Почему с set программа работает, а с list нет?

with open("27-62b.txt") as f:
    N = int(f.readline())
    arr = [int(s) for s in f]
 
res = 0
for i in arr:
    for j in range(1, 101):
        x = i
        cnt = 0
        while x in arr:
            x += j
            cnt += 1
        res = max(res, cnt)
print(res)

with open("27-62b.txt") as f:
    N = int(f.readline())
    arr = set([int(s) for s in f])
 
res = 0
for i in arr:
    for j in range(1, 101):
        x = i
        cnt = 0
        while x in arr:
            x += j
            cnt += 1
        res = max(res, cnt)
print(res)

import time
from bisect import bisect_left
def fun(a, elem):
    i = bisect_left(a, elem)
    if i < len(a):
        return a[i] == elem
    return False
    
    
t1 = time.time()
with open("27-62b.txt") as f:
    N = int(f.readline())
    arr = sorted([int(s) for s in f])
n = len(arr)
res = 0
for i in range(n-1):
    k = arr[i+1] - arr[i]
    x = arr[i]    
    for j in range(k, 101):
        cnt = 0
        ind = i
        while ind:
            cnt += 1
            x += j
            ind = fun(arr, x)
        res = max(res, cnt)
print(res)
print(time.time() - t1)

>>> a = list('abcdefecsab')
>>> len(a)
11
>>> len(set(a))
7
>>>