Here is a list of challenging CAT syllogisms along with their answers:

1. All cats are mammals. Some mammals are not dogs. Therefore, some cats are not dogs. (True)
2. All lawyers are intellectuals. Some intellectuals are not politicians. Therefore, some lawyers are not politicians. (False)
3. No flowers are animals. All roses are flowers. Therefore, no roses are animals. (True)
4. Some fruits are sweet. All sweet things are delicious. Therefore, some fruits are delicious. (True)
5. No politicians are honest. Some honest people are judges. Therefore, some judges are not politicians. (True)
6. All books are knowledge. Some knowledge is not wisdom. Therefore, some books are not wisdom. (False)
7. Some students are diligent. All diligent individuals are successful. Therefore, some students are successful. (True)
8. No actors are musicians. Some musicians are composers. Therefore, some composers are not actors. (False)
9. All birds can fly. Some flightless creatures are not birds. Therefore, some flightless creatures are not capable of flying. (True)
10. No athletes are lazy. All lazy individuals lack discipline. Therefore, no athletes lack discipline. (False)

These syllogisms involve complex logical relationships and require careful application of rules to determine the validity of the conclusions. Remember, practice is crucial for improving your skills in solving syllogisms.