3 files changed, 138 insertions, 0 deletions
diff --git a/include/atp/infer/resolution.h b/include/atp/infer/resolution.h
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+++ b/include/atp/infer/resolution.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 resolution.h
+/// @brief Binary resolution and factoring inference rules.
+
+#include "atp/core/clause.h"
+#include "atp/core/term_bank.h"
+
+#include <optional>
+#include <vector>
+
+namespace atp {
+
+/// Attempt binary resolution between two clauses on the specified literal indices.
+/// @return The resolvent clause if resolution succeeds, std::nullopt otherwise.
+std::optional<Clause> resolve(const TermBank& bank, const Clause& c1, size_t lit_idx1,
+                              const Clause& c2, size_t lit_idx2);
+
+/// Generate all possible resolvents between two clauses.
+std::vector<Clause> allResolvents(const TermBank& bank, const Clause& c1, const Clause& c2);
+
+/// Attempt factoring on a single clause (merge two unifiable literals).
+std::vector<Clause> factor(const TermBank& bank, const Clause& c);
+
+}  // namespace atp
diff --git a/include/atp/infer/substitution.h b/include/atp/infer/substitution.h
new file mode 100644
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+++ b/include/atp/infer/substitution.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 substitution.h
+/// @brief Variable binding map: Var -> Term.
+
+#include "atp/core/types.h"
+
+#include <vector>
+
+namespace atp {
+
+/// A substitution is a mapping from variable TermIds to their bound TermIds.
+/// Designed as a short-lived, stack-allocated object during unification.
+class Substitution {
+  public:
+    Substitution() = default;
+
+    /// Bind a variable to a term. Returns false if already bound to something different.
+    bool bind(TermId var, TermId term);
+
+    /// Look up what a variable is bound to. Returns kInvalidId if unbound.
+    [[nodiscard]] TermId lookup(TermId var) const;
+
+    /// Walk the binding chain to the final bound value.
+    [[nodiscard]] TermId resolve(TermId id) const;
+
+    /// Clear all bindings.
+    void clear();
+
+  private:
+    // TODO: Phase 2 implementation
+    std::vector<std::pair<TermId, TermId>> bindings_;
+};
+
+}  // namespace atp
diff --git a/include/atp/infer/unification.h b/include/atp/infer/unification.h
new file mode 100644
index 0000000..7d91aaf
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+++ b/include/atp/infer/unification.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 unification.h
+/// @brief Most General Unifier (MGU) computation.
+
+#include "atp/core/term_bank.h"
+#include "atp/infer/substitution.h"
+
+namespace atp {
+
+/// Configuration for the unification algorithm.
+struct UnificationConfig {
+    bool enable_occurs_check = false;  ///< Set true for sound but slower unification
+};
+
+/// Attempt to unify two terms, producing a most general unifier.
+/// @return true if unification succeeds, with the MGU in `subst`.
+bool unify(const TermBank& bank, TermId t1, TermId t2, Substitution& subst,
+           const UnificationConfig& config = {});
+
+}  // namespace atp