2 files changed, 135 insertions, 0 deletions
diff --git a/proofsearch/include/atp/search/clause_queue.h b/proofsearch/include/atp/search/clause_queue.h
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+++ b/proofsearch/include/atp/search/clause_queue.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 clause_queue.h
+/// @brief Priority queue for the Given Clause Loop.
+
+#include "atp/core/clause.h"
+
+#include <functional>
+
+namespace atp {
+
+/// Comparison function type for clause ordering.
+using ClauseComparator = std::function<bool(const Clause& a, const Clause& b)>;
+
+/// BFS comparator: prioritize shallower derivation depth.
+inline bool bfsCompare(const Clause& a, const Clause& b) {
+    return a.depth_ > b.depth_;  // min-heap by depth
+}
+
+/// Weight comparator: prioritize shorter (fewer literals) clauses.
+inline bool weightCompare(const Clause& a, const Clause& b) {
+    return a.literals_.size() > b.literals_.size();  // min-heap by literal count
+}
+
+}  // namespace atp
diff --git a/proofsearch/include/atp/search/prover.h b/proofsearch/include/atp/search/prover.h
new file mode 100644
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+++ b/proofsearch/include/atp/search/prover.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 prover.h
+/// @brief The Given Clause Loop — main saturation-based proof search.
+///
+/// V1: Uses a simple ProverConfig with hardcoded resolution + factoring.
+/// V2: Will be refactored to accept a Calculus object from strategy/ module
+///     for dynamic algorithm loading per problem type.
+
+#include "atp/core/clause.h"
+#include "atp/core/clause_store.h"
+#include "atp/core/term_bank.h"
+#include "atp/search/clause_queue.h"
+
+#include <optional>
+#include <queue>
+#include <vector>
+
+namespace atp {
+
+/// Result of a proof attempt.
+enum class ProverResult : uint8_t {
+    kTheorem,     ///< Empty clause derived — conjecture is a theorem
+    kSaturation,  ///< Search space saturated — cannot prove
+    kTimeout,     ///< Resource limit exceeded
+};
+
+/// V1 configuration — simple and direct.
+/// Future: replaced by strategy::Calculus for dynamic rule loading.
+struct ProverConfig {
+    ClauseComparator comparator_ = bfsCompare;
+    size_t max_clauses_ = 100000;     ///< Safety limit
+    size_t max_iterations_ = 500000;  ///< Safety limit
+    bool enable_occurs_check_ = false;
+};
+
+/// Main prover class implementing the Given Clause Loop.
+/// V1: hardcodes resolution + factoring + subsumption.
+/// V2: will accept a Calculus object for pluggable inference rules.
+class Prover {
+  public:
+    Prover(TermBank& bank, ClauseStore& store, ProverConfig config = {});
+
+    /// Add initial clauses (axioms + negated conjecture).
+    void addClauses(std::vector<Clause> clauses);
+
+    /// Run the proof search.
+    ProverResult prove();
+
+    /// After a successful proof, retrieve the empty clause ID.
+    [[nodiscard]] std::optional<ClauseId> getEmptyClauseId() const;
+
+    /// Access the underlying clause store.
+    [[nodiscard]] const ClauseStore& clauseStore() const { return store_; }
+
+  private:
+    [[nodiscard]] bool hitResourceLimit(size_t iterations) const;
+    [[nodiscard]] Clause popGivenClause();
+    [[nodiscard]] bool isForwardSubsumedByProcessed(const Clause& clause) const;
+    [[nodiscard]] bool shouldSkipGiven(const Clause& given) const;
+    void applyBackwardSubsumption(const Clause& given);
+    [[nodiscard]] std::vector<Clause> generateNewClauses(const Clause& given) const;
+    [[nodiscard]] uint16_t computeDepth(const Clause& clause) const;
+    [[nodiscard]] std::optional<ClauseId> processNewClauses(std::vector<Clause> new_clauses);
+
+    TermBank& bank_;
+    ClauseStore& store_;
+    ProverConfig config_;
+    std::priority_queue<Clause, std::vector<Clause>, ClauseComparator> unprocessed_;
+    std::vector<ClauseId> processed_;
+    std::optional<ClauseId> empty_clause_id_;
+};
+
+}  // namespace atp