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diff --git a/proofsearch/include/atp/simplify/subsumption.h b/proofsearch/include/atp/simplify/subsumption.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 subsumption.h
+/// @brief Forward and backward subsumption checks (backed by discrimination tree).
+
+#include "atp/core/clause.h"
+#include "atp/index/discrim_tree.h"
+
+#include <vector>
+
+namespace atp {
+
+/// Subsumption engine: checks if a new clause is subsumed by existing ones
+/// (forward) or subsumes existing ones (backward).
+class SubsumptionEngine {
+  public:
+    explicit SubsumptionEngine(const TermBank& bank);
+
+    /// Returns true if `candidate` is subsumed by any existing clause.
+    [[nodiscard]] bool isForwardSubsumed(const Clause& candidate) const;
+
+    /// Returns IDs of existing clauses that are subsumed by `new_clause`.
+    [[nodiscard]] std::vector<ClauseId> backwardSubsumed(const Clause& new_clause) const;
+
+    /// Add a clause to the subsumption index.
+    void addClause(const Clause& clause);
+
+    /// Remove a clause from the subsumption index.
+    void removeClause(ClauseId id);
+
+  private:
+    DiscrimTree index_;
+    // TODO: Phase 5 implementation
+};
+
+bool subsumes(const Clause& general, const Clause& specific);
+
+}  // namespace atp