diff --git a/src/smt/mam.cpp b/src/smt/mam.cpp
index ea2f50263..c71a6e21d 100644
--- a/src/smt/mam.cpp
+++ b/src/smt/mam.cpp
@@ -1847,7 +1847,10 @@ namespace smt {
         enode *             m_n2;
         enode *             m_app;
         const bind *        m_b;
-        ptr_vector<enode>   m_used_enodes;
+
+        // equalities used for pattern match. The first element of the tuple gives the argument (or null) of some term that was matched against some higher level
+        // structure of the trigger, the second element gives the term that argument is replaced with in order to match the trigger. Used for logging purposes only.
+        vector<std::tuple<enode *, enode *>> m_used_enodes;
         unsigned            m_curr_used_enodes_size;
         ptr_vector<enode>   m_pattern_instances; // collect the pattern instances... used for computing min_top_generation and max_top_generation
         unsigned_vector     m_min_top_generation, m_max_top_generation;
@@ -1864,11 +1867,11 @@ namespace smt {
             m_pool.recycle(v);
         }
 
-        void update_max_generation(enode * n) {
+        void update_max_generation(enode * n, enode * prev) {
             m_max_generation = std::max(m_max_generation, n->get_generation());
 
             if (m_ast_manager.has_trace_stream())
-                m_used_enodes.push_back(n);
+                m_used_enodes.push_back(std::make_tuple(prev, n));
         }
 
         // We have to provide the number of expected arguments because we have flat-assoc applications such as +.
@@ -1877,7 +1880,7 @@ namespace smt {
             enode * first = curr;
             do {
                 if (curr->get_decl() == lbl && curr->is_cgr() && curr->get_num_args() == num_expected_args) {
-                    update_max_generation(curr);
+                    update_max_generation(curr, first);
                     return curr;
                 }
                 curr = curr->get_next();
@@ -1890,7 +1893,7 @@ namespace smt {
             curr = curr->get_next();
             while (curr != first) {
                 if (curr->get_decl() == lbl && curr->is_cgr() && curr->get_num_args() == num_expected_args) {
-                    update_max_generation(curr);
+                    update_max_generation(curr, first);
                     return curr;
                 }
                 curr = curr->get_next();
@@ -1914,7 +1917,7 @@ namespace smt {
                 do {
                     if (n->get_decl() == f &&
                         n->get_arg(0)->get_root() == m_args[0]) {
-                        update_max_generation(n);
+                        update_max_generation(n, first);
                         return true;
                     }
                     n = n->get_next();
@@ -1929,7 +1932,7 @@ namespace smt {
                     if (n->get_decl() == f &&
                         n->get_arg(0)->get_root() == m_args[0] &&
                         n->get_arg(1)->get_root() == m_args[1]) {
-                        update_max_generation(n);
+                        update_max_generation(n, first);
                         return true;
                     }
                     n = n->get_next();
@@ -1949,7 +1952,7 @@ namespace smt {
                                 break;
                         }
                         if (i == num_args) {
-                            update_max_generation(n);
+                            update_max_generation(n, first);
                             return true;
                         }
                     }
@@ -2196,7 +2199,7 @@ namespace smt {
         if (bp.m_it == bp.m_end)
             return nullptr;
         m_top++;
-        update_max_generation(*(bp.m_it));
+        update_max_generation(*(bp.m_it), nullptr);
         return *(bp.m_it);
     }
 
@@ -2277,7 +2280,7 @@ namespace smt {
 
         if (m_ast_manager.has_trace_stream()) {
             m_used_enodes.reset();
-            m_used_enodes.push_back(n);
+            m_used_enodes.push_back(std::make_tuple(nullptr, n)); // null indicates that n was matched against the trigger at the top-level
         }
 
         m_pc             = t->get_root();
@@ -2382,6 +2385,10 @@ namespace smt {
             SASSERT(m_n2 != 0);
             if (m_n1->get_root() != m_n2->get_root())
                 goto backtrack;
+
+            // we used the equality m_n1 = m_n2 for the match and need to make sure it ends up in the log
+            m_used_enodes.push_back(std::make_tuple(m_n1, m_n2));
+
             m_pc = m_pc->m_next;
             goto main_loop;
 
@@ -2776,7 +2783,7 @@ namespace smt {
                     m_pattern_instances.pop_back();
                     m_pattern_instances.push_back(m_app);
                     // continue succeeded
-                    update_max_generation(m_app);
+                    update_max_generation(m_app, nullptr); // null indicates a top-level match
                     TRACE("mam_int", tout << "continue next candidate:\n" << mk_ll_pp(m_app->get_owner(), m_ast_manager););
                     m_num_args = c->m_num_args;
                     m_oreg     = c->m_oreg;
@@ -3878,7 +3885,7 @@ namespace smt {
         }
 #endif
 
-        void on_match(quantifier * qa, app * pat, unsigned num_bindings, enode * const * bindings, unsigned max_generation, ptr_vector<enode> & used_enodes) override {
+        void on_match(quantifier * qa, app * pat, unsigned num_bindings, enode * const * bindings, unsigned max_generation, vector<std::tuple<enode *, enode *>> & used_enodes) override {
             TRACE("trigger_bug", tout << "found match " << mk_pp(qa, m_ast_manager) << "\n";);
 #ifdef Z3DEBUG
             if (m_check_missing_instances) {
diff --git a/src/smt/mam.h b/src/smt/mam.h
index 635cb30e7..f6b2958c5 100644
--- a/src/smt/mam.h
+++ b/src/smt/mam.h
@@ -21,6 +21,7 @@ Revision History:
 
 #include "ast/ast.h"
 #include "smt/smt_types.h"
+#include <tuple>
 
 namespace smt {
     /**
@@ -57,7 +58,7 @@ namespace smt {
 
         virtual void display(std::ostream& out) = 0;
         
-        virtual void on_match(quantifier * q, app * pat, unsigned num_bindings, enode * const * bindings, unsigned max_generation, ptr_vector<enode> & used_enodes) = 0;
+        virtual void on_match(quantifier * q, app * pat, unsigned num_bindings, enode * const * bindings, unsigned max_generation, vector<std::tuple<enode *, enode *>> & used_enodes) = 0;
         
         virtual bool is_shared(enode * n) const = 0;
 
diff --git a/src/smt/smt_context.cpp b/src/smt/smt_context.cpp
index ac6482b95..70b55acee 100644
--- a/src/smt/smt_context.cpp
+++ b/src/smt/smt_context.cpp
@@ -562,6 +562,7 @@ namespace smt {
             invert_trans(n1);
             n1->m_trans.m_target        = n2;
             n1->m_trans.m_justification = js;
+            n1->m_proof_logged_status   = smt::logged_status::NOT_LOGGED;
             SASSERT(r1->trans_reaches(n1));
             // ---------------
             // r1 -> ..  -> n1 -> n2 -> ... -> r2
@@ -741,12 +742,14 @@ namespace smt {
         eq_justification js               = n->m_trans.m_justification;
         prev->m_trans.m_target            = nullptr;
         prev->m_trans.m_justification     = null_eq_justification;
+        prev->m_proof_logged_status       = smt::logged_status::NOT_LOGGED;
         while (curr != nullptr) {
             SASSERT(prev->trans_reaches(n));
             enode * new_curr              = curr->m_trans.m_target;
             eq_justification new_js       = curr->m_trans.m_justification;
             curr->m_trans.m_target        = prev;
             curr->m_trans.m_justification = js;
+            curr->m_proof_logged_status   = smt::logged_status::NOT_LOGGED;
             prev                          = curr;
             js                            = new_js;
             curr                          = new_curr;
@@ -1040,6 +1043,7 @@ namespace smt {
         SASSERT(r1->trans_reaches(n1));
         n1->m_trans.m_target        = nullptr;
         n1->m_trans.m_justification = null_eq_justification;
+        n1->m_proof_logged_status   = smt::logged_status::NOT_LOGGED;
         invert_trans(r1);
         // ---------------
         // n1 -> ... -> r1
@@ -1786,7 +1790,7 @@ namespace smt {
     }
 
     bool context::add_instance(quantifier * q, app * pat, unsigned num_bindings, enode * const * bindings, expr* def, unsigned max_generation,
-                               unsigned min_top_generation, unsigned max_top_generation, ptr_vector<enode> & used_enodes) {
+                               unsigned min_top_generation, unsigned max_top_generation, vector<std::tuple<enode *, enode *>> & used_enodes) {
         return m_qmanager->add_instance(q, pat, num_bindings, bindings, def, max_generation, min_top_generation, max_top_generation, used_enodes);
     }
 
diff --git a/src/smt/smt_context.h b/src/smt/smt_context.h
index 4f7c8073e..77b4ca79c 100644
--- a/src/smt/smt_context.h
+++ b/src/smt/smt_context.h
@@ -49,6 +49,7 @@ Revision History:
 #include "util/timer.h"
 #include "util/statistics.h"
 #include "solver/progress_callback.h"
+#include <tuple>
 
 // there is a significant space overhead with allocating 1000+ contexts in
 // the case that each context only references a few expressions.
@@ -970,7 +971,7 @@ namespace smt {
         bool contains_instance(quantifier * q, unsigned num_bindings, enode * const * bindings);
 
         bool add_instance(quantifier * q, app * pat, unsigned num_bindings, enode * const * bindings, expr* def, unsigned max_generation,
-                          unsigned min_top_generation, unsigned max_top_generation, ptr_vector<enode> & used_enodes);
+                          unsigned min_top_generation, unsigned max_top_generation, vector<std::tuple<enode *, enode*>> & used_enodes /*gives the equalities used for the pattern match, see mam.cpp for more info*/);
 
         void set_global_generation(unsigned generation) { m_generation = generation; }
 
diff --git a/src/smt/smt_context_pp.cpp b/src/smt/smt_context_pp.cpp
index 29c624bb2..3a2aacd26 100644
--- a/src/smt/smt_context_pp.cpp
+++ b/src/smt/smt_context_pp.cpp
@@ -577,7 +577,7 @@ namespace smt {
         case b_justification::BIN_CLAUSE: {
             literal l2 = j.get_literal();
             out << "bin-clause ";
-            display_literal_verbose(out, l2);
+            display_literal(out, l2);
             break;
         }
         case b_justification::CLAUSE: {
@@ -590,7 +590,7 @@ namespace smt {
             out << "justification " << j.get_justification()->get_from_theory() << ": ";
             literal_vector lits;
             const_cast<conflict_resolution&>(*m_conflict_resolution).justification2literals(j.get_justification(), lits);
-            display_literals_verbose(out, lits);
+            display_literals(out, lits);
             break;
         }
         default:
diff --git a/src/smt/smt_enode.cpp b/src/smt/smt_enode.cpp
index e09e83f6b..ca646974d 100644
--- a/src/smt/smt_enode.cpp
+++ b/src/smt/smt_enode.cpp
@@ -47,6 +47,7 @@ namespace smt {
         n->m_cgc_enabled      = cgc_enabled;
         n->m_iscope_lvl       = iscope_lvl;
         n->m_lbl_hash         = -1;
+        n->m_proof_logged_status = smt::logged_status::NOT_LOGGED;
         unsigned num_args     = n->get_num_args();
         for (unsigned i = 0; i < num_args; i++) {
             enode * arg  = app2enode[owner->get_arg(i)->get_id()];
diff --git a/src/smt/smt_enode.h b/src/smt/smt_enode.h
index 6c8d156b4..61fed786b 100644
--- a/src/smt/smt_enode.h
+++ b/src/smt/smt_enode.h
@@ -38,6 +38,15 @@ namespace smt {
         }
     };
 
+    /**
+       \brief Indicates whether the proof for membership in an equivalence class is already logged.
+    */
+    enum logged_status {
+        NOT_LOGGED, //!< Proof is not logged or logged information is not up-to-date.
+        BEING_LOGGED, //!< We are currently in the process of logging all relevant information. This is used to prevent looping when logging congruence steps.
+        LOGGED //!< Proof is logged and logged information is still up-to-date.
+    };
+
     /** \ brief Use sparse maps in SMT solver.
 
     Define this to use hash maps rather than vectors over ast
@@ -105,6 +114,7 @@ namespace smt {
         enode_vector        m_parents;          //!< Parent enodes of the equivalence class.
         theory_var_list     m_th_var_list;      //!< List of theories that 'care' about this enode.
         trans_justification m_trans;            //!< A justification for the enode being equal to its root.
+        logged_status       m_proof_logged_status;  //!< Indicates that the proof for the enode being equal to its root is in the log.
         signed char         m_lbl_hash;         //!< It is different from -1, if enode is used in a pattern
         approx_set          m_lbls;
         approx_set          m_plbls;
@@ -113,6 +123,7 @@ namespace smt {
         friend class context;
         friend class euf_manager;
         friend class conflict_resolution;
+        friend class quantifier_manager;
         
 
         theory_var_list * get_th_var_list() { 
@@ -361,6 +372,10 @@ namespace smt {
 
         theory_var get_th_var(theory_id th_id) const;
 
+        trans_justification get_trans_justification() {
+            return m_trans;
+        }
+
         unsigned get_generation() const {
             return m_generation;
         }
diff --git a/src/smt/smt_model_checker.cpp b/src/smt/smt_model_checker.cpp
index 06dd04846..f4c5c09d9 100644
--- a/src/smt/smt_model_checker.cpp
+++ b/src/smt/smt_model_checker.cpp
@@ -33,6 +33,7 @@ Revision History:
 #include "smt/smt_context.h"
 #include "smt/smt_model_finder.h"
 #include "model/model_pp.h"
+#include <tuple>
 
 namespace smt {
 
@@ -518,7 +519,7 @@ namespace smt {
     void model_checker::assert_new_instances() {
         TRACE("model_checker_bug_detail", tout << "assert_new_instances, inconsistent: " << m_context->inconsistent() << "\n";);
         ptr_buffer<enode> bindings;
-        ptr_vector<enode> dummy;
+        vector<std::tuple<enode *, enode *>> dummy;
         for (instance const& inst : m_new_instances) {
             quantifier * q  = inst.m_q;
             if (m_context->b_internalized(q)) {
diff --git a/src/smt/smt_quantifier.cpp b/src/smt/smt_quantifier.cpp
index 48c59003c..885157ab3 100644
--- a/src/smt/smt_quantifier.cpp
+++ b/src/smt/smt_quantifier.cpp
@@ -104,6 +104,90 @@ namespace smt {
             return m_plugin->is_shared(n);
         }
 
+        /**
+           \brief Ensures that all relevant proof steps to explain why the enode is equal to the root of its
+           equivalence class are in the log and up-to-date.
+        */
+        void log_justification_to_root(std::ostream & log, enode *en) {
+            enode *root = en->get_root();
+            for (enode *it = en; it != root; it = it->get_trans_justification().m_target) {
+                if (it->m_proof_logged_status == smt::logged_status::NOT_LOGGED) {
+                    it->m_proof_logged_status = smt::logged_status::BEING_LOGGED;
+                    log_single_justification(log, it);
+                    it->m_proof_logged_status = smt::logged_status::LOGGED;
+                } else if (it->m_proof_logged_status != smt::logged_status::BEING_LOGGED && it->get_trans_justification().m_justification.get_kind() == smt::eq_justification::kind::CONGRUENCE) {
+
+                    // When the justification of an argument changes m_proof_logged_status is not reset => We need to check if the proofs of all arguments are logged.
+                    it->m_proof_logged_status = smt::logged_status::BEING_LOGGED;
+                    const unsigned num_args = it->get_num_args();
+                    enode *target = it->get_trans_justification().m_target;
+
+                    for (unsigned i = 0; i < num_args; ++i) {
+                        log_justification_to_root(log, it->get_arg(i));
+                        log_justification_to_root(log, target->get_arg(i));
+                    }
+                    it->m_proof_logged_status = smt::logged_status::LOGGED;
+                }
+            }
+            if (root->m_proof_logged_status == smt::logged_status::NOT_LOGGED) {
+                log << "[eq-expl] #" << root->get_owner_id() << " root\n";
+                root->m_proof_logged_status = smt::logged_status::LOGGED;
+            }
+        }
+
+        /**
+          \brief Logs a single equality explanation step and, if necessary, recursively calls log_justification_to_root to log
+          equalities needed by the step (e.g. argument equalities for congruence steps).
+        */
+        void log_single_justification(std::ostream & out, enode *en) {
+            smt::literal lit;
+            unsigned num_args;
+            enode *target = en->get_trans_justification().m_target;
+            theory_id th_id;
+
+            switch (en->get_trans_justification().m_justification.get_kind()) {
+            case smt::eq_justification::kind::EQUATION:
+                lit = en->get_trans_justification().m_justification.get_literal();
+                out << "[eq-expl] #" << en->get_owner_id() << " lit #" << m_context.bool_var2expr(lit.var())->get_id() << " ; #" << target->get_owner_id() << "\n";
+                break;
+            case smt::eq_justification::kind::AXIOM:
+                out << "[eq-expl] #" << en->get_owner_id() << " ax ; #" << target->get_owner_id() << "\n";
+                break;
+            case smt::eq_justification::kind::CONGRUENCE:
+                if (!en->get_trans_justification().m_justification.used_commutativity()) {
+                    num_args = en->get_num_args();
+
+                    for (unsigned i = 0; i < num_args; ++i) {
+                        log_justification_to_root(out, en->get_arg(i));
+                        log_justification_to_root(out, target->get_arg(i));
+                    }
+
+                    out << "[eq-expl] #" << en->get_owner_id() << " cg";
+                    for (unsigned i = 0; i < num_args; ++i) {
+                        out << " (#" << en->get_arg(i)->get_owner_id() << " #" << target->get_arg(i)->get_owner_id() << ")";
+                    }
+                    out << " ; #" << target->get_owner_id() << "\n";
+
+                    break;
+                } else {
+                    out << "[eq-expl] #" << en->get_owner_id() << " nyi ; #" << target->get_owner_id() << "\n";
+                    break;
+                }
+            case smt::eq_justification::kind::JUSTIFICATION:
+                th_id = en->get_trans_justification().m_justification.get_justification()->get_from_theory();
+                if (th_id != null_theory_id) {
+                    symbol const theory = m().get_family_name(th_id);
+                    out << "[eq-expl] #" << en->get_owner_id() << " th " << theory.str() << " ; #" << target->get_owner_id() << "\n";
+                } else {
+                    out << "[eq-expl] #" << en->get_owner_id() << " unknown ; #" << target->get_owner_id() << "\n";
+                }
+                break;
+            default:
+                out << "[eq-expl] #" << en->get_owner_id() << " unknown ; #" << target->get_owner_id() << "\n";
+                break;
+            }
+        }
+
         bool add_instance(quantifier * q, app * pat,
                           unsigned num_bindings,
                           enode * const * bindings,
@@ -111,7 +195,7 @@ namespace smt {
                           unsigned max_generation,
                           unsigned min_top_generation,
                           unsigned max_top_generation,
-                          ptr_vector<enode> & used_enodes) {
+                          vector<std::tuple<enode *, enode *>> & used_enodes) {
             max_generation = std::max(max_generation, get_generation(q));
             if (m_num_instances > m_params.m_qi_max_instances) {
                 return false;
@@ -121,15 +205,39 @@ namespace smt {
             if (f) {
                 if (has_trace_stream()) {
                     std::ostream & out = trace_stream();
-                    out << "[new-match] " << static_cast<void*>(f) << " #" << q->get_id();
+
+                    // In the term produced by the quantifier instantiation the root of the equivalence class of the terms bound to the quantified variables
+                    // is used. We need to make sure that all of these equalities appear in the log.
+                    for (unsigned i = 0; i < num_bindings; ++i) {
+                        log_justification_to_root(out, bindings[i]);
+                    }
+
+                    for (auto n : used_enodes) {
+                        enode *orig = std::get<0>(n);
+                        enode *substituted = std::get<1>(n);
+                        if (orig != nullptr) {
+                            log_justification_to_root(out, orig);
+                            log_justification_to_root(out, substituted);
+                        }
+                    }
+
+                    // At this point all relevant equalities for the match are logged.
+                    out << "[new-match] " << static_cast<void*>(f) << " #" << q->get_id() << " #" << pat->get_id();
                     for (unsigned i = 0; i < num_bindings; i++) {
                         // I don't want to use mk_pp because it creates expressions for pretty printing.
                         // This nasty side-effect may change the behavior of Z3.
                         out << " #" << bindings[i]->get_owner_id();
                     }
                     out << " ;";
-                    for (enode* n : used_enodes) 
-                        out << " #" << n->get_owner_id();
+                    for (auto n : used_enodes) {
+                        enode *orig = std::get<0>(n);
+                        enode *substituted = std::get<1>(n);
+                        if (orig == nullptr)
+                            out << " #" << substituted->get_owner_id();
+                        else {
+                            out << " (#" << orig->get_owner_id() << " #" << substituted->get_owner_id() << ")";
+                        }
+                    }
                     out << "\n";
                 }
                 m_qi_queue.insert(f, pat, max_generation, min_top_generation, max_top_generation); // TODO
@@ -296,12 +404,12 @@ namespace smt {
                                           unsigned max_generation,
                                           unsigned min_top_generation,
                                           unsigned max_top_generation,
-                                          ptr_vector<enode> & used_enodes) {
+                                          vector<std::tuple<enode *, enode *>> & used_enodes) {
         return m_imp->add_instance(q, pat, num_bindings, bindings, def, max_generation, min_top_generation, max_generation, used_enodes);
     }
 
     bool quantifier_manager::add_instance(quantifier * q, unsigned num_bindings, enode * const * bindings, expr* def, unsigned generation) {
-        ptr_vector<enode> tmp;
+        vector<std::tuple<enode *, enode *>> tmp;
         return add_instance(q, nullptr, num_bindings, bindings, def, generation, generation, generation, tmp);
     }
 
diff --git a/src/smt/smt_quantifier.h b/src/smt/smt_quantifier.h
index dde7ec2c4..4f14c6853 100644
--- a/src/smt/smt_quantifier.h
+++ b/src/smt/smt_quantifier.h
@@ -23,6 +23,7 @@ Revision History:
 #include "util/statistics.h"
 #include "util/params.h"
 #include "smt/smt_types.h"
+#include <tuple>
 
 class proto_model;
 struct smt_params;
@@ -58,7 +59,7 @@ namespace smt {
                           unsigned max_generation,
                           unsigned min_top_generation,
                           unsigned max_top_generation,
-                          ptr_vector<enode> & used_enodes);
+                          vector<std::tuple<enode *, enode *>> & used_enodes /*gives the equalities used for the pattern match, see mam.cpp for more info*/);
         bool add_instance(quantifier * q, unsigned num_bindings, enode * const * bindings, expr* def, unsigned generation = 0);
 
         void init_search_eh();
diff --git a/src/smt/smt_quick_checker.cpp b/src/smt/smt_quick_checker.cpp
index 85c0ca183..14719c140 100644
--- a/src/smt/smt_quick_checker.cpp
+++ b/src/smt/smt_quick_checker.cpp
@@ -19,6 +19,7 @@ Revision History:
 #include "smt/smt_context.h"
 #include "smt/smt_quick_checker.h"
 #include "ast/ast_pp.h"
+#include <tuple>
 
 namespace smt {
 
@@ -197,7 +198,7 @@ namespace smt {
     }
 
     bool quick_checker::process_candidates(quantifier * q, bool unsat) {
-        ptr_vector<enode> empty_used_enodes;
+        vector<std::tuple<enode *, enode *>> empty_used_enodes;
         buffer<unsigned> szs;
         buffer<unsigned> it;
         for (unsigned i = 0; i < m_num_bindings; i++) {