if($_SESSION['valid_user'] != true){

header('Location: ../....php');

}else{