There are many versions of this song, I have at least five and the lyrics all diverge to some extent. It's an easy song to make up new verses to.

The original was by King Radio (Norman Span) but I think it crossed into American folk music quite early (possibly pre-war?) so there are versions by surprising artistes such as the Carpenters.

Belafonte alone had more than one version of the lyrics. He also added an extra part that goes "That's Right! The women are smarter!", this is an improvement to the song in my opinion.

So to do this song justice would require more of a concordance approach where each verse is annotated with the version(s) it appears in. That said, here's a few verses:

Let's put man and woman together
Find out which one is smarter
Some say men, I say no
The women beat the men long long ago.

Chorus:
Not me, the people say
The men leading the women astray
But I say the women of today
Smarter than a man in every way

Ever since the world began
Woman was always fooling man
But if you listen to my song attentively
I'll show you how a woman got the better of me

Chorus

I was friendly with a girl named Caroline
She called me honey-boy all the time
Just when everything was going fine
She was dealing me short with a friend of mine

Chorus

You meet a girl at a pretty dance
Thinking that you would stand a chance
You take her home thinking she's alone
Open the door to find the next man home

Chorus

Sampson was the strongest man long ago
No one could beat him as we all know
Till Delilah got him 'pon top of the bed
Found out the strength in his arms was in the hair of his head

Chorus

I was treating a girl independently
She say she make baby for me
When the child was born and I went to see
The eyes were blue, it was a Portugee

Chorus

[The above verses are the commonest in the versions by calypsonians. Some Belafonte verses follow.]

In the Garden of Eden Adam built a home
As soon as he finished Eve start to roam
Many a night Adam spent in pain
As soon as Eve was able she was raising cain

Chorus

The Garden of Eden was very nice
Adam didn't have to work in paradise
Eve meets snake, paradise gone
She made Adam work from that day on

Chorus

Methuselah spent all his life in tears
He hadn't met a woman in nine hundred years
One night he decided to have some fun
The poor man never lived to see nine hundred and one

Chorus