12. (12 points) As shown in the figure, there are four stations numbered $1, 2, 3, 4$ at the four vertices of a square ring road: Jia, Yi, Bing, and Ding start driving at the same time from stations numbered $A, B, C, D$ respectively $(A, B, C, D$ are all different), traveling clockwise at uniform speeds. The speeds of the cars starting from stations $1, 2, 3, 4$ are $1, 2, 3, 4$ respectively, and these speeds do not change. After driving, they have the following statements:

Jia says: "I caught up with Yi for the first time exactly at station (1)".
Yi says: "I caught up with Bing for the first time exactly at station (2)".
Bing says: "I caught up with Ding for the first time exactly at station (3)".
Ding says: "I caught up with Jia for the first time exactly at station (4)".
It is known that two of them are telling the truth, and two of them are lying. What is the four-digit number $\overline{\mathrm{ABCD}}=$
【Solution】Solution: 4 people have a total of 6 overtakes, let the side length of the square be $a$.
(4) The first time to catch up with (1) is $a \div(4-1)=\frac{a}{3}$,

so it should be between (1) and (2).
(4) The first time to catch up with (2) is $2a \div(4-2)=a$,

so it has traveled $2a$, at station (4).
Similarly, (4) first catches up with (3) at station (4).
(3) first catches up with (1) at station (2).
(3) first catches up with (2) at station (4).
(2) first catches up with (1) at station (4),

so the statements of A and C cannot be correct.
B first catches up with C at station (2),
so $B=3, C=1$.
D first catches up with A at station (4),
so $A=2, D=4$.
Therefore, the four-digit number $\overline{\mathrm{ABCD}}=2314$,
so the answer is 2314.