“Pickled Walnuts” Logic Problem

Question

Here's a problem by puzzle composer Hubert Phillips called “Pickled Walnuts”. What conclusions (if any) can be drawn about armadillos and picked walnuts, assuming all statements are true?

1. Pickled walnuts are always provided at Professor Piltdown’s parties.
2. No animal that does not prefer Beethoven to Mozart ever takes a taxi in Bond Street.
3. All armadillos can speak the Basque dialect.
4. No animal can be registered as a philatelist who does not carry a collapsible umbrella.
5. Any animal that can speak Basque is eligible for the Tintinnabulum Club.
6. Only animals that are registered philatelists are invited to Professor Piltdown’s parties.
7. All animals eligible for the Tintinnabulum Club prefer Mozart to Beethoven.
8. The only animals that enjoy pickled walnuts are those who get them at Professor Piltdown’s. (You can assume he's referring to Professor Piltdown's parties.)
9. Only animals that take taxis in Bond Street carry collapsible umbrellas.

Answer 1

From these statements, we can conclude that

Armadillos do not enjoy pickled walnuts

This can be determined by:

Using the following chain of logic from the following statements, sometimes using De Morgan's theorem

I'm using ">" to mean "implies"

enjoys pickled walnuts > invited to party (8 and 1?)
invited to party > philatelist (6)
philatelist > has collapsible umbrella (4)
has collapsible umbrella > takes taxis in Bond streets (9)
takes taxis in Bond streets > prefers Beethoven to Mozart (2)
prefers Beethoven to Mozart > NOT eligible for Tintinnabulum club (7)
NOT eligible for Tintinnabulum club > doesn't speak Basque (5)
doesn't speak Basque > not armadillo (3)

This gives us:

enjoys pickled walnuts > not armadillo (or, using contraposition, armadillo > DOESN'T enjoy pickled walnuts)

Answer 2

Here is my take on it. In a more human-readable form and, well, I don't get the same conclusion.

3. All armadillos can speak the Basque dialect.
=> ok, armadillos can speak Basque

5. Any animal that can speak Basque is eligible for the Tintinnabulum Club.
=> armadillos are eligible for the club

7. All animals eligible for the Tintinnabulum Club prefer Mozart to Beethoven.
=> armadillos prefer Mozart

2. No animal that does not prefer Beethoven to Mozart ever takes a taxi in Bond Street.
i.e. animals that prefer Mozart never take a taxi in Bond Street
=> armadillos never take a taxi there

9. Only animals that take taxis in Bond Street carry collapsible umbrellas.
i.e. animals that do not take taxis there do not carry such umbrellas
=> armadillos do not carry collapsible umbrellas

4. No animal can be registered as a philatelist who does not carry a collapsible umbrella.
i.e. an animal that doesn't carry such an umbrella cannot register
=> armadillos cannot be registered

6. Only animals that are registered philatelists are invited to Professor Piltdown’s parties.
=> armadillos are not invited to the parties

and

8. The only animals that enjoy pickled walnuts are those who get them at Professor Piltdown’s [parties].
=> armadillos who enjoy pickled walnuts get them at these parties

The conclusion is:

Armadillos who enjoy pickled walnuts get them at Professor Piltdown’s parties without being invited.

And you can note that sentence 1 is not necessary to reach that conclusion.