Description:
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Following the documentation, creating a new DateTime instance with the realtive format "first day" (without month) should result in "the day of the first of the current month" (although it's recommended to use it with the optional month): http://php.net/manual/en/datetime.formats.relative.php

In my tests (also in PHP 5.3.27 and PHP 5.4.7) a wrong date was created. As far as I can see, it's always the current time + 1 day.

Test script:
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<?php
echo PHP_VERSION . "\r\n";
$datetime1 = new DateTime('now');
echo $datetime1->format('Y-m-d H:i:s') . "\r\n";
$datetime2 = new DateTime('first day of this month');
echo $datetime2->format('Y-m-d H:i:s') . "\r\n";
$datetime3 = new DateTime('first day');
echo $datetime3->format('Y-m-d H:i:s') . "\r\n";

Expected result:
----------------
2013-09-30:
5.5.4
2013-09-30 07:59:29
2013-09-01 07:59:29
2013-09-01 07:59:29

2013-10-01:
5.5.4
2013-10-01 07:59:29
2013-10-01 07:59:29
2013-10-01 07:59:29

2013-10-02:
5.5.4
2013-10-02 07:59:29
2013-10-01 07:59:29
2013-10-01 07:59:29

Actual result:
--------------
2013-09-30:
5.5.4
2013-09-30 07:59:29
2013-09-01 07:59:29
2013-10-01 07:59:29

2013-10-01:
5.5.4
2013-10-01 07:59:29
2013-10-01 07:59:29
2013-10-02 07:59:29

2013-10-02:
5.5.4
2013-10-02 07:59:29
2013-10-01 07:59:29
2013-10-03 07:59:29