Description:
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strtotime("first day this month") gives a date for next month. 

Test script:
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<?php

$d = "first day this month";
echo "'$d': ".date("Y-m-d", strtotime($d)).PHP_EOL;

$d = "first day of this month";
echo "'$d': ".date("Y-m-d", strtotime($d)).PHP_EOL;

echo "Today: ".date("Y-m-d").PHP_EOL;


Expected result:
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'first day this month': 2017-11-01
'first day of this month': 2017-11-01
Today: 2017-11-30


Actual result:
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'first day this month': 2017-12-01
'first day of this month': 2017-11-01
Today: 2017-11-30