How to get all combinations of "sub"lists from a list

Now, this assumes you have a list of valid combinations that you can use. Using a recursive function, I am able to get the desired output.

Note: I have done 0 optimizations

import numpy


def build_combo(current_set, all_combos):
    global count, req_options
    for each in all_combos:
        if all(len(numpy.intersect1d(each, x)) == 0 for x in current_set):
            inner_set = current_set.copy()
            inner_set.append(each)
            flat = []
            for x in inner_set:
                flat.extend(x)
            if all(x in flat for x in req_options):
                built_combos.append(inner_set)
            else:
                build_combo(inner_set, all_combos)


req_options = ['a', 'b', 'c', 'd', 'e', 'f', 'g']

all_combos = [['a'], ['b'], ['c'], ['d'], ['e'], ['f'], ['g'],
              ['a', 'b'], ['c', 'd'], ['a', 'f'], ['f', 'g'],
              ['a', 'c', 'd'], ['g', 'f', 'e', 'b']]

built_combos = []
build_combo([], all_combos)

option_sets = set()
for combo in built_combos:
    newset = set()
    for element in combo:
        newset.add(frozenset(element))
    option_sets.add(frozenset(newset))

for option_set in option_sets:
    combo_str = ''
    for option in option_set:
        combo_str += '[{}]'.format('+'.join(option))
    print(combo_str)

Output ("+" sign added to printout for easier reading):

[e][g][c+d][b][f+a]
[a][c][d][f+e+g+b]
[f+g][e][c][d][a+b]
[f+g][e][c+d][a][b]
[f][e][c][g][a][b][d]
[c+a+d][f][e][g][b]
[b][e][f+g][c+a+d]
[f][e][g][c+d][a+b]
[f+g][e][a+b][c+d]
[f][e][g][c+d][a][b]
[e][c][g][b][f+a][d]
[f+g][e][c][a][b][d]
[f][e][c][g][d][a+b]
[a][f+e+g+b][c+d]
[c+a+d][f+e+g+b]