[sledge] Test: Move tests from Equality to Fol

Reviewed By: ngorogiannis

Differential Revision: D23459508

fbshipit-source-id: fc900ff09

sledge/src/fol_test.ml

@@ -15,9 +15,9 @@ let%test_module _ =
     (* let () =
      *   Trace.init ~margin:160
      *     ~config:(Result.ok_exn (Trace.parse "+Fol"))
-     *     ()
+     *     () *)
-     *
+
-     * [@@@warning "-32"] *)
+    [@@@warning "-32"]
 
     let printf pp = Format.printf "@\n%a@." pp
     let pp_raw = printf pp_raw
@@ -25,28 +25,24 @@ let%test_module _ =
     let ( ! ) i = Term.integer (Z.of_int i)
     let ( + ) = Term.add
     let ( - ) = Term.sub
-
+    let ( * ) i e = Term.mulq (Q.of_int i) e
-    (* let ( * ) i e = Term.mulq (Q.of_int i) e *)
     let wrt = Var.Set.empty
     let t_, wrt = Var.fresh "t" ~wrt
-
+    let u_, wrt = Var.fresh "u" ~wrt
-    (* let u_, wrt = Var.fresh "u" ~wrt *)
+    let v_, wrt = Var.fresh "v" ~wrt
-    (* let v_, wrt = Var.fresh "v" ~wrt *)
     let w_, wrt = Var.fresh "w" ~wrt
     let x_, wrt = Var.fresh "x" ~wrt
     let y_, wrt = Var.fresh "y" ~wrt
     let z_, wrt = Var.fresh "z" ~wrt
     let t = Term.var t_
-
+    let u = Term.var u_
-    (* let u = Term.var u_ *)
+    let v = Term.var v_
-    (* let v = Term.var v_ *)
     let w = Term.var w_
     let x = Term.var x_
     let y = Term.var y_
     let z = Term.var z_
-    let f = Term.mul t
+    let f = Term.splat
-
+    let g = Term.mul
-    (* let g = Term.mul u *)
 
     let of_eqs l =
       List.fold ~init:(wrt, empty)
@@ -54,42 +50,301 @@ let%test_module _ =
         l
       |> snd
 
-    (* let and_eq a b r = and_formula wrt (Formula.eq a b) r |> snd *)
+    let add_eq a b r = add wrt (Formula.eq a b) r |> snd
-    (* let and_ r s = and_ wrt r s |> snd *)
+    let union r s = union wrt r s |> snd
-    let or_ r s = interN wrt [r; s] |> snd
+    let inter r s = inter wrt r s |> snd
-    let difference x e f = Term.d_int (Context.normalize x (Term.sub e f))
+    let implies_eq r a b = implies r (Formula.eq a b)
+    let difference x e f = Term.d_int (normalize x (Term.sub e f))
+
+    (** tests *)
+
+    let f1 = of_eqs [(!0, !1)]
+
+    let%test _ = is_unsat f1
+
+    let%expect_test _ =
+      pp_raw f1 ;
+      [%expect {| {sat= false; rep= [[-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let%test _ = is_unsat (add_eq !1 !1 f1)
+
+    let f2 = of_eqs [(x, x + !1)]
+
+    let%test _ = is_unsat f2
+
+    let%expect_test _ =
+      pp_raw f2 ;
+      [%expect {| {sat= false; rep= [[%x_5 ↦ ]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let f3 = of_eqs [(x + !0, x + !1)]
+
+    let%test _ = is_unsat f3
+
+    let%expect_test _ =
+      pp_raw f3 ;
+      [%expect {| {sat= false; rep= [[%x_5 ↦ ]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let f4 = of_eqs [(x, y); (x + !0, y + !1)]
+
+    let%test _ = is_unsat f4
+
+    let%expect_test _ =
+      pp_raw f4 ;
+      [%expect
+        {| {sat= false; rep= [[%x_5 ↦ ]; [%y_6 ↦ %x_5]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let t1 = of_eqs [(!1, !1)]
+
+    let%test _ = is_empty t1
+
+    let t2 = of_eqs [(x, x)]
+
+    let%test _ = is_empty t2
+    let%test _ = is_unsat (union f3 t2)
+    let%test _ = is_unsat (union t2 f3)
+
     let r0 = empty
 
+    let%expect_test _ =
+      pp_raw r0 ;
+      [%expect {| {sat= true; rep= [[-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let%expect_test _ =
+      pp r0 ;
+      [%expect {||}]
+
     let%test _ = difference r0 (f x) (f x) |> Poly.equal (Some (Z.of_int 0))
     let%test _ = difference r0 !4 !3 |> Poly.equal (Some (Z.of_int 1))
 
     let r1 = of_eqs [(x, y)]
+
+    let%expect_test _ =
+      pp r1 ;
+      pp_raw r1 ;
+      [%expect
+        {|
+        %x_5 = %y_6
+
+      {sat= true; rep= [[%x_5 ↦ ]; [%y_6 ↦ %x_5]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let%test _ = implies_eq r1 x y
+
     let r2 = of_eqs [(x, y); (f x, y); (f y, z)]
 
-    let%test _ = difference (or_ r1 r2) x z |> Poly.equal None
+    let%expect_test _ =
+      pp r2 ;
+      pp_raw r2 ;
+      [%expect
+        {|
+        %x_5 = %y_6 = %z_7 = %x_5^
+
+      {sat= true;
+       rep= [[%x_5 ↦ ];
+             [%y_6 ↦ %x_5];
+             [%z_7 ↦ %x_5];
+             [%x_5^ ↦ %x_5];
+             [-1 ↦ ];
+             [0 ↦ ]]} |}]
+
+    let%test _ = implies_eq r2 x z
+    let%test _ = implies_eq (inter r1 r2) x y
+    let%test _ = not (implies_eq (inter r1 r2) x z)
+    let%test _ = difference (inter r1 r2) x z |> Poly.equal None
+    let%test _ = implies_eq (inter f1 r2) x z
+    let%test _ = implies_eq (inter r2 f3) x z
+    let%test _ = implies_eq r2 (f y) y
+    let%test _ = implies_eq r2 (f x) (f z)
+    let%test _ = implies_eq r2 (g x y) (g z y)
+
+    let%expect_test _ =
+      let r = of_eqs [(w, y); (y, z)] in
+      let s = of_eqs [(x, y); (y, z)] in
+      let rs = inter r s in
+      pp_raw r ;
+      pp_raw s ;
+      pp_raw rs ;
+      [%expect
+        {|
+        {sat= true;
+         rep= [[%w_4 ↦ ]; [%y_6 ↦ %w_4]; [%z_7 ↦ %w_4]; [-1 ↦ ]; [0 ↦ ]]}
+
+        {sat= true;
+         rep= [[%x_5 ↦ ]; [%y_6 ↦ %x_5]; [%z_7 ↦ %x_5]; [-1 ↦ ]; [0 ↦ ]]}
+
+        {sat= true; rep= [[%y_6 ↦ ]; [%z_7 ↦ %y_6]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let%test _ =
+      let r = of_eqs [(w, y); (y, z)] in
+      let s = of_eqs [(x, y); (y, z)] in
+      let rs = inter r s in
+      implies_eq rs y z
+
+    let r3 = of_eqs [(g y z, w); (v, w); (g y w, t); (x, v); (x, u); (u, z)]
+
+    let%expect_test _ =
+      pp r3 ;
+      pp_raw r3 ;
+      [%expect
+        {|
+        %z_7 = %u_2 = %v_3 = %w_4 = %x_5 = (%z_7 × %y_6)
+      ∧ (%z_7 × (%y_6 × %y_6)) = %t_1
+
+      {sat= true;
+       rep= [[%t_1 ↦ (%y_6^2 × %z_7)];
+             [%u_2 ↦ %z_7];
+             [%v_3 ↦ %z_7];
+             [%w_4 ↦ %z_7];
+             [%x_5 ↦ %z_7];
+             [%y_6 ↦ ];
+             [%z_7 ↦ ];
+             [(%y_6 × %z_7) ↦ %z_7];
+             [(%y_6^2 × %z_7) ↦ ];
+             [-1 ↦ ];
+             [0 ↦ ]]} |}]
+
+    let%test _ = not (implies_eq r3 t z) (* incomplete *)
+    let%test _ = implies_eq r3 x z
+    let%test _ = implies_eq (union r2 r3) x z
 
     let r4 = of_eqs [(w + !2, x - !3); (x - !5, y + !7); (y, z - !4)]
 
+    let%expect_test _ =
+      pp r4 ;
+      pp_raw r4 ;
+      [%expect
+        {|
+        (-4 + %z_7) = %y_6 ∧ (3 + %z_7) = %w_4 ∧ (8 + %z_7) = %x_5
+
+      {sat= true;
+       rep= [[%w_4 ↦ (%z_7 + 3)];
+             [%x_5 ↦ (%z_7 + 8)];
+             [%y_6 ↦ (%z_7 + -4)];
+             [%z_7 ↦ ];
+             [-1 ↦ ];
+             [0 ↦ ]]} |}]
+
+    let%test _ = implies_eq r4 x (w + !5)
     let%test _ = difference r4 x w |> Poly.equal (Some (Z.of_int 5))
 
+    let r5 = of_eqs [(x, y); (g w x, y); (g w y, f z)]
+
+    let%test _ = Var.Set.equal (fv r5) (Var.Set.of_list [w_; x_; y_; z_])
+
+    let r6 = of_eqs [(x, !1); (!1, y)]
+
+    let%expect_test _ =
+      pp r6 ;
+      pp_raw r6 ;
+      [%expect
+        {|
+        1 = %x_5 = %y_6
+
+      {sat= true; rep= [[%x_5 ↦ 1]; [%y_6 ↦ 1]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let%test _ = implies_eq r6 x y
+
+    let r7 = of_eqs [(v, x); (w, z); (y, z)]
+
+    let%expect_test _ =
+      pp r7 ;
+      pp_raw r7 ;
+      pp_raw (add_eq x z r7) ;
+      pp (add_eq x z r7) ;
+      [%expect
+        {|
+          %v_3 = %x_5 ∧ %w_4 = %y_6 = %z_7
+    
+        {sat= true;
+         rep= [[%v_3 ↦ ];
+               [%w_4 ↦ ];
+               [%x_5 ↦ %v_3];
+               [%y_6 ↦ %w_4];
+               [%z_7 ↦ %w_4];
+               [-1 ↦ ];
+               [0 ↦ ]]}
+
+        {sat= true;
+         rep= [[%v_3 ↦ ];
+               [%w_4 ↦ %v_3];
+               [%x_5 ↦ %v_3];
+               [%y_6 ↦ %v_3];
+               [%z_7 ↦ %v_3];
+               [-1 ↦ ];
+               [0 ↦ ]]}
+
+          %v_3 = %w_4 = %x_5 = %y_6 = %z_7 |}]
+
+    let%expect_test _ =
+      printf (List.pp " , " Term.pp) (class_of r7 t) ;
+      printf (List.pp " , " Term.pp) (class_of r7 x) ;
+      printf (List.pp " , " Term.pp) (class_of r7 z) ;
+      [%expect
+        {|
+        %t_1
+
+        %v_3 , %x_5
+
+        %w_4 , %z_7 , %y_6 |}]
+
+    let r7' = add_eq x z r7
+
+    let%expect_test _ =
+      pp r7' ;
+      pp_raw r7' ;
+      [%expect
+        {|
+        %v_3 = %w_4 = %x_5 = %y_6 = %z_7
+
+      {sat= true;
+       rep= [[%v_3 ↦ ];
+             [%w_4 ↦ %v_3];
+             [%x_5 ↦ %v_3];
+             [%y_6 ↦ %v_3];
+             [%z_7 ↦ %v_3];
+             [-1 ↦ ];
+             [0 ↦ ]]} |}]
+
+    let%test _ = normalize r7' w |> Term.equal v
+
+    let%test _ =
+      implies_eq (of_eqs [(g w x, g y z); (x, z)]) (g w x) (g w z)
+
+    let%test _ =
+      implies_eq (of_eqs [(g w x, g y w); (x, z)]) (g w x) (g w z)
+
+    let r8 = of_eqs [(x + !42, (3 * y) + (13 * z)); (13 * z, x)]
+
+    let%expect_test _ =
+      pp r8 ;
+      pp_raw r8 ;
+      [%expect
+        {|
+        14 = %y_6 ∧ (13 × %z_7) = %x_5
+    
+      {sat= true;
+       rep= [[%x_5 ↦ (13 × %z_7)]; [%y_6 ↦ 14]; [%z_7 ↦ ]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let%test _ = implies_eq r8 y !14
+
     let r9 = of_eqs [(x, z - !16)]
 
     let%expect_test _ =
-      pp r9 ;
+      pp_raw r9 ;
       pp_raw r9 ;
       [%expect
         {|
-        (-16 + %z_5) = %x_3
-    
       {sat= true;
-       rep= [[%x_3 ↦ (%z_5 + -16)]; [%z_5 ↦ ]; [-1 ↦ ]; [0 ↦ ]]} |}]
+       rep= [[%x_5 ↦ (%z_7 + -16)]; [%z_7 ↦ ]; [-1 ↦ ]; [0 ↦ ]]}
+
+      {sat= true;
+       rep= [[%x_5 ↦ (%z_7 + -16)]; [%z_7 ↦ ]; [-1 ↦ ]; [0 ↦ ]]} |}]
 
     let%test _ = difference r9 z (x + !8) |> Poly.equal (Some (Z.of_int 8))
 
     let r10 = of_eqs [(!16, z - x)]
 
     let%expect_test _ =
-      pp r10 ;
+      pp_raw r10 ;
       pp_raw r10 ;
       Format.printf "@.%a@." Term.pp (z - (x + !8)) ;
       Format.printf "@.%a@." Term.pp (normalize r10 (z - (x + !8))) ;
@@ -97,16 +352,17 @@ let%test_module _ =
       Format.printf "@.%a@." Term.pp (normalize r10 (x + !8 - z)) ;
       [%expect
         {|
-          (-16 + %z_5) = %x_3
-    
         {sat= true;
-         rep= [[%x_3 ↦ (%z_5 + -16)]; [%z_5 ↦ ]; [-1 ↦ ]; [0 ↦ ]]}
+         rep= [[%x_5 ↦ (%z_7 + -16)]; [%z_7 ↦ ]; [-1 ↦ ]; [0 ↦ ]]}
 
-        (%z_5 - (%x_3 + 8))
+        {sat= true;
+         rep= [[%x_5 ↦ (%z_7 + -16)]; [%z_7 ↦ ]; [-1 ↦ ]; [0 ↦ ]]}
+
+        (%z_7 - (%x_5 + 8))
 
         8
 
-        ((%x_3 + 8) - %z_5)
+        ((%x_5 + 8) - %z_7)
 
         -8 |}]
 
@@ -114,4 +370,129 @@ let%test_module _ =
 
     let%test _ =
       difference r10 (x + !8) z |> Poly.equal (Some (Z.of_int (-8)))
+
+    let r11 = of_eqs [(!16, z - x); (x + !8 - z, z - !16 + !8 - z)]
+
+    let%expect_test _ =
+      pp r11 ;
+      [%expect {| (-16 + %z_7) = %x_5 |}]
+
+    let r12 = of_eqs [(!16, z - x); (x + !8 - z, z + !16 + !8 - z)]
+
+    let%expect_test _ =
+      pp r12 ;
+      [%expect {| (-16 + %z_7) = %x_5 |}]
+
+    let r13 =
+      of_eqs
+        [ (Formula.inject (Formula.eq x !2), y)
+        ; (Formula.inject (Formula.dq x !2), z)
+        ; (y, z) ]
+
+    let%expect_test _ =
+      pp_raw r13 ;
+      [%expect
+        {| {sat= true; rep= [[%y_6 ↦ ]; [%z_7 ↦ %y_6]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let%test _ = not (is_unsat r13) (* incomplete *)
+
+    let a = Formula.inject (Formula.dq x !0)
+    let r14 = of_eqs [(a, a); (x, !1)]
+
+    let%expect_test _ =
+      pp_raw r14 ;
+      [%expect
+        {|
+          {sat= true; rep= [[%x_5 ↦ 1]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let%test _ = implies_eq r14 a (Formula.inject Formula.tt)
+
+    let b = Formula.inject (Formula.dq y !0)
+    let r14 = of_eqs [(a, b); (x, !1)]
+
+    let%expect_test _ =
+      pp_raw r14 ;
+      [%expect
+        {|
+          {sat= true;
+           rep= [[%x_5 ↦ 1];
+                 [%y_6 ↦ ];
+                 [(%x_5 ≠ 0) ↦ -1];
+                 [(%y_6 ≠ 0) ↦ -1];
+                 [-1 ↦ ];
+                 [0 ↦ ]]} |}]
+
+    let%test _ = implies_eq r14 a (Formula.inject Formula.tt)
+    let%test _ = implies_eq r14 b (Formula.inject Formula.tt)
+
+    let b = Formula.inject (Formula.dq x !0)
+    let r15 = of_eqs [(b, b); (x, !1)]
+
+    let%expect_test _ =
+      pp_raw r15 ;
+      [%expect
+        {|
+          {sat= true; rep= [[%x_5 ↦ 1]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    (* f(x−1)−1=x+1, f(y)+1=y−1, y+1=x ⊢ false *)
+    let r16 =
+      of_eqs [(f (x - !1) - !1, x + !1); (f y + !1, y - !1); (y + !1, x)]
+
+    let%expect_test _ =
+      pp_raw r16 ;
+      [%expect
+        {|
+      {sat= false;
+       rep= [[%x_5 ↦ (%y_6 + 1)];
+             [%y_6 ↦ ];
+             [%y_6^ ↦ (%y_6 + -2)];
+             [(%x_5 + -1)^ ↦ (%y_6 + 3)];
+             [-1 ↦ ];
+             [0 ↦ ]]} |}]
+
+    let%test _ = is_unsat r16
+
+    (* f(x) = x, f(y) = y − 1, y = x ⊢ false *)
+    let r17 = of_eqs [(f x, x); (f y, y - !1); (y, x)]
+
+    let%expect_test _ =
+      pp_raw r17 ;
+      [%expect
+        {|
+      {sat= false;
+       rep= [[%x_5 ↦ ];
+             [%y_6 ↦ %x_5];
+             [%x_5^ ↦ %x_5];
+             [%y_6^ ↦ (%x_5 + -1)];
+             [-1 ↦ ];
+             [0 ↦ ]]} |}]
+
+    let%test _ = is_unsat r17
+
+    let%expect_test _ =
+      let r18 = of_eqs [(f x, x); (f y, y - !1)] in
+      pp_raw r18 ;
+      pp r18 ;
+      [%expect
+        {|
+        {sat= true;
+         rep= [[%x_5 ↦ ];
+               [%y_6 ↦ ];
+               [%x_5^ ↦ %x_5];
+               [%y_6^ ↦ (%y_6 + -1)];
+               [-1 ↦ ];
+               [0 ↦ ]]}
+
+          %x_5 = %x_5^ ∧ (-1 + %y_6) = %y_6^ |}]
+
+    let r19 = of_eqs [(x, y + z); (x, !0); (y, !0)]
+
+    let%expect_test _ =
+      pp_raw r19 ;
+      [%expect
+        {|
+          {sat= true;
+           rep= [[%x_5 ↦ 0]; [%y_6 ↦ 0]; [%z_7 ↦ 0]; [-1 ↦ ]; [0 ↦ ]]} |}]
+
+    let%test _ = implies_eq r19 z !0
   end )

sledge/src/ses/equality_test.ml

@@ -22,10 +22,6 @@ let%test_module _ =
     let pp = printf pp
     let pp_classes = Format.printf "@\n@[<hv>  %a@]@." pp_classes
     let ( ! ) i = Term.integer (Z.of_int i)
-    let ( + ) = Term.add
-    let ( - ) = Term.sub
-    let ( * ) i e = Term.mulq (Q.of_int i) e
-    let f = Term.unsigned 8
     let g = Term.rem
     let wrt = Var.Set.empty
     let t_, wrt = Var.fresh "t" ~wrt
@@ -50,131 +46,9 @@ let%test_module _ =
       |> snd
 
     let implies_eq r a b = implies r (Term.eq a b)
-    let and_eq a b r = and_eq wrt a b r |> snd
-    let and_ r s = and_ wrt r s |> snd
-    let or_ r s = or_ wrt r s |> snd
-    let fv e = fold_vars e ~f:Var.Set.add ~init:Var.Set.empty
 
     (* tests *)
 
-    let f1 = of_eqs [(!0, !1)]
-
-    let%test _ = is_false f1
-
-    let%expect_test _ =
-      pp f1 ;
-      [%expect {| {sat= false; rep= [[-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let%test _ = is_false (and_eq !1 !1 f1)
-
-    let f2 = of_eqs [(x, x + !1)]
-
-    let%test _ = is_false f2
-
-    let%expect_test _ =
-      pp f2 ;
-      [%expect {| {sat= false; rep= [[%x_5 ↦ ]; [-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let f3 = of_eqs [(x + !0, x + !1)]
-
-    let%test _ = is_false f3
-
-    let%expect_test _ =
-      pp f3 ;
-      [%expect {| {sat= false; rep= [[%x_5 ↦ ]; [-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let f4 = of_eqs [(x, y); (x + !0, y + !1)]
-
-    let%test _ = is_false f4
-
-    let%expect_test _ =
-      pp f4 ;
-      [%expect
-        {|
-          {sat= false; rep= [[%x_5 ↦ ]; [%y_6 ↦ %x_5]; [-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let t1 = of_eqs [(!1, !1)]
-
-    let%test _ = is_true t1
-
-    let t2 = of_eqs [(x, x)]
-
-    let%test _ = is_true t2
-    let%test _ = is_false (and_ f3 t2)
-    let%test _ = is_false (and_ t2 f3)
-
-    let r0 = true_
-
-    let%expect_test _ =
-      pp r0 ;
-      [%expect {| {sat= true; rep= [[-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let%expect_test _ =
-      pp_classes r0 ;
-      [%expect {||}]
-
-    let r1 = of_eqs [(x, y)]
-
-    let%expect_test _ =
-      pp_classes r1 ;
-      pp r1 ;
-      [%expect
-        {|
-        %x_5 = %y_6
-
-      {sat= true; rep= [[%x_5 ↦ ]; [%y_6 ↦ %x_5]; [-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let%test _ = implies_eq r1 x y
-
-    let r2 = of_eqs [(x, y); (f x, y); (f y, z)]
-
-    let%expect_test _ =
-      pp_classes r2 ;
-      pp r2 ;
-      [%expect
-        {|
-        %x_5 = %y_6 = %z_7 = ((u8) %x_5)
-
-      {sat= true;
-       rep= [[%x_5 ↦ ];
-             [%y_6 ↦ %x_5];
-             [%z_7 ↦ %x_5];
-             [((u8) %x_5) ↦ %x_5];
-             [-1 ↦ ];
-             [0 ↦ ]]} |}]
-
-    let%test _ = implies_eq r2 x z
-    let%test _ = implies_eq (or_ r1 r2) x y
-    let%test _ = not (implies_eq (or_ r1 r2) x z)
-    let%test _ = implies_eq (or_ f1 r2) x z
-    let%test _ = implies_eq (or_ r2 f3) x z
-    let%test _ = implies_eq r2 (f y) y
-    let%test _ = implies_eq r2 (f x) (f z)
-    let%test _ = implies_eq r2 (g x y) (g z y)
-
-    let%expect_test _ =
-      let r = of_eqs [(w, y); (y, z)] in
-      let s = of_eqs [(x, y); (y, z)] in
-      let rs = or_ r s in
-      pp r ;
-      pp s ;
-      pp rs ;
-      [%expect
-        {|
-        {sat= true;
-         rep= [[%w_4 ↦ ]; [%y_6 ↦ %w_4]; [%z_7 ↦ %w_4]; [-1 ↦ ]; [0 ↦ ]]}
-
-        {sat= true;
-         rep= [[%x_5 ↦ ]; [%y_6 ↦ %x_5]; [%z_7 ↦ %x_5]; [-1 ↦ ]; [0 ↦ ]]}
-
-        {sat= true; rep= [[%y_6 ↦ ]; [%z_7 ↦ %y_6]; [-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let%test _ =
-      let r = of_eqs [(w, y); (y, z)] in
-      let s = of_eqs [(x, y); (y, z)] in
-      let rs = or_ r s in
-      implies_eq rs y z
-
     let r3 = of_eqs [(g y z, w); (v, w); (g y w, t); (x, v); (x, u); (u, z)]
 
     let%expect_test _ =
@@ -199,185 +73,6 @@ let%test_module _ =
              [0 ↦ ]]} |}]
 
     let%test _ = implies_eq r3 t z
-    let%test _ = implies_eq r3 x z
-    let%test _ = implies_eq (and_ r2 r3) x z
-
-    let r4 = of_eqs [(w + !2, x - !3); (x - !5, y + !7); (y, z - !4)]
-
-    let%expect_test _ =
-      pp_classes r4 ;
-      pp r4 ;
-      [%expect
-        {|
-        (%z_7 + -4) = %y_6 ∧ (%z_7 + 3) = %w_4 ∧ (%z_7 + 8) = %x_5
-
-      {sat= true;
-       rep= [[%w_4 ↦ (%z_7 + 3)];
-             [%x_5 ↦ (%z_7 + 8)];
-             [%y_6 ↦ (%z_7 + -4)];
-             [%z_7 ↦ ];
-             [-1 ↦ ];
-             [0 ↦ ]]} |}]
-
-    let%test _ = implies_eq r4 x (w + !5)
-
-    let r5 = of_eqs [(x, y); (g w x, y); (g w y, f z)]
-
-    let%test _ = Var.Set.equal (fv r5) (Var.Set.of_list [w_; x_; y_; z_])
-
-    let r6 = of_eqs [(x, !1); (!1, y)]
-
-    let%expect_test _ =
-      pp_classes r6 ;
-      pp r6 ;
-      [%expect
-        {|
-        1 = %x_5 = %y_6
-
-      {sat= true; rep= [[%x_5 ↦ 1]; [%y_6 ↦ 1]; [-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let%test _ = implies_eq r6 x y
-
-    let r7 = of_eqs [(v, x); (w, z); (y, z)]
-
-    let%expect_test _ =
-      pp_classes r7 ;
-      pp r7 ;
-      pp (and_eq x z r7) ;
-      pp_classes (and_eq x z r7) ;
-      [%expect
-        {|
-          %v_3 = %x_5 ∧ %w_4 = %y_6 = %z_7
-    
-        {sat= true;
-         rep= [[%v_3 ↦ ];
-               [%w_4 ↦ ];
-               [%x_5 ↦ %v_3];
-               [%y_6 ↦ %w_4];
-               [%z_7 ↦ %w_4];
-               [-1 ↦ ];
-               [0 ↦ ]]}
-
-        {sat= true;
-         rep= [[%v_3 ↦ ];
-               [%w_4 ↦ %v_3];
-               [%x_5 ↦ %v_3];
-               [%y_6 ↦ %v_3];
-               [%z_7 ↦ %v_3];
-               [-1 ↦ ];
-               [0 ↦ ]]}
-
-          %v_3 = %w_4 = %x_5 = %y_6 = %z_7 |}]
-
-    let%expect_test _ =
-      printf (List.pp " , " Term.pp) (Equality.class_of r7 t) ;
-      printf (List.pp " , " Term.pp) (Equality.class_of r7 x) ;
-      printf (List.pp " , " Term.pp) (Equality.class_of r7 z) ;
-      [%expect
-        {|
-        %t_1
-
-        %v_3 , %x_5
-
-        %w_4 , %z_7 , %y_6 |}]
-
-    let r7' = and_eq x z r7
-
-    let%expect_test _ =
-      pp_classes r7' ;
-      pp r7' ;
-      [%expect
-        {|
-        %v_3 = %w_4 = %x_5 = %y_6 = %z_7
-
-      {sat= true;
-       rep= [[%v_3 ↦ ];
-             [%w_4 ↦ %v_3];
-             [%x_5 ↦ %v_3];
-             [%y_6 ↦ %v_3];
-             [%z_7 ↦ %v_3];
-             [-1 ↦ ];
-             [0 ↦ ]]} |}]
-
-    let%test _ = normalize r7' w |> Term.equal v
-
-    let%test _ =
-      implies_eq (of_eqs [(g w x, g y z); (x, z)]) (g w x) (g w z)
-
-    let%test _ =
-      implies_eq (of_eqs [(g w x, g y w); (x, z)]) (g w x) (g w z)
-
-    let r8 = of_eqs [(x + !42, (3 * y) + (13 * z)); (13 * z, x)]
-
-    let%expect_test _ =
-      pp_classes r8 ;
-      pp r8 ;
-      [%expect
-        {|
-        (13 × %z_7) = %x_5 ∧ 14 = %y_6
-    
-      {sat= true;
-       rep= [[%x_5 ↦ (13 × %z_7)]; [%y_6 ↦ 14]; [%z_7 ↦ ]; [-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let%test _ = implies_eq r8 y !14
-
-    let r11 = of_eqs [(!16, z - x); (x + !8 - z, z - !16 + !8 - z)]
-
-    let%expect_test _ =
-      pp_classes r11 ;
-      [%expect {| (%z_7 + -16) = %x_5 |}]
-
-    let r12 = of_eqs [(!16, z - x); (x + !8 - z, z + !16 + !8 - z)]
-
-    let%expect_test _ =
-      pp_classes r12 ;
-      [%expect {| (%z_7 + -16) = %x_5 |}]
-
-    let r13 = of_eqs [(Term.eq x !2, y); (Term.dq x !2, z); (y, z)]
-
-    let%expect_test _ =
-      pp r13 ;
-      [%expect
-        {|
-      {sat= true;
-       rep= [[%x_5 ↦ ];
-             [%y_6 ↦ ];
-             [%z_7 ↦ %y_6];
-             [(%x_5 = 2) ↦ %y_6];
-             [(%x_5 ≠ 2) ↦ %y_6];
-             [-1 ↦ ];
-             [0 ↦ ]]} |}]
-
-    let%test _ = not (is_false r13) (* incomplete *)
-
-    let a = Term.dq x !0
-    let r14 = of_eqs [(a, a); (x, !1)]
-
-    let%expect_test _ =
-      pp r14 ;
-      [%expect
-        {|
-          {sat= true; rep= [[%x_5 ↦ 1]; [(%x_5 ≠ 0) ↦ -1]; [-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let%test _ = implies_eq r14 a Term.true_
-
-    let b = Term.dq y !0
-    let r14 = of_eqs [(a, b); (x, !1)]
-
-    let%expect_test _ =
-      pp r14 ;
-      [%expect
-        {|
-          {sat= true;
-           rep= [[%x_5 ↦ 1];
-                 [%y_6 ↦ ];
-                 [(%x_5 ≠ 0) ↦ -1];
-                 [(%y_6 ≠ 0) ↦ -1];
-                 [-1 ↦ ];
-                 [0 ↦ ]]} |}]
-
-    let%test _ = implies_eq r14 a Term.true_
-    let%test _ = implies_eq r14 b Term.true_
 
     let b = Term.dq x !0
     let r15 = of_eqs [(b, b); (x, !1)]
@@ -390,66 +85,4 @@ let%test_module _ =
 
     let%test _ = implies_eq r15 b (Term.signed 1 !1)
     let%test _ = implies_eq r15 (Term.unsigned 1 b) !1
-
-    (* f(x−1)−1=x+1, f(y)+1=y−1, y+1=x ⊢ false *)
-    let r16 =
-      of_eqs [(f (x - !1) - !1, x + !1); (f y + !1, y - !1); (y + !1, x)]
-
-    let%expect_test _ =
-      pp r16 ;
-      [%expect
-        {|
-      {sat= false;
-       rep= [[%x_5 ↦ (%y_6 + 1)];
-             [%y_6 ↦ ];
-             [((u8) %y_6) ↦ (%y_6 + -2)];
-             [((u8) (%x_5 + -1)) ↦ (%y_6 + 3)];
-             [-1 ↦ ];
-             [0 ↦ ]]} |}]
-
-    let%test _ = is_false r16
-
-    (* f(x) = x, f(y) = y − 1, y = x ⊢ false *)
-    let r17 = of_eqs [(f x, x); (f y, y - !1); (y, x)]
-
-    let%expect_test _ =
-      pp r17 ;
-      [%expect
-        {|
-      {sat= false;
-       rep= [[%x_5 ↦ ];
-             [%y_6 ↦ %x_5];
-             [((u8) %x_5) ↦ %x_5];
-             [((u8) %y_6) ↦ (%x_5 + -1)];
-             [-1 ↦ ];
-             [0 ↦ ]]} |}]
-
-    let%test _ = is_false r17
-
-    let%expect_test _ =
-      let r18 = of_eqs [(f x, x); (f y, y - !1)] in
-      pp r18 ;
-      pp_classes r18 ;
-      [%expect
-        {|
-        {sat= true;
-         rep= [[%x_5 ↦ ];
-               [%y_6 ↦ ];
-               [((u8) %x_5) ↦ %x_5];
-               [((u8) %y_6) ↦ (%y_6 + -1)];
-               [-1 ↦ ];
-               [0 ↦ ]]}
-
-          %x_5 = ((u8) %x_5) ∧ (%y_6 + -1) = ((u8) %y_6) |}]
-
-    let r19 = of_eqs [(x, y + z); (x, !0); (y, !0)]
-
-    let%expect_test _ =
-      pp r19 ;
-      [%expect
-        {|
-          {sat= true;
-           rep= [[%x_5 ↦ 0]; [%y_6 ↦ 0]; [%z_7 ↦ 0]; [-1 ↦ ]; [0 ↦ ]]} |}]
-
-    let%test _ = implies_eq r19 z !0
   end )