diff --git a/src/model/model_core.h b/src/model/model_core.h
index d705e432d..7f5051386 100644
--- a/src/model/model_core.h
+++ b/src/model/model_core.h
@@ -48,6 +48,14 @@ public:
     func_interp * get_func_interp(func_decl * d) const { func_interp * fi; return m_finterp.find(d, fi) ? fi : nullptr; }
 
     bool eval(func_decl * f, expr_ref & r) const;
+    bool is_true_decl(func_decl *f) const {
+        expr_ref r(m);
+        return eval(f, r) && m.is_true(r);
+    }
+    bool is_false_decl(func_decl *f) const {
+        expr_ref r(m);
+        return eval(f, r) && m.is_false(r);
+    }
 
     unsigned get_num_constants() const { return m_const_decls.size(); }
     unsigned get_num_functions() const { return m_func_decls.size(); }
diff --git a/src/muz/base/fp_params.pyg b/src/muz/base/fp_params.pyg
index c96a12ca2..31ab3a358 100644
--- a/src/muz/base/fp_params.pyg
+++ b/src/muz/base/fp_params.pyg
@@ -160,7 +160,6 @@ def_module_params('fp',
                            '2 = use Gaussian elimination optimization (broken), 3 = use additive IUC plugin'),
                           ('spacer.iuc.old_hyp_reducer', BOOL, False, 'use old hyp reducer instead of new implementation, for debugging only'),
                           ('spacer.validate_lemmas', BOOL, False, 'Validate each lemma after generalization'),
-                          ('spacer.reuse_pobs', BOOL, True, 'Reuse pobs'),
                           ('spacer.ground_pobs', BOOL, True, 'Ground pobs by using values from a model'),
                           ('spacer.iuc.print_farkas_stats', BOOL, False, 'prints for each proof how many Farkas lemmas it contains and how many of these participate in the cut (for debugging)'),
                           ('spacer.iuc.debug_proof', BOOL, False, 'prints proof used by unsat-core-learner for debugging purposes (debugging)'),
diff --git a/src/muz/spacer/spacer_context.cpp b/src/muz/spacer/spacer_context.cpp
index 40569295b..b034a8fd5 100644
--- a/src/muz/spacer/spacer_context.cpp
+++ b/src/muz/spacer/spacer_context.cpp
@@ -55,6 +55,8 @@ Notes:
 
 #include "muz/spacer/spacer_sat_answer.h"
 
+#define WEAKNESS_MAX 65535
+
 namespace spacer {
 
 /// pob -- proof obligation
@@ -66,8 +68,8 @@ pob::pob (pob* parent, pred_transformer& pt,
     m_binding(m_pt.get_ast_manager()),
     m_new_post (m_pt.get_ast_manager ()),
     m_level (level), m_depth (depth),
-    m_open (true), m_use_farkas (true), m_weakness(0),
-    m_blocked_lvl(0) {
+    m_open (true), m_use_farkas (true), m_in_queue(false),
+    m_weakness(0), m_blocked_lvl(0) {
     if (add_to_parent && m_parent) {
         m_parent->add_child(*this);
     }
@@ -79,6 +81,7 @@ void pob::set_post(expr* post) {
 }
 
 void pob::set_post(expr* post, app_ref_vector const &binding) {
+    SASSERT(!is_in_queue());
     normalize(post, m_post,
               m_pt.get_context().simplify_pob(),
               m_pt.get_context().use_euf_gen());
@@ -88,6 +91,7 @@ void pob::set_post(expr* post, app_ref_vector const &binding) {
 }
 
 void pob::inherit(pob const &p) {
+    SASSERT(!is_in_queue());
     SASSERT(m_parent == p.m_parent);
     SASSERT(&m_pt == &p.m_pt);
     SASSERT(m_post == p.m_post);
@@ -105,17 +109,10 @@ void pob::inherit(pob const &p) {
     m_derivation = nullptr;
 }
 
-void pob::clean () {
-    if (m_new_post) {
-        m_post = m_new_post;
-        m_new_post.reset();
-    }
-}
-
 void pob::close () {
     if (!m_open) { return; }
 
-    reset ();
+    m_derivation = nullptr;
     m_open = false;
     for (unsigned i = 0, sz = m_kids.size (); i < sz; ++i)
     { m_kids [i]->close(); }
@@ -137,17 +134,24 @@ void pob::get_skolems(app_ref_vector &v) {
 pob* pob_queue::top ()
 {
     /// nothing in the queue
-    if (m_obligations.empty()) { return nullptr; }
+    if (m_data.empty()) { return nullptr; }
     /// top queue element is above max level
-    if (m_obligations.top()->level() > m_max_level) { return nullptr; }
+    if (m_data.top()->level() > m_max_level) { return nullptr; }
     /// top queue element is at the max level, but at a higher than base depth
-    if (m_obligations.top ()->level () == m_max_level &&
-        m_obligations.top()->depth() > m_min_depth) { return nullptr; }
+    if (m_data.top ()->level () == m_max_level &&
+        m_data.top()->depth() > m_min_depth) { return nullptr; }
 
     /// there is something good in the queue
-    return m_obligations.top ().get ();
+    return m_data.top ();
 }
 
+void pob_queue::pop() {
+    pob *p = m_data.top();
+    p->set_in_queue(false);
+    m_data.pop();
+}
+
+
 void pob_queue::set_root(pob& root)
 {
     m_root = &root;
@@ -156,19 +160,28 @@ void pob_queue::set_root(pob& root)
     reset();
 }
 
-pob_queue::~pob_queue() {}
-
 void pob_queue::reset()
 {
-    while (!m_obligations.empty()) { m_obligations.pop(); }
-    if (m_root) { m_obligations.push(m_root); }
+    while (!m_data.empty()) {
+        pob *p = m_data.top();
+        m_data.pop();
+        p->set_in_queue(false);
+    }
+    if (m_root) {
+        SASSERT(!m_root->is_in_queue());
+        m_root->set_in_queue(true);
+        m_data.push(m_root.get());
+    }
 }
 
 void pob_queue::push(pob &n) {
-    TRACE("pob_queue",
-          tout << "pob_queue::push(" << n.post()->get_id() << ")\n";);
-    m_obligations.push (&n);
-    n.get_context().new_pob_eh(&n);
+    if (!n.is_in_queue()) {
+        TRACE("pob_queue",
+              tout << "pob_queue::push(" << n.post()->get_id() << ")\n";);
+        n.set_in_queue(true);
+        m_data.push (&n);
+        n.get_context().new_pob_eh(&n);
+    }
 }
 
 // ----------------
@@ -266,6 +279,8 @@ pob *derivation::create_next_child(model &mdl)
         m_evars.reset();
         pt().mbp(vars, m_trans, mdl,
                  true, pt().get_context().use_ground_pob());
+        CTRACE("spacer", !vars.empty(),
+               tout << "Failed to eliminate: " << vars << "\n";);
         m_evars.append (vars);
         vars.reset();
     }
@@ -295,6 +310,8 @@ pob *derivation::create_next_child(model &mdl)
         vars.append(m_evars);
         pt().mbp(vars, post, mdl,
                  true, pt().get_context().use_ground_pob());
+        CTRACE("spacer", !vars.empty(),
+               tout << "Failed to eliminate: " << vars << "\n";);
         //qe::reduce_array_selects (*mev.get_model (), post);
     }
     else {
@@ -398,6 +415,8 @@ pob *derivation::create_next_child ()
             this->pt().mbp(vars, m_trans, *mdl,
                            true, this->pt().get_context().use_ground_pob());
             // keep track of implicitly quantified variables
+            CTRACE("spacer", !vars.empty(),
+                   tout << "Failed to eliminate: " << vars << "\n";);
             m_evars.append (vars);
             vars.reset();
         }
@@ -462,8 +481,11 @@ void derivation::premise::set_summary (expr * summary, bool must,
 lemma::lemma (ast_manager &manager, expr * body, unsigned lvl) :
     m_ref_count(0), m(manager),
     m_body(body, m), m_cube(m),
-    m_zks(m), m_bindings(m), m_lvl(lvl), m_init_lvl(m_lvl),
-    m_pob(nullptr), m_ctp(nullptr), m_external(false), m_bumped(0) {
+    m_zks(m), m_bindings(m),
+    m_pob(nullptr), m_ctp(nullptr),
+    m_lvl(lvl), m_init_lvl(m_lvl),
+    m_bumped(0), m_weakness(WEAKNESS_MAX),
+    m_external(false), m_blocked(false) {
     SASSERT(m_body);
     normalize(m_body, m_body);
 }
@@ -471,8 +493,11 @@ lemma::lemma (ast_manager &manager, expr * body, unsigned lvl) :
 lemma::lemma(pob_ref const &p) :
     m_ref_count(0), m(p->get_ast_manager()),
     m_body(m), m_cube(m),
-    m_zks(m), m_bindings(m), m_lvl(p->level()), m_init_lvl(m_lvl),
-    m_pob(p), m_ctp(nullptr), m_external(false), m_bumped(0) {
+    m_zks(m), m_bindings(m),
+    m_pob(p), m_ctp(nullptr),
+    m_lvl(p->level()), m_init_lvl(m_lvl),
+    m_bumped(0), m_weakness(p->weakness()),
+    m_external(false), m_blocked(false) {
     SASSERT(m_pob);
     m_pob->get_skolems(m_zks);
     add_binding(m_pob->get_binding());
@@ -482,8 +507,11 @@ lemma::lemma(pob_ref const &p, expr_ref_vector &cube, unsigned lvl) :
     m_ref_count(0),
     m(p->get_ast_manager()),
     m_body(m), m_cube(m),
-    m_zks(m), m_bindings(m), m_lvl(p->level()), m_init_lvl(m_lvl),
-    m_pob(p), m_ctp(nullptr), m_external(false), m_bumped(0)
+    m_zks(m), m_bindings(m),
+    m_pob(p), m_ctp(nullptr),
+    m_lvl(p->level()), m_init_lvl(m_lvl),
+    m_bumped(0), m_weakness(p->weakness()),
+    m_external(false), m_blocked(false)
 {
     if (m_pob) {
         m_pob->get_skolems(m_zks);
@@ -820,7 +848,7 @@ const datalog::rule *pred_transformer::find_rule(model &model) {
 
     for (auto &kv : m_pt_rules) {
         app *tag = kv.m_value->tag();
-        if (model.eval(tag->get_decl(), val) && m.is_true(val)) {
+        if (model.is_true_decl(tag->get_decl())) {
             return &kv.m_value->rule();
         }
     }
@@ -1162,7 +1190,16 @@ expr_ref pred_transformer::get_origin_summary (model &mdl,
     }
 
     // bail out of if the model is insufficient
-    if (!mdl.is_true(summary)) return expr_ref(m);
+    // (skip quantified lemmas cause we can't validate them in the model)
+    // TBD: for quantified lemmas use current instances
+    flatten_and(summary);
+    for (auto *s : summary) {
+        if (!is_quantifier(s) && !mdl.is_true(s)) {
+            TRACE("spacer", tout << "Summary not true in the model: "
+                  << mk_pp(s, m) << "\n";);
+            return expr_ref(m);
+        }
+    }
 
     // -- pick an implicant
     expr_ref_vector lits(m);
@@ -1347,7 +1384,7 @@ lbool pred_transformer::is_reachable(pob& n, expr_ref_vector* core,
 
     if (is_sat == l_true || is_sat == l_undef) {
         if (core) { core->reset(); }
-        if (model) {
+        if (model && model->get()) {
             r = find_rule(**model, is_concrete, reach_pred_used, num_reuse_reach);
             TRACE ("spacer", tout << "reachable "
                    << "is_concrete " << is_concrete << " rused: ";
@@ -1387,7 +1424,12 @@ bool pred_transformer::is_ctp_blocked(lemma *lem) {
     // -- find rule of the ctp
     const datalog::rule *r;
     r = find_rule(*ctp);
-    if (r == nullptr) {return false;}
+    if (r == nullptr) {
+        // no rules means lemma is blocked forever because
+        // it does not satisfy some derived facts
+        lem->set_blocked(true);
+        return true;
+    }
 
     // -- find predicates along the rule
     find_predecessors(*r, m_predicates);
@@ -1410,6 +1452,8 @@ bool pred_transformer::is_invariant(unsigned level, lemma* lem,
                                     unsigned& solver_level,
                                     expr_ref_vector* core)
 {
+    if (lem->is_blocked()) return false;
+
     m_stats.m_num_is_invariant++;
     if (is_ctp_blocked(lem)) {
         m_stats.m_num_ctp_blocked++;
@@ -1451,7 +1495,7 @@ bool pred_transformer::is_invariant(unsigned level, lemma* lem,
         SASSERT (level <= solver_level);
     }
     else if (r == l_true) {
-        // optionally remove unused symbols from the model
+        // TBD: optionally remove unused symbols from the model
         if (mdl_ref_ptr) {lem->set_ctp(*mdl_ref_ptr);}
     }
     else {lem->reset_ctp();}
@@ -2120,16 +2164,10 @@ void pred_transformer::frames::simplify_formulas ()
 
 /// pred_transformer::pobs
 
-pob* pred_transformer::pobs::mk_pob(pob *parent,
-                                    unsigned level, unsigned depth,
-                                    expr *post, app_ref_vector const &b) {
-
-    if (!m_pt.ctx.reuse_pobs()) {
-        pob* n = alloc(pob, parent, m_pt, level, depth);
-        n->set_post(post, b);
-        return n;
-    }
-
+pob* pred_transformer::pob_manager::mk_pob(pob *parent,
+                                           unsigned level, unsigned depth,
+                                           expr *post,
+                                           app_ref_vector const &b) {
     // create a new pob and set its post to normalize it
     pob p(parent, m_pt, level, depth, false);
     p.set_post(post, b);
@@ -2138,7 +2176,7 @@ pob* pred_transformer::pobs::mk_pob(pob *parent,
         auto &buf = m_pobs[p.post()];
         for (unsigned i = 0, sz = buf.size(); i < sz; ++i) {
             pob *f = buf.get(i);
-            if (f->parent() == parent) {
+            if (f->parent() == parent && !f->is_in_queue()) {
                 f->inherit(p);
                 return f;
             }
@@ -2160,7 +2198,21 @@ pob* pred_transformer::pobs::mk_pob(pob *parent,
     return n;
 }
 
-
+pob* pred_transformer::pob_manager::find_pob(pob* parent, expr *post) {
+    pob p(parent, m_pt, 0, 0, false);
+    p.set_post(post);
+    pob *res = nullptr;
+    if (m_pobs.contains(p.post())) {
+        for (auto *f : m_pobs[p.post()]) {
+            if (f->parent() == parent) {
+                // try to find pob not already in queue
+                if (!f->is_in_queue()) return f;
+                res = f;
+            }
+        }
+    }
+    return res;
+}
 
 
 // ----------------
@@ -2207,7 +2259,6 @@ void context::updt_params() {
     m_use_ctp = m_params.spacer_ctp();
     m_use_inc_clause = m_params.spacer_use_inc_clause();
     m_blast_term_ite = m_params.spacer_blast_term_ite();
-    m_reuse_pobs = m_params.spacer_reuse_pobs();
     m_use_ind_gen = m_params.spacer_use_inductive_generalizer();
     m_use_array_eq_gen = m_params.spacer_use_array_eq_generalizer();
     m_validate_lemmas = m_params.spacer_validate_lemmas();
@@ -3055,27 +3106,19 @@ bool context::check_reachability ()
         }
 
         SASSERT (m_pob_queue.top ());
-        // -- remove all closed nodes and updated all dirty nodes
+        // -- remove all closed nodes
         // -- this is necessary because there is no easy way to
         // -- remove nodes from the priority queue.
-        while (m_pob_queue.top ()->is_closed () ||
-               m_pob_queue.top()->is_dirty()) {
-            pob_ref n = m_pob_queue.top ();
-            m_pob_queue.pop ();
-            if (n->is_closed()) {
-                IF_VERBOSE (1,
-                            verbose_stream () << "Deleting closed node: "
-                            << n->pt ().head ()->get_name ()
-                            << "(" << n->level () << ", " << n->depth () << ")"
-                            << " " << n->post ()->get_id () << "\n";);
-                if (m_pob_queue.is_root(*n)) { return true; }
-                SASSERT (m_pob_queue.top ());
-            } else if (n->is_dirty()) {
-                n->clean ();
-                // -- the node n might not be at the top after it is cleaned
-                m_pob_queue.push (*n);
-            } else
-            { UNREACHABLE(); }
+        while (m_pob_queue.top ()->is_closed ()) {
+            pob_ref n = m_pob_queue.top();
+            m_pob_queue.pop();
+            IF_VERBOSE (1,
+                        verbose_stream () << "Deleting closed node: "
+                        << n->pt ().head ()->get_name ()
+                        << "(" << n->level () << ", " << n->depth () << ")"
+                        << " " << n->post ()->get_id () << "\n";);
+            if (m_pob_queue.is_root(*n)) {return true;}
+            SASSERT (m_pob_queue.top ());
         }
 
         SASSERT (m_pob_queue.top ());
@@ -3169,6 +3212,7 @@ bool context::is_reachable(pob &n)
     unsigned num_reuse_reach = 0;
 
     unsigned saved = n.level ();
+    // TBD: don't expose private field
     n.m_level = infty_level ();
     lbool res = n.pt().is_reachable(n, nullptr, &mdl,
                                     uses_level, is_concrete, r,
@@ -3413,10 +3457,21 @@ lbool context::expand_pob(pob& n, pob_ref_buffer &out)
 
         // Optionally update the node to be the negation of the lemma
         if (v && m_use_lemma_as_pob) {
-            n.new_post (mk_and(lemma->get_cube()));
-            n.set_farkas_generalizer (false);
-            // XXX hack while refactoring is in progress
-            n.clean();
+            expr_ref c(m);
+            c = mk_and(lemma->get_cube());
+            // check that the post condition is different
+            if (c  != n.post()) {
+                pob *f = n.pt().find_pob(n.parent(), c);
+                // skip if a similar pob is already in the queue
+                if (f != &n && (!f || !f->is_in_queue())) {
+                    f = n.pt().mk_pob(n.parent(), n.level(),
+                                      n.depth(), c, n.get_binding());
+                    SASSERT(!f->is_in_queue());
+                    f->inc_level();
+                    //f->set_farkas_generalizer(false);
+                    out.push_back(f);
+                }
+            }
         }
 
         // schedule the node to be placed back in the queue
@@ -3434,7 +3489,7 @@ lbool context::expand_pob(pob& n, pob_ref_buffer &out)
     }
     case l_undef:
         // something went wrong
-        if (n.weakness() < 100 /* MAX_WEAKENSS */) {
+        if (n.weakness() < 10 /* MAX_WEAKENSS */) {
             bool has_new_child = false;
             SASSERT(m_weak_abs);
             m_stats.m_expand_pob_undef++;
@@ -3932,7 +3987,7 @@ bool context::is_inductive() {
 }
 
 /// pob_lt operator
-inline bool pob_lt::operator() (const pob *pn1, const pob *pn2) const
+inline bool pob_lt_proc::operator() (const pob *pn1, const pob *pn2) const
 {
     SASSERT (pn1);
     SASSERT (pn2);
diff --git a/src/muz/spacer/spacer_context.h b/src/muz/spacer/spacer_context.h
index 37b035b98..93c2337e6 100644
--- a/src/muz/spacer/spacer_context.h
+++ b/src/muz/spacer/spacer_context.h
@@ -122,12 +122,14 @@ class lemma {
     expr_ref_vector m_cube;
     app_ref_vector m_zks;
     app_ref_vector m_bindings;
+    pob_ref m_pob;
+    model_ref m_ctp;           // counter-example to pushing
     unsigned m_lvl;            // current level of the lemma
     unsigned m_init_lvl;       // level at which lemma was created
-    pob_ref m_pob;
-    model_ref m_ctp; // counter-example to pushing
-    bool m_external;
-    unsigned m_bumped;
+    unsigned m_bumped:16;
+    unsigned m_weakness:16;
+    unsigned m_external:1;
+    unsigned m_blocked:1;
 
     void mk_expr_core();
     void mk_cube_core();
@@ -154,12 +156,15 @@ public:
 
     bool has_pob() {return m_pob;}
     pob_ref &get_pob() {return m_pob;}
-    inline unsigned weakness();
+    unsigned weakness() {return m_weakness;}
 
     void add_skolem(app *zk, app* b);
 
-    inline void set_external(bool ext){m_external = ext;}
-    inline bool external() { return m_external;}
+    void set_external(bool ext){m_external = ext;}
+    bool external() { return m_external;}
+
+    bool is_blocked() {return m_blocked;}
+    void set_blocked(bool v) {m_blocked=v;}
 
     bool is_inductive() const {return is_infty_level(m_lvl);}
     unsigned level () const {return m_lvl;}
@@ -268,18 +273,31 @@ class pred_transformer {
     };
 
     /**
-        manager of proof-obligations (pobs)
+        manager of proof-obligations (pob_manager)
+
+        Pobs are determined uniquely by their post-condition and a parent pob.
+        They are managed by pob_manager and remain live through the
+        life of the manager
      */
-    class pobs {
+    class pob_manager {
+        // a buffer that contains space for one pob and allocates more
+        // space if needed
         typedef ptr_buffer<pob, 1> pob_buffer;
+        // Type for the map from post-conditions to pobs. The common
+        // case is that each post-condition corresponds to a single
+        // pob. Other cases are handled by expanding the buffer
         typedef obj_map<expr, pob_buffer > expr2pob_buffer;
 
+        // parent predicate transformer
         pred_transformer &m_pt;
 
+        // map from post-conditions to pobs
         expr2pob_buffer m_pobs;
+
+        // a store
         pob_ref_vector m_pinned;
     public:
-        pobs(pred_transformer &pt) : m_pt(pt) {}
+        pob_manager(pred_transformer &pt) : m_pt(pt) {}
         pob* mk_pob(pob *parent, unsigned level, unsigned depth,
                     expr *post, app_ref_vector const &b);
 
@@ -290,6 +308,7 @@ class pred_transformer {
         }
         unsigned size() const {return m_pinned.size();}
 
+        pob* find_pob(pob* parent, expr *post);
     };
 
     class pt_rule {
@@ -361,7 +380,7 @@ class pred_transformer {
     ptr_vector<datalog::rule>    m_rules;           // rules used to derive transformer
     scoped_ptr<prop_solver>      m_solver;          // solver context
     ref<solver>                  m_reach_solver;       // context for reachability facts
-    pobs                         m_pobs;            // proof obligations created so far
+    pob_manager                         m_pobs;            // proof obligations created so far
     frames                       m_frames;          // frames with lemmas
     reach_fact_ref_vector        m_reach_facts;     // reach facts
     unsigned                     m_rf_init_sz;      // number of reach fact from INIT
@@ -481,6 +500,9 @@ public:
                 expr *post, app_ref_vector const &b){
         return m_pobs.mk_pob(parent, level, depth, post, b);
     }
+    pob* find_pob(pob *parent, expr *post) {
+        return m_pobs.find_pob(parent, post);
+    }
 
     pob* mk_pob(pob *parent, unsigned level, unsigned depth,
                 expr *post) {
@@ -548,6 +570,7 @@ public:
  * A proof obligation.
  */
 class pob {
+    // TBD: remove this
     friend class context;
     unsigned m_ref_count;
     /// parent node
@@ -562,14 +585,15 @@ class pob {
     /// new post to be swapped in for m_post
     expr_ref                m_new_post;
     /// level at which to decide the post
-    unsigned                m_level;
-
-    unsigned                m_depth;
+    unsigned                m_level:16;
+    unsigned                m_depth:16;
 
     /// whether a concrete answer to the post is found
-    bool                    m_open;
+    unsigned                m_open:1;
     /// whether to use farkas generalizer to construct a lemma blocking this node
-    bool                    m_use_farkas;
+    unsigned                m_use_farkas:1;
+    /// true if this pob is in pob_queue
+    unsigned                m_in_queue:1;
 
     unsigned                m_weakness;
     /// derivation representing the position of this node in the parent's rule
@@ -584,17 +608,25 @@ class pob {
     // depth -> watch
     std::map<unsigned, stopwatch> m_expand_watches;
     unsigned m_blocked_lvl;
+
 public:
     pob (pob* parent, pred_transformer& pt,
          unsigned level, unsigned depth=0, bool add_to_parent=true);
 
     ~pob() {if (m_parent) { m_parent->erase_child(*this); }}
 
+    // TBD: move into constructor and make private
+    void set_post(expr *post, app_ref_vector const &binding);
+    void set_post(expr *post);
+
     unsigned weakness() {return m_weakness;}
     void bump_weakness() {m_weakness++;}
     void reset_weakness() {m_weakness=0;}
 
-    void inc_level () {m_level++; m_depth++;reset_weakness();}
+    void inc_level () {
+        SASSERT(!is_in_queue());
+        m_level++; m_depth++;reset_weakness();
+    }
 
     void inherit(pob const &p);
     void set_derivation (derivation *d) {m_derivation = d;}
@@ -614,32 +646,25 @@ public:
     unsigned level () const { return m_level; }
     unsigned depth () const {return m_depth;}
     unsigned width () const {return m_kids.size();}
-    unsigned blocked_at(unsigned lvl=0){return (m_blocked_lvl = std::max(lvl, m_blocked_lvl)); }
+    unsigned blocked_at(unsigned lvl=0){
+        return (m_blocked_lvl = std::max(lvl, m_blocked_lvl));
+    }
 
+    bool is_in_queue() const {return m_in_queue;}
+    void set_in_queue(bool v) {m_in_queue = v;}
     bool use_farkas_generalizer () const {return m_use_farkas;}
     void set_farkas_generalizer (bool v) {m_use_farkas = v;}
 
     expr* post() const { return m_post.get (); }
-    void set_post(expr *post);
-    void set_post(expr *post, app_ref_vector const &binding);
-
-    /// indicate that a new post should be set for the node
-    void new_post(expr *post) {if (post != m_post) {m_new_post = post;}}
-    /// true if the node needs to be updated outside of the priority queue
-    bool is_dirty () {return m_new_post;}
-    /// clean a dirty node
-    void clean();
-
-    void reset () {clean (); m_derivation = nullptr; m_open = true;}
 
     bool is_closed () const { return !m_open; }
     void close();
 
-    const ptr_vector<pob> &children() {return m_kids;}
+    const ptr_vector<pob> &children() const {return m_kids;}
     void add_child (pob &v) {m_kids.push_back (&v);}
     void erase_child (pob &v) {m_kids.erase (&v);}
 
-    const ptr_vector<lemma> &lemmas() {return m_lemmas;}
+    const ptr_vector<lemma> &lemmas() const {return m_lemmas;}
     void add_lemma(lemma* new_lemma) {m_lemmas.push_back(new_lemma);}
 
     bool is_ground () const { return m_binding.empty (); }
@@ -652,8 +677,14 @@ public:
      */
     void get_skolems(app_ref_vector& v);
 
-    void on_expand() { m_expand_watches[m_depth].start(); if (m_parent.get()){m_parent.get()->on_expand();} }
-    void off_expand() { m_expand_watches[m_depth].stop(); if (m_parent.get()){m_parent.get()->off_expand();} };
+    void on_expand() {
+        m_expand_watches[m_depth].start();
+        if (m_parent.get()){m_parent.get()->on_expand();}
+    }
+    void off_expand() {
+        m_expand_watches[m_depth].stop();
+        if (m_parent.get()){m_parent.get()->off_expand();}
+    }
     double get_expand_time(unsigned depth) { return m_expand_watches[depth].get_seconds();}
 
     void inc_ref () {++m_ref_count;}
@@ -672,25 +703,16 @@ public:
 };
 
 
-struct pob_lt :
-        public std::binary_function<const pob*, const pob*, bool>
-{bool operator() (const pob *pn1, const pob *pn2) const;};
-
-struct pob_gt :
-        public std::binary_function<const pob*, const pob*, bool> {
-    pob_lt lt;
-    bool operator() (const pob *n1, const pob *n2) const
-        {return lt(n2, n1);}
+struct pob_lt_proc : public std::binary_function<const pob*, const pob*, bool> {
+    bool operator() (const pob *pn1, const pob *pn2) const;
 };
 
-struct pob_ref_gt :
-        public std::binary_function<const pob_ref&, const model_ref &, bool> {
-    pob_gt gt;
-    bool operator() (const pob_ref &n1, const pob_ref &n2) const
-        {return gt (n1.get (), n2.get ());}
+struct pob_gt_proc : public std::binary_function<const pob*, const pob*, bool> {
+    bool operator() (const pob *n1, const pob *n2) const {
+        return pob_lt_proc()(n2, n1);
+    }
 };
 
-inline unsigned lemma::weakness() {return m_pob ? m_pob->weakness() : UINT_MAX;}
 /**
  */
 class derivation {
@@ -767,36 +789,41 @@ public:
 
 
 class pob_queue {
+
+    typedef std::priority_queue<pob*, std::vector<pob*>, pob_gt_proc> pob_queue_ty;
     pob_ref  m_root;
     unsigned m_max_level;
     unsigned m_min_depth;
 
-    std::priority_queue<pob_ref, std::vector<pob_ref>,
-                        pob_ref_gt>     m_obligations;
+    pob_queue_ty  m_data;
 
 public:
     pob_queue(): m_root(nullptr), m_max_level(0), m_min_depth(0) {}
-    ~pob_queue();
+    ~pob_queue() {}
 
     void reset();
-    pob * top ();
-    void pop () {m_obligations.pop ();}
+    pob* top();
+    void pop();
     void push (pob &n);
 
     void inc_level () {
-        SASSERT (!m_obligations.empty () || m_root);
+        SASSERT (!m_data.empty () || m_root);
         m_max_level++;
         m_min_depth++;
-        if (m_root && m_obligations.empty()) { m_obligations.push(m_root); }
+        if (m_root && m_data.empty()) {
+            SASSERT(!m_root->is_in_queue());
+            m_root->set_in_queue(true);
+            m_data.push(m_root.get());
+        }
     }
 
     pob& get_root() const {return *m_root.get ();}
     void set_root(pob& n);
-    bool is_root (pob& n) const {return m_root.get () == &n;}
+    bool is_root(pob& n) const {return m_root.get () == &n;}
 
     unsigned max_level() const {return m_max_level;}
     unsigned min_depth() const {return m_min_depth;}
-    size_t size() const {return m_obligations.size();}
+    size_t size() const {return m_data.size();}
 };
 
 
@@ -910,7 +937,6 @@ class context {
     bool                 m_use_ctp;
     bool                 m_use_inc_clause;
     bool                 m_blast_term_ite;
-    bool                 m_reuse_pobs;
     bool                 m_use_ind_gen;
     bool                 m_use_array_eq_gen;
     bool                 m_validate_lemmas;
@@ -1007,7 +1033,6 @@ public:
     bool use_ctp() {return m_use_ctp;}
     bool use_inc_clause() {return m_use_inc_clause;}
     bool blast_term_ite() {return m_blast_term_ite;}
-    bool reuse_pobs() {return m_reuse_pobs;}
     bool elim_aux() {return m_elim_aux;}
     bool reach_dnf() {return m_reach_dnf;}
 
diff --git a/src/muz/spacer/spacer_iuc_solver.cpp b/src/muz/spacer/spacer_iuc_solver.cpp
index a68db4c0a..27b8ee357 100644
--- a/src/muz/spacer/spacer_iuc_solver.cpp
+++ b/src/muz/spacer/spacer_iuc_solver.cpp
@@ -322,6 +322,24 @@ void iuc_solver::get_iuc(expr_ref_vector &core)
         // -- new hypothesis reducer
         else
         {
+#if 0
+            static unsigned bcnt = 0;
+            {
+                bcnt++;
+                TRACE("spacer", tout << "Dumping pf bcnt: " << bcnt << "\n";);
+                if (bcnt == 123) {
+                    std::ofstream ofs;
+                    ofs.open("/tmp/bpf_" + std::to_string(bcnt) + ".dot");
+                    iuc_proof iuc_pf_before(m, res.get(), core_lits);
+                    iuc_pf_before.display_dot(ofs);
+                    ofs.close();
+
+                    proof_checker pc(m);
+                    expr_ref_vector side(m);
+                    ENSURE(pc.check(res, side));
+                }
+            }
+#endif
             scoped_watch _t_ (m_hyp_reduce2_sw);
 
             // pre-process proof for better iuc extraction
@@ -356,6 +374,22 @@ void iuc_solver::get_iuc(expr_ref_vector &core)
 
         iuc_proof iuc_pf(m, res, core_lits);
 
+#if 0
+        static unsigned cnt = 0;
+        {
+            cnt++;
+            TRACE("spacer", tout << "Dumping pf cnt: " << cnt << "\n";);
+            if (cnt == 123) {
+                std::ofstream ofs;
+                ofs.open("/tmp/pf_" + std::to_string(cnt) + ".dot");
+                iuc_pf.display_dot(ofs);
+                ofs.close();
+                proof_checker pc(m);
+                expr_ref_vector side(m);
+                ENSURE(pc.check(res, side));
+            }
+        }
+#endif
         unsat_core_learner learner(m, iuc_pf);
 
         unsat_core_plugin* plugin;
diff --git a/src/muz/spacer/spacer_quant_generalizer.cpp b/src/muz/spacer/spacer_quant_generalizer.cpp
index f66fe7b29..95e884d42 100644
--- a/src/muz/spacer/spacer_quant_generalizer.cpp
+++ b/src/muz/spacer/spacer_quant_generalizer.cpp
@@ -114,7 +114,7 @@ void lemma_quantifier_generalizer::find_candidates(expr *e,
     if (!contains_selects(e, m)) return;
 
     app_ref_vector indices(m);
-    get_select_indices(e, indices, m);
+    get_select_indices(e, indices);
 
     app_ref_vector extra(m);
     expr_sparse_mark marked_args;
@@ -155,7 +155,7 @@ bool lemma_quantifier_generalizer::match_sk_idx(expr *e, app_ref_vector const &z
 
     if (!contains_selects(e, m)) return false;
     app_ref_vector indicies(m);
-    get_select_indices(e, indicies, m);
+    get_select_indices(e, indicies);
     if (indicies.size() > 2) return false;
 
     unsigned i=0;
@@ -255,15 +255,17 @@ void lemma_quantifier_generalizer::cleanup(expr_ref_vector &cube, app_ref_vector
 
    lb and ub are null if no bound was found
  */
-void lemma_quantifier_generalizer::mk_abs_cube(lemma_ref &lemma, app *term, var *var,
+void lemma_quantifier_generalizer::mk_abs_cube(lemma_ref &lemma, app *term,
+                                               var *var,
                                                expr_ref_vector &gnd_cube,
                                                expr_ref_vector &abs_cube,
-                                               expr *&lb, expr *&ub, unsigned &stride) {
+                                               expr *&lb, expr *&ub,
+                                               unsigned &stride) {
 
     // create an abstraction function that maps candidate term to variables
     expr_safe_replace sub(m);
     // term -> var
-    sub.insert(term , var);
+    sub.insert(term, var);
     rational val;
     if (m_arith.is_numeral(term, val)) {
         bool is_int = val.is_int();
@@ -285,19 +287,17 @@ void lemma_quantifier_generalizer::mk_abs_cube(lemma_ref &lemma, app *term, var
 
     for (expr *lit : m_cube) {
         expr_ref abs_lit(m);
-        sub (lit,  abs_lit);
-        if (lit == abs_lit) {
-            gnd_cube.push_back(lit);
-        }
+        sub(lit, abs_lit);
+        if (lit == abs_lit) {gnd_cube.push_back(lit);}
         else {
             expr *e1, *e2;
             // generalize v=num into v>=num
             if (m.is_eq(abs_lit, e1, e2) && (e1 == var || e2 == var)) {
-            if (m_arith.is_numeral(e1)) {
-                    abs_lit = m_arith.mk_ge (var, e1);
+                if (m_arith.is_numeral(e1)) {
+                    abs_lit = m_arith.mk_ge(var, e1);
                 } else if (m_arith.is_numeral(e2)) {
                     abs_lit = m_arith.mk_ge(var, e2);
-            }
+                }
             }
             abs_cube.push_back(abs_lit);
             if (contains_selects(abs_lit, m)) {
@@ -464,7 +464,7 @@ bool lemma_quantifier_generalizer::generalize (lemma_ref &lemma, app *term) {
           if (ub) tout << mk_pp(ub, m); else tout << "none";
           tout << "\n";);
 
-    if (!lb && !ub) 
+    if (!lb && !ub)
         return false;
 
     // -- guess lower or upper bound if missing
@@ -542,46 +542,50 @@ bool lemma_quantifier_generalizer::generalize (lemma_ref &lemma, app *term) {
     return false;
 }
 
-bool lemma_quantifier_generalizer::find_stride(expr_ref_vector &c, expr_ref &pattern, unsigned &stride) {
+bool lemma_quantifier_generalizer::find_stride(expr_ref_vector &cube,
+                                               expr_ref &pattern,
+                                               unsigned &stride) {
     expr_ref tmp(m);
-    tmp = mk_and(c);
+    tmp = mk_and(cube);
     normalize(tmp, tmp, false, true);
-    c.reset();
-    flatten_and(tmp, c);
+    cube.reset();
+    flatten_and(tmp, cube);
 
     app_ref_vector indices(m);
-    get_select_indices(pattern, indices, m);
+    get_select_indices(pattern, indices);
 
-    // TODO
-    if (indices.size() > 1)
-        return false;
+    CTRACE("spacer_qgen", indices.empty(),
+           tout << "Found no select indices in: " << pattern << "\n";);
+
+    // TBD: handle multi-dimensional arrays and literals with multiple
+    // select terms
+    if (indices.size() != 1) return false;
 
     app *p_index = indices.get(0);
-    if (is_var(p_index)) return false;
 
-    std::vector<unsigned> instances;
-    for (expr* lit : c) {
+    unsigned_vector instances;
+    for (expr* lit : cube) {
 
         if (!contains_selects(lit, m))
             continue;
 
         indices.reset();
-        get_select_indices(lit, indices, m);
+        get_select_indices(lit, indices);
 
-        // TODO:
-        if (indices.size() > 1)
+        // TBD: handle multi-dimensional arrays
+        if (indices.size() != 1)
             continue;
 
         app *candidate = indices.get(0);
 
         unsigned size = p_index->get_num_args();
         unsigned matched = 0;
-        for (unsigned p=0; p < size; p++) {
+        for (unsigned p = 0; p < size; p++) {
             expr *arg = p_index->get_arg(p);
             if (is_var(arg)) {
                 rational val;
-                if (p < candidate->get_num_args() && 
-                    m_arith.is_numeral(candidate->get_arg(p), val) && 
+                if (p < candidate->get_num_args() &&
+                    m_arith.is_numeral(candidate->get_arg(p), val) &&
                     val.is_unsigned()) {
                     instances.push_back(val.get_unsigned());
                 }
diff --git a/src/muz/spacer/spacer_util.cpp b/src/muz/spacer/spacer_util.cpp
index 42b40c665..3ea0917b7 100644
--- a/src/muz/spacer/spacer_util.cpp
+++ b/src/muz/spacer/spacer_util.cpp
@@ -900,17 +900,22 @@ namespace {
     struct collect_indices {
         app_ref_vector& m_indices;
         array_util      a;
-        collect_indices(app_ref_vector& indices): m_indices(indices), a(indices.get_manager()) {}
+        collect_indices(app_ref_vector& indices): m_indices(indices),
+                                                  a(indices.get_manager()) {}
         void operator()(expr* n) {}
         void operator()(app* n) {
-            if (a.is_select(n))
-                for (unsigned i = 1; i < n->get_num_args(); ++i)
-                    if (is_app(n->get_arg(i)))
-                        m_indices.push_back(to_app(n->get_arg(i)));
+            if (a.is_select(n)) {
+                // for all but first argument
+                for (unsigned i = 1; i < n->get_num_args(); ++i) {
+                    expr *arg = n->get_arg(i);
+                    if (is_app(arg))
+                        m_indices.push_back(to_app(arg));
+                }
+            }
         }
     };
 
-    void get_select_indices(expr* fml, app_ref_vector &indices, ast_manager& m) {
+    void get_select_indices(expr* fml, app_ref_vector &indices) {
         collect_indices ci(indices);
         for_each_expr(ci, fml);
     }
diff --git a/src/muz/spacer/spacer_util.h b/src/muz/spacer/spacer_util.h
index 9912769c5..8da574d0e 100644
--- a/src/muz/spacer/spacer_util.h
+++ b/src/muz/spacer/spacer_util.h
@@ -121,7 +121,7 @@ namespace spacer {
     void mbqi_project(model &mdl, app_ref_vector &vars, expr_ref &fml);
 
     bool contains_selects (expr* fml, ast_manager& m);
-    void get_select_indices (expr* fml, app_ref_vector& indices, ast_manager& m);
+    void get_select_indices (expr* fml, app_ref_vector& indices);
 
     void find_decls (expr* fml, app_ref_vector& decls, std::string& prefix);
 
diff --git a/src/qe/qe_term_graph.cpp b/src/qe/qe_term_graph.cpp
index 5cf1206a3..e9ec3d4b7 100644
--- a/src/qe/qe_term_graph.cpp
+++ b/src/qe/qe_term_graph.cpp
@@ -200,7 +200,8 @@ namespace qe {
         }
 
         std::ostream& display(std::ostream& out) const {
-            out << get_id() << ": " << m_expr << " - ";
+            out << get_id() << ": " << m_expr 
+                << (is_root() ? " R" : "") << " - ";
             term const* r = &this->get_next();
             while (r != this) {
                 out << r->get_id() << " ";
@@ -371,20 +372,20 @@ namespace qe {
     }
 
     void term_graph::merge(term &t1, term &t2) {
-        // -- merge might invalidate term2app cache
-        m_term2app.reset();
-        m_pinned.reset();
-
         term *a = &t1.get_root();
         term *b = &t2.get_root();
 
         if (a == b) return;
 
+        // -- merge might invalidate term2app cache
+        m_term2app.reset();
+        m_pinned.reset();
+
         if (a->get_class_size() > b->get_class_size()) {
             std::swap(a, b);
         }
 
-        // Remove parents of it from the cg table.
+        // Remove parents of b from the cg table.
         for (term* p : term::parents(b)) {
             if (!p->is_marked()) {
                 p->set_mark(true);
@@ -401,7 +402,7 @@ namespace qe {
         a->merge_eq_class(*b);
 
         // Insert parents of b's old equilvalence class into the cg table
-        for (term* p : term::parents(a)) {
+        for (term* p : term::parents(b)) {
             if (p->is_marked()) {
                 term* p_old = m_cg_table.insert_if_not_there(p);
                 p->set_mark(false);
@@ -412,6 +413,7 @@ namespace qe {
                 }
             }
         }
+        SASSERT(marks_are_clear());
     }
 
     expr* term_graph::mk_app_core (expr *e) {
@@ -484,10 +486,16 @@ namespace qe {
         }
     }
 
+    bool term_graph::marks_are_clear() {
+        for (term * t : m_terms) {
+            if (t->is_marked()) return false;
+        }
+        return true;
+    }
+
     /// Order of preference for roots of equivalence classes
     /// XXX This should be factored out to let clients control the preference
     bool term_graph::term_lt(term const &t1, term const &t2) {
-
         // prefer constants over applications
         // prefer uninterpreted constants over values
         // prefer smaller expressions over larger ones
@@ -521,6 +529,7 @@ namespace qe {
 
     /// Choose better roots for equivalence classes
     void term_graph::pick_roots() {
+        SASSERT(marks_are_clear());
         for (term* t : m_terms) {
             if (!t->is_marked() && t->is_root())
                 pick_root(*t);
@@ -589,7 +598,7 @@ namespace qe {
                 // prefer a node that resembles current child, 
                 // otherwise, pick a root representative, if present.
                 if (m_term2app.find(ch->get_id(), e))
-                    kids.push_back(e);
+                kids.push_back(e);
                 else if (m_root2rep.find(ch->get_root().get_id(), e)) 
                     kids.push_back(e);
                 else 
diff --git a/src/qe/qe_term_graph.h b/src/qe/qe_term_graph.h
index 2ab234a96..0c66f4193 100644
--- a/src/qe/qe_term_graph.h
+++ b/src/qe/qe_term_graph.h
@@ -75,6 +75,7 @@ namespace qe {
         void pick_roots();
 
         void reset_marks();
+        bool marks_are_clear();
 
         expr* mk_app_core(expr* a);
         expr_ref mk_app(term const &t);
diff --git a/src/solver/solver_pool.cpp b/src/solver/solver_pool.cpp
index 9dacfb5ce..598bb6c02 100644
--- a/src/solver/solver_pool.cpp
+++ b/src/solver/solver_pool.cpp
@@ -101,9 +101,11 @@ public:
     proof * get_proof() override {
         scoped_watch _t_(m_pool.m_proof_watch);
         if (!m_proof.get()) {
-            elim_aux_assertions pc(m_pred);
             m_proof = m_base->get_proof();
-            pc(m, m_proof, m_proof);
+            if (m_proof) {
+                elim_aux_assertions pc(m_pred);
+                pc(m, m_proof, m_proof);
+            }
         }
         return m_proof;
     }