Consider unifying the literal P(x, g(x)) with:

1. P(z,y) : unifies with {x/z, g(x)/y}
2. P(z, g(z)): unifies with {x/z} or {z/x}
3. P(Socrates, g(Socrates)) : unifies, {Socrates/x}
4. P(z, g(y)): unifies with {x/z, x/y} or {z/x, z/y}
5. P(g(y), z): unifies with {g(y)/x, g(g(y))/z}
6. P(Socrates, f(Socrates)) : does not unify: f and g do not match.
7. P(g(y), y) : does not unify: no substitution works.

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