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logic - How to translate sentences into FOL

I have a sentence:

Every Student who is taking a class taught by Prof. Tim is also taking a class taught by Prof. Jim.

I have translated it as:

Ax(Student(x)^(EyCourse(y)^teaches(Tim,y)^takes(x,y))=>(EzCourse(z)^teaches(Jim,z)^takes(x,z)))

Did I translate it correctly? Or Am I missing any logic here?

question from:https://stackoverflow.com/questions/65952998/how-to-translate-sentences-into-fol

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