Overlapping Times MySQL

<?php // RAY_mysqli_resource_calendar.php
ini_set('display_errors', TRUE);
error_reporting(E_ALL);
echo '<pre>';


// DEMONSTRATE A RESOURCE-SCHEDULING CALENDAR


// DATABASE CONNECTION AND SELECTION VARIABLES - GET THESE FROM YOUR HOSTING COMPANY
$db_host = "localhost"; // PROBABLY THIS IS OK
$db_name = "??";
$db_user = "??";
$db_word = "??";

// OPEN A CONNECTION TO THE DATA BASE SERVER AND SELECT THE DB
$mysqli = new mysqli($db_host, $db_user, $db_word, $db_name);

// DID THE CONNECT/SELECT WORK OR FAIL?
if ($mysqli->connect_errno)
{
    trigger_error("CONNECT FAIL: $mysqli->connect_errno $mysqli->connect_error", E_USER_ERROR);
}


// CREATING A TABLE FOR OUR TEST DATA
$sql
=
"
CREATE TEMPORARY TABLE my_calendar
( id    INT         NOT NULL AUTO_INCREMENT PRIMARY KEY
, rname VARCHAR(24) NOT NULL DEFAULT ''                    # RESOURCE NAME
, alpha DATETIME    NOT NULL DEFAULT '0000-00-00 00:00:00' # BEGINNING OF COMMITMENT
, omega DATETIME    NOT NULL DEFAULT '0000-00-00 00:00:00' # END OF COMMITMENT
)
"
;

// CREATE THE TABLE OR LOG AND SHOW THE ERROR
if (!$res = $mysqli->query($sql))
{
    $err
    = 'QUERY FAILURE:'
    . ' ERRNO: '
    . $mysqli->errno
    . ' ERROR: '
    . $mysqli->error
    . ' QUERY: '
    . $sql
    ;
    trigger_error($err, E_USER_ERROR);
}

// PRE-LOAD SOME SCHEDULED RESOURCES INTO THE CALENDAR
$mysqli->query("INSERT INTO my_calendar (rname, alpha, omega) VALUES ( 'One', '2013-06-20T08:00:00', '2013-06-20T09:59:59' )");
$mysqli->query("INSERT INTO my_calendar (rname, alpha, omega) VALUES ( 'Two', '2013-06-20T08:00:00', '2013-06-20T09:59:59' )");
$mysqli->query("INSERT INTO my_calendar (rname, alpha, omega) VALUES ( 'Two', '2013-06-20T11:00:00', '2013-06-20T12:59:59' )");


// SHOW THE CALENDAR
$res = $mysqli->query("SELECT * FROM my_calendar");
while ($row = $res->fetch_object()) { print_r($row); }


// SCHEDULE A RESOURCE FROM 1:00pm TO 3:00pm
$rname = 'One';
$alpha = date('c', strtotime('June 20, 2013 1:00pm'));
$omega = date('c', strtotime('June 20, 2013 3:00pm - 1 SECOND'));

$res = $mysqli->query("LOCK TABLES my_calendar");
$res = $mysqli->query("SELECT id FROM my_calendar WHERE rname = '$rname' AND ( (alpha BETWEEN '$alpha' AND '$omega') OR (omega BETWEEN '$alpha' AND '$omega') )  LIMIT 1");
$num = $res->num_rows;
if ($num == 0)
{
    $res = $mysqli->query("INSERT INTO my_calendar (rname, alpha, omega) VALUES ( '$rname', '$alpha', '$omega' )");
    echo "SCHEDULED $rname FROM $alpha TO $omega" . PHP_EOL;
}
else
{
    echo "CONFLICT! $rname FROM $alpha TO $omega" . PHP_EOL;
}
$res = $mysqli->query("UNLOCK TABLES my_calendar");


// TRY TO SCHEDULE THE SAME RESOURCE FROM 2:00pm TO 4:00pm
$rname = 'One';
$alpha = date('c', strtotime('June 20, 2013 2:00pm'));
$omega = date('c', strtotime('June 20, 2013 4:00pm - 1 SECOND'));

$res = $mysqli->query("LOCK TABLES my_calendar");
$res = $mysqli->query("SELECT id FROM my_calendar WHERE rname = '$rname' AND ( (alpha BETWEEN '$alpha' AND '$omega') OR (omega BETWEEN '$alpha' AND '$omega') )  LIMIT 1");
$num = $res->num_rows;
if ($num == 0)
{
    $mysqli->query("INSERT INTO my_calendar (rname, alpha, omega) VALUES ( '$rname', '$alpha', '$omega' )");
    echo "SCHEDULED $rname FROM $alpha TO $omega" . PHP_EOL;
}
else
{
    echo "CONFLICT! $rname FROM $alpha TO $omega" . PHP_EOL;
}
$res = $mysqli->query("UNLOCK TABLES my_calendar");


// TRY TO SCHEDULE A DIFFERENT RESOURCE FROM 2:00pm TO 4:00pm
$rname = 'Two';
$alpha = date('c', strtotime('June 20, 2013 2:00pm'));
$omega = date('c', strtotime('June 20, 2013 4:00pm - 1 SECOND'));

$res = $mysqli->query("LOCK TABLES my_calendar");
$res = $mysqli->query("SELECT id FROM my_calendar WHERE rname = '$rname' AND ( (alpha BETWEEN '$alpha' AND '$omega') OR (omega BETWEEN '$alpha' AND '$omega') )  LIMIT 1");
$num = $res->num_rows;
if ($num == 0)
{
    $mysqli->query("INSERT INTO my_calendar (rname, alpha, omega) VALUES ( '$rname', '$alpha', '$omega' )");
    echo "SCHEDULED $rname FROM $alpha TO $omega" . PHP_EOL;
}
else
{
    echo "CONFLICT! $rname FROM $alpha TO $omega" . PHP_EOL;
    while ($row = $res->fetch_object()) { var_dump($row); }
}
$res = $mysqli->query("UNLOCK TABLES my_calendar");


// SHOW THE RESULTING CALENDAR
$res = $mysqli->query("SELECT * FROM my_calendar");
while ($row = $res->fetch_object()) { print_r($row); }

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