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diff --git a/proofsearch/include/atp/utils/hash_utils.h b/proofsearch/include/atp/utils/hash_utils.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 hash_utils.h
+/// @brief Hash combination utilities.
+
+#include <cstddef>
+#include <cstdint>
+#include <functional>
+
+namespace atp {
+
+/// Combine a hash with a new value (boost::hash_combine style).
+inline void hashCombine(size_t& seed, size_t value) {
+    seed ^= value + 0x9e3779b9 + (seed << 6) + (seed >> 2);
+}
+
+/// Hash a span of values.
+template <typename T>
+size_t hashRange(const T* data, size_t count) {
+    size_t seed = 0;
+    std::hash<T> hasher;
+    for (size_t i = 0; i < count; ++i) {
+        hashCombine(seed, hasher(data[i]));
+    }
+    return seed;
+}
+
+}  // namespace atp