This isn't a proof, but the Drake equations are actually wrong. You can never add huge amounts of time to a probability statement. Otherwise you end up with monkeys typing Shakespeare. Multiplying odds by enough time guarantees shit happens, such as life.

For a better approach, still full of swag, start with today's number and count and assume.

If there are 10 to the 11th power stars in the Milky Way, then all I need are 11 events in a row with a 1 in 10 chance of occurring. Life doesn't seem so inevitable now. Rocky planet (1/10) in the right zone (1/10) in a stable orbit around a stable star (3.5 billion years of evolution requires stability 1/10). A big moon so water life can spread to land. 1/100 (having a moon is a biggie). Assume cyanobacteria happen. You still need eukaryotes and prekaryotes to evolve and combine, multicellular life to occur, life to move out of the ocean, a magnetic core to save land life from cosmic rays.

I think life is a lot more unlikely than folks assume. Regardless of what assumptions you do make, remember that multiplying probable odds by enough time is as invalid as dividing by zero. You can claim whatever results you want.