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Personally, I think A lied and Ding stole it.

Reason: On the condition that' only one person lies and one person steals', combined with the words of four people. It can be judged that the result is:

1. If A steals, A and D both lie;

2. If B steals, A, B and D all lie;

3. If C steals, A and D both lie;

4. If B lies, A also lies;

5. If C lies, B also lies;

6. If Ding lies, A also lies;

7. When A lies, B, C and D only have one sentence:' If B didn't steal it, I stole it'. If it is true, it will be found that he stole it.