Newbie C++ issue involving while loops and OR statements

I am having an issue learning C++ basics involving the while loop. When I run my program it works well, until I get to the while loop involving an OR (||) statement. while (totalhumanHP > 0 || totalskeletonHP > 0) should continue until one hits zero then stop correct? It is only keeping tabs on totalhumanHP and letting skeletonHP dip into the negatives without stopping. I am not sure how or why the OR statement isnt functioning in the while loop.

#include <iostream>
#include <string>
#include <random>
#include <ctime>

using namespace std;

int main()
{
    cout << "-----SKELETMANS V HOOMINS-----\n";
    int skeletonHP = 90;
    int humanHP = 100;
    int skeletonDMG = 1;
    int humanDMG = 1;
    int totalskeleton = 1;  //Inputted Skele's
    int totalhuman = 1; //Inputted hoomins
    int totalskeletonHP; //Overall Skele HP
    int totalhumanHP; //Overall Hoomin HP
    string battlecry;
    string battlecryenter;

    default_random_engine generator(time(0));
    uniform_int_distribution<int> skeletonrng(1, 22);
    uniform_int_distribution<int> humanrng(1, 20);

    cout << "How Many Skeletmans: ";
    cin >> totalskeleton;
    cout << "How Many Houmints: ";
    cin >> totalhuman;

    totalskeletonHP = totalskeleton * skeletonHP;
    totalhumanHP = totalhuman * humanHP;    

    cout << "Overall Skeleton HP= " << totalskeletonHP << endl;
    cout << "Overall Hoomint HP= " << totalhumanHP << endl;
    cout << endl;
    cout << "What is your battlecry?\n (You can use this to start the battle)";
    cout << endl;
    cin >> battlecry;
    battlecry == battlecryenter;

    cout << "Use Your Battlecry To Start The Fight!!!\n\n\n\n\n";    
    cout << "BattleCry: ";    
    cin >> battlecryenter;

    if (battlecryenter == battlecry)
    {
        cout << "THE FIGHT HAS COMMENCED!!!\n\n\n\n";
    }
    else{
        cout << "You 4got alreedy?  UR DOMB MING\n\n";    
        cout << "ACTUAL BattleCry: ";
        cin >> battlecryenter;

        if (battlecryenter == battlecry)
        {
            cout << "THE FIGHT HAS COMMENCED!!!\n\n\n\n";
        }
    }

    int endskeleton = 0;
    int endhuman = 0;

    while (totalhumanHP > 0 || totalskeleton > 0)
    {
        skeletonDMG = skeletonrng(generator);
        humanDMG = humanrng(generator);
        totalhumanHP = totalhumanHP - skeletonDMG;
        totalskeletonHP = totalskeletonHP - humanDMG;

        cout << "END SKELETON: " << totalskeletonHP << endl;
            cout << "END HOOMING: " << totalhumanHP << endl;

    }
    cout << "Skeleton Ramaining Health: " << totalskeletonHP << endl;
    cout << "Human Remaining Health: " <<  totalhumanHP << endl;
    system("PAUSE");
    return 0;
}