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\begin{align*} &\{x,f(y)\},\{y,f(u)\},\{u,\underline{v}\}, \{\underline{v},z\}, \{\underline{v},f(y)\}, \{f(x)\}, \{f(z)\}\\\ &\{x,\underline{f(y)}\},\{y,f(u)\},\{u,v,z,v,\underline{f(y)}, \{f(x)\}, \{f(z)\}\}\\ &\{\underline{x},f(y),u,v,\underline{z},v\},\{y,f(u)\}, \{\underline{f(x)}\}, \{\underline{f(z)}\}\\ &\{x,f(y),\underline{u},v,\underline{z},v\},\{y,\underline{f(u)}\}, \{f(x),\underline{f(z)}\}\\ &\{x,f(y),u,v,z,v\},\{y,f(u)\}, \{f(x),f(z)\}\end{align*}
Checking the disequality $f(x) \neq f(z)$ leads to the result that the assignment is UNSAT, since $f(x)$ and $f(z)$are in the same congruence class.
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