Не записывает в бд

<?php 
    $name = filter_var(trim($_POST['name']), FILTER_SANITIZE_STRING);
    $surname = filter_var(trim($_POST['surname']), FILTER_SANITIZE_STRING);
    $middle = filter_var(trim($_POST['middle']), FILTER_SANITIZE_STRING);
    $group = filter_var(trim($_POST['group']), FILTER_SANITIZE_STRING);
    $login = filter_var(trim($_POST['login']), FILTER_SANITIZE_STRING);
    $pass = filter_var(trim($_POST['pass']), FILTER_SANITIZE_STRING);
    $admin = 'none';
 
    require_once "connect.php"; 
    
    // $pass = md5(filter_var(trim($_POST['pass']), FILTER_SANITIZE_STRING).'geg2haj232');
 
    if (($name == '') or ($surname == '') or ($login == '') or ($pass == '')) {}
    else {
    connectDB();
    $mysqli->query("INSERT INTO `user` ( `name`, `surname`, `middle`,`stud_group`,`login`,`pass`, `admin` ) VALUES ('$name', '$surname', '$middle','$group','$login', '$pass', '$admin') ");
    closeDB();
    header('Location: ../../index.php');
    }
 
?>

<?php
    $mysqli = false;
    function connectDB() {
        global $mysqli;
        $mysql = new mysqli("localhost", "root", "", "test_stud");
  } 
    
 
    function closeDB () {
        global $mysqli;
        $mysqli-> close();
 
    }
?>

$mysql = new mysqli("localhost", "root", "", "test_stud");