diff --git a/src/ast/euf/ho_matcher.cpp b/src/ast/euf/ho_matcher.cpp
index f86d82b64..20b913b17 100644
--- a/src/ast/euf/ho_matcher.cpp
+++ b/src/ast/euf/ho_matcher.cpp
@@ -242,17 +242,72 @@ namespace euf {
     // We assume that m_rewriter should produce
     // something amounting to weak-head normal form WHNF
 
+    // Unfold a lambda-def application f(args) to the corresponding lambda expression.
+    // For a func_decl f with arity n and lambda-def quantifier (lambda (x1..xk) body),
+    // f(a1,...,an) is unfolded to (lambda (x1..xk) body[params := a1..an]).
+    // For a constant f (arity 0) that is a lambda-def, returns the lambda directly.
+    expr_ref ho_matcher::unfold_lambda_def(expr* e) const {
+        if (!is_app(e))
+            return expr_ref(e, m);
+        app* a = to_app(e);
+        func_decl* f = a->get_decl();
+        quantifier* lam = m.is_lambda_def(f);
+        if (!lam)
+            return expr_ref(e, m);
+        
+        unsigned arity = f->get_arity();
+        SASSERT(is_lambda(lam));
+        
+        if (arity == 0) {
+            // Constant lambda-def: just return the lambda expression
+            return expr_ref(lam, m);
+        }
+        
+        // f(a1,...,an) where lam = lambda (x1..xk) body
+        // The lambda body uses var(0)..var(k-1) for the lambda-bound vars
+        // and var(k)..var(k+n-1) for the function parameters.
+        // We substitute the function parameters with the actual arguments.
+        unsigned num_lambda_decls = lam->get_num_decls();
+        expr_ref body(lam->get_expr(), m);
+        
+        // Build substitution: var(num_lambda_decls + i) -> a->get_arg(arity - 1 - i) for i in [0, arity)
+        // var_subst replaces var(i) with subst[i]
+        expr_ref_vector subst(m);
+        subst.resize(num_lambda_decls + arity);
+        for (unsigned i = 0; i < num_lambda_decls; ++i)
+            subst[i] = m.mk_var(i, lam->get_decl_sort(num_lambda_decls - 1 - i));
+        for (unsigned i = 0; i < arity; ++i)
+            subst[num_lambda_decls + i] = a->get_arg(arity - 1 - i);
+        
+        var_subst vs(m, false);
+        body = vs(lam->get_expr(), subst);
+        
+        // Rebuild the lambda with the new body
+        ptr_buffer<sort> sorts;
+        vector<symbol> names;
+        for (unsigned i = 0; i < num_lambda_decls; ++i) {
+            sorts.push_back(lam->get_decl_sort(i));
+            names.push_back(lam->get_decl_name(i));
+        }
+        return expr_ref(m.mk_lambda(num_lambda_decls, sorts.data(), names.data(), body), m);
+    }
+
     void ho_matcher::reduce(match_goal& wi) {
         while (true) {
             expr_ref r = whnf(wi.pat, wi.pat_offset());
+            if (r == wi.pat) 
+                r = unfold_lambda_def(wi.pat);            
             if (r == wi.pat)
                 break;
             IF_VERBOSE(3, verbose_stream() << "ho_matcher::reduce: " << wi.pat << " -> " << r << "\n";);
             wi.pat = r;
         } 
 
+
         while (true) {
             expr_ref r = whnf(wi.t, wi.term_offset());
+            if (r == wi.t)
+                r = unfold_lambda_def(wi.t);
             if (r == wi.t)
                 break;
             IF_VERBOSE(3, verbose_stream() << "ho_matcher::reduce: " << wi.t << " -> " << r << "\n";);
@@ -656,16 +711,17 @@ namespace euf {
                 todo.pop_back();
                 continue;
             }
-            if (m_unitary.is_flex(0, t)) {
+            if (m_unitary.is_flex(0, t) || (is_app(t) && m.is_lambda_def(to_app(t)->get_decl())) || is_lambda(t)) {
                 m_pat2abs.insert_if_not_there(p, svector<std::pair<unsigned, expr*>>()).push_back({ nb, t });
                 auto v = m.mk_var(nb++, t->get_sort());
                 bound.push_back(v);
                 cache.setx(t->get_id(), v);
                 todo.pop_back();
                 continue;
-            }
+            }            
             if (is_app(t)) {
                 auto a = to_app(t);
+
                 unsigned sz = a->get_num_args();
                 ptr_buffer<expr> args;
                 for (auto arg : *a) {
@@ -737,7 +793,7 @@ namespace euf {
         trail().push(insert_map(m_pat2abs, p));
         trail().push(insert_map(m_q2hoq, q));
         trail().push(insert_map(m_hoq2q, q1));
-        trail().push(insert_map(m_hopat2free_vars, p1));        
+        trail().push(insert_map(m_hopat2free_vars, p1));
         return { q1, p1 };
     }
 
diff --git a/src/ast/euf/ho_matcher.h b/src/ast/euf/ho_matcher.h
index 65477078c..434900fa2 100644
--- a/src/ast/euf/ho_matcher.h
+++ b/src/ast/euf/ho_matcher.h
@@ -350,6 +350,8 @@ namespace euf {
 
         void reduce(match_goal& wi);
 
+        expr_ref unfold_lambda_def(expr* e) const;
+
         trail_stack& trail() { return m_trail; }
 
         std::ostream& display(std::ostream& out) const;
@@ -395,5 +397,13 @@ namespace euf {
 
         quantifier* hoq2q(quantifier* q) const { return m_hoq2q[q]; }
 
+
+        svector<std::pair<unsigned, expr*>> const* get_flex_subterms(app* p) const {
+            auto orig_p = m_hopat2pat.find_core(p);
+            if (!orig_p) return nullptr;
+            auto abs = m_pat2abs.find_core(orig_p->get_data().get_value());
+            return abs ? &abs->get_data().get_value() : nullptr;
+        }
+
     };
 }
diff --git a/src/ast/pattern/pattern_inference.cpp b/src/ast/pattern/pattern_inference.cpp
index 32b0546e8..8ec88096a 100644
--- a/src/ast/pattern/pattern_inference.cpp
+++ b/src/ast/pattern/pattern_inference.cpp
@@ -546,13 +546,13 @@ void pattern_inference_cfg::reset_pre_patterns() {
 
 
 bool pattern_inference_cfg::is_forbidden(app * n) const {
-    func_decl const * decl = n->get_decl();
+    func_decl * decl = n->get_decl();
     if (is_ground(n))
         return false;
     // Remark: skolem constants should not be used in patterns, since they do not
     // occur outside of the quantifier. That is, Z3 will never match this kind of
     // pattern.
-    if (m_params.m_pi_avoid_skolems && decl->is_skolem()) {
+    if (m_params.m_pi_avoid_skolems && decl->is_skolem() && !m.is_lambda_def(decl)) {
         CTRACE(pattern_inference_skolem, decl->is_skolem(), tout << "ignoring: " << mk_pp(n, m) << "\n";);
         return true;
     }
diff --git a/src/params/smt_params.cpp b/src/params/smt_params.cpp
index a80483d0f..a64075204 100644
--- a/src/params/smt_params.cpp
+++ b/src/params/smt_params.cpp
@@ -27,6 +27,7 @@ void smt_params::updt_local_params(params_ref const & _p) {
     m_random_seed = p.random_seed();
     m_relevancy_lvl = p.relevancy();
     m_ematching   = p.ematching();
+    m_ho_matching = p.ho_matching();
     m_induction   = p.induction();
     m_clause_proof = p.clause_proof();
     m_phase_selection = static_cast<phase_selection>(p.phase_selection());
diff --git a/src/params/smt_params.h b/src/params/smt_params.h
index 68ab50ffe..7b5efa991 100644
--- a/src/params/smt_params.h
+++ b/src/params/smt_params.h
@@ -109,6 +109,7 @@ struct smt_params : public preprocessor_params,
     bool             m_display_features = false;
     bool             m_new_core2th_eq = true;
     bool             m_ematching = true;
+    bool             m_ho_matching = false;
     bool             m_induction = false;
     bool             m_clause_proof = false;
     symbol           m_proof_log;
diff --git a/src/params/smt_params_helper.pyg b/src/params/smt_params_helper.pyg
index 6c8ce796d..cd52b989c 100644
--- a/src/params/smt_params_helper.pyg
+++ b/src/params/smt_params_helper.pyg
@@ -10,6 +10,7 @@ def_module_params(module_name='smt',
                           ('quasi_macros', BOOL, False, 'try to find universally quantified formulas that are quasi-macros'),
                           ('restricted_quasi_macros', BOOL, False, 'try to find universally quantified formulas that are restricted quasi-macros'),
                           ('ematching', BOOL, True, 'E-Matching based quantifier instantiation'),
+                          ('ho_matching', BOOL, False, 'higher-order matching for quantifier instantiation'),
                           ('phase_selection', UINT, 3, 'phase selection heuristic: 0 - always false, 1 - always true, 2 - phase caching, 3 - phase caching conservative, 4 - phase caching conservative 2, 5 - random, 6 - number of occurrences, 7 - theory'),
 	                  ('phase_caching_on', UINT, 400, 'number of conflicts while phase caching is on'),
 	                  ('phase_caching_off', UINT, 100, 'number of conflicts while phase caching is off'),
diff --git a/src/util/trace_tags.def b/src/util/trace_tags.def
index 67adb62c9..d343b2304 100644
--- a/src/util/trace_tags.def
+++ b/src/util/trace_tags.def
@@ -56,6 +56,7 @@ X(ctx_propagate_assertions, assert_eq_bug, "assert eq bug")
 X(ctx_solver_simplify_tactic, ctx_solver_simplify_tactic, "ctx solver simplify tactic")
 
 X(default_qm_plugin, default_qm_plugin, "default qm plugin")
+X(default_qm_plugin, ho_matching, "ho matching")
 X(default_qm_plugin, mam_stats, "mam stats")
 X(default_qm_plugin, quantifier, "quantifier")