better encodings for at-most-1, #755

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/ast/pb_decl_plugin.h

@@ -119,6 +119,8 @@ public:
 
     app* mk_fresh_bool();
 
+    expr_ref mk_at_most_1(unsigned num_args, expr * const * args);
+
 
 private:
     rational to_rational(parameter const& p) const;

src/opt/opt_solver.cpp

@@ -194,6 +194,11 @@ namespace opt {
         }
     }
 
+    lbool opt_solver::find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
+        return m_context.find_mutexes(vars, mutexes);
+    }
+
+
 
     /**
        \brief maximize the value of objective i in the current state.

src/opt/opt_solver.h

@@ -106,6 +106,7 @@ namespace opt {
         virtual expr * get_assertion(unsigned idx) const;
         virtual std::ostream& display(std::ostream & out) const;
         virtual ast_manager& get_manager() const { return m; } 
+        virtual lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes);
         void set_logic(symbol const& logic);
 
         smt::theory_var add_objective(app* term);

src/sat/sat_solver.cpp

@@ -3053,6 +3053,12 @@ namespace sat {
         return r;
     }
 
+    // -----------------------
+    //
+    // Extraction of mutexes
+    //
+    // -----------------------
+
     lbool solver::find_mutexes(literal_vector const& lits, vector<literal_vector> & mutexes) {
         literal_vector ps(lits);
         m_user_bin_clauses.reset();
@@ -3111,6 +3117,12 @@ namespace sat {
         }
     }
 
+    // -----------------------
+    //
+    // Consequence generation.
+    //
+    // -----------------------
+
     lbool solver::get_consequences(literal_vector const& asms, bool_var_vector const& vars, vector<literal_vector>& conseq) {
         literal_vector lits;
         lbool is_sat = check(asms.size(), asms.c_ptr());

src/smt/smt_consequences.cpp

@@ -251,191 +251,6 @@ namespace smt {
                                     expr_ref_vector& conseq, 
                                     expr_ref_vector& unfixed) {
 
-        m_antecedents.reset();
-        pop_to_base_lvl();
-        lbool is_sat = check(assumptions.size(), assumptions.c_ptr());
-        if (is_sat != l_true) {
-            return is_sat;
-        }
-        obj_map<expr, expr*> var2val;
-        index_set _assumptions;
-        for (unsigned i = 0; i < assumptions.size(); ++i) {
-            _assumptions.insert(get_literal(assumptions[i]).var());
-        }
-        model_ref mdl;
-        get_model(mdl);
-        ast_manager& m = m_manager;
-        expr_ref_vector trail(m);
-        model_evaluator eval(*mdl.get());
-        expr_ref val(m);
-        TRACE("context", model_pp(tout, *mdl););
-        for (unsigned i = 0; i < vars.size(); ++i) {
-            eval(vars[i], val);
-            if (m.is_value(val)) {
-                trail.push_back(val);
-                var2val.insert(vars[i], val);
-            } 
-            else {
-                unfixed.push_back(vars[i]);
-            }
-        }
-        unsigned num_units = 0;
-        extract_fixed_consequences(num_units, var2val, _assumptions, conseq);
-        app_ref eq(m);
-        TRACE("context", 
-              tout << "vars: " << vars.size() << "\n";
-              tout << "lits: " << num_units << "\n";);
-        m_case_split_queue->init_search_eh();
-        unsigned num_iterations = 0;
-        unsigned model_threshold = 2;
-        unsigned num_fixed_eqs = 0;
-        unsigned num_reiterations = 0;
-        while (!var2val.empty()) {
-            obj_map<expr,expr*>::iterator it = var2val.begin();
-            expr* e = it->m_key;
-            expr* val = it->m_value;
-
-            TRACE("context", tout << "scope level: " << get_scope_level() << "\n";);
-            SASSERT(!inconsistent());
-
-            //
-            // The current variable is checked to be a backbone
-            // We add the negation of the reference assignment to the variable.
-            // If the variable is a Boolean, it means adding literal that has
-            // the opposite value of the current reference model.
-            // If the variable is a non-Boolean, it means adding a disequality.
-            //
-            literal lit = mk_diseq(e, val);
-            mark_as_relevant(lit);
-            push_scope();
-            assign(lit, b_justification::mk_axiom(), true);
-            flet<bool> l(m_searching, true);
-
-            // 
-            // We check if the current assignment stack can be extended to a 
-            // satisfying assignment. bounded search may decide to restart, 
-            // in which case it returns l_undef and clears search failure.
-            //
-            while (true) {
-                is_sat = bounded_search();
-                TRACE("context", tout << "search result: " << is_sat << "\n";);
-                if (is_sat != l_true && m_last_search_failure != OK) {
-                    return is_sat;
-                }
-                if (is_sat == l_undef) {
-                    TRACE("context", tout << "restart\n";);
-                    inc_limits();
-                    continue;
-                }
-                break;
-            }
-            //
-            // If the state is satisfiable with the current variable assigned to 
-            // a different value from the reference model, it is unfixed.
-            // 
-            // If it is assigned above the search level we can't conclude anything
-            // about its value. 
-            // extract_fixed_consequences pops the assignment stack to the search level
-            // so this sets up the state to retry finding fixed values.
-            // 
-            // Otherwise, the variable is fixed.
-            // - it is either assigned at the search level to l_false, or
-            // - the state is l_false, which means that the variable is fixed by
-            //   the background constraints (and does not depend on assumptions).
-            // 
-            if (is_sat == l_true && get_assignment(lit) == l_true && is_relevant(lit)) { 
-                var2val.erase(e);
-                unfixed.push_back(e);
-                SASSERT(!are_equal(e, val));
-                TRACE("context", tout << mk_pp(e, m) << " is unfixed\n";
-                      display_literal_verbose(tout, lit); tout << "\n";
-                      tout << "relevant: " << is_relevant(lit) << "\n";
-                      display(tout););
-            }
-            else if (is_sat == l_true && (get_assign_level(lit) > get_search_level() || !is_relevant(lit))) {
-                TRACE("context", tout << "Retry fixing: " << mk_pp(e, m) << "\n";);
-                extract_fixed_consequences(num_units, var2val, _assumptions, conseq);
-                ++num_reiterations;
-                continue;
-            }
-            else {
-                //
-                // The state can be labeled as inconsistent when the implied consequence does
-                // not depend on assumptions, then the conflict level sits at the search level
-                // which causes the conflict resolver to decide that the state is unsat.
-                //
-                if (l_false == is_sat) {
-                    SASSERT(inconsistent());
-                    m_conflict = null_b_justification;
-                    m_not_l = null_literal;
-                }
-                TRACE("context", tout << "Fixed: " << mk_pp(e, m) << " " << is_sat << "\n";
-                      if (is_sat == l_false) display(tout););
-                
-            }
-            ++num_iterations;
-
-            //
-            // Check the slow pass: it retrieves an updated model and checks if the
-            // values in the updated model differ from the values in the reference
-            // model. 
-            // 
-            bool apply_slow_pass = model_threshold <= num_iterations || num_iterations <= 2;
-            if (apply_slow_pass && is_sat == l_true) {
-                delete_unfixed(var2val, unfixed);
-                // The next time we check the model is after 1.5 additional iterations.
-                model_threshold *= 3;
-                model_threshold /= 2;                                
-            }
-
-            //
-            // Walk the assignment stack at level 1 for learned consequences.
-            // The current literal should be assigned at the search level unless
-            // the state is is_sat == l_true and the assignment to lit is l_true.
-            // This condition is checked above.
-            // 
-            extract_fixed_consequences(num_units, var2val, _assumptions, conseq);
-
-            //
-            // Fixed equalities can be extracted by walking all variables and checking
-            // if the congruence roots are equal at the search level.
-            // 
-            if (apply_slow_pass) {
-                num_fixed_eqs += extract_fixed_eqs(var2val, conseq);
-                IF_VERBOSE(1, display_consequence_progress(verbose_stream(), num_iterations, var2val.size(), conseq.size(),
-                                                           unfixed.size(), num_fixed_eqs););
-                TRACE("context", display_consequence_progress(tout, num_iterations, var2val.size(), conseq.size(),
-                                                              unfixed.size(), num_fixed_eqs););
-            }
-            TRACE("context", tout << "finishing " << mk_pp(e, m) << "\n";);
-            SASSERT(!inconsistent());
-            
-            //
-            // This becomes unnecessary when the fixed consequence are 
-            // completely extracted.
-            // 
-            if (var2val.contains(e)) {
-                TRACE("context", tout << "Fixed value to " << mk_pp(e, m) << " was not processed\n";);
-                expr_ref fml(m);
-                fml = m.mk_eq(e, var2val.find(e));
-                if (!m_antecedents.contains(lit.var())) {
-                    extract_fixed_consequences(lit, var2val, _assumptions, conseq);
-                }
-                fml = m.mk_implies(antecedent2fml(m_antecedents[lit.var()]), fml);
-                conseq.push_back(fml);
-                var2val.erase(e);
-            }        
-        }
-        end_search();
-        DEBUG_CODE(validate_consequences(assumptions, vars, conseq, unfixed););
-        return l_true;
-    }
-
-    lbool context::get_consequences2(expr_ref_vector const& assumptions, 
-                                    expr_ref_vector const& vars, 
-                                    expr_ref_vector& conseq, 
-                                    expr_ref_vector& unfixed) {
-
         m_antecedents.reset();
         pop_to_base_lvl();
         lbool is_sat = check(assumptions.size(), assumptions.c_ptr());
@@ -552,6 +367,65 @@ namespace smt {
     }  
 
 
+    lbool context::find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
+        index_set lits;
+        for (unsigned i = 0; i < vars.size(); ++i) {
+            expr* n = vars[i];
+            bool neg = m_manager.is_not(n, n);
+            if (b_internalized(n)) {
+                lits.insert(literal(get_bool_var(n), !neg).index());
+            }
+        }
+        while (!lits.empty()) {
+            literal_vector mutex;
+            index_set other(lits);
+            while (!other.empty()) {
+                index_set conseq;
+                literal p = to_literal(*other.begin());
+                other.erase(p.index());
+                mutex.push_back(p);
+                if (other.empty()) {
+                    break;
+                }
+                get_reachable(p, other, conseq);
+                other = conseq;
+            }
+            if (mutex.size() > 1) {
+                expr_ref_vector mux(m_manager);
+                for (unsigned i = 0; i < mutex.size(); ++i) {
+                    expr_ref e(m_manager);
+                    literal2expr(mutex[i], e);
+                    mux.push_back(e);
+                }
+                mutexes.push_back(mux);
+            }
+            for (unsigned i = 0; i < mutex.size(); ++i) {
+                lits.remove(mutex[i].index());
+            }
+        }
+        return l_true;
+    }
+
+    void context::get_reachable(literal p, index_set& goal, index_set& reachable) {
+        index_set seen;
+        literal_vector todo;
+        todo.push_back(p);
+        while (!todo.empty()) {
+            p = todo.back();
+            todo.pop_back();
+            if (seen.contains(p.index())) {
+                continue;
+            }
+            seen.insert(p.index());
+            literal np = ~p;
+            if (goal.contains(np.index())) {
+                reachable.insert(np.index());
+            }
+            watch_list & w = m_watches[np.index()];
+            todo.append(static_cast<unsigned>(w.end_literals() - w.begin_literals()), w.begin_literals());
+        }
+    }
+
     //
     // Validate, in a slow pass, that the current consequences are correctly 
     // extracted.

src/smt/smt_context.h

@@ -1344,6 +1344,9 @@ namespace smt {
             literal lit, context& src_ctx, context& dst_ctx,
             vector<bool_var> b2v, ast_translation& tr);
         
+        /*
+          \brief Utilities for consequence finding.
+        */
         typedef hashtable<unsigned, u_hash, u_eq> index_set;
         //typedef uint_set index_set;
         u_map<index_set> m_antecedents;
@@ -1358,11 +1361,17 @@ namespace smt {
 
         expr_ref antecedent2fml(index_set const& ante);
 
+
         literal mk_diseq(expr* v, expr* val);
 
         void validate_consequences(expr_ref_vector const& assumptions, expr_ref_vector const& vars, 
                                    expr_ref_vector const& conseq, expr_ref_vector const& unfixed);
 
+        /*
+          \brief Auxiliry function for mutex finding.
+         */
+
+        void get_reachable(literal p, index_set& goal, index_set& reached);
 
     public:
         context(ast_manager & m, smt_params & fp, params_ref const & p = params_ref());
@@ -1404,7 +1413,8 @@ namespace smt {
         lbool check(unsigned num_assumptions = 0, expr * const * assumptions = 0, bool reset_cancel = true);        
 
         lbool get_consequences(expr_ref_vector const& assumptions, expr_ref_vector const& vars, expr_ref_vector& conseq, expr_ref_vector& unfixed);
-        lbool get_consequences2(expr_ref_vector const& assumptions, expr_ref_vector const& vars, expr_ref_vector& conseq, expr_ref_vector& unfixed);
+
+        lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes);
         
         lbool setup_and_check(bool reset_cancel = true);
         

src/smt/smt_kernel.cpp

@@ -112,7 +112,11 @@ namespace smt {
         }
 
         lbool get_consequences(expr_ref_vector const& assumptions, expr_ref_vector const& vars, expr_ref_vector& conseq, expr_ref_vector& unfixed) {
-            return m_kernel.get_consequences2(assumptions, vars, conseq, unfixed);
+            return m_kernel.get_consequences(assumptions, vars, conseq, unfixed);
+        }
+
+        lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
+            return m_kernel.find_mutexes(vars, mutexes);
         }
         
         void get_model(model_ref & m) const {
@@ -272,6 +276,10 @@ namespace smt {
         return m_imp->get_consequences(assumptions, vars, conseq, unfixed);
     }
 
+    lbool kernel::find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
+        return m_imp->find_mutexes(vars, mutexes);
+    }
+
     void kernel::get_model(model_ref & m) const {
         m_imp->get_model(m);
     }

src/smt/smt_kernel.h

@@ -132,6 +132,11 @@ namespace smt {
         lbool get_consequences(expr_ref_vector const& assumptions, expr_ref_vector const& vars, 
                                expr_ref_vector& conseq, expr_ref_vector& unfixed);
 
+        /*
+          \brief find mutually exclusive variables.
+         */
+        lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes);
+
         /**
            \brief Return the model associated with the last check command.
         */

src/smt/smt_solver.cpp

@@ -73,6 +73,10 @@ namespace smt {
             return m_context.get_consequences(assumptions, vars, conseq, unfixed);
         }
 
+        virtual lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
+            return m_context.find_mutexes(vars, mutexes);
+        }
+
         virtual void assert_expr(expr * t) {
             m_context.assert_expr(t);
         }
@@ -160,6 +164,7 @@ namespace smt {
             SASSERT(idx < get_num_assertions());
             return m_context.get_formulas()[idx];
         }   
+
     };
 };
 

src/smt/theory_pb.cpp

@@ -519,6 +519,7 @@ namespace smt {
             c->m_compilation_threshold = th;
             IF_VERBOSE(2, verbose_stream() << "(smt.pb setting compilation threhshold to " << th << ")\n";);
             TRACE("pb", tout << "compilation threshold: " << th << "\n";);
+            compile_ineq(*c);
         }
         else {
             c->m_compilation_threshold = UINT_MAX;
@@ -1216,7 +1217,7 @@ namespace smt {
 
     void theory_pb::inc_propagations(ineq& c) {
         ++c.m_num_propagations;
-        if (c.m_compiled == l_false && c.m_num_propagations > c.m_compilation_threshold) {
+        if (c.m_compiled == l_false && c.m_num_propagations >= c.m_compilation_threshold) {
             c.m_compiled = l_undef;
             m_to_compile.push_back(&c);
         }
@@ -1263,12 +1264,14 @@ namespace smt {
                 n -= rational::one();
             }
         }
+
+
         if (ctx.get_assignment(thl) == l_true  && 
             ctx.get_assign_level(thl) == ctx.get_base_level()) {
             psort_expr ps(ctx, *this);
             psort_nw<psort_expr> sortnw(ps);
             sortnw.m_stats.reset();
-            at_least_k = sortnw.ge(false, k, in.size(), in.c_ptr());
+            at_least_k = sortnw.ge(false, k, in.size(), in.c_ptr());            
             ctx.mk_clause(~thl, at_least_k, justify(~thl, at_least_k));
             m_stats.m_num_compiled_vars += sortnw.m_stats.m_num_compiled_vars;
             m_stats.m_num_compiled_clauses += sortnw.m_stats.m_num_compiled_clauses;

src/solver/solver.cpp

@@ -138,63 +138,6 @@ lbool solver::get_consequences_core(expr_ref_vector const& asms, expr_ref_vector
 
 lbool solver::find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
     return l_true;
-#if 0
-    // complete for literals, but inefficient.
-    // see more efficient (incomplete) version in sat_solver
-
-    mutexes.reset();
-    ast_manager& m = vars.get_manager();
-
-    typedef obj_hashtable<expr> expr_set;
-    
-    expr_set A, P;
-
-    for (unsigned i = 0; i < vars.size(); ++i) {
-        A.insert(vars[i]);
-    }
-
-    while (!A.empty()) {
-        P = A;
-        expr_ref_vector mutex(m);
-        while (!P.empty()) {
-            expr_ref_vector asms(m);
-            expr* p = *P.begin();
-            P.remove(p);
-            if (!is_literal(m, p)) {
-                break;
-            }
-            mutex.push_back(p);
-            asms.push_back(p);
-            expr_set Q;
-            expr_set::iterator it = P.begin(), end = P.end();
-            for (; it != end; ++it) {
-                expr* q = *it;
-                scoped_assumption_push _scoped_push(asms, q);
-                if (is_literal(m, q)) {
-                    lbool is_sat = check_sat(asms);
-                    switch (is_sat) {
-                    case l_false: 
-                        Q.insert(q);
-                        break;
-                    case l_true:
-                        break;
-                    case l_undef:
-                        return l_undef;
-                    }
-                }
-            }
-            P = Q;
-        }
-        if (mutex.size() > 1) {
-            mutexes.push_back(mutex);            
-        }
-        for (unsigned i = 0; i < mutex.size(); ++i) {
-            A.remove(mutex[i].get());
-        }
-    }
-    return l_true;
-#endif
-
 }
 
 bool solver::is_literal(ast_manager& m, expr* e) {

src/solver/solver_na2as.cpp

@@ -22,6 +22,7 @@ Notes:
 #include"solver_na2as.h"
 #include"ast_smt2_pp.h"
 
+
 solver_na2as::solver_na2as(ast_manager & m):
     m(m), 
     m_assumptions(m) {
@@ -71,6 +72,11 @@ lbool solver_na2as::get_consequences(expr_ref_vector const& asms, expr_ref_vecto
     return get_consequences_core(m_assumptions, vars, consequences);
 }
 
+lbool solver_na2as::find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes) {
+    return l_true;
+}
+
+
 void solver_na2as::push() {
     m_scopes.push_back(m_assumptions.size());
     push_core();

src/solver/solver_na2as.h

@@ -46,6 +46,7 @@ public:
     virtual unsigned get_num_assumptions() const { return m_assumptions.size(); }
     virtual expr * get_assumption(unsigned idx) const { return m_assumptions[idx]; }
     virtual lbool get_consequences(expr_ref_vector const& asms, expr_ref_vector const& vars, expr_ref_vector& consequences);
+    virtual lbool find_mutexes(expr_ref_vector const& vars, vector<expr_ref_vector>& mutexes);
 protected:
     virtual lbool check_sat_core(unsigned num_assumptions, expr * const * assumptions) = 0;
     virtual void push_core() = 0;

src/tactic/arith/card2bv_tactic.cpp

@@ -168,13 +168,39 @@ namespace pb {
             return BR_FAILED;
     }
 
-    expr_ref card2bv_rewriter::mk_atmost1(unsigned sz, expr * const* args) {
+    expr_ref card2bv_rewriter::mk_atmost1(unsigned n, expr * const* xs) {
-        expr_ref f1(m), f2(m), f3(m), result(m);
+        expr_ref_vector result(m), in(m);
-        f1 = bv.mk_bv(sz, args);
+        in.append(n, xs);
-        f2 = bv.mk_bv_sub(f1, bv.mk_numeral(rational(1), sz));
+        unsigned inc_size = 4;
-        f3 = m.mk_app(bv.get_fid(), OP_BAND, f1, f2);
+        while (!in.empty()) {
-        result = m.mk_eq(f3, bv.mk_numeral(rational(0), sz));
+            expr_ref_vector ors(m);
-        return result;
+            unsigned i = 0;
+            unsigned n = in.size();
+            bool last = n <= inc_size;
+            for (; i + inc_size < n; i += inc_size) {                    
+                mk_at_most_1_small(last, inc_size, in.c_ptr() + i, result, ors);
+            }
+            if (i < n) {
+                mk_at_most_1_small(last, n - i, in.c_ptr() + i, result, ors);
+            }
+            if (last) {
+                break;
+            }
+            in.reset();
+            in.append(ors);
+        }
+        return mk_and(result);
+    }
+
+    void card2bv_rewriter::mk_at_most_1_small(bool last, unsigned n, literal const* xs, expr_ref_vector& result, expr_ref_vector& ors) {
+        if (!last) {
+            ors.push_back(m.mk_or(n, xs));
+        }
+        for (unsigned i = 0; i < n; ++i) {
+            for (unsigned j = i + 1; j < n; ++j) {
+                result.push_back(m.mk_not(m.mk_and(xs[i], xs[j])));
+            }
+        }
     }
 
     bool card2bv_rewriter::is_atmost1(func_decl* f, unsigned sz, expr * const* args, expr_ref& result) {

src/tactic/arith/card2bv_tactic.h

@@ -54,6 +54,7 @@ namespace pb {
         bool is_and(func_decl* f);
         bool is_atmost1(func_decl* f, unsigned sz, expr * const* args, expr_ref& result);
         expr_ref mk_atmost1(unsigned sz, expr * const* args);
+        void mk_at_most_1_small(bool last, unsigned n, literal const* xs, expr_ref_vector& result, expr_ref_vector& ors);
 
     public:
         card2bv_rewriter(ast_manager& m);

src/test/sorting_network.cpp

@@ -332,7 +332,32 @@ void test_sorting5(unsigned n, unsigned k) {
     test_sorting_ge(n, k);
 }
 
+void test_at_most_1(unsigned n) {
+    ast_manager m;
+    reg_decl_plugins(m);
+    expr_ref_vector in(m), out(m);
+    for (unsigned i = 0; i < n; ++i) {
+        in.push_back(m.mk_fresh_const("a",m.mk_bool_sort()));
+    }
+
+    
+    ast_ext2 ext(m);
+    psort_nw<ast_ext2> sn(ext);
+    expr_ref result(m);
+    result = sn.le(false, 1, in.size(), in.c_ptr());
+    std::cout << result << "\n";
+    std::cout << ext.m_clauses << "\n";
+}
+
 void tst_sorting_network() {
+    test_at_most_1(1);
+    test_at_most_1(2);
+    test_at_most_1(3);
+    test_at_most_1(4);
+    test_at_most_1(5);
+    test_at_most_1(10);
+    return;
+
     test_sorting_eq(11,7);
     for (unsigned n = 3; n < 20; n += 2) {
         for (unsigned k = 1; k < n; ++k) {

src/util/sorting_network.h

@@ -201,7 +201,11 @@ Notes:
             if (dualize(k, n, xs, in)) {
                 return ge(full, k, n, in.c_ptr());
             }
+            else if (k == 1) {
+                return mk_at_most_1(full, n, xs);
+            }
             else {
+                std::cout << "sort " << k << "\n";
                 SASSERT(2*k <= n);
                 m_t = full?LE_FULL:LE;
                 card(k + 1, n, xs, out);
@@ -230,6 +234,54 @@ Notes:
         
     private:
 
+        literal mk_at_most_1(bool full, unsigned n, literal const* xs) {
+            literal_vector in(n, xs);
+            literal result = ctx.fresh();
+            unsigned inc_size = 4;
+            while (!in.empty()) {
+                literal_vector ors;
+                unsigned i = 0;
+                unsigned n = in.size();
+                bool last = n <= inc_size;
+                for (; i + inc_size < n; i += inc_size) {                    
+                    mk_at_most_1_small(full, last, inc_size, in.c_ptr() + i, result, ors);
+                }
+                if (i < n) {
+                    mk_at_most_1_small(full, last, n - i, in.c_ptr() + i, result, ors);
+                }
+                if (last) {
+                    break;
+                }
+                in.reset();
+                in.append(ors);
+                ors.reset();                
+            }
+            return result;
+        }
+
+        void mk_at_most_1_small(bool full, bool last, unsigned n, literal const* xs, literal result, literal_vector& ors) {
+            if (!last) {
+                literal ex = ctx.fresh();
+                for (unsigned j = 0; j < n; ++j) {
+                    add_clause(ctx.mk_not(xs[j]), ex);
+                }
+                if (full) {
+                    literal_vector lits(n, xs);
+                    lits.push_back(ctx.mk_not(ex));
+                    add_clause(lits.size(), lits.c_ptr());
+                }
+                ors.push_back(ex);
+            }
+            for (unsigned i = 0; i < n; ++i) {
+                for (unsigned j = i + 1; j < n; ++j) {
+                    add_clause(ctx.mk_not(result), ctx.mk_not(xs[i]), ctx.mk_not(xs[j]));
+                }
+                if (full) {
+                    add_clause(result, xs[i]);
+                }
+            }
+        }
+
         std::ostream& pp(std::ostream& out, unsigned n, literal const* lits) {
             for (unsigned i = 0; i < n; ++i) ctx.pp(out, lits[i]) << " ";
             return out;