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				https://github.com/Z3Prover/z3
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	Add cube tree optimization about resolving cores recursively up the path, to prune. Also integrate asms into the tree so they're not tracked separately (#7960)
* draft attempt at optimizing cube tree with resolvents. have not tested/ran yet * adding comments * fix bug about needing to bubble resolvent upwards to highest ancestor * fix bug where we need to cover the whole resolvent in the path when bubbling up * clean up comments * close entire tree when sibling resolvent is empty * integrate asms directly into cube tree, remove separate tracking * try to fix bug about redundant resolutions, merging close and try_resolve_upwards into once function * separate the logic again to avoid mutual recursion
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					 3 changed files with 156 additions and 55 deletions
				
			
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			@ -115,10 +115,6 @@ namespace smt {
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                    b.set_unsat(m_l2g, unsat_core);
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                    return;
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                }
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                // report assumptions used in unsat core, so they can be used in final core
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                for (expr *e : unsat_core)
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                    if (asms.contains(e))
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                        b.report_assumption_used(m_l2g, e);  
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                LOG_WORKER(1, " found unsat cube\n");
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                b.backtrack(m_l2g, unsat_core, node);
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			@ -260,8 +256,7 @@ namespace smt {
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        vector<cube_config::literal> g_core;
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        for (auto c : core) {
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            expr_ref g_c(l2g(c), m);
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            if (!is_assumption(g_c))
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                g_core.push_back(expr_ref(l2g(c), m));
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            g_core.push_back(expr_ref(l2g(c), m));
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        }
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        m_search_tree.backtrack(node, g_core);
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			@ -411,11 +406,6 @@ namespace smt {
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        cancel_workers();
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    }
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    void parallel::batch_manager::report_assumption_used(ast_translation &l2g, expr *assumption) {
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        std::scoped_lock lock(mux);
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        p.m_assumptions_used.insert(l2g(assumption));
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    }
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    lbool parallel::batch_manager::get_result() const {
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        if (m.limit().is_canceled())
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            return l_undef;  // the main context was cancelled, so we return undef.
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			@ -424,11 +414,12 @@ namespace smt {
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                                 // means all cubes were unsat
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            if (!m_search_tree.is_closed())
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                throw default_exception("inconsistent end state");
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            if (!p.m_assumptions_used.empty()) {
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                // collect unsat core from assumptions used, if any --> case when all cubes were unsat, but depend on
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                // nonempty asms, so we need to add these asms to final unsat core
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                SASSERT(p.ctx.m_unsat_core.empty());
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                for (auto a : p.m_assumptions_used)
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            // case when all cubes were unsat, but depend on nonempty asms, so we need to add these asms to final unsat core
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            // these asms are stored in the cube tree, at the root node
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            if (p.ctx.m_unsat_core.empty()) {
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                SASSERT(root && root->is_closed());
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                for (auto a : m_search_tree.get_core_from_root())
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                    p.ctx.m_unsat_core.push_back(a);
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            }
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            return l_false;
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			@ -496,16 +487,12 @@ namespace smt {
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            scoped_clear(parallel &p) : p(p) {}
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            ~scoped_clear() {
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                p.m_workers.reset();
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                p.m_assumptions_used.reset();
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                p.m_assumptions.reset();
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            }
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        };
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        scoped_clear clear(*this);
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        m_batch_manager.initialize();
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        m_workers.reset();
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        for (auto e : asms)
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            m_assumptions.insert(e);
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        scoped_limits sl(m.limit());
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        flet<unsigned> _nt(ctx.m_fparams.m_threads, 1);
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        SASSERT(num_threads > 1);
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			@ -79,10 +79,6 @@ namespace smt {
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            void init_parameters_state();
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            bool is_assumption(expr* e) const {
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                return p.m_assumptions.contains(e);
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            }
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        public:
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            batch_manager(ast_manager& m, parallel& p) : m(m), p(p), m_search_tree(expr_ref(m)) { }
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			@ -98,7 +94,6 @@ namespace smt {
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            void backtrack(ast_translation& l2g, expr_ref_vector const& core, node* n);
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            void split(ast_translation& l2g, unsigned id, node* n, expr* atom);
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            void report_assumption_used(ast_translation& l2g, expr* assumption);
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            void collect_clause(ast_translation& l2g, unsigned source_worker_id, expr* clause);
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            expr_ref_vector return_shared_clauses(ast_translation& g2l, unsigned& worker_limit, unsigned worker_id);
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			@ -162,8 +157,6 @@ namespace smt {
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        };
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        obj_hashtable<expr> m_assumptions_used; // assumptions used in unsat cores, to be used in final core
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        obj_hashtable<expr> m_assumptions;       // all assumptions
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        batch_manager m_batch_manager;
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        scoped_ptr_vector<worker> m_workers;
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			@ -41,6 +41,7 @@ namespace search_tree {
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        literal m_literal;
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        node* m_left = nullptr, * m_right = nullptr, * m_parent = nullptr;
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        status m_status;
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        vector<literal> m_core;
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    public:
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        node(literal const& l, node* parent) :
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            m_literal(l), m_parent(parent), m_status(status::open) {}
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			@ -96,6 +97,13 @@ namespace search_tree {
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            if (m_right)
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                m_right->display(out, indent + 2);
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        }
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        bool has_core() const { return !m_core.empty(); }
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        void set_core(vector<literal> const &core) { 
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            m_core = core;
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        }
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        vector<literal> const & get_core() const { return m_core; }
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        void clear_core() { m_core.clear(); }
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    };
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    template<typename Config>
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			@ -131,31 +139,139 @@ namespace search_tree {
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            return nullptr;
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        }
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        void close_node(node<Config>* n) {
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            if (!n)
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                return;
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            if (n->get_status() == status::closed)
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                return;
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            n->set_status(status::closed);
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            close_node(n->left());
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            close_node(n->right());
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            while (n) {
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                auto p = n->parent();
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                if (!p)
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                    return;
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                if (p->get_status() != status::open)
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                    return;
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                if (p->left()->get_status() != status::closed)
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                    return;
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                if (p->right()->get_status() != status::closed)
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                    return;
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                p->set_status(status::closed);
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                n = p;
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            }
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        }
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      // Invariants: 
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      // Cores labeling nodes are subsets of the literals on the path to the node and the (external) assumption literals.
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      // If a parent is open, then the one of the children is open.
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      void close_with_core(node<Config>* n, vector<literal> const &C, bool allow_resolve = true) {
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          if (!n || n->get_status() == status::closed)
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              return;
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          n->set_core(C);
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          n->set_status(status::closed);
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          close_with_core(n->left(), C, false);
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          close_with_core(n->right(), C, false);
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          // stop at root
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          if (!n->parent()) return;
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          node<Config>* p = n->parent();
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          if (!p) return; // root reached
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          auto is_literal_in_core = [](literal const& l, vector<literal> const& C) {
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              for (unsigned i = 0; i < C.size(); ++i)
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                  if (C[i] == l) return true;
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              return false;
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          };
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          // case 1: current splitting literal not in the conflict core
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          if (!is_literal_in_core(n->get_literal(), C)) {
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              close_with_core(p, C);
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          // case 2: both siblings closed -> resolve
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          } else if (allow_resolve && p->left()->get_status() == status::closed && p->right()->get_status() == status::closed) {
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              try_resolve_upwards(p);
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          }
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      }
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      // Given complementary sibling nodes for literals x and ¬x, sibling resolvent = (core_left ∪ core_right) \ {x, ¬x}
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        vector<literal> compute_sibling_resolvent(node<Config>* left, node<Config>* right) {
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          vector<literal> res;
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          if (!left->has_core() || !right->has_core()) return res;
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          bool are_sibling_complements = left->parent() == right->parent();
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          if (!are_sibling_complements)
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              return res;
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          auto &core_l = left->get_core();
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          auto &core_r = right->get_core();
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          auto contains = [](vector<literal> const &v, literal const &l) {
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              for (unsigned i = 0; i < v.size(); ++i)
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                  if (v[i] == l) return true;
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              return false;
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          };
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          auto lit_l = left->get_literal();
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          auto lit_r = right->get_literal();
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          // Add literals from left core, skipping lit_l
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          for (unsigned i = 0; i < core_l.size(); ++i) {
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              if (core_l[i] != lit_l && !contains(res, core_l[i]))
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                  res.push_back(core_l[i]);
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          }
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          // Add literals from right core, skipping lit_r
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          for (unsigned i = 0; i < core_r.size(); ++i) {
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              if (core_r[i] != lit_r && !contains(res, core_r[i]))
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                  res.push_back(core_r[i]);
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          }
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          return res;
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      }
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      void try_resolve_upwards(node<Config>* p) {
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          while (p) {
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              auto left = p->left();
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              auto right = p->right();
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              if (!left || !right) return;
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              // only attempt when both children are closed and each has a core
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              if (left->get_status() != status::closed || right->get_status() != status::closed) return;
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              if (!left->has_core() || !right->has_core()) return;
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              auto resolvent = compute_sibling_resolvent(left, right);
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              // empty resolvent of sibling complement (i.e. tautology) -> global UNSAT
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              if (resolvent.empty()) {
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                  close_with_core(m_root.get(), resolvent, false);
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                  return;
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              }
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              // if p already has the same core, nothing more to do
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              if (p->has_core() && resolvent == p->get_core())
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                  return;
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              // Bubble to the highest ancestor where ALL literals in the resolvent
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              // are present somewhere on the path from that ancestor to root
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              node<Config>* candidate = p;
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              node<Config>* attach_here = p; // fallback
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              while (candidate) {
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                  bool all_found = true;
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                  for (auto const& r : resolvent) {
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                      bool found = false;
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                      for (node<Config>* q = candidate; q; q = q->parent()) {
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                          if (q->get_literal() == r) {
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                              found = true;
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                              break;
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                          }
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                      }
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                      if (!found) {
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                          all_found = false;
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                          break;
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                      }
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                  }
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                  if (all_found) {
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                      attach_here = candidate;  // bubble up to this node
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                  }
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                  candidate = candidate->parent();
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              }
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              // attach the resolvent and close the subtree at attach_here
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              if (!attach_here->has_core() || attach_here->get_core() != resolvent) {
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                  close_with_core(attach_here, resolvent, false);
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              }
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              // continue upward from parent of attach_here
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              p = attach_here->parent();
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          }
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      }
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    public:
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        tree(literal const& null_literal) : m_null_literal(null_literal) {
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            reset();
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        }
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			@ -176,11 +292,10 @@ namespace search_tree {
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        }
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        // conflict is given by a set of literals.
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        // they are a subset of literals on the path from root to n
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        // they are subsets of the literals on the path from root to n AND the external assumption literals
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        void backtrack(node<Config>* n, vector<literal> const& conflict) {
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            if (conflict.empty()) {
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                close_node(m_root.get());
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                m_root->set_status(status::closed);
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                close_with_core(m_root.get(), conflict);
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                return;
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            }           
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            SASSERT(n != m_root.get());
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			@ -198,12 +313,14 @@ namespace search_tree {
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                };
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                SASSERT(all_of(conflict, [&](auto const& a) { return on_path(a); }));
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            );
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            while (n) {
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                if (any_of(conflict, [&](auto const& a) { return a == n->get_literal(); })) {
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                    close_node(n);
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                    // close the subtree under n (preserves core attached to n), and attempt to resolve upwards
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                    close_with_core(n, conflict);
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                    return;
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                }
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                n = n->parent();
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            }
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            UNREACHABLE();
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			@ -252,6 +369,10 @@ namespace search_tree {
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            return m_root->find_active_node();
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        }
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        vector<literal> const& get_core_from_root() const {
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            return m_root->get_core();
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        }
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        bool is_closed() const {
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            return m_root->get_status() == status::closed;
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        }
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