counterexample meaning in English

反例

The proof is easy, but the counterexamples are hard .
证明是容易的，但反例则甚难。
A brief discussion on the function of counterexample in discrete mathematics teaching
谈反例在离散数学教学中的作用
A counterexample on the existence of positive periodic solutions for two - species predator - prey diffusive systems
食饵系统正周期解存在性的一个反例
In a sense this program is a counterexample , in that it is never useful as a filter
从某种意义上，这个程序是一个可执行文件，因为对于作为过滤器来说，它决不会有任何用处。
There is an old saying : large wealth of a family can not last longer than three generations . is there any counterexample in the history
有句话是“富不过三代” 。历史上有没有富豪延续超过三代的例子？

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