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Given the following first-order formula with equality:
(f(X) ≐ g(X) ∨ q(X)) ∧
(f(X) ≐ X) ∧
(¬(X ≐ a) ∨ ¬q(X)) ∧
(¬p(g(f(a))) ∧
(p(f(a)) ∨ p(X))
Prove that this formula is unsatisfiable (1) by enriching the formula with equality axioms and standard FO-resolution or (2) with the resolution calculus with paramodulation.
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