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Given that:

$ \begin{gather} \ \text{ art}\hspace{1em}\Leftrightarrow\hspace{1em}\text{phi} \end{gather} $

Can you figure out the words that are missing?

$ \begin{gather} \text{imps}\hspace{1em}\Leftrightarrow\hspace{1em}\text{???}\\ \\ \text{???}\hspace{1em}\Leftrightarrow\hspace{1em}\text{pots}\\ \\ \text{aphid}\hspace{1em}\Leftrightarrow\hspace{1em}\text{???}\\ \\ \text{???}\hspace{1em}\Leftrightarrow\hspace{1em}\text{matzo}\\ \end{gather} $

Every answer is a common English word.

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From the given information we can guess that

aphid <-> part*
which suggests that d equals either s or y.
I don't have a conclusive path to disprove y, but if we choose s, we get
imps <-> t*ad and pots <-> a*id
The first of these suggests that m equals o, and the second seems to verify it, so we substitute into the last unknown to get
matzo <-> opi*m, and so z equals u.

Our words are

toad, amid, parts, and opium.

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