Questionnaire-2024/smt/1032_sol.tex

\begin{align*}
    & \{f(b),a\}, \{e,b\}, \{c,f(c)\}, \{f(e)\}, \{\underline{f(a)},f(d)\}, \{d,\underline{f(a)}\} \\
    & \{\underline{f(b)},a\}, \{\underline{e,b}\}, \{c,f(c)\}, \{\underline{f(e)}\}, \{f(a),f(d),d\} \\
    & \{f(b),a,f(e)\}, \{e,b\}, \{c,f(c)\}, \{f(a),f(d),d\}
\end{align*}

Checking the inequalities $d \neq f(e)$ and $a \neq f(c)$ leads to the result that the assignment is SAT, since neither $d$ and $f(e)$ nor $a$ and $f(c)$
are in the same congruence class.