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Mr. Woahhs is right. Just as mathematical proofs are available which show that consciousness cannot arise from purely algorithmic functions (i.e. computer programs), it is certainly possible that we might be able to show that life cannot spontaneously arise from its consituent parts. That is not proving a negative. It would be simply showing, as Mr. Woahhs points out, that there must be another explanation.

Just as mathematical proofs are available which show that consciousness cannot arise from purely algorithmic functions (i.e. computer programs),

Say what?! This is most definitely not the case. I would recommend that you don't make assertions about mathematics that you really don't understand. It always makes me ill every time discussions start in about even slightly advanced mathematics, because it makes it all too clear just how grossly ignorant most people are when it comes to math. Most of the really interesting parts cannot be digested into something that a layman can understand. Heck, many times math knowledge doesn't even translate well between mathematicians with expertise in unrelated specialties. In other words, it is probably safe to say that you don't know as much as you think you know.