diff --git a/src/muz/spacer/spacer_context.cpp b/src/muz/spacer/spacer_context.cpp
index 04f5834aa..05e8eeb70 100644
--- a/src/muz/spacer/spacer_context.cpp
+++ b/src/muz/spacer/spacer_context.cpp
@@ -2938,7 +2938,7 @@ expr_ref context::mk_unsat_answer() const
 }
 
 
-proof_ref context::get_ground_refutation() {
+proof_ref context::get_ground_refutation() const {
     if (m_last_result != l_true) {
         IF_VERBOSE(0, verbose_stream()
                    << "Sat answer unavailable when result is false\n";);
@@ -2948,142 +2948,45 @@ proof_ref context::get_ground_refutation() {
     ground_sat_answer_op op(*this);
     return op(*m_query);
 }
-expr_ref context::get_ground_sat_answer()  {
+
+expr_ref context::get_ground_sat_answer() const {
     if (m_last_result != l_true) {
         IF_VERBOSE(0, verbose_stream()
                    << "Sat answer unavailable when result is false\n";);
         return expr_ref(m);
     }
 
-    // treat the following as queues: read from left to right and insert at the right
-    reach_fact_ref_vector reach_facts;
-    ptr_vector<func_decl> preds;
-    ptr_vector<pred_transformer> pts;
-    expr_ref_vector cex (m); // pre-order list of ground instances of predicates
-    expr_ref_vector cex_facts (m); // equalities for the ground cex using signature constants
+    // convert a ground refutation into a linear counterexample
+    // only works for linear CHC systems
+    expr_ref_vector cex(m);
+    proof_ref pf = get_ground_refutation();
 
-    // temporary
-    reach_fact *reach_fact;
-    pred_transformer* pt;
-    expr_ref cex_fact (m);
-    datalog::rule const* r;
-
-    // get and discard query rule
-    reach_fact = m_query->get_last_rf ();
-    r = &reach_fact->get_rule ();
-
-    // initialize queues
-    reach_facts.append (reach_fact->get_justifications ());
-    if (reach_facts.size() != 1) {
-        // XXX Escape if an assertion is about to fail
-        IF_VERBOSE(1,
-                   verbose_stream () <<
-                   "Warning: counterexample is trivial or non-existent\n";);
-        return expr_ref(m.mk_true(), m);
+    proof_ref_vector premises(m);
+    expr_ref conclusion(m);
+    svector<std::pair<unsigned, unsigned>> positions;
+    vector<expr_ref_vector> substs;
+    unsigned count = 0;
+    while (m.is_hyper_resolve(pf, premises, conclusion, positions, substs)) {
+        // skip the first fact since it is query!X introduced by the encoding
+        // and not a user-visible predicate
+        if (count++ > 0)
+            cex.push_back(m.get_fact(pf));
+        if (premises.size() > 1) {
+            SASSERT(premises.size() == 2 && "Non linear CHC detected");
+            pf = premises.get(1);
+        } else {
+            pf.reset();
+            break;
     }
-    m_query->find_predecessors (*r, preds);
-    SASSERT (preds.size () == 1);
-    pts.push_back (&(get_pred_transformer (preds[0])));
-    cex_facts.push_back (m.mk_true ());
 
-    // XXX a hack to avoid assertion when query predicate is not nullary
-    if (preds[0]->get_arity () == 0)
-    { cex.push_back(m.mk_const(preds[0])); }
-
-    // smt context to obtain local cexes
-    ref<solver> cex_ctx =
-        mk_smt_solver(m, params_ref::get_empty(), symbol::null);
-
-    bool first = true;
-    // preorder traversal of the query derivation tree
-    for (unsigned curr = 0; curr < pts.size (); curr++) {
-        // pick next pt, fact, and cex_fact
-        pt = pts.get (curr);
-        reach_fact = reach_facts[curr];
-
-        cex_fact = cex_facts.get (curr);
-
-        ptr_vector<pred_transformer> child_pts;
-
-        // get justifying rule and child facts for the derivation of reach_fact at pt
-        r = &reach_fact->get_rule ();
-        const reach_fact_ref_vector &child_reach_facts =
-            reach_fact->get_justifications ();
-        // get child pts
-        preds.reset();
-        pt->find_predecessors(*r, preds);
-
-        for (unsigned j = 0; j < preds.size (); j++) {
-            child_pts.push_back (&(get_pred_transformer (preds[j])));
-        }
-        // update the queues
-        reach_facts.append (child_reach_facts);
-        pts.append (child_pts);
-
-        // update cex and cex_facts by making a local sat check:
-        // check consistency of reach facts of children, rule body, and cex_fact
-        cex_ctx->push ();
-        cex_ctx->assert_expr (cex_fact);
-        unsigned u_tail_sz = r->get_uninterpreted_tail_size ();
-        SASSERT (child_reach_facts.size () == u_tail_sz);
-        for (unsigned i = 0; i < u_tail_sz; i++) {
-            expr_ref ofml (m);
-            m_pm.formula_n2o(child_reach_facts[i]->get(), ofml, i);
-            cex_ctx->assert_expr (ofml);
-        }
-        cex_ctx->assert_expr(pt->transition());
-        cex_ctx->assert_expr(pt->rule2tag(r));
-        TRACE("cex", cex_ctx->display(tout););
-        lbool res = cex_ctx->check_sat(0, nullptr);
-        CTRACE("cex", res == l_false,
-               tout << "Cex fact: " << mk_pp(cex_fact, m) << "\n";
-               for (unsigned i = 0; i < u_tail_sz; i++)
-                   tout << "Pre" << i << " "
-                        << mk_pp(child_reach_facts[i]->get(), m) << "\n";
-               tout << "Rule: ";
-               get_datalog_context().get_rule_manager().display_smt2(*r, tout) << "\n";
-            );
-        VERIFY (res == l_true);
-        model_ref local_mdl;
-        cex_ctx->get_model (local_mdl);
-        cex_ctx->pop (1);
-        local_mdl->set_model_completion(true);
-        if (first) {
-            unsigned sig_size = pt->sig_size();
-            expr_ref_vector ground_fact_conjs(m);
-            expr_ref_vector ground_arg_vals(m);
-            for (unsigned j = 0; j < sig_size; j++) {
-                expr_ref sig_arg(m), sig_val(m);
-                sig_arg = m.mk_const (m_pm.o2n(pt->sig(j), 0));
-                sig_val = (*local_mdl)(sig_arg);
-                ground_arg_vals.push_back(sig_val);
-            }
-            cex.push_back(m.mk_app(pt->head(), sig_size, ground_arg_vals.c_ptr()));            
-            first = false;
-        }
-        for (unsigned i = 0; i < child_pts.size(); i++) {
-            pred_transformer& ch_pt = *(child_pts.get(i));
-            unsigned sig_size = ch_pt.sig_size();
-            expr_ref_vector ground_fact_conjs(m);
-            expr_ref_vector ground_arg_vals(m);
-            for (unsigned j = 0; j < sig_size; j++) {
-                expr_ref sig_arg(m), sig_val(m);
-                sig_arg = m.mk_const (m_pm.o2o(ch_pt.sig(j), 0, i));
-                sig_val = (*local_mdl)(sig_arg);
-                ground_fact_conjs.push_back(m.mk_eq(sig_arg, sig_val));
-                ground_arg_vals.push_back(sig_val);
-            }
-            if (!ground_fact_conjs.empty()) {
-                expr_ref ground_fact(m);
-                ground_fact = mk_and(ground_fact_conjs);
-                m_pm.formula_o2n(ground_fact, ground_fact, i);
-                cex_facts.push_back (ground_fact);
-            } else {
-                cex_facts.push_back (m.mk_true ());
-            }
-            cex.push_back(m.mk_app(ch_pt.head(),
-                                   sig_size, ground_arg_vals.c_ptr()));
+        premises.reset();
+        conclusion.reset();
+        positions.reset();
+        substs.reset();
         }
+    SASSERT(!pf || !m.is_hyper_resolve(pf));
+    if (pf) {
+        cex.push_back(m.get_fact(pf));
     }
 
     TRACE ("spacer", tout << "ground cex\n" << cex << "\n";);
@@ -3091,7 +2994,7 @@ expr_ref context::get_ground_sat_answer()  {
     return mk_and(cex);
 }
 
-void context::display_certificate(std::ostream &out)  {
+void context::display_certificate(std::ostream &out) const {
     switch(m_last_result) {
     case l_false:
         out << mk_pp(mk_unsat_answer(), m);
diff --git a/src/muz/spacer/spacer_context.h b/src/muz/spacer/spacer_context.h
index cb9063c52..76813895c 100644
--- a/src/muz/spacer/spacer_context.h
+++ b/src/muz/spacer/spacer_context.h
@@ -1006,7 +1006,7 @@ class context {
     /**
        \brief Retrieve satisfying assignment with explanation.
     */
-    expr_ref mk_sat_answer() {return get_ground_sat_answer();}
+    expr_ref mk_sat_answer() const {return get_ground_sat_answer();}
     expr_ref mk_unsat_answer() const;
     unsigned get_cex_depth ();
 
@@ -1065,6 +1065,7 @@ public:
 
     ast_manager&      get_ast_manager() const {return m;}
     manager&          get_manager() {return m_pm;}
+    const manager &   get_manager() const {return m_pm;}
     decl2rel const&   get_pred_transformers() const {return m_rels;}
     pred_transformer& get_pred_transformer(func_decl* p) const {return *m_rels.find(p);}
 
@@ -1082,8 +1083,8 @@ public:
      * get bottom-up (from query) sequence of ground predicate instances
      * (for e.g. P(0,1,0,0,3)) that together form a ground derivation to query
      */
-    expr_ref get_ground_sat_answer ();
-    proof_ref get_ground_refutation();
+    expr_ref get_ground_sat_answer () const;
+    proof_ref get_ground_refutation() const;
     void get_rules_along_trace (datalog::rule_ref_vector& rules);
 
     void collect_statistics(statistics& st) const;
@@ -1091,7 +1092,7 @@ public:
     void reset();
 
     std::ostream& display(std::ostream& out) const;
-    void display_certificate(std::ostream& out);
+    void display_certificate(std::ostream& out) const;
 
     pob& get_root() const {return m_pob_queue.get_root();}
     void set_query(func_decl* q) {m_query_pred = q;}
diff --git a/src/muz/spacer/spacer_sat_answer.cpp b/src/muz/spacer/spacer_sat_answer.cpp
index 30241230f..7b54260f5 100644
--- a/src/muz/spacer/spacer_sat_answer.cpp
+++ b/src/muz/spacer/spacer_sat_answer.cpp
@@ -1,7 +1,7 @@
 #include "muz/spacer/spacer_sat_answer.h"
 #include "muz/base/dl_context.h"
 #include "muz/base/dl_rule.h"
-
+#include "ast/scoped_proof.h"
 #include "smt/smt_solver.h"
 
 namespace spacer {
@@ -44,15 +44,16 @@ struct ground_sat_answer_op::frame {
     pred_transformer &pt() {return m_pt;}
 };
 
-ground_sat_answer_op::ground_sat_answer_op(context &ctx) :
+ground_sat_answer_op::ground_sat_answer_op(const context &ctx) :
     m_ctx(ctx), m(m_ctx.get_ast_manager()), m_pm(m_ctx.get_manager()),
     m_pinned(m) {
-    m_solver = mk_smt_solver(m, params_ref::get_empty(), symbol::null);
 }
 
 proof_ref ground_sat_answer_op::operator()(pred_transformer &query) {
+    // -- turn on proof mode so that proof constructing API in ast_manager work correctly
+    scoped_proof _pf(m);
 
-
+    m_solver = mk_smt_solver(m, params_ref::get_empty(), symbol::null);
     vector<frame> todo, new_todo;
 
     // -- find substitution for a query if query is not nullary
diff --git a/src/muz/spacer/spacer_sat_answer.h b/src/muz/spacer/spacer_sat_answer.h
index 6cfd3b14c..daf2e5da0 100644
--- a/src/muz/spacer/spacer_sat_answer.h
+++ b/src/muz/spacer/spacer_sat_answer.h
@@ -29,9 +29,9 @@ Revision History:
 namespace spacer {
 
 class ground_sat_answer_op {
-    context &m_ctx;
+    const context &m_ctx;
     ast_manager &m;
-    manager &m_pm;
+    const manager &m_pm;
 
     expr_ref_vector m_pinned;
     obj_map<expr, proof*> m_cache;
@@ -46,7 +46,7 @@ class ground_sat_answer_op {
                                    model_ref &mdl, expr_ref_vector &subst);
 
 public:
-    ground_sat_answer_op(context &ctx);
+    ground_sat_answer_op(const context &ctx);
 
     proof_ref operator() (pred_transformer &query);
 };