These are just my personal thoughts about the topic and about that website, to add something to the debate.

proofthatgodexists.org kept on debating, in despite of being owned many times, btw, I am completely against that website even if I do believe in God's existence, that does mean that I'm going to blindly accept that brainwashing logic as a proof.

Let me tell you this tale:
A scholar, who'd later become a saint was trying to find the truth behind god's existence. He readed countless books trying to understand the real nature of god.

One day as he was walking on the beach, he found a young boy, who was digging an hole in the beach. The boy kept went back and forth trying to fill this hole with the water taken from the sea, using a small cup.

The scholar asked him: "What are you doing?"
and the boy: "I'm trying to put the sea into that hole I've digged"
The scholar laughed at him:
"You're trying to dry the sea by using that cup?"
And the boy replied smiling:
"Aren't you trying to uncover the truth behind god by using your science as well?"
--------------------------------------------------------------

Allow me to use a different approach:
1)Think about someone you truly love

2)Prove me that you do really love that person like you can prove any physics or maths law.

I could do anything for the person I'm in love with, but if we take like 100 people, there may still be that 1% that won't believe me.
And that 1% may be right because there's not absolute way to be 100% sure of someone else feeling like you can do with math.

That's just to say that we cannot determine god's existence using science or logic in my opinion. I believe that only with our innermost thoughts and feelings, with that part of us that's "more than human" we can grasps the truth about god's existance and nature for ourselves.

So in the end: you can believe in god because "you feel it" with your soul, but you cannot scientifically prove neither your feeling or god's existance to anyone else.