The expression Ayil Meshulash is from the Pasuk Bereshit 15:9,
which mentions three sacrifices, the Eglah Meshuleshet, the Ez Meshuleshet, and the Ayil Meshulash, which correspond to three three-fold "wars" in our time. One of the three fits the three parts of Ayil Meshulash, and the other two three-fold wars are as follows.
The first three-fold war is Eglah Meshuleshet. The first part of it is the war of independence. It was "predicted" to be related to טצ"ץ, in the sense that the gematria of the date is 999.
Indeed, year 5708 is the year that 999/2 was reached by the exile count.
Likewise, the other great wars, the six-day war of 5727, and the Yom Kippur war of 5734 were טצ"ץ wars.
In short, all of the above wars were in the years in which the three counts, the exile count, the count of Din, and the count of Chesed, reached the value 999/2. They were part of Eglah Meshuleshet, which is all history now.
The three counts reach 507 in accordance with the first Pasuk of this week's Parasha, Tetzaveh. It contains the number 507, ז"ך, along side three numbers כ"ת, י"ת, זי"ת. These numbers, seen as years that elapsed since the year 5366, exactly fit the years in which 507 is reached by the three counts. This is Ez Meshuleshet. It starts in the current year, 5776.