How to format text with gq by cutting long lines but without joining shorter lines?

Question

I don't understand what shall I set (I guess fo, but how?) for cutting lines that are longer than textwidth but without joining lines that are shorter.

For example, assume that I have textwidth option set to 78 and I have the following text:

This text is just an example to show what I want to achieve. 

However, I am failing in that and therefore I am asking for help.
Let's add a random enumerated list to make the example more complete.

    1. frog
    2. cow
    3. donkey

And let me add another line, just to make something more complete.
Now, let me add a very long line that it is not formatted at all and I want to cut it happened to be way too long

Hello,
My name
Is John Nash

If I type gggqG, I have the following:

This text is just an example to show what I want to achieve. 

However, I am failing in that and therefore I am asking for help.  Let's add a
random enumerated list to make the example more complete.

    1. frog 2. cow 3. donkey

And let me add another line, just to make something more complete.  Now, let
me add a very long line that it is not formatted at all and I want to cut it
happened to be way too long

hello My name Is John Nash

but what I want instead is the following:

This text is just an example to show what I want to achieve. 

However, I am failing in that and therefore I am asking for help.
Let's add a random enumerated list to make the example more complete.

    1. frog
    2. cow
    3. donkey

And let me add another line, just to make something more complete.  Now, let
me add a very long line that it is not formatted at all and I want to cut it
happened to be way too long

Hello,
My name
Is John Nash

Namely, I want that longer lines than textwidth are cut, but shorter lines are left untouched.

Answer 1

I would do:

:g/^.\{80\}/normal gqq

Or more generic as suggested by @Barzi2002

:execute 'g/^.\{' .. &textwidth ..'\}/normal gqq'

Answer 2

Adding w to the default value of 'formatoptions' gives you the desired behavior:

:set formatoptions+=w

You shouldn't have stopped trying at set fo=tc. :help fo-t and :help fo-c are not related to the problem at hand… and :help fo-w is a few lines below.