How to correctly convert a file with utf-32 encoding to utf-8 using the UTF8-CPP library?

Question

linux

I have a file in utf-32 encoding and I need to convert it to utf-8, here is my program code:

#include "source/utf8.h"
using namespace std;

int main(int argc, char** argv)
{
    const char* sourceFilePath = "/home/user/utf32.txt";

    ifstream sourceFile(sourceFilePath, std::ifstream::binary);
    ofstream outFile("/home/user/utf8result.txt");

    vector<unsigned char> utf8result;
       utf8::utf32to8(std::istreambuf_iterator<char>(sourceFile),
                      std::istreambuf_iterator<char>(),
                      back_inserter(utf8result));
       outFile.write((char*)&utf8result[0], utf8result.size());

    return 0;
}

There are no errors, but for some reason the new file is still encoded in utf-32, this can be seen from the fact that the sizes of the received and the old file are the same, I also looked in the HEX Editor - it also shows that each character in utf8result.txt takes 4 bytes.
The utf8result.txt file must be in utf-8 encoding and must be 24 bytes long. Why is it so? I used this simple but famous library:
utfcpp.sourceforge.net
Please help me. I've been trying all day to find the right solution, although it shouldn't be hard.

Answer 1

utf8::utf32to8(std::istreambuf_iterator<char32_t>(sourceFile),
                      std::istreambuf_iterator<char32_t>(),
                      back_inserter(utf8result));

Answer 2

Why use a third party library? Linux has an iconv function (from glibc) that encodes utf and other encodings