diff --git a/src/cmd_context/extra_cmds/proof_cmds.cpp b/src/cmd_context/extra_cmds/proof_cmds.cpp
index c95e5cc18..e464e6ecb 100644
--- a/src/cmd_context/extra_cmds/proof_cmds.cpp
+++ b/src/cmd_context/extra_cmds/proof_cmds.cpp
@@ -45,6 +45,7 @@ Proof checker for clauses created during search.
 #include "smt/smt_solver.h"
 #include "sat/sat_solver.h"
 #include "sat/sat_drat.h"
+#include "sat/sat_proof_trim.h"
 #include "sat/smt/euf_proof_checker.h"
 #include "cmd_context/cmd_context.h"
 #include "params/solver_params.hpp"
@@ -181,203 +182,57 @@ public:
 
 };
 
-namespace sat {
-    /**
-     * Replay proof entierly, then walk backwards extracting reduced proof.
-     */
-    class proof_trim {
-        cmd_context& ctx;
-        ast_manager& m;
-        solver s;
-        literal_vector m_clause;
-
-        vector<std::tuple<literal_vector, clause*, bool, bool>> m_trail;
+/**
+ * Replay proof entierly, then walk backwards extracting reduced proof.
+ */
+class proof_trim {
+    cmd_context& ctx;
+    ast_manager& m;
+    sat::proof_trim trim;
         
-        struct hash {
-            unsigned operator()(literal_vector const& v) const {
-                return string_hash((char const*)v.begin(), v.size()*sizeof(literal), 3);
-            }
-        };
-        struct eq {
-            bool operator()(literal_vector const& a, literal_vector const& b) const {
-                return a == b;
-            }
-        };
-        map<literal_vector, clause_vector, hash, eq> m_clauses;
+    void mk_clause(expr_ref_vector const& clause) {
+        trim.init_clause();
+        for (expr* arg: clause)
+            add_literal(arg);
+    }
         
-        void mk_clause(expr_ref_vector const& clause) {
-            m_clause.reset();
-            for (expr* arg: clause)
-                add_literal(arg);
-            std::sort(m_clause.begin(), m_clause.end());
-        }
+    sat::bool_var mk_var(expr* arg) {
+        while (arg->get_id() >= trim.num_vars())
+            trim.mk_var();
+        return arg->get_id();
+    }
         
-        bool_var mk_var(expr* arg) {
-            while (arg->get_id() >= s.num_vars())
-                s.mk_var(true, true);
-            return arg->get_id();
-        }
-        
-        void add_literal(expr* arg) {
-            bool sign = m.is_not(arg, arg);
-            m_clause.push_back(literal(mk_var(arg), sign));
-        }
-
-
-        /**
-           Pseudo-code from Gurfinkel, Vizel, FMCAD 2014
-           Input: trail (a0,d0), ..., (an,dn) = ({},bot)
-           Output: reduced trail - result 
-           result = []
-           C = { an }
-           for i = n to 0 do
-               if s.is_deleted(ai) then s.revive(ai)
-               else 
-                  if s.isontrail(ai) then
-                     s.undotrailcore(ai,C)
-                  s.delete(ai)
-                  if ai in C then 
-                      if ai is not initial then
-                         s.savetrail()
-                         s.enqueue(not ai)
-                         c = s.propagate()
-                         s.conflictanalysiscore(c, C)
-                         s.restoretrail()
-                       result += [ai]
-            reverse(result)
-            
-            is_deleted(ai):
-               clause was detached
-            revive(ai):
-               attach clause ai
-            isontrail(ai):
-                some literal on the current trail in s is justified by ai
-            undotrailcore(ai, C):
-                pop the trail until dependencies on ai are gone
-            savetrail:
-                store current trail so it can be restored
-            enqueue(not ai):
-                assert negations of ai at a new decision level
-            conflictanalysiscore(c, C):
-                ?
-            restoretrail:
-                restore the trail to the position before enqueue
-                
-                                                           
-        */        
-        void trim() {            
-            vector<literal_vector> result, clauses;
-            clauses.push_back(literal_vector());
-            for (unsigned i = m_trail.size(); i-- > 0; ) {
-                auto const& [cl, clp, is_add, is_initial] = m_trail[i];
-                if (!is_add) {
-                    revive(cl, clp);
-                    continue;
-                }
-                prune_trail(cl, clp);
-                del(cl, clp);
-                if (!clauses.contains(cl))
-                    continue;
-                if (!is_initial) {
-                    s.push();
-                    unsigned lvl = s.scope_lvl();
-                    for (auto lit : cl)
-                        s.assign(~lit, justification(lvl));
-                    s.propagate(false);
-                    SASSERT(s.inconsistent());
-                    conflict_analysis(clauses);
-                    s.pop(1);
-                }
-                result.push_back(cl);
-            }
-            result.reverse();
-        }
-
-        void del(literal_vector const& cl, clause* cp) {
-            if (cp) 
-                s.detach_clause(*cp);
-            else 
-                del(cl);
-        }
-
-        void prune_trail(literal_vector const& cl, clause* cp) {
-
-        }
-
-        void conflict_analysis(vector<literal_vector> const& clauses) {
-            
-        }
-
-
-        void revive(literal_vector const& cl, clause* cp) {
-            if (cp) 
-                s.attach_clause(*cp);
-            else 
-                s.mk_clause(cl, status::redundant());            
-        }
-
-
-        clause* del(literal_vector const& cl) {
-            clause* cp = nullptr;
-            IF_VERBOSE(3, verbose_stream() << "del: " << cl << "\n");
-            if (m_clause.size() == 2) {
-                s.detach_bin_clause(cl[0], cl[1], true);
-                return cp;
-            }
-            auto* e = m_clauses.find_core(cl);            
-            if (!e)
-                return cp;
-            auto& v = e->get_data().m_value;
-            if (!v.empty()) {
-                cp = v.back();
-                IF_VERBOSE(3, verbose_stream() << "del: " << *cp << "\n");
-                s.detach_clause(*cp);
-                v.pop_back();
-            }
-            return cp;
-        }
-
-        void save(literal_vector const& lits, clause* cl) {
-            if (!cl)                
-                return;
-            IF_VERBOSE(3, verbose_stream() << "add: " << *cl << "\n");
-            auto& v = m_clauses.insert_if_not_there(lits, clause_vector());            
-            v.push_back(cl);
-        }
-        
-    public:
-        proof_trim(cmd_context& ctx):
-            ctx(ctx),
-            m(ctx.m()),
-            s(gparams::get_module("sat"), m.limit()) {            
-        }
-        
-        void assume(expr_ref_vector const& _clause, bool is_initial = true) {        
-            mk_clause(_clause);
-            IF_VERBOSE(3, verbose_stream() << "add: " << m_clause << "\n");
-            auto* cl = s.mk_clause(m_clause, status::redundant());
-            m_trail.push_back({ m_clause, cl, true, is_initial });
-            s.propagate(false);
-            save(m_clause, cl);
-        }
-        
-        void del(expr_ref_vector const& _clause) {
-            mk_clause(_clause);
-            clause* cp = del(m_clause);
-            m_trail.push_back({ m_clause, cp, false, true });
-        }
-        
-        void infer(expr_ref_vector const& _clause, app*) {
-            assume(_clause, false);
-        }
-
-        void updt_params(params_ref const& p) {
-            s.updt_params(p);
-        }
-
-    };
-}
-
+    void add_literal(expr* arg) {
+        bool sign = m.is_not(arg, arg);
+        trim.add_literal(mk_var(arg), sign);
+    }
+      
+public:
+    proof_trim(cmd_context& ctx):
+        ctx(ctx),
+        m(ctx.m()),
+        trim(gparams::get_module("sat"), m.limit()) {            
+    }
+    
+    void assume(expr_ref_vector const& _clause, bool is_initial = true) {        
+        mk_clause(_clause);
+        trim.assume(true);
+    }
+    
+    void del(expr_ref_vector const& _clause) {
+        mk_clause(_clause);
+        trim.del();
+    }
+    
+    void infer(expr_ref_vector const& _clause, app*) {
+        mk_clause(_clause);
+        trim.infer();
+    }
+    
+    void updt_params(params_ref const& p) {
+        trim.updt_params(p);
+    }    
+};
 
 class proof_saver {
     cmd_context& ctx;
@@ -415,11 +270,11 @@ class proof_cmds_imp : public proof_cmds {
     bool            m_trim   = false;
     scoped_ptr<smt_checker>     m_checker;
     scoped_ptr<proof_saver>     m_saver;
-    scoped_ptr<sat::proof_trim>      m_trimmer;
+    scoped_ptr<proof_trim>      m_trimmer;
     
     smt_checker& checker() { if (!m_checker) m_checker = alloc(smt_checker, m); return *m_checker; }
     proof_saver& saver() { if (!m_saver) m_saver = alloc(proof_saver, ctx); return *m_saver; }
-    sat::proof_trim& trim() { if (!m_trimmer) m_trimmer = alloc(sat::proof_trim, ctx); return *m_trimmer; }
+    proof_trim& trim() { if (!m_trimmer) m_trimmer = alloc(proof_trim, ctx); return *m_trimmer; }
     
 public:
     proof_cmds_imp(cmd_context& ctx): ctx(ctx), m(ctx.m()), m_lits(m), m_proof_hint(m) {
diff --git a/src/sat/CMakeLists.txt b/src/sat/CMakeLists.txt
index b16a15482..b6f6a6f94 100644
--- a/src/sat/CMakeLists.txt
+++ b/src/sat/CMakeLists.txt
@@ -30,6 +30,7 @@ z3_add_component(sat
     sat_parallel.cpp
     sat_prob.cpp
     sat_probing.cpp
+    sat_proof_trim.cpp
     sat_scc.cpp
     sat_simplifier.cpp
     sat_solver.cpp
diff --git a/src/sat/sat_proof_trim.cpp b/src/sat/sat_proof_trim.cpp
new file mode 100644
index 000000000..b8ecec04e
--- /dev/null
+++ b/src/sat/sat_proof_trim.cpp
@@ -0,0 +1,326 @@
+/*++
+  Copyright (c) 2020 Microsoft Corporation
+
+  Module Name:
+
+   sat_proof_trim.cpp
+
+  Abstract:
+   
+    proof replay and trim
+
+  Author:
+
+    Nikolaj Bjorner 2023-10-04
+
+  Notes:
+  
+
+--*/
+
+#include "sat/sat_proof_trim.h"
+
+namespace sat {
+
+
+    /**
+       Pseudo-code from Gurfinkel, Vizel, FMCAD 2014
+       Input: trail (a0,d0), ..., (an,dn) = ({},bot)
+       Output: reduced trail - result 
+       result = []
+       C = { an }
+       for i = n to 0 do
+           if s.is_deleted(ai) then s.revive(ai)
+           else 
+              if s.isontrail(ai) then
+                  s.undotrailcore(ai,C)
+              s.delete(ai)
+              if ai in C then 
+                  if ai is not initial then
+                      s.savetrail()
+                      s.enqueue(not ai)
+                      c = s.propagate()
+                      s.conflictanalysiscore(c, C)
+                      s.restoretrail()
+                   result += [ai]
+       reverse(result)
+            
+       is_deleted(ai):
+          clause was detached
+       revive(ai):
+          attach clause ai
+       isontrail(ai):
+          some literal on the current trail in s is justified by ai
+       undotrailcore(ai, C):
+          pop the trail until dependencies on ai are gone
+       savetrail:
+          store current trail so it can be restored
+       enqueue(not ai):
+          assert negations of ai at a new decision level
+       conflictanalysiscore(c, C):
+          ?
+       restoretrail:
+          restore the trail to the position before enqueue
+                                                                          
+    */        
+
+    void proof_trim::trim() {
+        vector<literal_vector> result, clauses;
+        clauses.push_back(literal_vector());
+        for (unsigned i = m_trail.size(); i-- > 0; ) {
+            auto const& [cl, clp, is_add, is_initial] = m_trail[i];
+            if (!is_add) {
+                revive(cl, clp);
+                continue;
+            }
+            prune_trail(cl, clp);
+            del(cl, clp);
+            if (!clauses.contains(cl))
+                continue;
+            result.push_back(cl);
+            if (is_initial)
+                continue;
+            s.push();
+            unsigned init_sz = s.m_trail.size();
+            unsigned lvl = s.scope_lvl();
+            for (auto lit : cl)
+                s.assign(~lit, justification(lvl));
+            s.propagate(false);
+            SASSERT(s.inconsistent());
+            conflict_analysis_core(init_sz, clauses);
+            s.pop(1);                
+        }
+        result.reverse();
+    }
+    
+    void proof_trim::del(literal_vector const& cl, clause* cp) {
+        if (cp) 
+            s.detach_clause(*cp);
+        else 
+            del(cl);
+    }
+    
+    bool proof_trim::match_clause(literal_vector const& cl, literal l1, literal l2) const {
+        return cl.size() == 2 && ((l1 == cl[0] && l2 == cl[1]) || (l1 == cl[1] && l2 == cl[0]));
+    }
+    
+    bool proof_trim::match_clause(literal_vector const& cl, literal l1, literal l2, literal l3) const {
+        return cl.size() == 3 &&
+            ((l1 == cl[0] && l2 == cl[1] && l3 == cl[2]) ||
+             (l1 == cl[0] && l2 == cl[2] && l3 == cl[1]) ||
+             (l1 == cl[1] && l2 == cl[0] && l3 == cl[2]) ||
+             (l1 == cl[1] && l2 == cl[2] && l3 == cl[0]) ||
+             (l1 == cl[2] && l2 == cl[1] && l3 == cl[0]) ||
+             (l1 == cl[2] && l2 == cl[0] && l3 == cl[1]));
+    }
+
+            /**
+         * cl is on the trail if there is some literal l that is implied by cl
+         * Remove all clauses after cl that are in the cone of influence of cl.
+         * The coi is defined inductively: C is in coi of cl if it contains ~l
+         * or it contains ~l' where l' is implied by a clause in the coi of cl.
+         * Possible optimization: 
+         * - check if clause contains a literal that is on implied on the trail
+         *   if it doesn't contain any such literal, bypass the trail adjustment.
+         */
+
+    void proof_trim::prune_trail(literal_vector const& cl, clause* cp) {
+        m_in_clause.reset();
+        m_in_coi.reset();
+        
+        for (literal lit : cl) 
+            m_in_clause.insert(lit.index());
+        
+        bool on_trail = false;
+        unsigned j = 0;
+        for (unsigned i = 0; i < s.trail_size(); ++i) {
+            literal l = s.trail_literal(i);
+            if (m_in_clause.contains(l.index())) {
+                SASSERT(!on_trail);
+                on_trail = true;
+                m_in_coi.insert((~l).index());
+                s.m_assignment[l.index()] = l_undef;
+                s.m_assignment[(~l).index()] = l_undef;
+                continue;
+            }
+            if (!on_trail) {
+                s.m_trail[j++] = s.m_trail[i];
+                continue;
+            }
+            
+            auto js = s.get_justification(l);
+            bool in_coi = false;
+            if (js.is_clause())
+                for (literal lit : s.get_clause(j))
+                    in_coi |= m_in_coi.contains(lit.index());                
+            else if (js.is_binary_clause())
+                in_coi = m_in_coi.contains(js.get_literal().index());
+            else if (js.is_ternary_clause())
+                in_coi = m_in_coi.contains(js.get_literal1().index()) || m_in_coi.contains(js.get_literal2().index());
+            else
+                UNREACHABLE(); // approach does not work for external justifications
+            
+            if (in_coi) {
+                m_in_coi.insert((~l).index());
+                s.m_assignment[l.index()] = l_undef;
+                s.m_assignment[(~l).index()] = l_undef;
+            }
+            else
+                s.m_trail[j++] = s.m_trail[i];
+        }            
+        s.m_trail.shrink(j);
+    }
+
+
+    /**
+       The current state is in conflict.
+       Chase justifications for conflict to extract clauses that are in coi of conflict.
+
+       Assume:
+       F | G, ~C |- []
+       Let T (trail) be the extension of G, ~C that derives the empty clause.
+       T := G, ~C, l1:j1, l2:j2, ..., lk:jk
+       The goal is to extract clauses in T that are used to derive C.
+       - some of the literals in ~C that are not set to true already (they must be unassigned relative)
+       are used to derive the empty clause.
+       - some literals in ~C that are assigned to true may also be used to derive the empty clause.
+             
+       Example:
+       C = c or d or e
+       G = a
+       F = { ~a or ~b, c or d or b, ... }
+       T = ~b : ~a or ~b, ~c: D ~d : D , ~e : D, b : c or d or b 
+       where D is a decision marker (justification::NONE)
+       The conflict depends on the first two clauses in F.
+             
+       All literals that are are used in clauses leading to the conflict are
+       queried for their explanation. Their explanation is added to the clauses.
+       
+    */
+    void proof_trim::conflict_analysis_core(unsigned init_sz, vector<literal_vector>& clauses) {
+        justification j = s.m_conflict;
+        literal consequent = null_literal;
+        unsigned idx = s.m_trail.size() - 1;
+        unsigned old_sz = s.m_unmark.size();
+        bool_var c_var;
+        auto add_dependency = [&](bool_var v) {
+            auto j = s.m_justification[v];
+            literal lit = literal(v, s.value(v) == l_false);
+            add_core(lit, j, clauses);            
+        };
+        
+        if (s.m_not_l != null_literal) {
+            s.process_antecedent_for_unsat_core(s.m_not_l);
+            add_core(s.m_not_l, s.m_justification[s.m_not_l.var()], clauses);
+            add_core(~s.m_not_l, j, clauses);
+            consequent = ~s.m_not_l;                
+        }
+        while (true) {
+            s.process_consequent_for_unsat_core(consequent, j);
+            while (idx >= init_sz) {
+                consequent = s.m_trail[idx];
+                c_var = consequent.var();
+                if (s.is_marked(c_var))
+                    break;
+                --idx;
+            }
+            if (idx < init_sz)
+                break;
+            j = s.m_justification[c_var];
+            --idx;
+        }
+        for (unsigned i = s.m_mark.size(); i-- > old_sz; ) 
+            add_dependency(s.m_unmark[i]);
+        s.reset_unmark(old_sz);
+    }
+
+    void proof_trim::add_core(literal l, justification j, vector<literal_vector>& clauses) {
+        m_clause.reset();
+        switch (j.get_kind()) {
+        case justification::NONE:
+            return;                
+        case justification::BINARY:
+            m_clause.push_back(l);
+            m_clause.push_back(j.get_literal());
+            break;
+        case justification::TERNARY:
+            m_clause.push_back(l);
+            m_clause.push_back(j.get_literal1());
+            m_clause.push_back(j.get_literal2());
+            break;
+        case justification::CLAUSE: 
+            for (auto lit : s.get_clause(j))
+                m_clause.push_back(lit);
+            break;
+        default:
+            UNREACHABLE();
+            break;
+        }
+        std::sort(m_clause.begin(), m_clause.end());
+        clauses.insert(m_clause);            
+    }
+
+
+    void proof_trim::revive(literal_vector const& cl, clause* cp) {
+        if (cp) 
+            s.attach_clause(*cp);
+        else 
+            s.mk_clause(cl, status::redundant());            
+    }
+
+
+    clause* proof_trim::del(literal_vector const& cl) {
+        clause* cp = nullptr;
+        IF_VERBOSE(3, verbose_stream() << "del: " << cl << "\n");
+        if (m_clause.size() == 2) {
+            s.detach_bin_clause(cl[0], cl[1], true);
+            return cp;
+        }
+        auto* e = m_clauses.find_core(cl);            
+        if (!e)
+            return cp;
+        auto& v = e->get_data().m_value;
+        if (!v.empty()) {
+            cp = v.back();
+            IF_VERBOSE(3, verbose_stream() << "del: " << *cp << "\n");
+            s.detach_clause(*cp);
+            v.pop_back();
+        }
+        return cp;
+    }
+
+    void proof_trim::save(literal_vector const& lits, clause* cl) {
+        if (!cl)                
+            return;
+        IF_VERBOSE(3, verbose_stream() << "add: " << *cl << "\n");
+        auto& v = m_clauses.insert_if_not_there(lits, clause_vector());            
+        v.push_back(cl);
+    }
+
+    
+
+    proof_trim::proof_trim(params_ref const& p, reslimit& lim):
+        s(p, lim)
+    {}
+
+    void proof_trim::assume(bool is_initial) {
+        std::sort(m_clause.begin(), m_clause.end());
+        IF_VERBOSE(3, verbose_stream() << "add: " << m_clause << "\n");
+        auto* cl = s.mk_clause(m_clause, status::redundant());
+        m_trail.push_back({ m_clause, cl, true, is_initial });
+        s.propagate(false);
+        save(m_clause, cl);
+    }
+    
+    void proof_trim::del() {
+        std::sort(m_clause.begin(), m_clause.end());
+        clause* cp = del(m_clause);
+        m_trail.push_back({ m_clause, cp, false, true });
+    }
+    
+    void proof_trim::infer() {
+        assume(false);        
+    }
+
+
+}
diff --git a/src/sat/sat_proof_trim.h b/src/sat/sat_proof_trim.h
new file mode 100644
index 000000000..c7b871df7
--- /dev/null
+++ b/src/sat/sat_proof_trim.h
@@ -0,0 +1,79 @@
+/*++
+  Copyright (c) 2020 Microsoft Corporation
+
+  Module Name:
+
+   sat_trim.h
+
+  Abstract:
+   
+    proof replay and trim
+
+  Author:
+
+    Nikolaj Bjorner 2023-10-04
+
+  Notes:
+  
+
+--*/
+
+#pragma once
+
+#include "util/params.h"
+#include "util/statistics.h"
+#include "sat/sat_clause.h"
+#include "sat/sat_types.h"
+#include "sat/sat_solver.h"
+
+namespace sat {
+
+    class proof_trim {
+        solver         s;
+        literal_vector m_clause;
+        uint_set       m_in_clause;
+        uint_set       m_in_coi;
+        vector<std::tuple<literal_vector, clause*, bool, bool>> m_trail;
+        
+        struct hash {
+            unsigned operator()(literal_vector const& v) const {
+                return string_hash((char const*)v.begin(), v.size()*sizeof(literal), 3);
+            }
+        };
+        struct eq {
+            bool operator()(literal_vector const& a, literal_vector const& b) const {
+                return a == b;
+            }
+        };
+        map<literal_vector, clause_vector, hash, eq> m_clauses;
+
+        void del(literal_vector const& cl, clause* cp);
+
+        bool match_clause(literal_vector const& cl, literal l1, literal l2) const;
+        bool match_clause(literal_vector const& cl, literal l1, literal l2, literal l3) const;
+
+        void prune_trail(literal_vector const& cl, clause* cp);
+        void conflict_analysis_core(unsigned init_sz, vector<literal_vector>& clauses);
+        void add_core(literal l, justification j, vector<literal_vector>& clauses);
+        void revive(literal_vector const& cl, clause* cp);        
+        clause* del(literal_vector const& cl);
+        void save(literal_vector const& lits, clause* cl);
+        
+    public:
+
+        proof_trim(params_ref const& p, reslimit& lim);
+
+        bool_var mk_var() { return s.mk_var(true, true); }
+        void init_clause() { m_clause.reset(); }
+        void add_literal(bool_var v, bool sign) { m_clause.push_back(literal(v, sign)); }
+        unsigned num_vars() { return s.num_vars(); }
+
+        void assume(bool is_initial = true);
+        void del();
+        void infer();
+        void updt_params(params_ref const& p) { s.updt_params(p); }
+
+        void trim();
+
+    };
+}