I see no need for the "if".
I would be grateful if you could help me put this formula into simple words
. . .
Could I in this instance read it as follows?
X proceeds or equals y and y between Aug 1 2010 and July 2011
X succeeds y and x between Aug 1 2010 and July 2011
I would be careful with the word "between".
Some may assume that it means literally between,
. . not including the end dates.