I think we can find three exceptions Marcin, but let's just confirm the more normal patterns first of all.
first conditional - future possibility / probability
if-clause = present tense/modal; main clause = will/going to/modal
The normal patterns in the first conditional when we are discussing future possibility, as you suggest,
Marcin, is for the if-clause to be in the present tense or to contain a modal verb.
It is then the main clause that includes the will future or possibly the going to future
or a further modal verb. Here are some examples:
In all of these examples, we are talking about conditions that must apply for something to happen.
If I don't see you at the match on Saturday, I'll pop round on Sunday morning.
If the conditions are good over Christmas or the New Year, we may go skiing.
If you go to the pub again tonight, I'm going to lock you out of the house.
If you can't come to see us next weekend, we'll come and visit you.
If you complete the work by lunchtime, you can take the afternoon off.
However, if we are talking about future results rather than conditions, an if - will clause is used.
So here is your first exception to the rule, Marcin:
if you will... = if you insist on...
If (you think) it will save our marriage, I'll try to give up drinking.
I'll help to pay the course fees, if that will persuade you to apply to university.
Take the whole of next week off, if that will help you to recover.
This could be the second exception to the rule, but this use of will in the if-clause does not refer
to future possibility, but instead has the same meaning as the verb insist on. In this usage a lot of word stress if placed upon will:
if you won't... = if you refuse to...
If you will smoke twenty a day, it's not surprising you have a hacking cough. =
If you insist on smoking so much, it's not surprising you have a hacking cough
If she will eat so many chocolates, it's hardly surprising she has a spotty face.
Similarly, the negative of will in the if-clause has the same meaning as refuse to.
As you read these examples, remember to place heavier word stress than normal on won't:
if you will / would = if you wouldn't mind...
If she won't come to Sardinia with us, there's nothing we can do to make her.
If she refuses to come to Sardinia with us, there's nothing we can do to make her.
What shall we do, if she won't agree to have the operation?
This third exception to the rule doesn't have a conditional meaning either.
This helps to explain why they are exceptions. Here we are using if + will or if + would as polite requests with
the same meaning as if you wouldn't mind:
If you'll just fill in this form before you go, you can hand it in to reception. =
If you wouldn't mind filling in this form before you go, you can leave it with reception.
If you would take a seat, the doctor will see you in five minutes.
If you wouldn't mind taking a seat, the doctor will see you in five minutes.
If you'd be so kind as to take a seat, the consultant will see you in five minutes.