Assuming your tasks return bool you can do something like this:

CancellationTokenSource source = new CancellationTokenSource();
CancellationToken stoppingToken = source.Token;
Task<bool> task1 = Task.Run(() => Task1(stoppingToken));
....

var tasks = new List<Task<bool>>
{
    task1, task2, task3, ...
};

bool taskResult = false;
do
{
    var finished = await Task.WhenAny(tasks);
    taskResult = finished.Result;
    tasks.Remove(finished);
} while (tasks.Any() && !taskResult);

source.Cancel();

Here's a solution based on continuation tasks. The idea is to append continuation tasks to each of the original (provided) tasks, and check the result there. If it's a match, the completion source will be set with a result (if there's no match, the result won't be set at all).

Then, the code will wait for whatever happens first: either all the continuation tasks complete, or the task completion result will be set. Either way, we'll be ready to check the result of the task associated with task completion source (that's why we wait for the continuation tasks to complete, not the original tasks) and if it's set, it's pretty much an indication that we have a match (the additional check at the end is a little paranoid, but better safe than sorry I guess... :D)

public static async Task<bool> WhenAnyHasResult<T>(Predicate<T> isExpectedResult, params Task<T>[] tasks)
{
    const TaskContinuationOptions continuationTaskFlags = TaskContinuationOptions.ExecuteSynchronously | TaskContinuationOptions.OnlyOnRanToCompletion | TaskContinuationOptions.AttachedToParent;
         
    // Prepare TaskCompletionSource to be set only when one of the provided tasks
    // completes with expected result
    var tcs = new TaskCompletionSource<T>();

    // For every provided task, attach a continuation task that fires
    // once the original task was completed
    var taskContinuations = tasks.Select(task =>
    {
        return task.ContinueWith(x =>
        {
            var taskResult = x.Result;
            if (isExpectedResult(taskResult))
            {
                tcs.SetResult(taskResult);
            }
        },
        continuationTaskFlags);
    });

    // We either wait for all the continuation tasks to be completed 
    // (it's most likely an indication that none of the provided tasks completed with the expected result)
    // or for the TCS task to complete (which means a failure)
    await Task.WhenAny(Task.WhenAll(taskContinuations), tcs.Task);

    // If the task from TCS has run to completion, it means the result has been set from
    // the continuation task attached to one of the tasks provided in the arguments
    var completionTask = tcs.Task;
    if (completionTask.IsCompleted)
    {
        // We will check once more to make sure the result is set as expected 
        // and return this as our outcome
        var tcsResult = completionTask.Result;
        return isExpectedResult(tcsResult);
    }

    // TCS result was never set, which means we did not find a task matching the expected result.
    tcs.SetCanceled();
    return false;
}

Now, the usage will be as follows:

static async Task ExampleWithBooleans()
{
    Console.WriteLine("Example with booleans");

    var task1 = SampleTask(3000, true);
    var task2 = SampleTask(5000, false);

    var finalResult = await TaskUtils.WhenAnyHasResult(result => result == true, task1, task2);

    // go ahead and cancel your cancellation token here

    Console.WriteLine("Final result: " + finalResult);
    Debug.Assert(finalResult == true);
    Console.WriteLine();
}

What's nice about putting it into a generic method, is that it works with any type, not only booleans, as a result of the original task.

You could use an asynchronous method that wraps a Task<bool> to another Task<bool>, and cancels a CancellationTokenSource if the result of the input task is true. In the example below this method is the IfTrueCancel, and it is implemented as local function. This way it captures the CancellationTokenSource, and so you don't have to pass it as argument on every call:

var cts = new CancellationTokenSource();
var stoppingToken = cts.Token;

var task1 = IfTrueCancel(Task.Run(() => Task1(stoppingToken)));
var task2 = IfTrueCancel(Task.Run(() => Task2(stoppingToken)));
var task3 = IfTrueCancel(Task.Run(() => Task3(stoppingToken)));
var task4 = IfTrueCancel(Task.Run(() => Task4(stoppingToken)));
var task5 = IfTrueCancel(Task.Run(() => Task5(stoppingToken)));
var task6 = IfTrueCancel(Task.Run(() => Task6(stoppingToken)));

Task.WaitAll(task1, task2, task3, task4, task5, task6);

async Task<bool> IfTrueCancel(Task<bool> task)
{
    bool result = await task.ConfigureAwait(false);
    if (result) cts.Cancel();
    return result;
}

Another, quite different, solution to this problem could be to use PLINQ instead of explicitly created Tasks. PLINQ requires an IEnumerable of something in order to do parallel work on it, and in your case this something is the Task1, Task2 etc functions that you want to invoke. You could put them in an array of Func<CancellationToken, bool>, and solve the problem this way:

var functions = new Func<CancellationToken, bool>[]
{
    Task1, Task2, Task3, Task4, Task5, Task6
};

bool success = functions
    .AsParallel()
    .WithDegreeOfParallelism(4)
    .Select(function =>
    {
        try
        {
            bool result = function(stoppingToken);
            if (result) cts.Cancel();
            return result;
        }
        catch (OperationCanceledException)
        {
            return false;
        }
    })
    .Any(result => result);

The advantage of this approach is that you can configure the degree of parallelism, and you don't have to rely on the ThreadPool availability for limiting the concurrency of the whole operation. The disadvantage is that all functions should have the same signature. You could overcome this disadvantage by declaring the functions as lambda expressions like this:

var functions = new Func<CancellationToken, bool>[]
{
    ct => Task1(arg1, ct),
    ct => Task2(arg1, arg2, ct),
    ct => Task3(ct),
    ct => Task4(arg1, arg2, arg3, ct),
    ct => Task5(arg1, ct),
    ct => Task6(ct)
};