diff --git a/src/sat/sat_extension.h b/src/sat/sat_extension.h
index d6a956a32..653ea4039 100644
--- a/src/sat/sat_extension.h
+++ b/src/sat/sat_extension.h
@@ -127,6 +127,8 @@ namespace sat {
         virtual bool tracking_assumptions() { return false; }
         virtual bool enable_self_propagate() const { return false; }
 
+        virtual void add_xor(literal_vector const& lits) { throw default_exception("solver does not support adding xor clauses"); }
+
         virtual bool extract_pb(std::function<void(unsigned sz, literal const* c, unsigned k)>& card,
                                 std::function<void(unsigned sz, literal const* c, unsigned const* coeffs, unsigned k)>& pb) {                                
             return false;
diff --git a/src/sat/smt/euf_internalize.cpp b/src/sat/smt/euf_internalize.cpp
index 9f747090a..6f49fb35d 100644
--- a/src/sat/smt/euf_internalize.cpp
+++ b/src/sat/smt/euf_internalize.cpp
@@ -31,6 +31,7 @@ Notes:
 
 #include "ast/pb_decl_plugin.h"
 #include "sat/smt/euf_solver.h"
+#include "sat/smt/xor_solver.h"
 
 namespace euf {
 
@@ -498,4 +499,17 @@ namespace euf {
         }
     }
 
+    void solver::add_xor(sat::literal_vector const& lits) {
+        family_id fid = m.mk_family_id("xor");
+        auto* ext = m_id2solver.get(fid, nullptr);
+        th_solver* xr;
+        if (!ext) {
+            xr = alloc(xr::solver, *this);
+            add_solver(xr);
+            ext = xr;
+        }
+        xr = dynamic_cast<xr::solver*>(ext);
+        xr->add_xor(lits);
+    }
+
 }
diff --git a/src/sat/smt/euf_solver.h b/src/sat/smt/euf_solver.h
index beb0809fb..64577430c 100644
--- a/src/sat/smt/euf_solver.h
+++ b/src/sat/smt/euf_solver.h
@@ -451,6 +451,7 @@ namespace euf {
         void set_bool_var2expr(sat::bool_var v, expr* e) { m_var_trail.push_back(v);  m_bool_var2expr.setx(v, e, nullptr); }
         expr* bool_var2expr(sat::bool_var v) const { return m_bool_var2expr.get(v, nullptr); }
         expr_ref literal2expr(sat::literal lit) const { expr* e = bool_var2expr(lit.var()); return (e && lit.sign()) ? expr_ref(mk_not(m, e), m) : expr_ref(e, m); }
+        void add_xor(sat::literal_vector const& lits) override;
         unsigned generation() const { return m_generation; }
 
         sat::literal attach_lit(sat::literal lit, expr* e);
diff --git a/src/sat/smt/xor_solver.h b/src/sat/smt/xor_solver.h
index 76c8f1ee8..337b679b9 100644
--- a/src/sat/smt/xor_solver.h
+++ b/src/sat/smt/xor_solver.h
@@ -177,6 +177,10 @@ namespace xr {
         solver(ast_manager& m, sat::sat_internalizer& si, euf::theory_id id);
         th_solver* clone(euf::solver& ctx) override;
 
+
+        void add_xor(sat::literal_vector const& lits) override { NOT_IMPLEMENTED_YET(); }
+
+
         sat::literal internalize(expr* e, bool sign, bool root)  override { UNREACHABLE(); return sat::null_literal; }
 
         void internalize(expr* e) override { UNREACHABLE(); }
diff --git a/src/sat/tactic/goal2sat.cpp b/src/sat/tactic/goal2sat.cpp
index 0ca46c2dd..09b720383 100644
--- a/src/sat/tactic/goal2sat.cpp
+++ b/src/sat/tactic/goal2sat.cpp
@@ -612,7 +612,93 @@ struct goal2sat::imp : public sat::sat_internalizer {
         }
     }
 
+    unsigned get_num_args(app* t) {
+        if (!m_xor || (!m.is_iff(t) && !m.is_xor(t))) 
+            return t->get_num_args();
+
+        unsigned n = 2;
+        while (m.is_iff(t->get_arg(1)) || m.is_xor(t->get_arg(1))) {
+            ++n;
+            t = to_app(t->get_arg(1));
+        }
+        return n;
+    }
+
+    expr* get_arg(app* t, unsigned idx) {
+        if (!m_xor || (!m.is_iff(t) && !m.is_xor(t))) 
+            return t->get_arg(idx);
+        
+        while (idx >= 1) {
+            SASSERT(m.is_iff(t) || m.is_xor(t));
+            t = to_app(t->get_arg(1));
+            --idx;
+        }
+        if (m.is_iff(t) || m.is_xor(t)) 
+            return t->get_arg(idx);
+        else 
+            return t;
+    }
+
+    bool is_iff(app* t) {
+        bool r = true;
+        expr* e = t, *x = nullptr;
+        do {
+            if (m.is_iff(e, x, e))
+                continue;
+            if (m.is_xor(e, x, e)) {
+                r = !r;
+                continue;
+            }
+            break;
+        }
+        while (true);
+        return r;
+    }
+
+    /**
+     * Convert xor expressions to native xor solver directly.
+     */
+
+    void convert_iff_native(app * t, bool root, bool sign) {
+        unsigned sz = m_result_stack.size();
+        unsigned num_args = get_num_args(t);
+        ptr_buffer<expr> args;
+        SASSERT(sz >= num_args && num_args >= 2);
+        sat::literal_vector lits;
+        sat::bool_var v = add_var(true, t);
+        lits.push_back(sat::literal(v, is_iff(t)));
+        for (unsigned i = 0; i < num_args; ++i) {
+            sat::literal lit(m_result_stack[sz - num_args + i]);
+            m_solver.set_external(lit.var());
+            lits.push_back(lit);
+        }
+        // ensure that = is converted to xor
+        for (unsigned i = 1; i + 1 < lits.size(); ++i) 
+            lits[i].neg();
+        TRACE("goal2sat", tout << "convert-xor " << mk_bounded_pp(t, m, 8) << " " << lits << "\n");
+
+        ensure_xor();
+        m_solver.get_extension()->add_xor(lits);
+        if (aig()) 
+            aig()->add_xor(~lits.back(), lits.size() - 1, lits.data() + 1);
+        sat::literal lit(v, sign);
+        if (root) {            
+            m_result_stack.reset();
+            mk_root_clause(lit);
+        }
+        else {
+            m_result_stack.shrink(sz - num_args);
+            m_result_stack.push_back(lit);
+        }
+    }
+
+
     void convert_iff(app * t, bool root, bool sign) {
+        if (m_xor) {
+            convert_iff_native(t, root, sign);
+            return;
+        }
+            
         if (t->get_num_args() != 2)            
             throw default_exception("unexpected number of arguments to " + mk_pp(t, m));
         SASSERT(t->get_num_args() == 2);
@@ -824,9 +910,9 @@ struct goal2sat::imp : public sat::sat_internalizer {
                 visit(t->get_arg(0), root, !sign);
                 continue;
             }
-            unsigned num = t->get_num_args();
+            unsigned num = get_num_args(t);
             while (m_frame_stack[fsz-1].m_idx < num) {
-                expr * arg = t->get_arg(m_frame_stack[fsz-1].m_idx);
+                expr * arg = get_arg(t, m_frame_stack[fsz-1].m_idx);
                 m_frame_stack[fsz - 1].m_idx++;
                 if (!visit(arg, false, false))
                     goto loop;