The two stories contradict each other.

这两种说法相互抵触。

《牛津词典》

There are several hypotheses trying to explain that outbreaks but none have elements of the truth because they contradict each other.

有几种假说试图解释这种疾病的爆发，但没有一种假说是正确的，因为它们相互矛盾。

youdao

These two goals contradict each other.

这两个目标是相互矛盾的。

youdao

We have all of these common sayings that contradict each other and then empirically, some of them turn out to have more evidence supporting them than others.

有很多俗语表达的意思,相互矛盾,经过实证，其中一些比其他的,更有说服力。

耶鲁公开课 - 心理学导论课程节选

The nature of technical analysis dictates that some indicators may often contradict each other.

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That allows some plaintiffs to hit up multiple trusts with claims that may contradict each other.

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Investment analysts have two theories on volatility and market performance, and unfortunately they contradict each other.

ECONOMIST: Collywobbles