Find common time in list of time ranges?

Question

I have two lists:

lis1 = [(datetime.datetime(2022, 6, 2, 9, 0), datetime.datetime(2022, 6, 2, 9, 30)), (datetime.datetime(2022, 6, 2, 11, 0), datetime.datetime(2022, 6, 2, 12, 10))],
lis2 = [(datetime.datetime(2022, 6, 2, 5, 9), datetime.datetime(2022, 6, 2, 6, 56)), (datetime.datetime(2022, 6, 2, 15, 37), datetime.datetime(2022, 6, 2, 17, 24)),  (datetime.datetime(2022, 6, 2, 9, 5), datetime.datetime(2022, 6, 2, 9, 25))]

and I have a event duration of 10 minutes. I want a common time range that resembles with both the list, meaning it should return a time which is available in both lists and is greater than the event duration for example in the above lists: datetime.datetime(2022, 6, 2, 9, 5) is the time which is available. what i've tried

def compare_lists(list1, list2, duration):
    
    gap_list = []
    for x in list1:
        for y in list2:
            if x[0] < y[0] and y[0] < x[1] < y[1]:
                gap_list.append((y[0], x[1]))

            if y[0] < x[0] < y[1] and y[0] < x[1] < y[1]:
                gap_list.append((y[0], y[1]))

            if y[0] < x[0] < y[1] and y[1] > x[1]:
                gap_list.append((x[0], x[1]))

            if x[0] < y[0] < x[1] and x[0] < y[1] < x[1]:
                gap_list.append((y[0], y[1]))
                
    common_time = [t for t in gap_list if (t[1] - t[0]) > duration]
    return common_time


duration = timedelta(minutes=20)
ranges = [
    [(datetime.datetime(2022, 6, 2, 9, 0), datetime.datetime(2022, 6, 2, 9, 30)),(datetime.datetime(2022, 6, 2, 11, 0), datetime.datetime(2022, 6, 2, 12, 10))],
    [(datetime.datetime(2022, 6, 2, 5, 9), datetime.datetime(2022, 6, 2, 6, 56)), (datetime.datetime(2022, 6, 2, 15, 37),datetime.datetime(2022, 6, 2, 17, 24)),  (datetime.datetime(2022, 6, 2, 15, 37), datetime.datetime(2022, 6, 2, 9, 25))],
]

ret = compare_lists(ranges[0], ranges[1], duration)
print(ret)

the results is an empty list weather i have an common time or not.