We are the only life form of the univers. Not even the only intelligent, but the only one. My arguments are:
Life is absolutely everywhere on earth. There is not a single isolated island or deep trench in the ocean that is not covered by life. If life can live elsewhere, univers would be covered by life. Some bacteria would have been ejected into space by some cataclysme and had colinized nearby planets. Kind of Fermi's paradoxes.
Antropic argument. Our universe is suitable for life because if it weren't, we simply wouldn't be there. Add it to Okam razor. If a smaller, simpler, universe could handle life, we would be in that one. Not our current one.
"Our universe is so huge, so there must be other life form" is not the right statement. Our universe is so huge because it is the smallest universe where life could potentially appear.
Only my opinion, not a scientific demonstration.
Your 2nd paragraph is potentially flawed, but maybe just incomplete.
We have areas that are exceptionally dry, exceptionally hot, or exceptionally acidic, among other things that have been found to be devoid of life. Even the geothermal vents example everyone points to needs a clarifier. Life lives near the vents, not on them. The temperature at the vent gets too hot for basic chemical process or even proteins to make sense.
I think watching the Pale Blue Dot video from Carl Sagan is also worth a watch just as a reminder of how big the universe is for the 'ejected into space' point too. The fastest we've ever traveled is around 25,000 mph briefly and life has been around for we think around 3.7 billion years. If we had been traveling as fast as we have ever traveled for the entirety of the time we think life has existed, we could make it around 140,000 light years (someone please check my math) compared to the observable universe being about 100 billion light years across. I think you at least get from one end of the milky way to the other with a bit to spare, just have to worry about anything that wasn't on that straight line and at least 200 billion galaxies to go (probably dramatically more).
Also, like, there's a reason the Weak Anthropic Principle was created along side the standard one and there's a reason we talk about the weak a lot more. The standard Anthropic Principle is really someone just saying that they don't want to talk about that anymore. It doesn't prove anything on it's own anymore than saying 'It is what it is'.
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