Is the down casting right, and why dynamic_cast fails?

[QtCrawler]

Hello guys,
here I have a snippet of code and it would be very helpful, if you can explain why the second dynamic_cast fails and if the static_cast is the way to do it.

There are three classes Base, MyString and MyList. MyString and MyList are derived from Base. MyList is a template-class

#include <QCoreApplication>
#include <QDebug>
 
class Base
{
public:
    Base(){
 
    }
 
    virtual ~Base(){
        qDebug() << "~Base()";
    }
};
 
class MyString : public Base
{
public:
    QString str;
 
public:
    MyString(const QString& str) : Base(), str(str){
 
    }
 
    virtual ~MyString(){
        qDebug() << "~MyString()";
    }
};
 
template <class T>
class MyList : public QList<T>, public Base
{
public:
    MyList<T>():QList<T>(){
 
    }
 
    MyList<T>(QList<T> h):QList<T>(h){
 
    }
 
    virtual ~MyList<T>(){
        qDebug() << "~MyList()";
    }
};
 
Base* createMyList()
{
    MyList<Base*>* myList = new MyList<Base*>();
    myList->append(new MyString("joey potter"));
    myList->append(new MyString("allen harper"));
    myList->append(new MyString("charlie harper"));
    myList->append(new MyString("john mcclane"));
 
    return myList;
}
 
int main(int argc, char *argv[])
{
    QCoreApplication a(argc, argv);
    Q_UNUSED(a);
 
    MyList<Base*>* myList = new MyList<Base*>();
    myList->append(new MyString("string1"));
 
    //I know that first element is from class MyString so static_cast is sufficient
    Q_ASSERT(dynamic_cast<MyString*>(myList->first()) != NULL);// ok
    Q_ASSERT(static_cast<MyString*>(myList->first()) != NULL);// ok
 
    MyList<MyString*>* anotherList = static_cast<MyList<MyString*>*>(createMyList());
    Q_ASSERT(anotherList != NULL);// ok
 
    MyList<MyString*>* differentList = dynamic_cast<MyList<MyString*>*>(createMyList());
    Q_ASSERT(differentList != NULL);// ASSERT: "differentList != NULL" in file ../dynamic_cast_test/main.cpp, line 74
 
 
 
 
 
 
 
    //free ram
    QListIterator<Base*> lit1(*myList);
    while(lit1.hasNext()){
        delete lit1.next();
    }
    delete myList;
 
    QListIterator<MyString*> lit2(*anotherList);
    while(lit2.hasNext()){
        delete lit2.next();
    }
    delete anotherList;
 
    QListIterator<MyString*> lit3(*differentList);
    while(lit3.hasNext()){
        delete lit3.next();
    }
    delete differentList;
 
    return 0;
}

#include <QCoreApplication>
#include <QDebug>

class Base
{
public:
    Base(){

    }

    virtual ~Base(){
        qDebug() << "~Base()";
    }
};

class MyString : public Base
{
public:
    QString str;

public:
    MyString(const QString& str) : Base(), str(str){

    }

    virtual ~MyString(){
        qDebug() << "~MyString()";
    }
};

template <class T>
class MyList : public QList<T>, public Base
{
public:
    MyList<T>():QList<T>(){

    }

    MyList<T>(QList<T> h):QList<T>(h){

    }

    virtual ~MyList<T>(){
        qDebug() << "~MyList()";
    }
};

Base* createMyList()
{
    MyList<Base*>* myList = new MyList<Base*>();
    myList->append(new MyString("joey potter"));
    myList->append(new MyString("allen harper"));
    myList->append(new MyString("charlie harper"));
    myList->append(new MyString("john mcclane"));

    return myList;
}

int main(int argc, char *argv[])
{
    QCoreApplication a(argc, argv);
    Q_UNUSED(a);

    MyList<Base*>* myList = new MyList<Base*>();
    myList->append(new MyString("string1"));

    //I know that first element is from class MyString so static_cast is sufficient
    Q_ASSERT(dynamic_cast<MyString*>(myList->first()) != NULL);// ok
    Q_ASSERT(static_cast<MyString*>(myList->first()) != NULL);// ok

    MyList<MyString*>* anotherList = static_cast<MyList<MyString*>*>(createMyList());
    Q_ASSERT(anotherList != NULL);// ok

    MyList<MyString*>* differentList = dynamic_cast<MyList<MyString*>*>(createMyList());
    Q_ASSERT(differentList != NULL);// ASSERT: "differentList != NULL" in file ../dynamic_cast_test/main.cpp, line 74







    //free ram
    QListIterator<Base*> lit1(*myList);
    while(lit1.hasNext()){
        delete lit1.next();
    }
    delete myList;

    QListIterator<MyString*> lit2(*anotherList);
    while(lit2.hasNext()){
        delete lit2.next();
    }
    delete anotherList;

    QListIterator<MyString*> lit3(*differentList);
    while(lit3.hasNext()){
        delete lit3.next();
    }
    delete differentList;

    return 0;
}

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Why does following cast fail?

MyList<MyString*>* differentList = dynamic_cast<MyList<MyString*>*>(createMyList())

MyList<MyString*>* differentList = dynamic_cast<MyList<MyString*>*>(createMyList())

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Cause MyList<Base*>* is completely different from MyList<MyString*>* and the dynamic check is technically impossible ?

But can I do a static_cast(no dynamic checks), cause I know it's a MyList<MyString*>*? Is this cast is safe?

thank you