I do believe the algorithm in the pervious answer and in the OP does not do what the OP wanted. It test for the longest string starting with the line's first character, and then repeat from the first non repeating string. For example if the string is

abcaefgb

The algorithm given will return

abc

while the right answer should be

bcaefg

I believe the following algorithm will find the right string. Note that if there are several equal length longest strings it will return the first

def scantillrepeat(line):
    found = ''
    for char in line:
        if not char in found:
            found = found + char
        else:
            break
    return(found)


def findlongest(f):
    for line in f:
        longestfound = ''
        longestfoundlen = 0
        for k in range(len(line)):
            candidate = scantillrepeat(line[k:])
            if len(candidate) > longestfoundlen:
                longestfound = candidate
                longestfoundlen = len(candidate)
    return(longestfound)

To test

In [39]: f = ['abcaefgb']

In [40]: findlongest(f)
Out[40]: 'bcaefg'

Note that my version does not allow joining lines separated by newline \n. This should be altered if needed.

I do believe the algorithm in the pervious answer and in the OP does not do what the OP wanted. It test for the longest string starting with the line's first character, and then repeat from the first non repeating string. For example if the string is

abcaefgb

The algorithm given will return

abc

while the right answer should be

bcaefg

I believe the following algorithm will find the right string. Note that if there are several equal length longest strings it will return the first

def scantillrepeat(line):
    found = ''
    for char in line:
        if not char in found:
            found = found + char
        else:
            break
    return found


def findlongest(f):
    for line in f:
        longestfound = ''
        longestfoundlen = 0
        for k in range(len(line)):
            candidate = scantillrepeat(line[k:])
            if len(candidate) > longestfoundlen:
                longestfound = candidate
                longestfoundlen = len(candidate)
    return longestfound

To test

In [39]: f = ['abcaefgb']

In [40]: findlongest(f)
Out[40]: 'bcaefg'

Note that my version does not allow joining lines separated by newline \n. This should be altered if needed.