Initial condition of Schmitt Trigger Circuit
There seems to be an original idea in this &quot;ladder&quot; - the comparators are turned on sequentially and each of them allows the next.
Okay, here are some more tips to think about:

Is it Inverting Schmitt Trigger comparator circuit?

Yes, it is as the input voltage is applied to the inverting input.

Which Output will be High or Low at first? Out A or D?

It seems all the outputs will be HIGH at first.

How other Outputs will switch accordingly?

They should switch sequentially.

The voltage dividers are not firmly connected to Vcc and ground; instead their ends are &quot;movable&quot;. Let's see what happens when Vin begins increasing above zero.
Vin = 0. In the beginning, the outputs of the all comparators are HIGH. It is convenient to check this by going from back to front.
Output D is HIGH since R31 is firmly connected to 7 V... and regardless of the previous output C, the input voltage of the non-inverting input is positive (&gt; 0.7 V). We continue up and see that, for the same reason, the outputs C, B and A are HIGH.
Vin &gt; VH.  When the high threshold  is exceeded, the first comparator  switches and its output A becomes LOW; the 3 k R21 of the second voltage divider is grounded.
Since R23 is connected to HIGH, the second comparator switches and its output B becomes LOW; so the 3 k R26 of the third voltage divider is grounded.
Then, since R27 is connected to HIGH, the third comparator switches and its output C becomes LOW; so the 3 k R30 of the fourth voltage divider is grounded.
Finally, since R31 is connected to 7 V, the fourth comparator switches and its output D becomes LOW.
Vin &lt; VL.  When the low threshold  is reached, the fourth comparator  switches and its output D becomes HIGH; the 6.8 k R27 of the third voltage divider is connected to HIGH.
Since the 3 k R26 is connected to LOW, the third comparator switches and its output C becomes HIGH and R23 of the second voltage divider is connected to HIGH... and so on...
Conclusion
Like a domino effect, once the input voltage exceeds the upper threshold, the comparators start switching from HIGH to LOW in sequence A -&gt; B -&gt; C -&gt; D. When the input voltage goes below the lower threshold, they start switching from LOW to HIGH in the reverse sequence D -&gt; C -&gt; B - &gt; A.