"The cat exists and at the same time does not exist."
Translation:그 고양이는 있으면서 없습니다.
“그 고양이는 있으면서 없습니다.”
- 그: the / that
- 고양이는: cat (with topic marker 는)
- 있으면서: while exists
- 없습니다: not exist
Literally: the cat, while it exists, (also) does not exist.
The A(으)면서 B pattern is used to mean while A, B (when A and B happen at the same time). Example:
- 먹으면서 공부해요.
- While eating (I) study. → (I) eat while I study.
Since Korean has no corresponding word for the, it is sometimes (actually very often) impossible to tell whether it is an apple or the apple that they are talking about, from the context. Then chances are it is an apple, as it is normal to use 그 in lieu of the in such cases.