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diff --git a/proofsearch/include/atp/rewrite/paramodulation.h b/proofsearch/include/atp/rewrite/paramodulation.h
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+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+#pragma once
+
+/// @file paramodulation.h
+/// @brief Paramodulation inference rule for equality reasoning.
+///
+/// Paramodulation replaces a subterm in one clause with an equal term
+/// from an equation in another clause. Combined with term orderings,
+/// this gives a complete calculus for first-order logic with equality
+/// (the Superposition calculus).
+
+#include "atp/core/clause.h"
+#include "atp/core/term_bank.h"
+#include "atp/rewrite/ordering.h"
+
+#include <vector>
+
+namespace atp {
+
+/// Generate all paramodulants between two clauses.
+/// Uses the term ordering to restrict to ordered paramodulation (superposition).
+std::vector<Clause> paramodulate(const TermBank& bank, const Clause& c1, const Clause& c2,
+                                 const TermOrdering& ordering);
+
+/// Simplify a clause by demodulation (rewriting with unit equalities).
+/// Returns true if the clause was modified.
+bool demodulate(TermBank& bank, Clause& clause, const Clause& unit_eq,
+                const TermOrdering& ordering);
+
+}  // namespace atp