He should have left by the time you arrive.

这个句子中should为推测性用法。by介词短语给出一个将来时间点，说话人推测在这个将来时间点，主语he已经在此之前离开了。你可以对比一下将来完成时：He will have left by the time you arrive. 其实将来时态中的will就是情态动词的推测性用法。should 表示推测时，说话人的信心没有用will时那么足而已。你还可以用may来表示这种推测，此时推测的信心更弱一些：He may have left by the time you arrive. 

He【主语】// should have left 【谓语动词】// by the time you arrive【时间状语】// .

网友提供的英语句子属于下列4种用法中的第2种用法

主语+should have+过去分词(done)有以下4种用法供网友参考

【1】主语本应该做某事,实际上没有做某事(属于虚拟语气一种)

You should have told me so before.你早就应该告诉我。

You should have reported them to the police.  你应当向警方控告他(们的。

The problem should have been ironed out months ago.这个问题几个月前就该解决了。

We should have been at the theatre ten minutes ago.我们本应该十分钟前就到戏院了。

I should have thought of that.我本应当想到这一点的。

【2】用于推测过去已经发生的事情或者情况意思“应该/大概已经做了某事”

He should have arrived by now.此时他应该/大概已经该到了。

The letter should have arrived by now.信现在应该/大概已经到了。

The train should have already left.火车应该/大概已经开走了吧。

【3】表示与过去事实不相符或相反的假设虚拟语气”。

If I had seen Mary I should have invited her.我当时要是看到玛丽的话我本会邀请她的。

If I had received the present, I should have thanked him.如果我收到了礼物，我是应当向他道谢的。

备注:以上should可以用would替换

【4】表示过去发生发生的事情或者情况感到惊讶,后悔,难过,不理解,不可思议”等情绪，意思为“竟然/居然”。

I am surprised that you should have acted so indiscreetly.你竟然/居然表现得如此轻率，我感到惊讶。

It is amazing that she should have said nothing about the murder.令人惊奇是,她竟然/居然对这桩凶杀案不置一词。

I'm sorry you should have gone to so much trouble.很抱歉,让你费了这么大事。