请教一个问题：关于be动词的省略！！

按照BY的讲解：两个或三个句子并列，第一句有be动词或者become，第二句和第三句中的be和become必须省略，包括重复的名词、形容词甚至连词都可以省略。但是有时候我还是比较迷惑，比如：

Once the economic and social usefullness of the motor car was demonstrated and with its superiority to the horse being proved, much of the early hostility to it in rural regions disappeared.

A: with its superiority to the horse being

B: and its superiority over the horse had been

C: and its superiority to the horse

D: its superiority over the horse

E: with its superiority to the horse having been

答案是B. 我不明白为什么时态突然发生变化，因为找不到变化的理由。

我觉得是C. BY 解释 and 连接once 从句和名词短语 its superiority形式上不对称。但是我觉得可以认为was 承前省略。

而在下题中，be就承前省略了：

Despite protests from some waste-disposal companies, state health officals have ordered the levels of bacteria in seawater at popular beaches to be measured and that the results be published.

答案是：that the level of bacteria in seawater at popular beaches be measured and the results

我明白这个题为什么是这个答案，但是对于上题我就有点不明白，请牛牛们指点！！！万分感激！