Merge remote-tracking branch 'proofsearch-import/master'

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diff --git a/proofsearch/include/atp/proof/proof_trace.h b/proofsearch/include/atp/proof/proof_trace.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 proof_trace.h
+/// @brief Proof reconstruction from the empty clause back to axioms.
+
+#include "atp/core/clause.h"
+#include "atp/core/clause_store.h"
+#include "atp/core/term_bank.h"
+
+#include <string>
+#include <vector>
+
+namespace atp {
+
+/// A single step in a reconstructed proof.
+struct ProofStep {
+    ClauseId clause_id_;
+    InferenceRule rule_;
+    ClauseId parent1_;
+    ClauseId parent2_;
+};
+
+/// Reconstruct the proof trace from the empty clause.
+/// Returns steps in topological order: axioms first, empty clause last.
+std::vector<ProofStep> extractProof(const ClauseStore& store, ClauseId empty_clause_id);
+
+/// Convert a TermId back to a human-readable string.
+std::string termToString(TermId id, const TermBank& bank);
+
+/// Convert a Clause to a human-readable string.
+std::string clauseToString(const Clause& clause, const TermBank& bank);
+
+/// Format a proof as a human-readable string.
+std::string formatProof(const std::vector<ProofStep>& proof, const ClauseStore& store,
+                        const TermBank& bank);
+
+}  // namespace atp