7 files changed, 434 insertions, 0 deletions
diff --git a/proofsearch/include/atp/core/clause.h b/proofsearch/include/atp/core/clause.h
new file mode 100644
index 0000000..6387adf
--- /dev/null
+++ b/proofsearch/include/atp/core/clause.h
@@ -0,0 +1,52 @@
+/*
+ * 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.h
+/// @brief A clause is a disjunction of literals, with provenance tracking.
+///
+/// NOTE: V1 uses std::vector<Literal> for simplicity.
+/// Future optimization: migrate to a Clause Arena with contiguous storage.
+
+#include "atp/core/literal.h"
+#include "atp/core/types.h"
+
+#include <vector>
+
+namespace atp {
+
+/// A clause: a disjunction of literals plus provenance for proof reconstruction.
+struct Clause {
+    ClauseId id_ = kInvalidId;
+    std::vector<Literal> literals_;
+
+    // Provenance (for proof trace)
+    InferenceRule rule_ = InferenceRule::kInput;
+    ClauseId parent1_ = kInvalidId;
+    ClauseId parent2_ = kInvalidId;
+    uint16_t depth_ = 0;  ///< Derivation depth (for BFS scheduling)
+
+    /// True if the clause has no literals (contradiction).
+    [[nodiscard]] bool isEmpty() const { return literals_.empty(); }
+
+    /// Number of literals.
+    [[nodiscard]] size_t size() const { return literals_.size(); }
+};
+
+}  // namespace atp
diff --git a/proofsearch/include/atp/core/clause_store.h b/proofsearch/include/atp/core/clause_store.h
new file mode 100644
index 0000000..5d6562a
--- /dev/null
+++ b/proofsearch/include/atp/core/clause_store.h
@@ -0,0 +1,64 @@
+/*
+ * 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_store.h
+/// @brief Central clause storage — owns all clauses, assigns ClauseIds.
+///
+/// Extracted from Prover to separate storage responsibility from search logic.
+/// This enables swapping search strategies (OTTER loop / DISCOUNT loop)
+/// without touching clause lifecycle management.
+
+#include "atp/core/clause.h"
+#include "atp/core/types.h"
+
+#include <functional>
+#include <vector>
+
+namespace atp {
+
+/// Central clause store. Owns all clauses and assigns unique ClauseIds.
+/// All modules access clauses through this store via ClauseId references.
+class ClauseStore {
+  public:
+    ClauseStore() = default;
+
+    /// Add a clause, assign it a ClauseId, and return the ID.
+    ClauseId addClause(Clause clause);
+
+    /// Access a clause by its ID. UB if id is out of range.
+    [[nodiscard]] const Clause& getClause(ClauseId id) const;
+
+    /// Mutable access (for marking clauses as deleted, etc.)
+    [[nodiscard]] Clause& getMutableClause(ClauseId id);
+
+    /// Total number of stored clauses.
+    [[nodiscard]] size_t size() const;
+
+    /// Iterate over all clauses with a visitor.
+    void forEach(const std::function<void(const Clause&)>& visitor) const;
+    // function may have type erasure overhead, consider using a template
+    // template <typename Visitor>
+    // void forEach(Visitor&& visitor) const;
+
+  private:
+    std::vector<Clause> clauses_;
+};
+
+}  // namespace atp
diff --git a/proofsearch/include/atp/core/literal.h b/proofsearch/include/atp/core/literal.h
new file mode 100644
index 0000000..e58b185
--- /dev/null
+++ b/proofsearch/include/atp/core/literal.h
@@ -0,0 +1,39 @@
+/*
+ * 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 literal.h
+/// @brief A literal is a (possibly negated) atomic formula.
+
+#include "atp/core/types.h"
+
+namespace atp {
+
+/// A literal: a polarity flag plus the TermId of the atom.
+struct Literal {
+    TermId atom_;       ///< TermId of the predicate application
+    bool is_positive_;  ///< true = positive, false = negated
+
+    /// Complement: flip polarity, same atom.
+    [[nodiscard]] Literal complement() const { return {.atom_ = atom_, .is_positive_ = !is_positive_}; }
+
+    bool operator==(const Literal& other) const = default;
+};
+
+}  // namespace atp
diff --git a/proofsearch/include/atp/core/symbol_table.h b/proofsearch/include/atp/core/symbol_table.h
new file mode 100644
index 0000000..a646f78
--- /dev/null
+++ b/proofsearch/include/atp/core/symbol_table.h
@@ -0,0 +1,71 @@
+/*
+ * 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 symbol_table.h
+/// @brief Bidirectional mapping between symbol names and SymbolIds,
+///        with kind and sort metadata.
+
+#include "atp/core/types.h"
+
+#include <deque>
+#include <string>
+#include <string_view>
+#include <unordered_map>
+
+namespace atp {
+
+/// Metadata associated with an interned symbol.
+struct SymbolInfo {
+    std::string name_;
+    SymbolKind kind_ = SymbolKind::kFunction;
+    uint16_t arity_ = 0;
+    SortId sort_ = kUnsorted;  ///< Result sort (for sorted logic)
+};
+
+/// Interns symbol names so that each unique string is stored exactly once.
+/// Also tracks symbol metadata (kind, arity, sort).
+/// Thread-safety: NOT thread-safe (single-threaded prover design).
+class SymbolTable {
+  public:
+    SymbolTable() = default;
+
+    /// Intern a symbol name with metadata. Returns existing ID if already present.
+    SymbolId intern(std::string_view name, SymbolKind kind, uint16_t arity = 0,
+                    SortId sort = kUnsorted);
+
+    /// Look up the name for a given SymbolId. UB if id is out of range.
+    [[nodiscard]] std::string_view getName(SymbolId id) const;
+
+    /// Look up full metadata for a SymbolId.
+    [[nodiscard]] const SymbolInfo& getInfo(SymbolId id) const;
+
+    /// Check if a symbol is a variable.
+    [[nodiscard]] bool isVariable(SymbolId id) const;
+
+    /// Number of interned symbols.
+    [[nodiscard]] size_t size() const;
+
+  private:
+    // TODO: Phase 1 implementation
+    std::deque<SymbolInfo> infos_;
+    std::unordered_map<std::string_view, SymbolId> name_to_id_;
+};
+
+}  // namespace atp
diff --git a/proofsearch/include/atp/core/term.h b/proofsearch/include/atp/core/term.h
new file mode 100644
index 0000000..d35c753
--- /dev/null
+++ b/proofsearch/include/atp/core/term.h
@@ -0,0 +1,43 @@
+/*
+ * 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 term.h
+/// @brief Core Term data structure — hash-consed, immutable.
+///
+/// V1 uses vector<TermId> for args.
+/// Future: flat arena with contiguous arg storage for cache locality.
+
+#include "atp/core/types.h"
+
+#include <vector>
+
+namespace atp {
+
+/// A term is a function/predicate application: f(t1, t2, ..., tn).
+/// Variables are 0-arity terms whose symbol has SymbolKind::kVariable.
+struct Term {
+    SymbolId symbol_id_;        ///< Index into the SymbolTable
+    std::vector<TermId> args_;  ///< Argument sub-term IDs
+
+    /// Number of arguments.
+    [[nodiscard]] uint16_t arity() const { return static_cast<uint16_t>(args_.size()); }
+};
+
+}  // namespace atp
diff --git a/proofsearch/include/atp/core/term_bank.h b/proofsearch/include/atp/core/term_bank.h
new file mode 100644
index 0000000..ca12759
--- /dev/null
+++ b/proofsearch/include/atp/core/term_bank.h
@@ -0,0 +1,86 @@
+/*
+ * 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 term_bank.h
+/// @brief Hash-consing term pool — guarantees structural sharing.
+
+#include "atp/core/symbol_table.h"
+#include "atp/core/term.h"
+#include "atp/core/types.h"
+
+#include <span>
+#include <unordered_map>
+#include <vector>
+
+namespace atp {
+
+/// Global term pool with hash-consing.
+/// Every structurally identical term maps to the same TermId.
+///
+/// Holds a reference to SymbolTable for variable detection.
+class TermBank {
+  public:
+    /// TermBank needs the SymbolTable to distinguish variables from constants
+    /// (both have 0 args, but SymbolKind differs).
+        explicit TermBank(SymbolTable& symbols) : symbols_(&symbols) {}
+
+    /// Create or retrieve a term. Returns the canonical TermId.
+    TermId makeTerm(SymbolId symbol, std::span<const TermId> args);
+
+    /// Create a variable term. Convenience for makeTerm(var, {}).
+    TermId makeVar(SymbolId var_symbol);
+
+    /// Look up a term by its ID.
+    [[nodiscard]] const Term& getTerm(TermId id) const;
+
+    /// Check if a TermId represents a variable (delegates to SymbolTable).
+    [[nodiscard]] bool isVariable(TermId id) const;
+
+    /// Total number of unique terms stored.
+    [[nodiscard]] size_t size() const;
+
+    /// Access the underlying SymbolTable.
+    [[nodiscard]] const SymbolTable& symbols() const { return *symbols_; }
+    [[nodiscard]] SymbolTable& mutableSymbols() { return *symbols_; }
+
+  private:
+    struct TermKey {
+        SymbolId symbol_;
+        std::vector<TermId> args_;
+
+        bool operator==(const TermKey& other) const = default;
+    };
+
+    struct TermKeyHash {
+        size_t operator()(const TermKey& key) const {
+            size_t seed = std::hash<uint32_t>{}(key.symbol_);
+            for (const TermId arg : key.args_) {
+                seed ^= std::hash<TermId>{}(arg) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
+            }
+            return seed;
+        }
+    };
+
+    SymbolTable* symbols_;
+    std::vector<Term> terms_;
+    std::unordered_map<TermKey, TermId, TermKeyHash> term_to_id_;
+};
+
+}  // namespace atp
diff --git a/proofsearch/include/atp/core/types.h b/proofsearch/include/atp/core/types.h
new file mode 100644
index 0000000..23f2322
--- /dev/null
+++ b/proofsearch/include/atp/core/types.h
@@ -0,0 +1,79 @@
+/*
+ * 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 types.h
+/// @brief Core type aliases for the ATP engine.
+
+#include <cstdint>
+
+namespace atp {
+
+/// Unique identifier for an interned symbol (predicate/function/constant name).
+using SymbolId = uint32_t;
+
+/// Unique identifier for a term in the Term Bank (hash-consed).
+using TermId = uint32_t;
+
+/// Unique identifier for a clause in the Clause Store.
+using ClauseId = uint32_t;
+
+/// Unique identifier for a sort/type (for sorted logic).
+using SortId = uint16_t;
+
+/// Sentinel value indicating an invalid / unassigned ID.
+inline constexpr uint32_t kInvalidId = UINT32_MAX;
+
+/// Default sort (unsorted logic).
+inline constexpr SortId kUnsorted = 0;
+
+/// Symbol kind — distinguishes variables from function/predicate symbols.
+enum class SymbolKind : uint8_t {
+    kVariable,   ///< Universally quantified variable
+    kConstant,   ///< 0-arity function symbol (constant)
+    kFunction,   ///< Function symbol (arity >= 1)
+    kPredicate,  ///< Predicate symbol (returns bool)
+    kSkolem,     ///< Skolem function/constant (introduced by Skolemization)
+};
+
+/// Inference rule that produced a clause.
+/// Deliberately uses uint16_t for extensibility toward algebra/analysis rules.
+enum class InferenceRule : uint16_t {
+    // ── Core resolution rules ──
+    kInput = 0,       ///< Original input clause (axiom / negated conjecture)
+    kResolution = 1,  ///< Binary resolution
+    kFactoring = 2,   ///< Factoring
+
+    // ── Equality rules (algebra) ──
+    kParamodulation = 100,      ///< Paramodulation (equality resolution)
+    kDemodulation = 101,        ///< Demodulation (simplification by rewriting)
+    kEqualityResolution = 102,  ///< s != t resolved with unifier
+    kEqualityFactoring = 103,   ///< Factoring with equality
+
+    // ── Simplification rules ──
+    kSubsumption = 200,      ///< Removed by subsumption
+    kTautologyElim = 201,    ///< Removed as tautology
+    kPureLiteralElim = 202,  ///< Pure literal elimination
+
+    // ── Theory rules (analysis, arithmetic) ──
+    kTheoryResolution = 300,  ///< Theory-specific resolution
+    kTheoryRewrite = 301,     ///< Theory-driven rewriting
+};
+
+}  // namespace atp