diff --git a/lib/prolog/tests/programs/member.pl b/lib/prolog/tests/programs/member.pl
new file mode 100644
index 00000000..ca078b78
--- /dev/null
+++ b/lib/prolog/tests/programs/member.pl
@@ -0,0 +1,4 @@
+%% member/2 — list membership.
+%% Generates all solutions on backtracking when the element is unbound.
+member(X, [X|_]).
+member(X, [_|T]) :- member(X, T).
diff --git a/lib/prolog/tests/programs/member.sx b/lib/prolog/tests/programs/member.sx
new file mode 100644
index 00000000..51e7846f
--- /dev/null
+++ b/lib/prolog/tests/programs/member.sx
@@ -0,0 +1,91 @@
+;; lib/prolog/tests/programs/member.sx — member/2 generator.
+
+(define pl-mb-test-count 0)
+(define pl-mb-test-pass 0)
+(define pl-mb-test-fail 0)
+(define pl-mb-test-failures (list))
+
+(define
+  pl-mb-test!
+  (fn
+    (name got expected)
+    (begin
+      (set! pl-mb-test-count (+ pl-mb-test-count 1))
+      (if
+        (= got expected)
+        (set! pl-mb-test-pass (+ pl-mb-test-pass 1))
+        (begin
+          (set! pl-mb-test-fail (+ pl-mb-test-fail 1))
+          (append!
+            pl-mb-test-failures
+            (str name "\n    expected: " expected "\n    got:      " got)))))))
+
+(define
+  pl-mb-goal
+  (fn
+    (src env)
+    (pl-instantiate (nth (first (pl-parse (str "g :- " src "."))) 2) env)))
+
+(define pl-mb-prog-src "member(X, [X|_]). member(X, [_|T]) :- member(X, T).")
+
+(define pl-mb-db (pl-mk-db))
+(pl-db-load! pl-mb-db (pl-parse pl-mb-prog-src))
+
+(pl-mb-test!
+  "member(2, [1, 2, 3]) succeeds"
+  (pl-solve-once!
+    pl-mb-db
+    (pl-mb-goal "member(2, [1, 2, 3])" {})
+    (pl-mk-trail))
+  true)
+
+(pl-mb-test!
+  "member(4, [1, 2, 3]) fails"
+  (pl-solve-once!
+    pl-mb-db
+    (pl-mb-goal "member(4, [1, 2, 3])" {})
+    (pl-mk-trail))
+  false)
+
+(pl-mb-test!
+  "member(X, []) fails"
+  (pl-solve-once!
+    pl-mb-db
+    (pl-mb-goal "member(X, [])" {})
+    (pl-mk-trail))
+  false)
+
+(pl-mb-test!
+  "member(X, [a, b, c]) generates 3 solutions"
+  (pl-solve-count!
+    pl-mb-db
+    (pl-mb-goal "member(X, [a, b, c])" {})
+    (pl-mk-trail))
+  3)
+
+(define pl-mb-env-1 {})
+(define pl-mb-goal-1 (pl-mb-goal "member(X, [11, 22, 33])" pl-mb-env-1))
+(pl-solve-once! pl-mb-db pl-mb-goal-1 (pl-mk-trail))
+
+(pl-mb-test!
+  "member(X, [11, 22, 33]) first solution X = 11"
+  (pl-num-val (pl-walk-deep (dict-get pl-mb-env-1 "X")))
+  11)
+
+(pl-mb-test!
+  "member(2, [1, 2, 3, 2, 1]) matches twice on backtrack"
+  (pl-solve-count!
+    pl-mb-db
+    (pl-mb-goal "member(2, [1, 2, 3, 2, 1])" {})
+    (pl-mk-trail))
+  2)
+
+(pl-mb-test!
+  "member with unbound list cell unifies"
+  (pl-solve-once!
+    pl-mb-db
+    (pl-mb-goal "member(a, [X, b, c])" {})
+    (pl-mk-trail))
+  true)
+
+(define pl-member-tests-run! (fn () {:failed pl-mb-test-fail :passed pl-mb-test-pass :total pl-mb-test-count :failures pl-mb-test-failures}))
diff --git a/plans/prolog-on-sx.md b/plans/prolog-on-sx.md
index edf2b979..a4dcf3cb 100644
--- a/plans/prolog-on-sx.md
+++ b/plans/prolog-on-sx.md
@@ -58,7 +58,7 @@ Representation choices (finalise in phase 1, document here):
 - [ ] Classic programs in `lib/prolog/tests/programs/`:
   - [x] `append.pl` — list append (with backtracking) — `lib/prolog/tests/programs/append.{pl,sx}`. 6 tests cover: build (`append([], L, X)`, `append([1,2], [3,4], X)`), check ground match/mismatch, full split-backtracking (`append(X, Y, [1,2,3])` → 4 solutions), single-deduce (`append(X, [3], [1,2,3])` → X=[1,2]).
   - [x] `reverse.pl` — naive reverse — `lib/prolog/tests/programs/reverse.{pl,sx}`. Naive reverse via append: `reverse([H|T], R) :- reverse(T, RT), append(RT, [H], R)`. 6 tests cover empty, singleton, 3-list, 4-atom-list, ground match, ground mismatch.
-  - [ ] `member.pl` — generate all solutions via backtracking
+  - [x] `member.pl` — generate all solutions via backtracking — `lib/prolog/tests/programs/member.{pl,sx}`. Classic 2-clause `member(X, [X|_])` + `member(X, [_|T]) :- member(X, T)`. 7 tests cover bound-element hit/miss, empty list, generator (count = list length), first-solution binding, duplicate matches counted twice, anonymous head-cell unification.
   - [ ] `nqueens.pl` — 8-queens
   - [ ] `family.pl` — facts + rules (parent/ancestor)
 - [ ] `lib/prolog/conformance.sh` + runner, `scoreboard.json` + `scoreboard.md`
@@ -88,6 +88,7 @@ Representation choices (finalise in phase 1, document here):
 
 _Newest first. Agent appends on every commit._
 
+- 2026-04-25 — `member.pl` third classic program. Standard 2-clause definition; 7 tests cover bound-element hit/miss, empty-list fail, generator-count = list length, first-solution binding (X=11), duplicate elements matched twice on backtrack, anonymous-head unification (`member(a, [X, b, c])` binds X=a). Total 167 (+7).
 - 2026-04-25 — `reverse.pl` second classic program. Naive reverse defined via append. 6 tests (empty/singleton/3-list/4-atom-list/ground match/ground mismatch). Confirms the solver handles non-trivial recursive composition: `reverse([1,2,3], R)` recurses to depth 3 then unwinds via 3 nested `append`s. Total 160 (+6).
 - 2026-04-25 — `append.pl` first classic program. `lib/prolog/tests/programs/append.pl` is the canonical 2-clause source; `append.sx` embeds the source as a string (no file-read primitive in SX yet) and runs 6 tests covering build, check, full split-backtrack (4 solutions), and deduction modes. Helpers `pl-ap-list-to-sx` / `pl-ap-term-to-sx` convert deep-walked Prolog lists (`("compound" "." (h t))` / `("atom" "[]")`) to SX lists for structural assertion. Total 154 (+6).
 - 2026-04-25 — `is/2` arithmetic landed. `pl-eval-arith` recursively evaluates ground RHS expressions (binary `+ - * /`, `mod`; binary+unary `-`; unary `abs`); `is/2` wraps the value as `("num" v)` and unifies via `pl-solve-eq!`, so it works in all three modes — bind unbound LHS, check ground LHS for equality, propagate from earlier var bindings on RHS. 11 tests, total 148 (+11). Without operator support, expressions must be written prefix: `is(X, +(2, *(3, 4)))`.