势不两立的英文：
[Literal Meaning]
situation/not/both exist
to be mutually exclusive

[解释]
指敌对的双方不能同时存在。比喻矛盾不可调和。

[Explanation]
irreconcilable

[例子]
由于水井的纠纷, 目前这两个家族已经势不两立。

[Example]
Because of the conflict over the well, the two families became irreconcilable.

[英文等价词]
at daggers drawn

There was no compatibility between Begin and Sadat on which to base any progress
贝京和萨达特势不两立，不可能取得什么进展。