You want to play with semantics?

Ok, let's play.

Let's take a human, the super-hero kind, who can:
 a/ Calculate a 32-bit operation in 10 seconds
 b/ Work from midnight to midnight everyday
 c/ Calculate a 32-bit operation without any errors

A hash takes about 5000 32-bit operations. So make it 10000 for ripemd160(sha256()).
That makes (10*10000) = 100k seconds = 38.4 hours = 1.6 day non-stop.
Possible.

Now here comes the fun.

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This time we take a real human, the super smart kind.

A/ He calculates a 32-bit operation in 30 seconds (please try a 32-bit addition and tell me how much time it took)
This raises the total time to calculate one hash to 115.2 hours

B/ The guy must sleep, so he can "only" work from 8am to midnight.
This makes the total time to calculate one hash equal to 4.8 days.
Still possible.

C/ The lower brain failure rate in the best conditions is 5%. As he's super smart his is only 1%.
The probability of him finding the correct hash on one try is P = 1/2^(100000*1%) = 1/2^1000 ~ 1/10^300

D/ He starts the hashing calculation at birth and will stop at 100 years old.
This is (100*365) = 36500 days of calculation.
One try is 4.8 days, so he has 7604 tries available.
The odd of our super smart guy FINDING AT LEAST ONCE the correct hash in his entire lifetime is then:
  R = 1-Q where Q = (1-P)^7604 = ( 1 - 1/2^1000 )^7604

Basic maths gives that Q > 1 - 7604/2^1000 = 1 - 10^(-297.149) > 1 - 10^(-297)
So R < 10^(-297) < 1/2^986
Yes, R < 1/2^986

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TLDR

It's easier to crack 6 different bitcoin addresses with only 6 guesses than to a human to calculate a correct bitcoin address hash in his lifetime
Yes, I call that impossible

Anyway, it is not possible to derive the public key and the address without using using a computer

when are they checked for double spends or false coins?  Is that when the miners put them in the block?

In a sense but your chances of winning tho lotto is 1000000 times better then mining 25 bitcoins, mining at that speed.
1 block=25 coins