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7 months ago
7 months ago
  1. \begin{align*}
  2. & \{k,\underline{f(o)}\}, \{l\}, \{m,f(k)\}, \{f(k),\underline{f(o)}\}, \{f(n)\}, \{n,o\}, \{o,f(m)\} \\
  3. & \{k,f(k),f(o)\}, \{l\}, \{m,f(k)\}, \{f(n)\}, \{n,\underline{o}\}, \{\underline{o},f(m)\} \\
  4. & \{k,\underline{f(k)},f(o)\}, \{l\}, \{m,\underline{f(k)}\}, \{f(n)\}, \{n,o,f(m)\} \\
  5. & \{k,m,f(k),\underline{f(o)}\}, \{l\}, \{\underline{f(n)}\}, \{\underline{n,o},f(m)\} \\
  6. & \{\underline{k,m},\underline{f(k)},f(n),f(o)\}, \{l\}, \{n,o,\underline{f(m)}\} \\
  7. & \{k,m,n,o,f(k),f(m),f(n),f(o)\}, \{l\} \\
  8. \end{align*}
  9. Checking the inequalities $o \neq k$, $f(m) \neq k$, $m \neq f(m)$ leads to the result that the assignment is UNSAT, since $o$ and $k$, $f(m)$ and $k$, $m$ and $f(m)$
  10. are in the same congruence class.