Mathematical reasoning! Urgent!

In the sixth grade, A, B, C and D took part in the calligraphy competition. A, B and C predicted the result of the game. A: "I think A can only win the third place and C can win the championship." B: "C can only take the second place, and B can take the third place." C: "D can take the second place, and A can take the first place." After the game, I found that they were half right. The first place is (c), the second place is (d), the third place is (b), and the fourth place is (a).

Reasoning process;

1, assuming that A can only take the third place, it is wrong for C to take the championship.

Then it is wrong for C to say that A gets the first place and it is correct for D to get the second place.

Then it is wrong for B to say that C won the second place, and it is correct for B to win the third place.

This contradicts A's statement that A won the third place.

It is wrong to say that A can only win the third place, so C is right to win the championship.

Then it is wrong for C to say that A gets the first place and it is correct for D to get the second place.

It is wrong for B to say that C won the second place, and it is not contradictory for B to win the third place.

So the answer is: the first place is (c), the second place is (d), the third place is (b), and the fourth place is (a).