Basic maths are this ...
1. Ohms Law == P = I * V - or Power (Watts) = Current (A) x Voltage (V)
Another way to say that is I = P / V (Current = Power / Volts)
so 1000W / 12V = 84A
if you lose 5% due in inefficiencies, add 5% to the current, so the current drawn is 84A *105% = 90A (I rounded up to 90A as 95% efficient is pretty optimistic)
2. 1AH = 1A drawn for 1 hour. so 90A would be 90AH if drawn for 1 Hour.
you are drawing for 1/4 of an hour, so AHs used will be 1/4 of 90A = 22.5AH
Those are the theoretical numbers. a 12V system is not actually 12V of course.
With a Lead Acid
Battery system with that load, that Voltage would probably drop down to under 12V (and the lower the voltage, the greater the current to deliver 1000W - remember P = I * V).
With a Lithium
Battery system like you have, the Voltage drop does not occur and your batteries will be greater than 12V (so there will actually be a lower current draw to achieve that 1000W and a corresponding decrease in AHs consumed)