Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/graphs/   (PVS Prover Version 6.0.9©)  Datei vom 28.9.2014 mit Größe 7 MB image not shown  

Impressum k_menger.prf   Sprache: Lisp

 

(k_menger
 (sep_num_B 0
  (sep_num_B-1 nil 3375303932
   ("" (skosimp*)
    (("" (expand "B")
      (("" (prop)
        (("" (copy -1)
          (("" (inst -3 "min_sep_set(G!1,s!1,t!1)")
            (("" (expand "sep_num")
              (("" (lemma "min_sep_set_card")
                (("" (inst?)
                  (("1" (bddsimp)
                    (("1" (lemma "min_sep_set_seps")
                      (("1" (inst?)
                        (("1" (prop)
                          (("1" (expand "good?") (("1" (prop) nil nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (expand "good?") (("2" (bddsimp) nil nil)) nil)
                   ("3" (expand "good?") (("3" (bddsimp) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((B const-decl "bool" k_menger nil)
    (sep_num const-decl "nat" sep_sets nil)
    (G!1 skolem-const-decl "graph[T]" k_menger nil)
    (s!1 skolem-const-decl "T" k_menger nil)
    (t!1 skolem-const-decl "T" k_menger nil)
    (min_sep_set_seps formula-decl nil sep_sets nil)
    (good? const-decl "bool" k_menger nil)
    (min_sep_set_card formula-decl nil sep_sets nil)
    (min_sep_set const-decl "finite_set[T]" sep_sets nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil k_menger nil))
   shostak))
 (sep_num_implies 0
  (sep_num_implies-1 nil 3379680344
   ("" (skosimp*)
    (("" (expand "B")
      (("" (prop)
        (("" (skosimp*)
          (("" (lemma "min_sep_set_card")
            (("" (inst?)
              (("1" (expand "sep_num")
                (("1" (prop) (("1" (assert) nil nil)) nil)) nil)
               ("2" (expand "good?") (("2" (prop) nil nil)) nil)
               ("3" (expand "good?") (("3" (prop) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((B const-decl "bool" k_menger nil)
    (s!1 skolem-const-decl "T" k_menger nil)
    (G!1 skolem-const-decl "graph[T]" k_menger nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (t!1 skolem-const-decl "T" k_menger nil)
    (is_finite const-decl "bool" finite_sets nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (sep_num const-decl "nat" sep_sets nil)
    (good? const-decl "bool" k_menger nil)
    (min_sep_set_card formula-decl nil sep_sets nil)
    (T formal-type-decl nil k_menger nil))
   shostak))
 (card_extension_W 0
  (card_extension_W-1 nil 3389097760
   ("" (skosimp*)
    (("" (lemma "card_extension[T,(W!1)]")
      (("" (inst -1 "V!1")
        (("" (expand "restrict")
          (("" (expand "extend")
            ((""
              (case "(LAMBDA (t: T): IF (W!1)(t) THEN V!1(t) ELSE FALSE ENDIF)=V!1")
              (("1" (replace -1 1 lr) (("1" (propax) nil nil)) nil)
               ("2" (hide 2)
                (("2" (apply-extensionality 1 :hide? t)
                  (("2" (iff)
                    (("2" (prop)
                      (("2" (expand "subset?")
                        (("2" (inst? -3)
                          (("2" (expand "member")
                            (("2" (prop) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil k_menger nil)
    (card_extension formula-decl nil finite_sets_card_from nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (FALSE const-decl "bool" booleans nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (extend const-decl "R" extend nil)
    (restrict const-decl "R" restrict nil)
    (finite_restrict application-judgement "finite_set[S]"
     restrict_set_props nil))
   shostak))
 (card_extension_same 0
  (card_extension_same-1 nil 3389098779
   ("" (skosimp*)
    (("" (lemma "card_extension_W")
      (("" (inst -1 "W!1" "W!1")
        (("" (prop) (("" (hide 2) (("" (grind) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((card_extension_W formula-decl nil k_menger nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil k_menger nil))
   shostak))
 (easy_menger_B 0
  (easy_menger_B-2 "sec" 3379689668
   ("" (skosimp*)
    (("" (lemma "easy_menger[T]")
      (("" (expand "many_ind")
        (("" (skosimp*)
          (("" (inst -1 "G!1" "s!1" "t!1" "ips!1")
            (("" (expand "B")
              (("" (prop)
                (("1" (expand "st_path_set?")
                  (("1"
                    (lemma
                     "finite_sets_card_eq[prewalk,Path_from[T](G!1, s!1, t!1)].card_eq_bij")
                    (("1" (expand "restrict")
                      (("1"
                        (inst -1 "ips!1"
                         "LAMBDA (s: Path_from[T](G!1, s!1, t!1)): ips!1(s)")
                        (("1" (prop)
                          (("1" (replace -1 -3 rl)
                            (("1" (replace -7 -3 lr)
                              (("1"
                                (lemma "min_sep_set_card")
                                (("1"
                                  (skosimp*)
                                  (("1"
                                    (inst?)
                                    (("1"
                                      (expand "sep_num")
                                      (("1"
                                        (prop)
                                        (("1" (assert) nil nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (expand "good?")
                                      (("2" (prop) nil nil))
                                      nil)
                                     ("3"
                                      (expand "good?")
                                      (("3" (prop) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (hide -1 -3 -5 2 3)
                            (("2" (inst 1 "LAMBDA (p1:(ips!1)) :p1")
                              (("1" (grind) nil nil)
                               ("2" (grind) nil nil))
                              nil))
                            nil))
                          nil)
                         ("2" (hide -1 -3 -5 2)
                          (("2" (typepred "ips!1")
                            (("2"
                              (lemma
                               "restrict_set_props[prewalk,Path_from[T](G!1, s!1, t!1)].restrict_finite")
                              (("2"
                                (inst -1 "ips!1")
                                (("2"
                                  (prop)
                                  (("2"
                                    (expand "restrict")
                                    (("2" (propax) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (expand "good?") (("2" (prop) nil nil)) nil)
                 ("3" (hide -4 1) (("3" (grind) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil k_menger nil)
    (easy_menger formula-decl nil easy_menger nil)
    (B const-decl "bool" k_menger nil)
    (ind_prewalk_set? const-decl "bool" k_menger nil)
    (ind_path_set? const-decl "bool" ind_paths nil)
    (independent? const-decl "bool" ind_paths nil)
    (st_path_set? const-decl "bool" k_menger nil)
    (restrict_finite formula-decl nil restrict_set_props nil)
    (good? const-decl "bool" k_menger nil)
    (sep_num const-decl "nat" sep_sets nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (min_sep_set_card formula-decl nil sep_sets nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (odd_plus_even_is_odd application-judgement "odd_int" integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (from? const-decl "bool" walks nil)
    (path? const-decl "bool" paths nil)
    (walk? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (verts_in? const-decl "bool" walks nil)
    (separable? const-decl "bool" sep_sets nil)
    (edge? const-decl "bool" graphs nil)
    (bijective? const-decl "bool" functions nil)
    (surjective? const-decl "bool" functions nil)
    (injective? const-decl "bool" functions nil)
    (nil application-judgement "finite_set[T]" k_menger nil)
    (nil application-judgement "finite_set[T]" graphs nil)
    (ips!1 skolem-const-decl "set_of_prewalks" k_menger nil)
    (t!1 skolem-const-decl "T" k_menger nil)
    (s!1 skolem-const-decl "T" k_menger nil)
    (G!1 skolem-const-decl "graph[T]" k_menger nil)
    (card_eq_bij formula-decl nil finite_sets_card_eq "finite_sets/")
    (set_of_prewalks type-eq-decl nil k_menger nil)
    (restrict const-decl "R" restrict nil)
    (set_of_paths type-eq-decl nil ind_paths nil)
    (is_finite const-decl "bool" finite_sets nil)
    (Path_from type-eq-decl nil paths nil)
    (path_from? const-decl "bool" paths nil)
    (prewalk type-eq-decl nil walks nil)
    (> const-decl "bool" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (finite_restrict application-judgement "finite_set[S]"
     restrict_set_props nil)
    (many_ind const-decl "bool" k_menger nil))
   shostak)
  (easy_menger_B-1 nil 3379687287
   ("" (skosimp*)
    (("" (lemma "easy_menger")
      (("" (expand "many_ind")
        (("" (skosimp*)
          (("" (inst -1 "G!1" "s!1" "t!1" "ips!1")
            (("" (prop)
              (("1" (expand "B")
                (("1" (prop)
                  (("1" (postpone) nil nil) ("2" (postpone) nil nil))
                  nil))
                nil)
               ("2" (postpone) nil nil) ("3" (postpone) nil nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   nil shostak))
 (sep_set_small 0
  (sep_set_small-1 nil 3379682439
   ("" (skosimp*)
    (("" (expand "B")
      (("" (prop)
        (("" (inst?)
          (("" (prop)
            (("1" (assert) nil nil)
             ("2" (expand "separates")
              (("2" (expand "green?")
                (("2" (prop)
                  (("2" (skosimp*)
                    (("2" (lemma "walk_to_path")
                      (("2" (inst -1 "del_verts(G!1,V!1)" "s!1" "t!1")
                        (("2" (prop)
                          (("1" (skosimp*)
                            (("1" (hide -3 -4 -5)
                              (("1"
                                (expand "walk_from?")
                                (("1"
                                  (prop)
                                  (("1"
                                    (inst 3 "p!1")
                                    (("1"
                                      (expand "path_from?")
                                      (("1"
                                        (prop)
                                        (("1"
                                          (expand "from?")
                                          (("1" (assert) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (hide -2 -3 4)
                            (("2" (inst 1 "w!1") nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((B const-decl "bool" k_menger nil)
    (T formal-type-decl nil k_menger nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (separates const-decl "bool" sep_sets nil)
    (walk_to_path formula-decl nil path_ops nil)
    (path_from? const-decl "bool" paths nil)
    (from? const-decl "bool" walks nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (walk_from? const-decl "bool" walks nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (green? const-decl "bool" k_menger nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
 (B_many_1 0
  (B_many_1-1 nil 3379681920
   ("" (skosimp*)
    (("" (expand "B_many")
      (("" (prop)
        (("" (expand "many_ind")
          (("" (lemma "sep_set_small")
            (("" (expand "B")
              (("" (prop)
                (("" (inst -1 "G!1" "_" "1" "s!1" "t!1")
                  (("" (inst -1 "emptyset[T]")
                    (("" (prop)
                      (("1" (expand "del_verts")
                        (("1" (expand "difference")
                          (("1" (expand "member")
                            (("1" (assert)
                              (("1"
                                (expand "emptyset")
                                (("1"
                                  (skosimp*)
                                  (("1"
                                    (inst 1 "singleton[prewalk](p!1)")
                                    (("1"
                                      (hide -2 -3)
                                      (("1"
                                        (lemma
                                         "card_singleton[prewalk]")
                                        (("1"
                                          (inst -1 "p!1")
                                          (("1"
                                            (prop)
                                            (("1"
                                              (expand
                                               "ind_prewalk_set?")
                                              (("1"
                                                (skosimp*)
                                                (("1"
                                                  (expand "singleton")
                                                  (("1"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (expand "st_path_set?")
                                              (("2"
                                                (hide -1)
                                                (("2"
                                                  (skosimp*)
                                                  (("2"
                                                    (expand
                                                     "singleton")
                                                    (("2"
                                                      (replace -1 * lr)
                                                      (("2"
                                                        (install-rewrites
                                                         "paths")
                                                        (("2"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (hide -1 -2 2)
                        (("2" (lemma "card_emptyset[T]")
                          (("2" (assert)
                            (("2" (expand "green?")
                              (("2"
                                (prop)
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "emptyset")
                                    (("1" (propax) nil nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (expand "emptyset")
                                  (("2" (propax) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("3" (lemma "card_emptyset[T]")
                        (("3" (assert) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((B_many const-decl "bool" k_menger nil)
    (many_ind const-decl "bool" k_menger nil)
    (B const-decl "bool" k_menger nil)
    (T formal-type-decl nil k_menger nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (difference const-decl "set" sets nil)
    (st_path_set? const-decl "bool" k_menger nil)
    (path_from? const-decl "bool" paths nil)
    (from? const-decl "bool" walks nil)
    (path? const-decl "bool" paths nil)
    (walk? const-decl "bool" walks nil)
    (edge? const-decl "bool" graphs nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (verts_in? const-decl "bool" walks nil)
    (nil application-judgement "finite_set[T]" graphs nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nil application-judgement "finite_set[T]" k_menger nil)
    (ind_prewalk_set? const-decl "bool" k_menger nil)
    (card_singleton formula-decl nil finite_sets nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (set_of_prewalks type-eq-decl nil k_menger nil)
    (singleton? const-decl "bool" sets nil)
    (singleton const-decl "(singleton?)" sets nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set" finite_sets nil)
    (member const-decl "bool" sets nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (card_emptyset formula-decl nil finite_sets nil)
    (green? const-decl "bool" k_menger nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (is_finite const-decl "bool" finite_sets nil)
    (emptyset const-decl "set" sets nil)
    (finite_emptyset name-judgement "finite_set" finite_sets nil)
    (finite_emptyset name-judgement "finite_set[T]" k_menger nil)
    (sep_set_small formula-decl nil k_menger nil))
   shostak))
 (sub_tight 0
  (sub_tight-1 nil 3379015166
   ("" (skosimp*)
    (("" (expand "tight?")
      (("" (expand "subset?")
        (("" (skosimp*)
          (("" (expand "member")
            (("" (inst -1 "x!1")
              (("" (inst -2 "x!1") (("" (prop) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((tight? const-decl "bool" k_menger nil)
    (T formal-type-decl nil k_menger nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil))
   shostak))
 (smaller_tight 0
  (smaller_tight-3 "good" 3378204176
   ("" (skosimp*)
    (("" (expand "tight?")
      (("" (expand "subset?")
        (("" (expand "member")
          (("" (skosimp*)
            (("" (expand "intersection")
              (("" (expand "member")
                (("" (inst 2 "remove(x!1,W!1)")
                  (("" (prop)
                    (("1" (skosimp*)
                      (("1" (expand "remove")
                        (("1" (prop)
                          (("1" (expand "member")
                            (("1" (propax) nil nil)) nil))
                          nil))
                        nil))
                      nil)
                     ("2" (expand "remove")
                      (("2" (expand "member")
                        (("2" (hide -2 1)
                          (("2" (grind)
                            (("2" (decompose-equality -1)
                              (("2"
                                (inst -1 "x!1")
                                (("2"
                                  (iff)
                                  (("2" (prop) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("3" (expand "separates")
                      (("3" (prop)
                        (("1" (expand "remove")
                          (("1" (expand "member")
                            (("1" (prop) nil nil)) nil))
                          nil)
                         ("2" (expand "remove")
                          (("2" (expand "member")
                            (("2" (prop) nil nil)) nil))
                          nil)
                         ("3" (skosimp*)
                          (("3" (expand "walk_from?")
                            (("3" (prop)
                              (("3"
                                (inst 4 "w!1")
                                (("3"
                                  (prop)
                                  (("3"
                                    (case "verts_of(w!1)(x!1)")
                                    (("1"
                                      (hide -4)
                                      (("1"
                                        (hide 1)
                                        (("1"
                                          (expand "path_verts")
                                          (("1"
                                            (expand "verts_of")
                                            (("1"
                                              (skosimp*)
                                              (("1"
                                                (expand "finseq_appl")
                                                (("1"
                                                  (inst
                                                   1
                                                   "w!1^(0,i!1)")
                                                  (("1"
                                                    (expand
                                                     "walk_from?")
                                                    (("1"
                                                      (prop)
                                                      (("1"
                                                        (expand*
                                                         "^"
                                                         min
                                                         empty_seq)
                                                        nil
                                                        nil)
                                                       ("2"
                                                        (expand*
                                                         "^"
                                                         min
                                                         empty_seq)
                                                        nil
                                                        nil)
                                                       ("3"
                                                        (reveal -1)
                                                        (("3"
                                                          (lemma
                                                           "walk?_caret")
                                                          (("3"
                                                            (inst
                                                             -1
                                                             "G!1"
                                                             "0"
                                                             "i!1"
                                                             "w!1")
                                                            (("3"
                                                              (typepred
                                                               "i!1")
                                                              (("3"
                                                                (assert)
                                                                (("3"
                                                                  (lemma
                                                                   "walk?_subgraph")
                                                                  (("3"
                                                                    (inst
                                                                     -1
                                                                     "G!1"
                                                                     "del_verts(G!1, remove(x!1, W!1))"
                                                                     "w!1")
                                                                    (("3"
                                                                      (prop)
                                                                      (("3"
                                                                        (hide
                                                                         -2
                                                                         2
                                                                         3)
                                                                        (("3"
                                                                          (assert)
                                                                          (("3"
                                                                            (install-rewrites
                                                                             "finite_sets[T]")
                                                                            (("3"
                                                                              (assert)
                                                                              (("3"
                                                                                (prop)
                                                                                (("1"
                                                                                  (skosimp*)
                                                                                  nil
                                                                                  nil)
                                                                                 ("2"
                                                                                  (skosimp*)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (grind)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (hide 3)
                                      (("2"
                                        (install-rewrites "walks")
                                        (("2"
                                          (expand "walk?")
                                          (("2"
                                            (expand "finseq_appl")
                                            (("2"
                                              (prop)
                                              (("1"
                                                (expand "verts_in?")
                                                (("1"
                                                  (skosimp*)
                                                  (("1"
                                                    (expand
                                                     "del_verts")
                                                    (("1"
                                                      (typepred "i!1")
                                                      (("1"
                                                        (hide -5)
                                                        (("1"
                                                          (inst
                                                           -4
                                                           "i!1")
                                                          (("1"
                                                            (expand
                                                             "verts_of")
                                                            (("1"
                                                              (expand
                                                               "finseq_appl")
                                                              (("1"
                                                                (expand
                                                                 "difference")
                                                                (("1"
                                                                  (expand
                                                                   "member")
                                                                  (("1"
                                                                    (prop)
                                                                    (("1"
                                                                      (inst
                                                                       1
                                                                       "i!1")
                                                                      (("1"
                                                                        (expand
                                                                         "remove")
                                                                        (("1"
                                                                          (expand
                                                                           "member")
                                                                          (("1"
                                                                            (prop)
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (skosimp*)
                                                (("2"
                                                  (inst -5 "n!1")
                                                  (("2"
                                                    (prop)
                                                    (("2"
                                                      (expand
                                                       "verts_of")
                                                      (("2"
                                                        (expand
                                                         "finseq_appl")
                                                        (("2"
                                                          (expand
                                                           "edge?")
                                                          (("2"
                                                            (prop)
                                                            (("2"
                                                              (hide -5)
                                                              (("2"
                                                                (expand
                                                                 "del_verts")
                                                                (("2"
                                                                  (prop)
                                                                  (("2"
                                                                    (skosimp*)
                                                                    (("2"
                                                                      (copy
                                                                       -4)
                                                                      (("2"
                                                                        (inst
                                                                         -1
                                                                         "seq(w!1)(n!1)")
                                                                        (("2"
                                                                          (inst
                                                                           -5
                                                                           "seq(w!1)(n!1 + 1)")
                                                                          (("1"
                                                                            (prop)
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil)
                                                                             ("2"
                                                                              (assert)
                                                                              nil
                                                                              nil)
                                                                             ("3"
                                                                              (assert)
                                                                              nil
                                                                              nil)
                                                                             ("4"
                                                                              (assert)
                                                                              (("4"
                                                                                (prop)
                                                                                (("1"
                                                                                  (assert)
                                                                                  nil
                                                                                  nil)
                                                                                 ("2"
                                                                                  (assert)
                                                                                  nil
                                                                                  nil)
                                                                                 ("3"
                                                                                  (assert)
                                                                                  nil
                                                                                  nil)
                                                                                 ("4"
                                                                                  (assert)
                                                                                  (("4"
                                                                                    (inst
                                                                                     3
                                                                                     "1+n!1")
                                                                                    (("4"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("5"
                                                                                  (inst
                                                                                   3
                                                                                   "n!1")
                                                                                  (("5"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil)
                                                                                 ("6"
                                                                                  (inst
                                                                                   3
                                                                                   "n!1")
                                                                                  (("6"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil)
                                                                                 ("7"
                                                                                  (replace
                                                                                   -1
                                                                                   -2
                                                                                   lr)
                                                                                  (("7"
                                                                                    (propax)
                                                                                    nil
                                                                                    nil))
                                                                                  nil)
                                                                                 ("8"
                                                                                  (replace
                                                                                   -1
                                                                                   -2
                                                                                   lr)
                                                                                  (("8"
                                                                                    (propax)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (grind)
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("4" (skosimp*)
                      (("4" (hide -2 2)
                        (("4" (expand "remove")
                          (("4" (expand "member")
                            (("4" (prop) nil nil)) nil))
                          nil))
                        nil))
                      nil)
                     ("5" (hide -2 1)
                      (("5" (expand "remove")
                        (("5" (decompose-equality -1)
                          (("5" (inst?)
                            (("5" (expand "member")
                              (("5" (propax) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("6" (expand "separates")
                      (("6" (prop)
                        (("1" (expand "remove")
                          (("1" (expand "member")
                            (("1" (prop) nil nil)) nil))
                          nil)
                         ("2" (expand "remove")
                          (("2" (expand "member")
                            (("2" (prop) nil nil)) nil))
                          nil)
                         ("3" (skosimp*)
                          (("3" (expand "walk_from?")
                            (("3" (prop)
                              (("3"
                                (inst 4 "w!1")
                                (("3"
                                  (prop)
                                  (("3"
                                    (case "verts_of(w!1)(x!1)")
                                    (("1"
                                      (hide -4)
                                      (("1"
                                        (hide 1)
                                        (("1"
                                          (expand "path_verts")
                                          (("1"
                                            (expand "verts_of")
                                            (("1"
                                              (expand "finseq_appl")
                                              (("1"
                                                (skosimp*)
                                                (("1"
                                                  (inst
                                                   1
                                                   "rev(w!1)^(0,length(w!1)-1-i!1)")
                                                  (("1"
                                                    (expand
                                                     "walk_from?")
                                                    (("1"
                                                      (prop)
                                                      (("1"
                                                        (expand "rev")
                                                        (("1"
                                                          (expand*
                                                           "^"
                                                           min
                                                           empty_seq)
                                                          nil
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (expand "rev")
                                                        (("2"
                                                          (expand*
                                                           "^"
                                                           min
                                                           empty_seq)
                                                          nil
                                                          nil))
                                                        nil)
                                                       ("3"
                                                        (reveal -1)
                                                        (("3"
                                                          (lemma
                                                           "walk?_caret")
                                                          (("3"
                                                            (lemma
                                                             "walk?_rev")
                                                            (("3"
                                                              (inst
                                                               -1
                                                               "G!1"
                                                               "w!1")
                                                              (("3"
                                                                (inst
                                                                 -2
                                                                 "G!1"
                                                                 "0"
                                                                 "length(w!1)-1-i!1"
                                                                 "rev(w!1)")
                                                                (("1"
                                                                  (typepred
                                                                   "i!1")
                                                                  (("1"
                                                                    (assert)
                                                                    (("1"
                                                                      (lemma
                                                                       "walk?_subgraph")
                                                                      (("1"
                                                                        (inst
                                                                         -1
                                                                         "G!1"
                                                                         "del_verts(G!1, remove(x!1, W!1))"
                                                                         "w!1")
                                                                        (("1"
                                                                          (prop)
                                                                          (("1"
                                                                            (lemma
                                                                             "walk?_caret")
                                                                            (("1"
                                                                              (inst
                                                                               -1
                                                                               "G!1"
                                                                               "0"
                                                                               "length(w!1)-1-i!1"
                                                                               "rev(w!1)")
                                                                              (("1"
                                                                                (assert)
                                                                                (("1"
                                                                                  (expand
                                                                                   "rev")
                                                                                  (("1"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (expand
                                                                             "rev")
                                                                            (("2"
                                                                              (assert)
                                                                              nil
                                                                              nil))
                                                                            nil)
                                                                           ("3"
                                                                            (expand
                                                                             "rev")
                                                                            (("3"
                                                                              (assert)
                                                                              nil
                                                                              nil))
                                                                            nil)
                                                                           ("4"
                                                                            (hide
                                                                             -2
                                                                             1
                                                                             2
                                                                             4)
                                                                            (("4"
                                                                              (grind)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil)
                                                                 ("2"
                                                                  (expand
                                                                   "rev")
                                                                  (("2"
                                                                    (assert)
                                                                    nil
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (expand "rev")
                                                    (("2"
                                                      (expand*
                                                       "^"
                                                       min
                                                       empty_seq)
                                                      (("2"
                                                        (typepred
                                                         "i!1")
                                                        (("2"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (assert)
                                      (("2"
                                        (hide 3)
                                        (("2"
                                          (install-rewrites "walks")
                                          (("2"
                                            (expand "walk?")
                                            (("2"
                                              (expand "finseq_appl")
                                              (("2"
                                                (prop)
                                                (("1"
                                                  (expand "verts_in?")
                                                  (("1"
                                                    (skosimp*)
                                                    (("1"
                                                      (expand
                                                       "del_verts")
                                                      (("1"
                                                        (typepred
                                                         "i!1")
                                                        (("1"
                                                          (hide -5)
                                                          (("1"
                                                            (inst
                                                             -4
                                                             "i!1")
                                                            (("1"
                                                              (expand
                                                               "verts_of")
                                                              (("1"
                                                                (expand
                                                                 "finseq_appl")
                                                                (("1"
                                                                  (expand
                                                                   "difference")
                                                                  (("1"
                                                                    (expand
                                                                     "member")
                                                                    (("1"
                                                                      (prop)
                                                                      (("1"
                                                                        (inst
                                                                         1
                                                                         "i!1")
                                                                        (("1"
                                                                          (expand
                                                                           "remove")
                                                                          (("1"
                                                                            (expand
                                                                             "member")
                                                                            (("1"
                                                                              (prop)
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (skosimp*)
                                                  (("2"
                                                    (inst -5 "n!1")
                                                    (("2"
                                                      (prop)
                                                      (("2"
                                                        (expand
                                                         "verts_of")
                                                        (("2"
                                                          (expand
                                                           "finseq_appl")
                                                          (("2"
                                                            (expand
                                                             "edge?")
                                                            (("2"
                                                              (prop)
                                                              (("2"
                                                                (hide
                                                                 -5)
                                                                (("2"
                                                                  (expand
                                                                   "del_verts")
                                                                  (("2"
                                                                    (prop)
                                                                    (("2"
                                                                      (skosimp*)
                                                                      (("2"
                                                                        (copy
                                                                         -4)
                                                                        (("2"
                                                                          (inst
                                                                           -1
                                                                           "seq(w!1)(n!1)")
                                                                          (("2"
                                                                            (inst
                                                                             -5
                                                                             "seq(w!1)(n!1 + 1)")
                                                                            (("1"
                                                                              (prop)
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil)
                                                                               ("2"
                                                                                (assert)
                                                                                nil
                                                                                nil)
                                                                               ("3"
                                                                                (assert)
                                                                                nil
                                                                                nil)
                                                                               ("4"
                                                                                (assert)
                                                                                (("4"
                                                                                  (prop)
                                                                                  (("1"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil)
                                                                                   ("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil)
                                                                                   ("3"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil)
                                                                                   ("4"
                                                                                    (assert)
                                                                                    (("4"
                                                                                      (inst
                                                                                       3
                                                                                       "1+n!1")
                                                                                      (("4"
                                                                                        (assert)
                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("5"
                                                                                    (inst
                                                                                     3
                                                                                     "n!1")
                                                                                    (("5"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil)
                                                                                   ("6"
                                                                                    (inst
                                                                                     3
                                                                                     "n!1")
                                                                                    (("6"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil)
                                                                                   ("7"
                                                                                    (replace
                                                                                     -1
                                                                                     -2
                                                                                     lr)
                                                                                    (("7"
                                                                                      (propax)
                                                                                      nil
                                                                                      nil))
                                                                                    nil)
                                                                                   ("8"
                                                                                    (replace
                                                                                     -1
                                                                                     -2
                                                                                     lr)
                                                                                    (("8"
                                                                                      (propax)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil)
                                                                             ("2"
                                                                              (grind)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((tight? const-decl "bool" k_menger nil)
    (member const-decl "bool" sets nil)
    (intersection const-decl "set" sets nil)
    (finite_remove application-judgement "finite_set[T]" k_menger nil)
    (T formal-type-decl nil k_menger nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (remove const-decl "set" sets nil)
    (n!1 skolem-const-decl "nat" k_menger nil)
    (rev const-decl "finseq[T]" doubletons nil)
    (w!1 skolem-const-decl "prewalk[T]" k_menger nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (i!1 skolem-const-decl "below(length(w!1))" k_menger nil)
    (walk?_rev formula-decl nil walks nil)
    (separates const-decl "bool" sep_sets nil)
    (walk? const-decl "bool" walks nil)
    (verts_in? const-decl "bool" walks nil)
    (nil application-judgement "finite_set[T]" k_menger nil)
    (edge? const-decl "bool" graphs nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (n!1 skolem-const-decl "nat" k_menger nil)
    (path_verts const-decl "set[T]" paths nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (^ const-decl "finseq" finite_sequences nil)
    (w!1 skolem-const-decl "prewalk[T]" k_menger nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (i!1 skolem-const-decl "below(length(w!1))" k_menger nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (walk?_caret formula-decl nil walks nil)
    (walk?_subgraph formula-decl nil subgraph_paths nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (finite_difference application-judgement "finite_set[T]" k_menger
     nil)
    (difference const-decl "set" sets nil)
    (subgraph? const-decl "bool" subgraphs nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (verts_of const-decl "finite_set[T]" walks nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (walk_from? const-decl "bool" walks nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (subset? const-decl "bool" sets nil))
   shostak)
  (smaller_tight-2 "sec" 3378155661
   ("" (skosimp*)
    (("" (expand "tight?")
      (("" (expand "subset?")
        (("" (expand "member")
          (("" (skosimp*)
            (("" (expand "intersection")
              (("" (expand "member")
                (("" (inst 2 "remove(x!1,W!1)")
                  (("" (prop)
                    (("1" (skosimp*)
                      (("1" (expand "remove")
                        (("1" (prop)
                          (("1" (expand "member")
                            (("1" (propax) nil nil)) nil))
                          nil))
                        nil))
                      nil)
                     ("2" (expand "remove")
                      (("2" (expand "member")
                        (("2" (hide -2 1)
                          (("2" (grind)
                            (("2" (decompose-equality -1)
                              (("2"
                                (inst -1 "x!1")
                                (("2"
                                  (iff)
                                  (("2" (prop) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("3" (expand "separates")
                      (("3" (prop)
                        (("1" (expand "remove")
                          (("1" (expand "member")
                            (("1" (prop) nil nil)) nil))
                          nil)
                         ("2" (expand "remove")
                          (("2" (expand "member")
                            (("2" (prop) nil nil)) nil))
                          nil)
                         ("3" (skosimp*)
                          (("3" (expand "walk_from?")
                            (("3" (prop)
                              (("3"
                                (inst 4 "w!1")
                                (("3"
                                  (prop)
                                  (("3"
                                    (case "verts_of(w!1)(x!1)")
                                    (("1"
                                      (hide -4)
                                      (("1"
                                        (hide 1)
                                        (("1"
                                          (expand "path_verts")
                                          (("1"
                                            (expand "verts_of")
                                            (("1"
                                              (skosimp*)
                                              (("1"
                                                (inst 1 "w!1^(0,i!1)")
                                                (("1"
                                                  (expand "walk_from?")
                                                  (("1"
                                                    (prop)
                                                    (("1"
                                                      (expand*
                                                       "^"
                                                       min
                                                       empty_seq)
                                                      (("1"
                                                        (propax)
                                                        nil
                                                        nil))
                                                      nil)
                                                     ("2"
                                                      (expand*
                                                       "^"
                                                       min
                                                       empty_seq)
                                                      (("2"
                                                        (propax)
                                                        nil
                                                        nil))
                                                      nil)
                                                     ("3"
                                                      (reveal -1)
                                                      (("3"
                                                        (lemma
                                                         "walk?_caret")
                                                        (("3"
                                                          (inst
                                                           -1
                                                           "G!1"
                                                           "0"
                                                           "i!1"
                                                           "w!1")
                                                          (("3"
                                                            (typepred
                                                             "i!1")
                                                            (("3"
                                                              (assert)
                                                              (("3"
                                                                (lemma
                                                                 "walk?_subgraph")
                                                                (("3"
                                                                  (inst
                                                                   -1
                                                                   "G!1"
                                                                   "del_verts(G!1, remove(x!1, W!1))"
                                                                   "w!1")
                                                                  (("3"
                                                                    (prop)
                                                                    (("3"
                                                                      (hide
                                                                       -2
                                                                       2
                                                                       3)
                                                                      (("3"
                                                                        (assert)
                                                                        (("3"
                                                                          (install-rewrites
                                                                           "finite_sets[T]")
                                                                          (("3"
                                                                            (assert)
                                                                            (("3"
                                                                              (prop)
                                                                              (("1"
                                                                                (skosimp*)
                                                                                nil
                                                                                nil)
                                                                               ("2"
                                                                                (skosimp*)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2" (grind) nil nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (hide 3)
                                      (("2"
                                        (install-rewrites "walks")
                                        (("2"
                                          (expand "walk?")
                                          (("2"
                                            (prop)
                                            (("1"
                                              (expand "verts_in?")
                                              (("1"
                                                (skosimp*)
                                                (("1"
                                                  (expand "del_verts")
                                                  (("1"
                                                    (typepred "i!1")
                                                    (("1"
                                                      (hide -5)
                                                      (("1"
                                                        (inst -4 "i!1")
                                                        (("1"
                                                          (expand
                                                           "verts_of")
                                                          (("1"
                                                            (expand
                                                             "difference")
                                                            (("1"
                                                              (expand
                                                               "member")
                                                              (("1"
                                                                (prop)
                                                                (("1"
                                                                  (inst
                                                                   1
                                                                   "i!1")
                                                                  (("1"
                                                                    (expand
                                                                     "remove")
                                                                    (("1"
                                                                      (expand
                                                                       "member")
                                                                      (("1"
                                                                        (prop)
                                                                        (("1"
                                                                          (assert)
                                                                          nil
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (skosimp*)
                                              (("2"
                                                (inst -5 "n!1")
                                                (("2"
                                                  (prop)
                                                  (("2"
                                                    (expand "verts_of")
                                                    (("2"
                                                      (expand "edge?")
                                                      (("2"
                                                        (prop)
                                                        (("2"
                                                          (hide -5)
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                                                                (("2"
                                                                  (copy
                                                                   -4)
                                                                  (("2"
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                                                                     -1
                                                                     "seq(w!1)(n!1)")
                                                                    (("2"
                                                                      (inst
                                                                       -5
                                                                       "seq(w!1)(n!1 + 1)")
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                                                                             ("4"
                                                                              (assert)
                                                                              (("4"
                                                                                (inst
                                                                                 3
                                                                                 "1+n!1")
                                                                                (("4"
                                                                                  (assert)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              nil)
                                                                             ("5"
                                                                              (inst
                                                                               3
                                                                               "n!1")
                                                                              (("5"
                                                                                (assert)
                                                                                nil
                                                                                nil))
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                                                                              (inst
                                                                               3
                                                                               "n!1")
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                                                                                (assert)
                                                                                nil
                                                                                nil))
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                                                                              (replace
                                                                               -1
                                                                               -2
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                                                                                (propax)
                                                                                nil
                                                                                nil))
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                                                                             ("8"
                                                                              (replace
                                                                               -1
                                                                               -2
                                                                               lr)
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                                                                                nil
                                                                                nil))
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                                                                       ("2"
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                      nil)
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                        (("4" (expand "remove")
                          (("4" (expand "member")
                            (("4" (prop) nil nil)) nil))
                          nil))
                        nil))
                      nil)
                     ("5" (hide -2 1)
                      (("5" (expand "remove")
                        (("5" (decompose-equality -1)
                          (("5" (inst?)
                            (("5" (expand "member")
                              (("5" (propax) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("6" (expand "separates")
                      (("6" (prop)
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                          (("1" (expand "member")
                            (("1" (prop) nil nil)) nil))
                          nil)
                         ("2" (expand "remove")
                          (("2" (expand "member")
                            (("2" (prop) nil nil)) nil))
                          nil)
                         ("3" (skosimp*)
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                                      (hide -4)
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                                        (hide 1)
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                                              (("1"
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                                                 1
                                                 "rev(w!1)^(0,length(w!1)-1-i!1)")
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                                                  (expand "walk_from?")
                                                  (("1"
                                                    (prop)
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                                                      (("1"
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                                                         "^"
                                                         min
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                                                          (propax)
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                                                     ("2"
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                                                         "^"
                                                         min
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                                                          (propax)
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                                                        nil))
                                                      nil)
                                                     ("3"
                                                      (reveal -1)
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                                                        (lemma
                                                         "walk?_caret")
                                                        (("3"
                                                          (lemma
                                                           "walk?_rev")
                                                          (("3"
                                                            (inst
                                                             -1
                                                             "G!1"
                                                             "w!1")
                                                            (("3"
                                                              (inst
                                                               -2
                                                               "G!1"
                                                               "0"
                                                               "length(w!1)-1-i!1"
                                                               "rev(w!1)")
                                                              (("1"
                                                                (typepred
                                                                 "i!1")
                                                                (("1"
                                                                  (assert)
                                                                  (("1"
                                                                    (typepred
                                                                     "w!1")
                                                                    (("1"
                                                                      (postpone)
                                                                      nil
                                                                      nil))
                                                                    nil))
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                                                               ("2"
                                                                (postpone)
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                                                  (postpone)
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                                                  (postpone)
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                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((walk?_rev formula-decl nil walks nil)
    (separates const-decl "bool" sep_sets nil)
    (walk? const-decl "bool" walks nil)
    (edge? const-decl "bool" graphs nil)
    (verts_in? const-decl "bool" walks nil)
    (graph type-eq-decl nil graphs nil)
    (pregraph type-eq-decl nil graphs nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (subgraph? const-decl "bool" subgraphs nil)
    (walk?_caret formula-decl nil walks nil)
    (verts_of const-decl "finite_set[T]" walks nil)
    (prewalk type-eq-decl nil walks nil)
    (walk_from? const-decl "bool" walks nil))
   shostak)
  (smaller_tight-1 nil 3378121587
   ("" (skosimp*)
    (("" (expand "tight?")
      (("" (expand "subset?")
        (("" (expand "member")
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              (("" (expand "member")
                (("" (inst 2 "remove(x!1,W!1)")
                  (("" (prop)
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                        (("1" (prop)
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                            (("1" (propax) nil nil)) nil))
                          nil))
                        nil))
                      nil)
                     ("2" (expand "remove")
                      (("2" (expand "member")
                        (("2" (hide -2 1)
                          (("2" (grind)
                            (("2" (decompose-equality -1)
                              (("2"
                                (inst -1 "x!1")
                                (("2"
                                  (iff)
                                  (("2" (prop) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
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                      nil)
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                          (("1" (expand "member")
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                          nil)
                         ("2" (expand "remove")
                          (("2" (expand "member")
                            (("2" (prop) nil nil)) nil))
                          nil)
                         ("3" (skosimp*)
                          (("3" (expand "walk_from?")
                            (("3" (prop)
                              (("3"
                                (inst 4 "w!1")
                                (("3"
                                  (prop)
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                                    (case "verts_of(w!1)(x!1)")
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                                      (hide -4)
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                                        (hide 1)
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                                          (expand "path_verts")
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                                                      (reveal -1)
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                                                         "walk?_caret")
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                                                          (inst
                                                           -1
                                                           "G!1"
                                                           "0"
                                                           "i!1"
                                                           "w!1")
                                                          (("3"
                                                            (typepred
                                                             "i!1")
                                                            (("3"
                                                              (assert)
                                                              (("3"
                                                                (lemma
                                                                 "walk?_subgraph")
                                                                (("3"
                                                                  (inst
                                                                   -1
                                                                   "G!1"
                                                                   "del_verts(G!1, remove(x!1, W!1))"
                                                                   "w!1")
                                                                  (("3"
                                                                    (prop)
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                                                                      (hide
                                                                       -2
                                                                       2
                                                                       3)
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                                                                        (assert)
                                                                        (("3"
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                                                                            (assert)
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                                                                                nil
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                                          (expand "walk?")
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                                                      (hide -5)
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                                                          (("1"
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                                                             "difference")
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                                                              (expand
                                                               "member")
                                                              (("1"
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                                                                   1
                                                                   "i!1")
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                                             ("2"
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                                                (inst -5 "n!1")
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                                                          (hide -5)
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                                                                (("2"
                                                                  (copy
                                                                   -4)
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                                                                    (inst
                                                                     -1
                                                                     "seq(w!1)(n!1)")
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                                                                      (inst
                                                                       -5
                                                                       "seq(w!1)(n!1 + 1)")
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                                                                          (assert)
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                                                                          (assert)
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                                                                         ("4"
                                                                          (assert)
                                                                          (("4"
                                                                            (prop)
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                                                                             ("3"
                                                                              (assert)
                                                                              nil
                                                                              nil)
                                                                             ("4"
                                                                              (assert)
                                                                              (("4"
                                                                                (inst
                                                                                 3
                                                                                 "1+n!1")
                                                                                (("4"
                                                                                  (assert)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              nil)
                                                                             ("5"
                                                                              (inst
                                                                               3
                                                                               "n!1")
                                                                              (("5"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil)
                                                                             ("6"
                                                                              (inst
                                                                               3
                                                                               "n!1")
                                                                              (("6"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil)
                                                                             ("7"
                                                                              (replace
                                                                               -1
                                                                               -2
                                                                               lr)
                                                                              (("7"
                                                                                (propax)
                                                                                nil
                                                                                nil))
                                                                              nil)
                                                                             ("8"
                                                                              (replace
                                                                               -1
                                                                               -2
                                                                               lr)
                                                                              (("8"
                                                                                (propax)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (grind)
                                                                        nil
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("4" (skosimp*)
                      (("4" (hide -2 2)
                        (("4" (expand "remove")
                          (("4" (expand "member")
                            (("4" (prop) nil nil)) nil))
                          nil))
                        nil))
                      nil)
                     ("5" (hide -2 1)
                      (("5" (expand "remove")
                        (("5" (decompose-equality -1)
                          (("5" (inst?)
                            (("5" (expand "member")
                              (("5" (propax) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("6" (postpone) nil nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   nil shostak))
 (small_tight 0
  (small_tight-1 nil 3378206435
   ("" (lemma "finite_set_induction_gen")
    (("" (skosimp*)
      ((""
        (inst -1
         "lambda W: (separates(G!1,W,s!1,t!1) implies (exists V1 : subset?(V1,W) and separates(G!1,V1,s!1,t!1) and tight?(G!1,s!1,t!1,V1)))")
        (("" (prop)
          (("1" (inst -1 "W!1") (("1" (prop) nil nil)) nil)
           ("2" (skosimp*)
            (("2" (lemma "smaller_tight")
              (("2" (inst -1 "G!1" "S!1" "s!1" "t!1")
                (("2" (hide -4 2)
                  (("2" (prop)
                    (("1" (inst 1 "S!1")
                      (("1" (hide -2)
                        (("1" (prop)
                          (("1" (install-rewrites "finite_sets[T]")
                            (("1" (assert)
                              (("1"
                                (hide-all-but 1)
                                (("1" (grind) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (skosimp*)
                      (("2" (case "card(V!1)<card(S!1)")
                        (("1" (inst -4 "V!1")
                          (("1" (prop)
                            (("1" (skosimp*)
                              (("1"
                                (inst 2 "V1!1")
                                (("1"
                                  (prop)
                                  (("1"
                                    (hide-all-but (-1 -5 1))
                                    (("1"
                                      (install-rewrites
                                       "finite_sets[T]")
                                      (("1"
                                        (assert)
                                        (("1"
                                          (skosimp*)
                                          (("1"
                                            (inst?)
                                            (("1"
                                              (inst?)
                                              (("1" (prop) nil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (hide-all-but (-1 1 2))
                          (("2" (lemma "same_card_subset")
                            (("2" (inst -1 "V!1" "S!1")
                              (("2"
                                (prop)
                                (("2"
                                  (lemma "card_subset")
                                  (("2"
                                    (inst -1 "V!1" "S!1")
                                    (("2" (assert) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((smaller_tight formula-decl nil k_menger nil)
    (card_subset formula-decl nil finite_sets nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (same_card_subset formula-decl nil finite_sets nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (< const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (Card const-decl "nat" finite_sets nil)
    (card const-decl "{n: nat | n = Card(S)}" finite_sets nil)
    (nil application-judgement "finite_set[T]" graphs nil)
    (nil application-judgement "finite_set[T]" k_menger nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (member const-decl "bool" sets nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (walk_from? const-decl "bool" walks nil)
    (path_verts const-decl "set[T]" paths nil)
    (intersection const-decl "set" sets nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (difference const-decl "set" sets nil)
    (tight? const-decl "bool" k_menger nil)
    (subset? const-decl "bool" sets nil)
    (separates const-decl "bool" sep_sets nil)
    (graph type-eq-decl nil graphs nil)
    (pregraph type-eq-decl nil graphs nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pred type-eq-decl nil defined_types nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (finite_set_induction_gen formula-decl nil finite_sets_inductions
     "finite_sets/")
    (T formal-type-decl nil k_menger nil))
   shostak))
 (exists_tight 0
  (exists_tight-2 nil 3378222865
   ("" (skosimp*)
    (("" (expand "good?")
      (("" (expand "separable?")
        (("" (prop)
          (("" (lemma "small_tight")
            (("" (inst?)
              ((""
                (inst -1
                 "{t: T | vert(G!1)(t)  AND t /= s!1 AND t /= t!1}"
                 "s!1" "t!1")
                (("1" (prop)
                  (("1" (skosimp*)
                    (("1" (inst 3 "V!1") (("1" (prop) nil nil)) nil))
                    nil)
                   ("2" (hide 4)
                    (("2" (expand "separates")
                      (("2" (skosimp*)
                        (("2" (expand "walk_from?")
                          (("2" (flatten)
                            (("2" (case "length(w!1) = 1")
                              (("1"
                                (replace -1)
                                (("1"
                                  (hide -1)
                                  (("1" (assert) nil nil))
                                  nil))
                                nil)
                               ("2"
                                (case-replace "length(w!1) = 2")
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "walk?")
                                    (("1"
                                      (expand "finseq_appl")
                                      (("1"
                                        (flatten)
                                        (("1"
                                          (inst -5 "0")
                                          (("1"
                                            (assert)
                                            (("1"
                                              (hide -4)
                                              (("1"
                                                (replace -2 * lr)
                                                (("1"
                                                  (replace -3 * lr)
                                                  (("1"
                                                    (hide 1)
                                                    (("1"
                                                      (expand "edge?")
                                                      (("1"
                                                        (expand
                                                         "del_verts")
                                                        (("1"
                                                          (prop)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (case
                                   "FORALL (i: below(length(w!1))): seq(w!1)(i) = s!1 OR seq(w!1)(i) = t!1")
                                  (("1"
                                    (expand "walk?")
                                    (("1"
                                      (expand "finseq_appl")
                                      (("1"
                                        (flatten)
                                        (("1"
                                          (inst -5 "0")
                                          (("1"
                                            (assert)
                                            (("1"
                                              (expand "edge?")
                                              (("1"
                                                (expand "del_verts")
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (inst -1 "1")
                                                    (("1"
                                                      (assert)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (lemma "walk_verts_in")
                                    (("2"
                                      (inst?)
                                      (("1"
                                        (split -1)
                                        (("1"
                                          (hide -4)
                                          (("1"
                                            (expand "verts_in?")
                                            (("1"
                                              (expand "del_verts")
                                              (("1"
                                                (expand "difference")
                                                (("1"
                                                  (expand "member")
                                                  (("1"
                                                    (skosimp*)
                                                    (("1"
                                                      (inst?)
                                                      (("1"
                                                        (flatten)
                                                        (("1"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2" (propax) nil nil))
                                        nil)
                                       ("2"
                                        (hide -1 -2 -3 2 3 4 5 6)
                                        (("2"
                                          (lemma "finite_subset[T]")
                                          (("2"
                                            (inst?)
                                            (("2"
                                              (inst -1 "vert(G!1)")
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (hide 2)
                                                  (("2"
                                                    (grind)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (hide 3 4)
                  (("2" (lemma "finite_subset[T]")
                    (("2" (inst?)
                      (("2" (inst -1 "vert(G!1)")
                        (("2" (assert)
                          (("2" (hide 2) (("2" (grind) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((good? const-decl "bool" k_menger nil)
    (T formal-type-decl nil k_menger nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil)
    (separates const-decl "bool" sep_sets nil)
    (walk_from? const-decl "bool" walks nil)
    (number nonempty-type-decl nil numbers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (finite_difference application-judgement "finite_set[T]" k_menger
     nil)
    (member const-decl "bool" sets nil)
    (difference const-decl "set" sets nil)
    (verts_in? const-decl "bool" walks nil)
    (finite_subset formula-decl nil finite_sets nil)
    (subset? const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (walk_verts_in formula-decl nil walks nil)
    (even_minus_odd_is_odd application-judgement "odd_int" integers
     nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (>= const-decl "bool" reals nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (nil application-judgement "finite_set[T]" k_menger nil)
    (edge? const-decl "bool" graphs nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (walk? const-decl "bool" walks nil)
    (is_finite const-decl "bool" finite_sets nil)
    (G!1 skolem-const-decl "graph[T]" k_menger nil)
    (s!1 skolem-const-decl "T" k_menger nil)
    (t!1 skolem-const-decl "T" k_menger nil)
    (small_tight formula-decl nil k_menger nil)
    (separable? const-decl "bool" sep_sets nil))
   nil)
  (exists_tight-1 nil 3378222242
   ("" (skosimp*)
    (("" (lemma "sep_set_exists")
      (("" (inst?)
        (("" (inst?)
          (("" (inst?) (("" (skosimp*) (("" (postpone) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   nil shostak))
 (close_tight 0
  (close_tight-1 nil 3378932482
   ("" (skosimp*)
    (("" (install-rewrites "k_menger")
      (("" (expand "tight?")
        (("" (expand "subset?")
          (("" (skosimp*)
            (("" (expand "member")
              (("" (expand "intersection")
                (("" (expand "member")
                  (("" (prop)
                    (("1" (expand "close?")
                      (("1" (inst -1 "x!1")
                        (("1" (prop)
                          (("1" (skosimp*)
                            (("1" (expand "intersection")
                              (("1"
                                (expand "member")
                                (("1"
                                  (decompose-equality -2)
                                  (("1"
                                    (inst -1 "x!1")
                                    (("1"
                                      (iff)
                                      (("1"
                                        (expand "singleton")
                                        (("1"
                                          (prop)
                                          (("1"
                                            (expand "internal_verts")
                                            (("1"
                                              (expand "finseq_appl")
                                              (("1"
                                                (skosimp*)
                                                (("1"
                                                  (expand "path_verts")
                                                  (("1"
                                                    (inst
                                                     1
                                                     "p!1^(0,i!1)")
                                                    (("1"
                                                      (expand*
                                                       "^"
                                                       min
                                                       empty_seq)
                                                      (("1"
                                                        (expand
                                                         "walk_from?")
                                                        (("1"
                                                          (prop)
                                                          (("1"
                                                            (install-rewrites
                                                             "paths")
                                                            (("1"
                                                              (assert)
                                                              nil
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (expand
                                                             "path_from?")
                                                            (("2"
                                                              (prop)
                                                              (("2"
                                                                (expand
                                                                 "path?")
                                                                (("2"
                                                                  (expand
                                                                   "finseq_appl")
                                                                  (("2"
                                                                    (prop)
                                                                    (("2"
                                                                      (lemma
                                                                       "walk?_caret")
                                                                      (("2"
                                                                        (inst
                                                                         -1
                                                                         "G!1"
                                                                         "0"
                                                                         "i!1"
                                                                         "p!1")
                                                                        (("2"
                                                                          (prop)
                                                                          (("1"
                                                                            (install-rewrites
                                                                             "walks")
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (assert)
                                                                            nil
                                                                            nil)
                                                                           ("3"
                                                                            (assert)
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("3"
                                                            (lift-if)
                                                            (("3"
                                                              (assert)
                                                              (("3"
                                                                (prop)
                                                                (("1"
                                                                  (skosimp)
                                                                  (("1"
                                                                    (inst?)
                                                                    nil
                                                                    nil))
                                                                  nil)
                                                                 ("2"
                                                                  (skosimp)
                                                                  (("2"
                                                                    (inst
                                                                     -7
                                                                     "n!1")
                                                                    (("2"
                                                                      (assert)
                                                                      nil
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("2"
                                                      (install-rewrites
                                                       "walks")
                                                      (("2"
                                                        (assert)
                                                        (("2"
                                                          (expand
                                                           "min")
                                                          (("2"
                                                            (assert)
                                                            nil
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (expand "close?")
                      (("2" (inst -1 "x!1")
                        (("2" (prop)
                          (("2" (skosimp*)
                            (("2" (expand "intersection")
                              (("2"
                                (expand "member")
                                (("2"
                                  (decompose-equality -2)
                                  (("2"
                                    (inst -1 "x!1")
                                    (("2"
                                      (iff)
                                      (("2"
                                        (expand "singleton")
                                        (("2"
                                          (prop)
                                          (("2"
                                            (expand "internal_verts")
                                            (("2"
                                              (expand "finseq_appl")
                                              (("2"
                                                (skosimp*)
                                                (("2"
                                                  (expand "path_verts")
                                                  (("2"
                                                    (inst
                                                     1
                                                     "rev(p!1^(i!1,length(p!1)-1))")
                                                    (("1"
                                                      (expand*
                                                       "^"
                                                       min
                                                       empty_seq)
                                                      (("1"
                                                        (expand "rev")
                                                        (("1"
                                                          (expand
                                                           "walk_from?")
                                                          (("1"
                                                            (prop)
                                                            (("1"
                                                              (install-rewrites
                                                               "walks")
                                                              (("1"
                                                                (assert)
                                                                (("1"
                                                                  (prop)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil)
                                                             ("2"
                                                              (install-rewrites
                                                               "walks")
                                                              (("2"
                                                                (assert)
                                                                nil
                                                                nil))
                                                              nil)
                                                             ("3"
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                                                              (("3"
                                                                (expand
                                                                 "path_from?")
                                                                (("3"
                                                                  (prop)
                                                                  (("3"
                                                                    (expand
                                                                     "path?")
                                                                    (("3"
                                                                      (expand
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                                                                      (("3"
                                                                        (prop)
                                                                        (("3"
                                                                          (lemma
                                                                           "walk?_caret")
                                                                          (("3"
                                                                            (inst
                                                                             -1
                                                                             "G!1"
                                                                             "i!1"
                                                                             "length(p!1)-1"
                                                                             "p!1")
                                                                            (("3"
                                                                              (prop)
                                                                              (("1"
                                                                                (lemma
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                                                                                (("1"
                                                                                  (inst
                                                                                   -1
                                                                                   "G!1"
                                                                                   " p!1 ^ (i!1, length(p!1) - 1)")
                                                                                  (("1"
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                                                                                     -8
                                                                                     -9)
                                                                                    (("1"
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                                                                                            (("1"
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                                                                                              nil
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                                                                               ("2"
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                                                     ("2"
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                                                        (("2"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
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              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((subset? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (empty_seq const-decl "finseq" finite_sequences nil)
    (walk?_rev formula-decl nil walks nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (i!1 skolem-const-decl "nat" k_menger nil)
    (p!1 skolem-const-decl "prewalk[T]" k_menger nil)
    (rev const-decl "finseq[T]" doubletons nil)
    (close? const-decl "bool" k_menger nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (internal_verts const-decl "finite_set[T]" ind_paths nil)
    (singleton? const-decl "bool" sets nil)
    (singleton const-decl "(singleton?)" sets nil)
    (verts_in? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (/= const-decl "boolean" notequal nil)
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (path? const-decl "bool" paths nil)
    (from? const-decl "bool" walks nil)
    (path_from? const-decl "bool" paths nil)
    (walk_from? const-decl "bool" walks nil)
    (path_verts const-decl "set[T]" paths nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" k_menger nil)
    (nil application-judgement "finite_set[T]" graphs nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nil application-judgement "finite_set[T]" k_menger nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (walk?_caret formula-decl nil walks nil)
    (nat_min application-judgement "{k: nat | k <= i AND k <= j}"
     real_defs nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (int_min application-judgement "{k: int | k <= i AND k <= j}"
     real_defs nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (below type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (i!1 skolem-const-decl "nat" k_menger nil)
    (p!1 skolem-const-decl "prewalk[T]" k_menger nil)
    (^ const-decl "finseq" finite_sequences nil)
    (>= const-decl "bool" reals nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (T formal-type-decl nil k_menger nil)
    (intersection const-decl "set" sets nil)
    (tight? const-decl "bool" k_menger nil))
   shostak))
 (smaller_close 0
  (smaller_close-1 nil 3379013579
   ("" (skosimp*)
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                     ("3" (expand "separates")
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                          nil)
                         ("2" (expand "remove")
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                            (("2" (prop) nil nil)) nil))
                          nil)
                         ("3" (skosimp*)
                          (("3" (hide -2 3)
                            (("3" (lemma "walk_to_path_from")
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                                 -1
                                 "del_verts(G!1, remove(w!1, W!1))"
                                 "s!1"
                                 "t!1"
                                 "w!2")
                                (("3"
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                                      (hide -2)
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                                        (("3"
                                          (lemma "path?_subgraph")
                                          (("3"
                                            (inst
                                             -1
                                             "G!1"
                                             "del_verts(G!1, remove(w!1, W!1))"
                                             "p!1")
                                            (("3"
                                              (prop)
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                                                nil)
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                                                        (("2"
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                                                            (("2"
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                                                                (("2"
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                                                                   1
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                                                                   t)
                                                                  (("1"
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                                                                          (inst
                                                                           -5
                                                                           "i!1")
                                                                          (("1"
                                                                            (rop
                                                                            work forjava.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
                                                                              (inst
                                                                               -7
                                                                               "i!1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                
                                                                              nil)
                                                                             >.toolsaccessor/java.lang.StringIndexOutOfBoundsException: Range [59, 58) out of bounds for length 59
                                                                              (inst
                                                                               -6
                                                                               "i!1")
                                                                              (("2"
                                                                                (assert)
                                                                                nil
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                                                                         2)
                                                                        (("3"
                                                                          (inst
                                                                           1
                                                                           "p!1")
                                                                          (("3"
                                                                            (expand
                                                                             "walk_from?")
                                                                            (("3"
                                                                              (prop)
                                                                              (("1"
                                                                                (reveal
                                                                                 -3)
                                                                                (("1"
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                                                                                   "from?")
                                                                                  (("1"
                                                                                    (prop)
                                                                                    nil
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                                                                                nil)
                                                                               ("2"
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                                                                                 -3)
                                                                                (("2"
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                                                                                   "from?")
                                                                                  (("2"
                                                                                    (prop)
                                                                                    nil
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                                                                                nil)
                                                                               ("3"
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                                                                                 "walk?")
                                                                                (("3"
                                                                                  (expand
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                                                                                  (("3"
                                                                                    (prop)
                                                                                    (("1"
                                                                                      (expand
                                                                                       "verts_in?")
                                                                                      (("1"
                                                                                        (skosimp*)
                                                                                        (("1"
                                                                                          (inst
                                                                                           -2
                                                                                           "i!1")
                                                                                          (("1"
                                                                                            (inst
                                                                                             -3
                                                                                             "i!1")
                                                                                            (("1"
                                                                                              (prop)
                                                                                              (("1"
                                                                                                (typepred
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                                                                                                (("1"
                                                                                                  (inst
                                                                                                   -3
                                                                                                   "x!1")
                                                                                                  (("1"
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                                                                                                        (reveal
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                                                                                                          (("1"
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                                                                                                              (inst
                                                                                                               3
                                                                                                               "i!1")
                                                                                                              (("1"
                                                                                                                (replace
                                                                                                                 -6
                                                                                                                 *
                                                                                                                 rl)
                                                                                                                (("1"
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                                                                                                                  nil
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                                                                                                                nil))
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                                                                                               ("2"
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                                                                                                  (("2"
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                                                                                                    (("2"
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                                                                                                        (case
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                                                                                                        (("1"
                                                                                                          (replace
                                                                                                           -1
                                                                                                           *
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                                                                                                          (("1"
                                                                                                            (replace
                                                                                                             -3
                                                                                                             *
                                                                                                             lr)
                                                                                                            (("1"
                                                                                                              (assert)
                                                                                                              nil
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                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("2"
                                                                                                          (assert)
                                                                                                          nil
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                                                                                                        nil))
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                                                                                               ("3"
                                                                                                (hide
                                                                                                 -1
                                                                                                 -2
                                                                                                 -5
                                                                                                 1
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                                                                                                (("3"
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                                                                                                  nil
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                                                                                               ("4"
                                                                                                (hide
                                                                                                 -3
                                                                                                 4)
                                                                                                (("4"
                                                                                                  (grind)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
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                                                                                      nil)
                                                                                     ("2"
                                                                                      (skosimp*)
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                                                                                         -4
                                                                                         "n!1")
                                                                                        (("2"
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                                                                                          (("2"
                                                                                            (expand
                                                                                             "edge?")
                                                                                            (("2"
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                                                                                                (("2"
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                                                                                                    (("2"
                                                                                                      (inst
                                                                                                       -4
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                                                                                                          (hide
                                                                                                           -3
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                                                                                                           -7
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                                                                                                          (("1"
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                                                                                                         ("2"
                                                                                                          (copy
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                                                                                                            (("2"
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                                                                                                              (("2"
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                                                                                                                   -1
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                                                                                                                    (("2"
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                                                                                                                          (("1"
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                                                                                                                            (("1"
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                                                                                                                              (("1"
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                                                                                                                            nil)
                                                                                                                           ("2"
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                                                                                                                         ("2"
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                                                                                                                         ("3"
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                                                                                                                         ("4"
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                                                                                                                             "from?")
                                                                                                                            (("4"
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                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (skosimp*)
                                                                    (("2"
                                                                      (assert)
                                                                      nil
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("3"
                                                (assert)
                                                (("3"
                                                  (expand "path_from?")
                                                  (("3"
                                                    (lemma
                                                     "path?_subgraph")
                                                    (("3"
                                                      (inst
                                                       -1
                                                       "G!1"
                                                       "del_verts(G!1, remove(w!1, W!1))"
                                                       "p!1")
                                                      (("3"
                                                        (prop)
                                                        (("3"
                                                          (hide 3)
                                                          (("3"
                                                            (hide
                                                             -1
                                                             -2
                                                             1)
                                                            (("3"
                                                              (install-rewrites
                                                               "graphs")
                                                              (("3"
                                                                (assert)
                                                                (("3"
                                                                  (prop)
                                                                  (("1"
                                                                    (skosimp*)
                                                                    nil
                                                                    nil)
                                                                   ("2"
                                                                    (skosimp*)
                                                                    nil
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("4"
                                                (hide -1 1)
                                                (("4"
                                                  (install-rewrites
                                                   "graphs")
                                                  (("4"
                                                    (assert)
                                                    (("4"
                                                      (prop)
                                                      (("1"
                                                        (skosimp*)
                                                        nil
                                                        nil)
                                                       ("2"
                                                        (skosimp*)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("5"
                                                (expand "path_from?")
                                                (("5" (prop) nil nil))
                                                nil)
                                               ("6"
                                                (expand "path_from?")
                                                (("6" (prop) nil nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("4" (hide 2)
                      (("4" (lemma "sub_tight")
                        (("4"
                          (inst -1 "G!1" "remove(w!1,W!1)" "W!1" "s!1"
                           "t!1")
                          (("4" (prop)
                            (("4" (hide -1 -2 2)
                              (("4"
                                (install-rewrites "finite_sets")
                                (("4"
                                  (assert)
                                  (("4" (skosimp*) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((close? const-decl "bool" k_menger nil)
    (member const-decl "bool" sets nil)
    (intersection const-decl "set" sets nil)
    (finite_remove application-judgement "finite_set[T]" k_menger nil)
    (T formal-type-decl nil k_menger nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (remove const-decl "set" sets nil)
    (sub_tight formula-decl nil k_menger nil)
    (separates const-decl "bool" sep_sets nil)
    (walk_to_path_from formula-decl nil path_ops nil)
    (path?_subgraph formula-decl nil subgraph_paths nil)
    (path_from? const-decl "bool" paths nil)
    (path? const-decl "bool" paths nil)
    (singleton? const-decl "bool" sets nil)
    (singleton const-decl "(singleton?)" sets nil)
    (p!1 skolem-const-decl "prewalk[T]" k_menger nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (W!1 skolem-const-decl "finite_set[T]" k_menger nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (walk? const-decl "bool" walks nil)
    (edge? const-decl "bool" graphs nil)
    (verts_in? const-decl "bool" walks nil)
    (difference const-decl "set" sets nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" k_menger nil)
    (finite_difference application-judgement "finite_set[T]" k_menger
     nil)
    (nil application-judgement "finite_set[T]" k_menger nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (from? const-decl "bool" walks nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (walk_from? const-decl "bool" walks nil)
    (internal_verts const-decl "finite_set[T]" ind_paths nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (subgraph? const-decl "bool" subgraphs nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (prewalk type-eq-decl nil walks nil)
    (> const-decl "bool" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (graph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pregraph type-eq-decl nil graphs nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (subset? const-decl "bool" sets nil))
   nil))
 (small_close 0
  (small_close-3 "variabl" 3379069981
   ("" (lemma "finite_set_induction_gen")
    (("" (skosimp*)
      ((""
        (inst -1
         "lambda W: (separates(G!1,W,s!1,t!1) implies (exists V1 : subset?(V1,W) and separates(G!1,V1,s!1,t!1) and close?(G!1,s!1,t!1,V1)))")
        (("" (prop)
          (("1" (inst -1 "W!1") (("1" (prop) nil nil)) nil)
           ("2" (skosimp*)
            (("2" (hide -3 2)
              (("2" (lemma "smaller_close")
                (("2" (lemma "small_tight")
                  (("2" (inst -1 "G!1" "S!1" "s!1" "t!1")
                    (("2" (prop)
                      (("2" (skosimp*)
                        (("2" (inst -4 "G!1" "V!1" "s!1" "t!1")
                          (("2" (prop)
                            (("1" (inst 1 "V!1") (("1" (prop) nil nil))
                              nil)
                             ("2" (skosimp*)
                              (("2"
                                (inst -7 "V!2")
                                (("2"
                                  (prop)
                                  (("1"
                                    (skosimp*)
                                    (("1"
                                      (inst 2 "V1!1")
                                      (("1"
                                        (prop)
                                        (("1"
                                          (hide-all-but (-1 -4 -7 1 2))
                                          (("1"
                                            (install-rewrites
                                             "finite_sets[T]")
                                            (("1"
                                              (assert)
                                              (("1"
                                                (skosimp*)
                                                (("1"
                                                  (inst?)
                                                  (("1"
                                                    (inst?)
                                                    (("1"
                                                      (inst?)
                                                      (("1"
                                                        (prop)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (hide (-2 -3 -5 -6 -7 3))
                                    (("2"
                                      (lemma "same_card_subset")
                                      (("2"
                                        (lemma "card_subset")
                                        (("2"
                                          (copy -1)
                                          (("2"
                                            (copy -3)
                                            (("2"
                                              (inst -1 "V!2" "V!1")
                                              (("2"
                                                (inst -4 "V!1" "S!1")
                                                (("2"
                                                  (inst -2 "V!2" "V!1")
                                                  (("2"
                                                    (inst
                                                     -3
                                                     "V!1"
                                                     "S!1")
                                                    (("2"
                                                      (prop)
                                                      (("1"
                                                        (replace
                                                         -1
                                                         *
                                                         lr)
                                                        (("1"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (assert)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((small_tight formula-decl nil k_menger nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (member const-decl "bool" sets nil)
    (same_card_subset formula-decl nil finite_sets nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (card_subset formula-decl nil finite_sets nil)
    (smaller_close formula-decl nil k_menger nil)
    (close? const-decl "bool" k_menger nil)
    (subset? const-decl "bool" sets nil)
    (separates const-decl "bool" sep_sets nil)
    (graph type-eq-decl nil graphs nil)
    (pregraph type-eq-decl nil graphs nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (pred type-eq-decl nil defined_types nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (finite_set_induction_gen formula-decl nil finite_sets_inductions
     "finite_sets/")
    (T formal-type-decl nil k_menger nil))
   shostak)
  (small_close-2 "put_in_tight" 3379067892
   ("" (lemma "finite_set_induction_gen")
    (("" (skosimp*)
      ((""
        (inst -1
         "lambda W: (separates(G!1,W,s!1,t!1) implies (exists V1 : subset?(V1,W) and separates(G!1,V1,s!1,t!1) and close?(G!1,s!1,t!1,V1)))")
        (("" (prop)
          (("1" (inst -1 "W!1") (("1" (prop) nil nil)) nil)
           ("2" (skosimp*)
            (("2" (lemma "smaller_close")
              (("2" (lemma "small_tight")
                (("2" (inst -1 "G!1" "S!1" "s!1" "t!1")
                  (("2" (prop)
                    (("2" (skosimp*)
                      (("2" (inst -4 "G!1" "V!1" "s!1" "t!1")
                        (("2" (prop)
                          (("1" (inst 1 "V!1") (("1" (prop) nil nil))
                            nil)
                           ("2" (skosimp*)
                            (("2" (case "card(V!1)<card(S!1)")
                              (("1"
                                (inst -8 "V!1")
                                (("1"
                                  (prop)
                                  (("1"
                                    (skosimp*)
                                    (("1"
                                      (inst 2 "V1!1")
                                      (("1"
                                        (prop)
                                        (("1"
                                          (hide-all-but (-1 -8 1))
                                          (("1"
                                            (install-rewrites
                                             "finite_sets[T]")
                                            (("1"
                                              (assert)
                                              (("1"
                                                (skosimp*)
                                                (("1"
                                                  (inst?)
                                                  (("1"
                                                    (inst?)
                                                    (("1"
                                                      (prop)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2" (postpone) nil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   nil shostak)
  (small_close-1 nil 3379064658
   ("" (lemma "finite_set_induction_gen")
    (("" (skosimp*)
      ((""
        (inst -1
         "lambda W: (separates(G!1,W,s!1,t!1) implies (exists V1 : subset?(V1,W) and separates(G!1,V1,s!1,t!1) and tight?(G!1,s!1,t!1,V1)))")
        (("" (prop)
          (("1" (inst -1 "W!1") (("1" (prop) nil)))
           ("2" (skosimp*)
            (("2" (lemma "smaller_tight")
              (("2" (inst -1 "G!1" "S!1" "s!1" "t!1")
                (("2" (hide -4 2)
                  (("2" (prop)
                    (("1" (inst 1 "S!1")
                      (("1" (hide -2)
                        (("1" (prop)
                          (("1" (install-rewrites "finite_sets[T]")
                            (("1" (assert)
                              (("1"
                                (hide-all-but 1)
                                (("1" (grind) nil)))))))))))))
                     ("2" (skosimp*)
                      (("2" (case "card(V!1)<card(S!1)")
                        (("1" (inst -4 "V!1")
                          (("1" (prop)
                            (("1" (skosimp*)
                              (("1"
                                (inst 2 "V1!1")
                                (("1"
                                  (prop)
                                  (("1"
                                    (hide-all-but (-1 -5 1))
                                    (("1"
                                      (install-rewrites
                                       "finite_sets[T]")
                                      (("1"
                                        (assert)
                                        (("1"
                                          (skosimp*)
                                          (("1"
                                            (inst?)
                                            (("1"
                                              (inst?)
                                              (("1"
                                                (prop)
                                                nil)))))))))))))))))))))))
                         ("2" (hide-all-but (-1 1 2))
                          (("2" (lemma "same_card_subset")
                            (("2" (inst -1 "V!1" "S!1")
                              (("2"
                                (prop)
                                (("2"
                                  (lemma "card_subset")
                                  (("2"
                                    (inst -1 "V!1" "S!1")
                                    (("2"
                                      (assert)
                                      nil))))))))))))))))))))))))))))))))))
    nil)
   nil nil))
 (exists_close 0
  (exists_close-3 "copied from exists tight" 3379073276
   ("" (skosimp*)
    (("" (expand "good?")
      (("" (expand "separable?")
        (("" (prop)
          (("" (lemma "small_close")
            (("" (inst?)
              ((""
                (inst -1
                 "{t: T | vert(G!1)(t)  AND t /= s!1 AND t /= t!1}"
                 "s!1" "t!1")
                (("1" (prop)
                  (("1" (skosimp*)
                    (("1" (inst 3 "V!1") (("1" (prop) nil nil)) nil))
                    nil)
                   ("2" (hide 4)
                    (("2" (expand "separates")
                      (("2" (skosimp*)
                        (("2" (expand "walk_from?")
                          (("2" (flatten)
                            (("2" (case "length(w!1) = 1")
                              (("1"
                                (replace -1)
                                (("1"
                                  (hide -1)
                                  (("1" (assert) nil nil))
                                  nil))
                                nil)
                               ("2"
                                (case-replace "length(w!1) = 2")
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "walk?")
                                    (("1"
                                      (expand "finseq_appl")
                                      (("1"
                                        (flatten)
                                        (("1"
                                          (inst -5 "0")
                                          (("1"
                                            (assert)
                                            (("1"
                                              (hide -4)
                                              (("1"
                                                (replace -2 * lr)
                                                (("1"
                                                  (replace -3 * lr)
                                                  (("1"
                                                    (hide 1)
                                                    (("1"
                                                      (expand "edge?")
                                                      (("1"
                                                        (expand
                                                         "del_verts")
                                                        (("1"
                                                          (prop)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (case
                                   "FORALL (i: below(length(w!1))): seq(w!1)(i) = s!1 OR seq(w!1)(i) = t!1")
                                  (("1"
                                    (expand "walk?")
                                    (("1"
                                      (expand "finseq_appl")
                                      (("1"
                                        (flatten)
                                        (("1"
                                          (inst -5 "0")
                                          (("1"
                                            (assert)
                                            (("1"
                                              (expand "edge?")
                                              (("1"
                                                (expand "del_verts")
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (inst -1 "1")
                                                    (("1"
                                                      (assert)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (lemma "walk_verts_in")
                                    (("2"
                                      (inst?)
                                      (("1"
                                        (split -1)
                                        (("1"
                                          (hide -4)
                                          (("1"
                                            (expand "verts_in?")
                                            (("1"
                                              (expand "del_verts")
                                              (("1"
                                                (expand "difference")
                                                (("1"
                                                  (expand "member")
                                                  (("1"
                                                    (skosimp*)
(("1
                        instjava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
                                                      AcquireSampleRowsFuncBlockNumberrelpages
                                                        (flatten)
                                                        (("1"
                                                           
                                                          nil
                                                          nil))
nil)
                )
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2*probablynot to  .(We dont  ;
                                        nil
                                       (
                                        (- -2-32 34 )
                                        (("2"
(lemmafinite_subset[T"
((""
                                            (inst?)
                                            (("2" java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 19
( 1"G!1))
                                              (
                                                (assert)
                                                (("2"
                                                  (hide 2)
                                                  (2java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
                                                       rows
                                                    
 /*
                                                       ALLOCSET_DEFAULT_SIZES);
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                 )java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
                                nil))
                                (i =1i =attr_cnt i+)
                            nil))
                          nil))
                        nil)
                      nil))
                    nil))
                  nil)
                 ("java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 15
(("2"( finite_subset[T])
                    (("2" (instjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                      (("2" (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                                  (""(ssert)
                          (("2" (hide 2) (("2" (grind) nil nil)) nil))
                          nil))
                        nil)
                      nil))
                    nil))
                  nil))
                nil 
              nil))
            nil))
          nil))
        nil))
      nil))
   nil)
   ((good? const-decl "bool" k_menger nil)
    (T  if (n_dist =00)
( -decl java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 49
     --q-declnil  )
    (set type-eq-decl nil sets nil)
    (AND constjava.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T    
(bl constdecl setT" doubletons )
    (doubleton type-eq-decl nil doubletons nil)
    (finite_set type-eq-decl      InvalidTransactionId,
    (pregraph type-eq-decl nilIrel[]
    IMPLIES -decl "bool bool -> bool]" booleans nil)
    (graph type-eq-  *theirentries except  java.lang.StringIndexOutOfBoundsException: Range [52, 51) out of bounds for length 68
    (separates const-decl "bool" sep_sets nil)
    (walk_from? const-decl "bool" walks nil)
    (number nonempty-type-decl nil numbers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (number_field_pred ))
     java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
    (number_field nonempty-type-from/* Log the action if appropriate */
    (eal_pred const-decl "[number_field ->boolean]" reals nil)
    (real nonempty-type- total_blks_dirtied = buff.+
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
(application-"ven_int"integers
     nil)
    (< const-decl "bool" reals nil)
    eq- nil naturalnumbersnil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (java.lang.StringIndexOutOfBoundsException: Range [3, 2) out of bounds for length 4
     nil)
    constb nil
    (difference const-decl "set" sets nil)
    (verts_in? const-decl "bool" walks nil)
    (finite_subset formula-decl nil finite_sets nil)
    (subset? const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set  pfree(.;
     sets_lemmas nil)
    (walk_verts_in formula-decl    * int java.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 43
    (even_minus_odd_is_odd java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 43
     
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
>-java.lang.StringIndexOutOfBoundsException: Range [20, 18) out of bounds for length 36
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 46
    (rational nonempty-type-from-decl nil rationals nil)
r java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 64
    (nil application-judgement "finite_set[T]" k_menger nil)
e? onst- "bool graphs niljava.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
    (del_verts     tcnt] false;
    (real_lt_is_strict_total_order name-judgement
     "( thisdata-tupleFract=(double) numindexrows / (double) numrows;
    (int_minus_int_is_int application-judgement "int" integers nil)
 "ool"walksnil)
    (is_finite const-decl "bool" finite_sets nil)
    (G MemoryContextDelete();
    (!1 -onst-""k_menger java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
    (t!1 skolem-const-decl "T" k_menger nil)
    (small_close formula-decl nil k_menger nil)
    (separable? const-decl "bool  ok;
   shostak))
 (closed_minimal 0
(closed_minimal-1 nil 3379073798
java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
    (("" (expand "close?")
      (("" (expand "separates")
        (("" (prop)
          (("" (expand "subset?")
            (("" (expand "member")
              (("" (apply-extensionality 7 :hide? t)
                (("" (inst -2 "x!1")
                  (("" (iff)
                    (("" (prop)
                      (("1" (hide -1)
                        (("1" (inst -2 "x!1")
                          ((" >java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 48
                            (("1" (skosimp*)

                                (hide/
                                (("1"
                                  java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
                                  java.lang.StringIndexOutOfBoundsException: Range [46, 45) out of bounds for length 73
                                    (expand "path_from?")
                                    (("1"
                                      "")
                                      (("1"
                                        (prop)
                                        "
                                          (expand "from?")
                                          (("1" (prop) nil nil))
                                          java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 70
                                         ("2"
                                          (expand "from?")
                                          (("2" (prop) nil nil))
                                          nil)
                                         ("3"
                                          (hide -2)
                                          (
                                            (expand "walk?")
                                            (("3"
                                              (expand "finseq_appl")
                                              (("3"
                                                (prop)
                                                (("1"
                                                  (expand "verts_in?")
                                                  (("1"
                                                    (expand
                                                     d)
                                                    (""
                                                      (expand
                                                       )
                                                      (1java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
                                                        (expand
                                                         "member")
                                                        (("1t  scanned is
(skosimp*)
""
                                                            (expand
                                                             ""s":scanned d  % pages,"
                                                            "
                                                              (expand
                                                                  cHeapTuple )java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
                                                              (("1"
                                                                (expand
                                                                 "finseq_appl")
                                                                (("1"
                                                                  (prop)
                                                                  (("1"
                                                                    (expand
                                                                     "walk?")  i;
                                                                    "
                                                                      (expand
                                                                       
                                                                      (("1 *java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 74
                                                                        (expand
                                                                         "verts_in?")
                                                                        
                                                                          (prop)
                                                                          (("1"
                                                                            
                                                                             
                                                                             "i!1")
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                     supports .
                                                                   ("    *
                                                                    (hide
                                                                     
                                                                    (("2"
                                                                      decompose-equality
                                                                       
                                                                      (("2"
                                                                        
                                                                         -1)
                                                     2"
                                                                          (inst
                                                                           -1
                                                                             
    get_namespace_name(RelationGetNamespace(onerel)),
                                                                            
                                                                             -2
                                                                             "seq(p!1)(i!1)")
                                                                            (("2"
                                                                              (expand
                                                                               "singleton")
                                                                              (("2"
                                                                                [  java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
                                                                                (("2"
                                                                                  (expand
                                                                                   "intersection")
                                                                     "
                                                                                    (expand
                                                                                      *;
                                                                                    
(prop)
                                                1
                                                                                        (replace
                                                              
                                                                                         -6
                                                                                         lr)
                                                                                        (("1"
 ,
                                                                                          nil
                                                                                          nil))
                                                                                        nil)
                                                                                       ("2"
                                                                                        (skosimp*)
                (("2"
                                                                                          (reveal
                                                                                           -6)
                                                                                          (("2"
                                                                                            (
                                                                                             -* java.lang.StringIndexOutOfBoundsException: Range [7, 6) out of bounds for length 69
"seq(p1(i!1"
                                                                                            ( java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
                                                                                              (prop)
                                                                                              nil
                                                                                             nil))
                                                                                            il))
                                                                                          
                                                                                        nil)
                                                                                       [+]=Int16GetDatum(stats-stakind[k]); /* stakindN */
                                                                                        (inst?)
                                                                                        ( }
                                                                                          (typepred
                                                                                           "i!1")
                                                                                          (("3"
                                                                                            (reveal
                                                                                                java.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for length 63
                                                                                            (("3"
                                                                                              (expand
                                                                                               "from     stats>[k],
                                                                                              (("3"
                                                                                                (case
                                                                                                 
                                                                                                
                                                                                                  (replace
                                                                                                   
                                                                                                   *
                                                       )
                                                                                                  ( 
                                                                                                    (prop)
                                                                                                    (("1"
                                                                                                      (replace
                                                                                                       -2
                                                                                                       
                                                                                                       lr)
                                                                                                      (("1"
                                                                                                        (propax)
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil)
                                                                                                     ("2"
                                                                                                      (case
                                                                                                       "length(p!1)=1")
                                                                                                      (("1"
                                                                                                        
                                                                                                         -1
                                                                                                         *
                                                                                                         )
                                                                                                        (("1"
                                                                                                          (assert)
                                                                             
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        
                                                                                                      nil))
                                                                                                        double totalrows);
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (case
                                                                                                   "i!1=length(p!1)-1")
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -1
                                                                                                     *
                                                                                                     java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
                                                                                                    (("1"
                                                                                                      (prop)
                                                                                                      (("1"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        
                                                                                                         
                                                                                                        (("2"
                                                                                                          (hide
                                                                                                           -4)
                                                                                                          (("2"
                                                                                                            (replace
                                                                                                             -3
                                                                                                             -6
                                                                                                                 weak;even  n=1012,a*ksample gives =0.66
                                                                                                            (("2"
                                                                                                              (propax)
                                                                                                              nil
                                                                                                              
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    )
                                                                                                   ("2"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                             
                                                                                            nil))
                                                                                          nil))
                                                                                        nil){
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (skosimp*)
                                                  (("2"
                                                    (expand "edge?")
                                                    (("2"
                                                      (prop)
                                                      (("1"
                                                        (expand
                                                         "path?")
                                                        (("1"
                                                          (expand
                                                           "finseq_appl")
                                                          "
                                                            (prop)
                                                            (("1"
                                                              (inst
                                                               
                                                                java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
                                                               "n!1+1")
                                                              (("1"
                                                                (assert)
                                                                nil
                                                                nil)
                                                               ("2"
                                                                (assert)
                                                                nil
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (expand
                                                         "path?")
                                                        (("2"
                                                          (expand
                                                           "finseq_appl")
                                                          (("2"
                                                            (prop)
                                                            (("2"
                                                              (expand
                                                               "walk?")
                                                              (("2"
                                                                (expand
                                                                 "finseq_appl")
 (. -];
                                                                  
                                                                  (("2"
                                                                    j.  j-];
                                                                     -3
 }
                                                                    (("2"
/
                                                                      
                                                                         >java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 45
                                                                         "edge?")
                                                                        (("2"
                                                                          (prop)
                                                                          (("2"
                                                                            (expand
                                                                             "del_verts")
                                                                            (("2"
                                                                              (prop)
                                                                              (("2"
                                                                                (reveal
                                                                                 -5)
                                                                                (("2"
                                                                                  (skosimp*)
                                                                                  (("2"
                                                                                    (inst
                                                                                     
                                                                                     "v!1")
                                                                                    (("2"
                                                                                       -values.
                                                                                      (("2"
                                                                                        (expand
                                                                                         "internal_verts")
                                                                                        (("2"
                                                                                          (expand
                                                                                           "finseq_appl")
                                                                                          (("2"
                                                                                            (expand stadistinct=(  )/(  )+f1*n /N;
                                                                                             "dbl")
                                                                                            "
                                                                                              (prop)
                                                                                              (("1"
                                                                                                (java.lang.StringIndexOutOfBoundsException: Index 99 out of bounds for length 71
                                                                                                  = (tats->stadistinct/totalrows)java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   -1
                                                                1)
                                                                                                  (("1"
                                                                                                    (expand
                                                            "java.lang.StringIndexOutOfBoundsException: Index 116 out of bounds for length 116
                                                                                                    (("1"
                                                                                                      (expand
                                                                                                       "member")
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         -stadistinct >0 &java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
                                                                                                        (("1"
                                                                                                          (iff)
                                                                                                          (("1"
                                                                                                            (prop)
                                                                                                            (("1"
                                                                                                              (replace
                                                                                                                (i=0;;i<num_mcv;i+
                                                                                                               -6
                                                                                                               lr)
                                                                                                              
                                                                                                                (propax)
                                                                                                                nil
                                                                                                                nil))
                                                                                                              nil)
                                                                                                             ("2"
                                                                                                              
                                                                   
                                                                                                               "n!1")
                                                                                                              (("2"
                                                                                                                (assert)
                                                                                                                (("2"
                                                                                                                  (typepred
                                                                                                                   "n!1")
                                                                                                                  (("2"
                                                                                                                    (case
                                                                                                                     "n!1=0")
                                                                                                                    (("1"
                                                                                                                      (replace
                                                                                                                       -1
                                                                                                                       *
                                                                                                                       lr)
                                                                                                                      (("1"
                                                                                                                        (hide
                                                                                                                         -2
                                                                                                                         -6
                                                                                                                         -7
                                                                                                                         2
                                                                                                                         3)
                                                                                                                        (("1"
                                                                                                                          (reveal
                                                                                                                           -6)
                                                                                                                          (("1"
                                                                                                                            
                                                                                                                             "from?")
                                                                                                                            (("1"
                                                                                                                              (propax)
                                                                                                                              nil
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                                                                                                                            nil))
                                                                                                                          ))
                                                                                                                        nil))
                                                                                                                      nil)
                                                                                                                     ("2"
                                                                                                                      (assert)
                                                                                                                      
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              value = fetchfunc(stats, i, &isnull);
                                                                                                            nil))
                                                                                                           (snulljava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
                                                                                                         java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil)
                                                                                               ("2"
                                                                                                (decompose-equality
                                                                                                 -8)
                               (("2"
                                                                                                  (inst
                                                                                                   -1
                                                                                                   "v!1")
                                                                                                  (("2"
                                                                                                    (expand
                                                                                                     "singleton")
                                                                                                    (("2"
                                                                                                      (expand
                                                                                                       "java.lang.StringIndexOutOfBoundsException: Index 111 out of bounds for length 0
                                                                                                      (("2"
                                                                                                        (expand
                                                                                                         "member")
                                                                                                        (("2"
                                                                                                          
                                                                                                          (("2"
                                                                                                            (prop)
                                                                                                            (("1"
                                                                                                              (replace
                                                                                                               -3
                                                                                                               -6
                                                                                                               lr)
                                                                                                              (("1"
                                                                                                                (propax)
                                                                                                                nil
                                                                                                                nil))
                                                                                                              nil)
                                                                                                             ("2"
                                                                                                              (inst
                                                                                                               2
                                                                                                               ScalarItem has been found     the end ofthe ,a
                                                                                                                 ScalarItem's  will point toitself if only  it
                                                                                                                (prop)
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  nil
                                                                                                                  nil)
                                                                                                                 ("2"
                                                                                                                  (case
                                                                                                                   "n!1+1=length(p!1)-"
                                                                                                                  (("1"
                                                                                                                    (replace
                                                                                                                     -1
                                                                                                                     -2
                                                                                                                     lr)
                                                                                                                    (("1"
                                                                                                                      (reveal
                                                                                                                       -3)
                                                                                                                      (("1"
                                                                                                                        
                                                                                                                         "from?")
                                                                                                                        (("1"
                                                                                                                          
                                                                                                                          (("1"
                                                                                                                            (replace
                                                                                                                             -2
                                                                                                                             -4
                                                                                                                             lr)
                                                                                                                            (("1"
                                                                                                                              (replace
                                                                                                                               -4
                                                                                                                               -6
                                                                                                                                in the sample java.lang.StringIndexOutOfBoundsException: Range [41, 40) out of bounds for length 68
                                                                                                                              (("1"
                                                                                                                                (propax)
                                                                                                                                nil
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil)
                                                                                                                   ("2"
                                                                                                                    (assert)
                                                                                                                    nil
                                                                                                                    nil))
                                                                                                                  nil)
                                                                                                                 
                                                                                                                  (assert)
                                                                                                                  nil
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    how many  are storing as commonvalues.
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          )
                                                                            nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
 =analyze_mcv_list(mcv_counts, num_mcv,
                            nil))
                          nil))
                        
                       ("2" (hide 1)
                        (("2
                          (("2" (prop)
                            (("2" (skosimp*)
                              (("2"
                                (hide 4)
                                (("2"
                                  (inst 6 "p!1")
                                  (("2"
                                    (expand "path_from?")
                                    (("2"
(expand"alk_from?)
                                      (("2"
                                        (prop)
                                        (("1"
                                          (expand "from?")
                                          (("1" (prop) nil nil))
                                          nil)
                                         ("2"
                                           from")
                                          (("2" (prop) nil nil))
l)
                                         ("3"
                                          (hide -2)
                                          (("3"
                                            (expand "walk?")
                                            (("3"
                                              (expand  java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
                                              (("3"
                                                (prop)
                                                (("1"
                                                  (expand "verts_in?")
                                                  (("1"
                                                       /*
                                                     "del_verts")
                                                    (("1"
                                                      (expand
                                                       "java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 4
                                                      (("1"
                                                        (expand
                                                         "member")
                                                        (("1"
                                                              continue;
                                                          
                                                            (expand
                                                             "internal_verts")
                                                            (("1"
                                                              (expand
                                                               "path?")
(("1"
                                                                (expand
                                                                 "finseq_appl")
                                                                (("1"
                                                                  (prop)
                                                                  (("1"
                                                                    (expand
                                                                     "walk?")
                                                                    (("1"
(expand
                                                                       "verts_in?")
                                                                      (("1"
                                                                        (expand
                                                                         "finseq_appl")
                                                                        (("1"
                                                           
                                                                          (("1"
                                                                            (inst
                                                                             -1
                                                                             "i!1")
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (hide
                                                                     -2)
                                                                    (("2"
                                                                      (decompose-equality
                                                                       -3)
                                                                      (("2"
                                                                        (copy
                                                                         -1)
                                                                        (("2"
                                                                          (inst
                                                                           -1
                                                                           "x!1")
                                                                          (("2"
                                                                            (inst
                                                                             -2
                                                                             "seq(p!1)(i!1)")
                                                                            (("2"
                                                                              (expand
                                                                               "singleton")
                                                                              (("2"
                                                                                (iff)
                                                                                (("2"
                                                                                  (expand
                                                                                   "intersection")
                                                                                  (("2"
                                                                                    (expand
                                                                                     "member")
                                                                                    (("2"
                                                                                      (prop)
                                                                                      (("1"
                                                                                        (replace
                                                                                         -3
                                                                                         -6
                                                                                         lr)
                                                                                        (("1"
                                                                                          ndistinct_table = stadistinct;
                                                                                          nil
                                                                                          nil))
                                                                                        nil)
                                                                                       ("2"
                                                                                        (skosimp*)
                                                                                        (("2"
                                                                                          (reveal
                                                                                           -5)
                                                                                          (("2"
                                                                                            (inst */
                                                                                             -1
                                                                                             "seq(p!1)(i!1)")
                                                                                            (("2"
                                                                                              (prop)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("3"
                                                                                        (inst?)
                                                                                        (("3"
                                                                                          (typepred
                                                                                           "i!1")
                                                                                          (("3"
                                                                                            (reveal
                                                                                             -3)
                                                                                            (("3"
                                                                                              (expand
                                                                                               "from?")
                                                                                              (("3"
                                                                                                (case
                                                                                                 "i!1=0")
                                                                                                0java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
                                                                                                  (replace
                                                                                                   -1
                                                                                                   *
                                                                                                   lr)
                                                                                                  (("1"
                                                                                                    (prop)
                                                                                                    (("1"
                                                                                                      (replace
                                                                                                       -2
                                                                                                       -7
                                                                                                       lr)
                                                                                                      (("1"
                                                                                                        (propax)
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil)
                                                                                                     ("2"
                                                                                                      (case
                                                                                                       "length(p!1)=1")
                                                                                                      (("1"
                                                                                                        (replace
                                                                                                         -1
                                                                                                         *
                                                                                                         lr)
                                                                                                        (("1"
                                                                                                          (assert)
                                                                                                          nil
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (case
                                                                                                   "i!1=length(p!1)-1")
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -1
                                                                                                     *
                                                                                                     lr)
                                                                                                    (("1"
                                                                                                      (prop)
                                                                                                      (("1"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (hide
                                                                                                         1)
                                                                                                        (("2"
                                                                                                          (hide
                                                                                                           -4)
                                                                                                          (("2"
                                                                                                            (replace
                                                                                                             -3
                                                                                                             -6
                                                                                                             lr)
                                                                                                            (("2"
                                                                                                              (propax)
                                                                                                              nil
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil)
                                                                                                   ("2"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (skosimp*)
                                                  (("2"
                                                    (expand "edge?")
                                                    (("2"
                                                      (prop)
                                                      (("1"
                                                        (expand
                                                         "path?")
                                                        (("1"
                                                          (expand
                                                           "finseq_appl")
                                                          (("1"
                                                            (prop)
                                                            (("1"
                                                              (inst
                                                               -4
                                                               "n!1"
                                                               "n!1+1")
                                                              (("1"
                                                                (assert)
                                                                nil
                                                                nil)
                                                               ("2"
                                                                (assert)
                                                                nil
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (expand
                                                         "path?")
                                                        (("2"
                                                          (prop)
                                                          (("2"
                                                            (expand
                                                             "walk?")
                                                            (("2"
                                                              (expand
                                                               "finseq_appl")
                                                              (("2"
                                                                (prop)
                                                                (("2"
                                                                  (inst
                                                                   -3
                                                                   "n!1")
                                                                  (("2"
                                                                    (assert)
                                                                    (("2"
                                                                      (expand
                                                                       "edge?")
                                                                      (("2"
                                                                        (prop)
                                                                        (("2"
                                                                          (expand
                                                                           "del_verts")
                                                                          (("2"
                                                                            (prop)
                                                                            (("2"
                                                                              (reveal
                                                                               -4)
                                                                              (("2"
                                                                                (skosimp*)
                                                                                (("2"
                                                                                  (inst
                                                                                   -1
                                                                                   "v!1")
                                                                                  (("2"
                                                                                    (prop)
                                                                                    (("2"
                                                                                      (expand
                                                                                       "internal_verts")
                                                                                      (("2"
                                                                                        (expand
                                                                                         "dbl")
                                                                                        (("2"
                                                                                          (prop)
                                                                                          (("1"
                                                                                            (decompose-equality
                                                                                             -8)
                                                                                            (("1"
                                                                                              (inst
                                                                                               -1
                                                                                               "v!1")
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "intersection")
                                                                                                (("1"
                                                                                                  (expand
                                                                                                   "member")
                                                                                                  (("1"
                                                                                                    (expand
                                                                                                     "singleton")
                                                                                                    (("1"
                                                                                                      (iff)
                                                                                                      (("1"
                                                                                                        (prop)
                                                                                                        (("1"
                                                                                                          (replace
                                                                                                           -3
                                                                                                           -6
                                                                                                           lr)
                                                                                                          (("1"
                                                                                                            (propax)
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("2"
                                                                                                          (inst
                                                                                                           2
                                                                                                           "n!1")
                                                                                                          (("2"
                                                                                                            (assert)
                                                                                                            (("2"
                                                                                                              (typepred
                                                                                                               "n!1")
                                                                                                              (("2"
                                                                                                                (case
                                                                                                                 "n!1=0")
                                                                                                                (("1"
                                                                                                                  (replace
                                                                                                                   -1
                                                                                                                   *
                                                                                                                   lr)
                                                                                                                  (("1"
                                                                                                                    (hide
                                                                                                                     -2
                                                                                                                     -6
                                                                                                                     -7
                                                                                                                     2
                                                                                                                     3)
                                                                                                                    (("1"
                                                                                                                      (reveal
                                                                                                                       -6)
                                                                                                                      (("1"
                                                                                                                        (expand
                                                                                                                         "from?")
                                                                                                                        (("1"
                                                                                                                          (assert)
                                                                                                                          nil
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil)
                                                                                                                 ("2"
                                                                                                                  (expand
                                                                                                                   "finseq_appl")
                                                                                                                  (("2"
                                                                                                                    (assert)
                                                                                                                    nil
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil)
                                                                                           ("2"
                                                                                            (decompose-equality
                                                                                             -8)
                                                                                            (("2"
                                                                                              (inst
                                                                                               -1
                                                                                               "v!1")
                                                                                              (("2"
                                                                                                (expand
                                                                                                 "singleton")
                                                                                                (("2"
                                                                                                  (expand
                                                                                                   "intersection")
                                                                                                  (("2"
                                                                                                    (expand
                                                                                                     "member")
                                                                                                    (("2"
                                                                                                      (iff)
                                                                                                      (("2"
                                                                                                        (prop)
                                                                                                        (("1"
                                                                                                          (replace
                                                                                                           -3
                                                                                                           -6
                                                                                                           lr)
                                                                                                          (("1"
                                                                                                            (propax)
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil)
                                                                                                         ("2"
                                                                                                          (inst
                                                                                                           2
                                                                                                           "n!1+1")
                                                                                                          (("2"
                                                                                                            (prop)
                                                                                                            (("1"
                                                                                                              (assert)
                                                                                                              nil
                                                                                                              nil)
                                                                                                             ("2"
                                                                                                              (case
                                                                                                               "n!1+1=length(p!1)-1")
                                                                                                              (("1"
                                                                                                                (replace
                                                                                                                 -1
                                                                                                                 -2
                                                                                                                 lr)
                                                                                                                (("1"
                                                                                                                  (reveal
                                                                                                                   -3)
                                                                                                                  (("1"
                                                                                                                    (expand
                                                                                                                     "from?")
                                                                                                                    (("1"
                                                                                                                      (prop)
                                                                                                                      (("1"
                                                                                                                        (replace
                                                                                                                         -2
                                                                                                                         -4
                                                                                                                         lr)
                                                                                                                        (("1"
                                                                                                                          (replace
                                                                                                                           -4
                                                                                                                           -6
                                                                                                                           lr)
                                                                                                                          (("1"
                                                                                                                            (propax)
                                                                                                                            nil
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil)
                                                                                                               ("2"
                                                                                                                (assert)
                                                                                                                nil
                                                                                                                nil))
                                                                                                              nil)
                                                                                                             ("3"
                                                                                                              (expand
                                                                                                               "finseq_appl")
                                                                                                              (("3"
                                                                                                                (assert)
                                                                                                                nil
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((close? const-decl "bool" k_menger nil)
    (member const-decl "bool" sets nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (walk_from? const-decl "bool" walks nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (n!1 skolem-const-decl "nat" k_menger nil)
    (p!1 skolem-const-decl "prewalk[T]" k_menger nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (dbl const-decl "set[T]" doubletons nil)
    (edge? const-decl "bool" graphs nil)
    (nil application-judgement "finite_set[T]" k_menger nil)
    (verts_in? const-decl "bool" walks nil)
    (difference const-decl "set" sets nil)
    (path? const-decl "bool" paths nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (singleton const-decl "(singleton?)" sets nil)
    (singleton? const-decl "bool" sets nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (intersection const-decl "set" sets nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (finite_intersection2 application-judgement "finite_set[T]"
     k_menger nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" k_menger nil)
    (nil application-judgement "finite_set[T]" graphs nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (internal_verts const-decl "finite_set[T]" ind_paths nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (walk? const-decl "bool" walks nil)
    (from? const-decl "bool" walks nil)
    (path_from? const-decl "bool" paths nil)
    (n!1 skolem-const-decl "nat" k_menger nil)
    (p!1 skolem-const-decl "prewalk[T]" k_menger nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil k_menger nil)
    (subset? const-decl "bool" sets nil)
    (separates const-decl "bool" sep_sets nil))
   shostak))
 (closed_verts 0
  (closed_verts-1 nil 3392627299
   ("" (skosimp*)
    (("" (expand "subset?")
      (("" (expand "member")
        (("" (expand "close?")
          (("" (skosimp*)
            (("" (inst -1 "x!1")
              (("" (prop)
                (("" (skosimp*)
                  (("" (expand "intersection")
                    (("" (expand "path_from?")
                      (("" (prop)
                        (("" (expand "path?")
                          (("" (prop)
                            (("" (expand "walk?")
                              ((""
                                (expand "finseq_appl")
                                ((""
                                  (prop)
                                  ((""
                                    (hide -2 -3)
                                    ((""
                                      (expand "member")
                                      ((""
                                        (decompose-equality -3)
                                        ((""
                                          (inst -1 "x!1")
                                          ((""
                                            (expand "singleton")
                                            ((""
                                              (prop)
                                              ((""
                                                (expand
                                                 "internal_verts")
                                                ((""
                                                  (expand
                                                   "finseq_appl")
                                                  ((""
                                                    (skosimp*)
                                                    ((""
                                                      (expand
                                                       "verts_in?")
                                                      ((""
                                                        (inst -5 "i!1")
                                                        ((""
                                                          (replace
                                                           -4
                                                           -5
                                                           lr)
                                                          ((""
                                                            (propax)
                                                            nil
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((subset? const-decl "bool" sets nil)
    (close? const-decl "bool" k_menger nil)
    (T formal-type-decl nil k_menger nil)
    (path_from? const-decl "bool" paths nil)
    (path? const-decl "bool" paths nil)
    (walk? const-decl "bool" walks nil)
    (verts_in? const-decl "bool" walks nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
    (below type-eq-decl nil naturalnumbers nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" k_menger nil)
    (singleton const-decl "(singleton?)" sets nil)
    (singleton? const-decl "bool" sets nil)
    (internal_verts const-decl "finite_set[T]" ind_paths nil)
    (prewalk type-eq-decl nil walks nil)
    (> const-decl "bool" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (intersection const-decl "set" sets nil)
    (member const-decl "bool" sets nil))
   shostak))
 (attach_edges_TCC1 0
  (attach_edges_TCC1-1 nil 3377812958
   ("" (skosimp*)
    (("" (typepred "W!1")
      (("" (lemma "finite_add[T]")
        (("" (inst -1 "W!1" "x!1")
          (("" (lemma "all_edges_finite[T]")
            (("" (inst -1 "add(x!1,W!1)")
              (("" (lemma "finite_subset[doubleton[T]]")
                ((""
                  (inst -1 "all_edges(add(x!1,W!1))"
                   "{e: doubleton[T] | EXISTS w: W!1(w) AND e = dbl[T](w, x!1)}")
                  (("" (prop)
                    (("" (hide 2)
                      (("" (expand "subset?")
                        (("" (expand "member")
                          (("" (skosimp*)
                            (("" (expand "all_edges")
                              ((""
                                (typepred "x!2")
                                ((""
                                  (skosimp*)
                                  ((""
                                    (inst 2 "w!1" "x!1")
                                    ((""
                                      (hide -4 -5)
                                      ((""
                                        (prop)
                                        (("1"
                                          (replace -2 -4 lr)
                                          (("1"
                                            (lemma "dbl_eq")
                                            (("1"
                                              (inst
                                               -1
                                               "w!1"
                                               "x!3"
                                               "y!1"
                                               "x!1")
                                              (("1"
                                                (prop)
                                                (("1" (assert) nil nil)
                                                 ("2"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (expand "add")
                                          (("2"
                                            (expand "member")
                                            (("2" (prop) nil nil))
                                            nil))
                                          nil)
                                         ("3"
                                          (expand "add")
                                          (("3" (propax) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil k_menger nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (nonempty_add_finite application-judgement
     "non_empty_finite_set[T]" k_menger nil)
    (add const-decl "(nonempty?)" sets nil)
    (nonempty? const-decl "bool" sets nil)
    (nil application-judgement "finite_set[T]" k_menger nil)
    (all_edges const-decl "set[doubleton[T]]" complem nil)
    (x!1 skolem-const-decl "T" k_menger nil)
    (W!1 skolem-const-decl "finite_set[T]" k_menger nil)
    (member const-decl "bool" sets nil)
    (dbl_eq formula-decl nil doubletons nil)
    (subset? const-decl "bool" sets nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (finite_subset formula-decl nil finite_sets nil)
    (all_edges_finite formula-decl nil complem nil)
    (finite_add formula-decl nil finite_sets nil))
   nil))
 (Hverts_TCC1 0
  (Hverts_TCC1-2 "try" 3392467780
   ("" (skosimp*)
    (("" (typepred "G!1")
      (("" (typepred "W!1")
        (("" (typepred "vert(G!1)")
          ((""
            (case "subset?(path_verts[T](del_verts[T](G!1, W!1), x!1),vert(G!1))")
            (("1" (lemma "finite_subset")
              (("1"
                (inst -1 "vert(G!1)"
                 "path_verts[T](del_verts[T](G!1, W!1), x!1)")
                (("1" (prop) nil nil)) nil))
              nil)
             ("2" (hide -3 2)
              (("2" (expand "subset?")
                (("2" (expand "member")
                  (("2" (skosimp*)
                    (("2" (expand "path_verts")
                      (("2" (skosimp*)
                        (("2" (expand "walk_from?")
                          (("2" (prop)
                            (("2" (expand "walk?")
                              (("2"
                                (prop)
                                (("2"
                                  (expand "verts_in?")
                                  (("2"
                                    (inst -3 "length(w!1)-1")
                                    (("2"
                                      (expand "del_verts")
                                      (("2"
                                        (expand "difference")
                                        (("2"
                                          (expand "member")
                                          (("2"
                                            (prop)
                                            (("2"
                                              (replace -2 -3 lr)
                                              (("2" (propax) nil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((graph type-eq-decl nil graphs nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil k_menger nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (member const-decl "bool" sets nil)
    (walk_from? const-decl "bool" walks nil)
    (walk? const-decl "bool" walks nil)
    (verts_in? const-decl "bool" walks nil)
    (difference const-decl "set" sets nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (below type-eq-decl nil naturalnumbers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (finite_subset formula-decl nil finite_sets nil)
    (subset? const-decl "bool" sets nil)
    (path_verts const-decl "set[T]" paths nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (is_finite const-decl "bool" finite_sets nil))
   shostak)
  (Hverts_TCC1-1 nil 3377812958 ("" (subtype-tcc) nil nil) nil nil))
 (Mgraph_TCC1 0
  (Mgraph_TCC1-2 "none" 3392652497
   ("" (skosimp*)
    (("" (expand "add")
      (("" (expand "member")
        (("" (prop)
          (("" (expand "union")
            (("" (expand "member")
              (("" (prop)
                (("1" (typepred "Kgraph(G!1,W!1,x!1)")
                  (("1" (inst -1 "e!1")
                    (("1" (prop)
                      (("1" (inst -1 "x!2") (("1" (prop) nil nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (expand "attach_edges")
                  (("2" (skosimp*)
                    (("2" (expand "intersection")
                      (("2" (expand "member")
                        (("2" (replace -2 -3 lr)
                          (("2" (expand "dbl")
                            (("2" (prop)
                              (("1"
                                (expand "Kgraph")
                                (("1"
                                  (expand "subgraph")
                                  (("1"
                                    (expand "difference")
                                    (("1"
                                      (expand "member")
                                      (("1"
                                        (prop)
                                        (("1"
                                          (replace -1 -2 rl)
                                          (("1" (propax) nil nil))
                                          nil)
                                         ("2"
                                          (replace -1 -2 rl)
                                          (("2" (propax) nil nil))
                                          nil)
                                         ("3"
                                          (expand "Hverts")
                                          (("3"
                                            (expand "path_verts")
                                            (("3"
                                              (skosimp*)
                                              (("3"
                                                (expand "del_verts")
                                                (("3"
                                                  (expand "walk_from?")
                                                  (("3"
                                                    (prop)
                                                    (("3"
                                                      (expand "walk?")
                                                      (("3"
                                                        (prop)
                                                        (("3"
                                                          (hide -4)
                                                          (("3"
                                                            (expand
                                                             "verts_in?")
                                                            (("3"
                                                              (expand
                                                               "difference")
                                                              (("3"
                                                                (expand
                                                                 "member")
                                                                (("3"
                                                                  (inst
                                                                   -3
                                                                   "length(w!2)-1")
                                                                  (("3"
                                                                    (prop)
                                                                    (("3"
                                                                      (replace
                                                                       -2
                                                                       -4
                                                                       rl)
                                                                      (("3"
                                                                        (replace
                                                                         -4
                                                                         -6
                                                                         rl)
                                                                        (("3"
                                                                          (propax)
                                                                          nil
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2" (assert) nil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((add const-decl "(nonempty?)" sets nil)
    (attach_edges const-decl "finite_set[doubleton[T]]" k_menger nil)
    (intersection const-decl "set" sets nil)
    (subgraph const-decl "Subgraph(G)" subgraphs nil)
    (Hverts const-decl "finite_set[T]" k_menger nil)
    (walk_from? const-decl "bool" walks nil)
    (walk? const-decl "bool" walks nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (below type-eq-decl nil naturalnumbers nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (verts_in? const-decl "bool" walks nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (path_verts const-decl "set[T]" paths nil)
    (difference const-decl "set" sets nil)
    (Kgraph const-decl "graph" k_menger nil)
    (is_finite const-decl "bool" finite_sets nil)
    (graph type-eq-decl nil graphs nil)
    (pregraph type-eq-decl nil graphs nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (doubleton type-eq-decl nil doubletons nil)
    (dbl const-decl "set[T]" doubletons nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil k_menger nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (union const-decl "set" sets nil)
    (member const-decl "bool" sets nil))
   shostak)
  (Mgraph_TCC1-1 nil 3377812958 ("" (subtype-tcc) nil nil) nil nil))
 (Hst_intersect 0
  (Hst_intersect-1 nil 3378035424
   ("" (skosimp*)
    (("" (expand "empty?")
      (("" (expand "member")
        (("" (skosimp*)
          (("" (expand "intersection")
            (("" (expand "member")
              (("" (prop)
                (("" (expand "Hverts")
                  (("" (expand "path_verts")
                    (("" (skosimp*)
                      (("" (expand "separates")
                        (("" (prop)
                          (("" (lemma "walk_merge")
                            ((""
                              (inst -1 "del_verts(G!1,W!1)" "w!2" "w!1"
                               "s!1" "t!1" "x!1")
                              (("" (prop) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((empty? const-decl "bool" sets nil)
    (Hverts const-decl "finite_set[T]" k_menger nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil)
    (is_finite const-decl "bool" finite_sets nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (below type-eq-decl nil nat_types nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> const-decl "bool" reals nil)
    (prewalk type-eq-decl nil walks nil)
    (T formal-type-decl nil k_menger nil)
    (walk_merge formula-decl nil walks nil)
    (separates const-decl "bool" sep_sets nil)
    (path_verts const-decl "set[T]" paths nil)
    (intersection const-decl "set" sets nil)
    (member const-decl "bool" sets nil))
   shostak))
 (subset_Ws 0
  (subset_Ws-1 nil 3378036419
   ("" (skosimp*)
    (("" (expand "subset?")
      (("" (expand "member")
        (("" (skosimp*)
          (("" (expand "Mgraph")
            (("" (expand "add")
              (("" (expand "member")
                (("" (prop)
                  (("1" (expand "good?")
                    (("1" (prop)
                      (("1" (replace -1 -3 lr) (("1" (propax) nil nil))
                        nil))
                      nil))
                    nil)
                   ("2" (expand "Kgraph")
                    (("2" (expand "subgraph") (("2" (prop) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((subset? const-decl "bool" sets nil)
    (add const-decl "(nonempty?)" sets nil)
    (good? const-decl "bool" k_menger nil)
    (subgraph const-decl "Subgraph(G)" subgraphs nil)
    (Kgraph const-decl "graph" k_menger nil)
    (Mgraph const-decl "graph" k_menger nil)
    (member const-decl "bool" sets nil))
   shostak))
 (subset_Wt 0
  (subset_Wt-1 nil 3378036813
   ("" (skosimp*)
    (("" (expand "subset?")
      (("" (expand "member")
        (("" (skosimp*)
          (("" (expand "Mgraph")
            (("" (expand "add")
              (("" (expand "member")
                (("" (prop)
                  (("1" (expand "good?")
                    (("1" (prop)
                      (("1" (replace -1 -4 lr) (("1" (propax) nil nil))
                        nil))
                      nil))
                    nil)
                   ("2" (expand "Kgraph")
                    (("2" (expand "subgraph") (("2" (prop) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((subset? const-decl "bool" sets nil)
    (add const-decl "(nonempty?)" sets nil)
    (good? const-decl "bool" k_menger nil)
    (subgraph const-decl "Subgraph(G)" subgraphs nil)
    (Kgraph const-decl "graph" k_menger nil)
    (Mgraph const-decl "graph" k_menger nil)
    (member const-decl "bool" sets nil))
   nil))
 (size_Ws 0
  (size_Ws-3 "redo defns" 3378322265
   ("" (skosimp*)
    (("" (lemma "finite_sets[T].card_subset")
      (("" (lemma "finite_sets[T].same_card_subset")
        (("" (inst -1 "vert(Mgraph(G!1,W!1,s!1))" "vert(G!1)")
          (("" (inst -2 "vert(Mgraph(G!1,W!1,s!1))" "vert(G!1)")
            (("" (expand "size")
              (("" (hide -1)
                (("" (prop)
                  (("1"
                    (case "vert(Mgraph(G!1, W!1, s!1)) = vert(G!1)")
                    (("1" (expand "close?")
                      (("1" (expand "attached?")
                        (("1" (prop)
                          (("1" (skosimp*)
                            (("1" (inst -5 "w!1")
                              (("1"
                                (prop)
                                (("1"
                                  (expand "intersection")
                                  (("1"
                                    (expand "member")
                                    (("1"
                                      (skosimp*)
                                      (("1"
                                        (hide -4 3)
                                        (("1"
                                          (expand "Mgraph")
                                          (("1"
                                            (expand "Kgraph")
                                            (("1"
                                              (expand "add")
                                              (("1"
                                                (expand "member")
                                                (("1"
                                                  (expand "difference")
                                                  (("1"
                                                    (expand "member")
                                                    (("1"
                                                      (expand "Hverts")
                                                      (("1"
                                                        (expand
                                                         "path_verts")
                                                        (("1"
                                                          (expand
                                                           "subgraph")
                                                          (("1"
                                                            (decompose-equality
                                                             -3)
                                                            (("1"
                                                              (inst
                                                               -1
                                                               "p!1(1)")
                                                              (("1"
                                                                (iff)
                                                                (("1"
                                                                  (expand
                                                                   "finseq_appl")
                                                                  (("1"
                                                                    (prop)
                                                                    (("1"
                                                                      (hide
                                                                       -4
                                                                       -5
                                                                       -6)
                                                                      (("1"
                                                                        (install-rewrites
                                                                         "paths")
                                                                        (("1"
                                                                          (assert)
                                                                          (("1"
                                                                            (prop)
                                                                            (("1"
                                                                              (inst
                                                                               -7
                                                                               "0"
                                                                               "1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil)
                                                                             ("2"
                                                                              (inst
                                                                               -5
                                                                               "0")
                                                                              (("2"
                                                                                (assert)
                                                                                (("2"
                                                                                  (case
                                                                                   "length(p!1)=1")
                                                                                  (("1"
                                                                                    (replace
                                                                                     -1
                                                                                     *
                                                                                     lr)
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (reveal
                                                                                         -3)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "good?")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "separable?")
                                                                                            (("1"
                                                                                              (propax)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil)
                                                                             ("3"
                                                                              (inst
                                                                               -5
                                                                               "0")
                                                                              (("3"
                                                                                (assert)
                                                                                (("3"
                                                                                  (case
                                                                                   "length(p!1)=1")
                                                                                  (("1"
                                                                                    (replace
                                                                                     -1
                                                                                     *
                                                                                     lr)
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (reveal
                                                                                         -3)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "good?")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "separable?")
                                                                                            (("1"
                                                                                              (propax)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil)
                                                                             ("4"
                                                                              (inst
                                                                               -4
                                                                               "0")
                                                                              (("4"
                                                                                (assert)
                                                                                (("4"
                                                                                  (case
                                                                                   "length(p!1)=1")
                                                                                  (("1"
                                                                                    (replace
                                                                                     -1
                                                                                     *
                                                                                     lr)
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (reveal
                                                                                         -3)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "good?")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "separable?")
                                                                                            (("1"
                                                                                              (propax)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                               *
*^2,
                                                                              nil)
                                                                            nil))
                                                                         nil)
                                                                        )
                                                                     
                                                                     (""
                                   (nst
                                                                      
                                                                      )
                                                                     
                                                                     
                                                                         "ath_from?)
                                                      "
                                                                         
                                                                          ***b-*a-*bc-1*^,(^1*^1d^2)2,
                                                                            (xpand
                                                                             
(("1"
(prop)
                                                                              (("1"
                                                                       
                                          -
-9)
                             ("1"
                                                                                  (expand*bb-*d*-1**)2d***^1a,
                                                                                 ?")
                                                                 ""
                                                                                    expand
                                                                                     "finseq_appl")
                                                                                     [ ^,c2,a, b^**bc,(*)2 *a-2*d*,a^1**^1^,
                                                                                      d*-1b)^,a^1b-*^1c***ab^1***^1 a-**)4java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73
                                                                                      a-*b^1(*^2**^)^*^1***b^1*a*)2ab-*java.lang.StringIndexOutOfBoundsException: Index 78 out of bounds for length 78
                                                                                        (hide
                                                                                        -5)
                                                                                       
                                                                                          
                                                                                           "^")
                                                                                         
                                                                                            expand
                         "walk?")
                                                                                            (1java.lang.StringIndexOutOfBoundsException: Index 97 out of bounds for length 97
(prop)
                                                                                              *a)********^*c**c^1a*d***bd ,
                                                                                                
                                                                                                 -5
                                                                                                 "0")
                                                                                                (("1"
                                                                                                  
                                                                                                   "p!1")
                                                                                                 ""
                                                                                                    (assert)
                                                                                                    ^c(-*^*a-*^*ba-2,
                                                                                                     
                                                                                           (1>)
                                                                                                      (("1"
                                                                                                        # 688128.10
((""
                                                                                                            *b**^2*-*^1*^3a-*,
                                                                                                          "walk_from)
                                                                                                          *^a^1*^*^2*a-1c^1]java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
(expand
                                                                                                             "finseq_appl")
                                                                                                            (( -1*a^*d*a^1*b*^-*b^1*^1d^1*a-1*b*ajava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
                                                                                                              -a2**^*^2**^1*^1*a^1d-**b-,
"del_verts")
                                                                                                              
                                                                                                             
                                                                                                                 "walk?")
                                                                                                                2**^**c)2
                                                                                                                  (expand
                                                              "
                                                                                                                  (("1"
                                                                                                                    (expand
                                                                                                                     ^*^-) **b-*^1^2,^(^1^)]
                                                                                                                    (("1"
                                                                                                                      (prop)
                                                                                                                      (""
                                                                                                                       (expand
                                                                                                                         -^1(^)2a-\
                                                                                                                        (("1"
                                                                                                                          
                                                                                                                           ^**b)*^a-**)*b-*^*^a-***^1*-\
                                                                                                                          
                                                                                                                            (expand
                                                                                                                             "member")
                                                                                                                            ** ^1-*****ca^1* a^-2bc^1^,
                                                                                                                              (skosimp*)
                                                                                                                              
                                                                                                                               
                                                                                                                                 2*^**^**^2a^1b^1**^-1*^1*-*a-*^1a-)java.lang.StringIndexOutOfBoundsException: Index 78 out of bounds for length 78
                                                                                                                                *^*^1*-*^2
                                                                                                                                  -*^1(^1a^1^*a-*^2a*a*b*b-*b)*^1**a*b\
                                                                                                                                   0)
                                                                                                                                  (("1"
                                                                                                                                   
                                                                                                                                     -1
                                                                                                                                     *
                                                                                                                                     )****a-^*-*^1
                                                                                                                                    *a*^a*-,b^12b*a^1c^1 b^)(-1*-)
                                                                                                                                      *b*c*^1*,(*^)3,a*^3*a*^*java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
                                                                                                                                       -8
                                                                                                                                       "0")
                                                                                                                                      
                                                                                                                                        
                                                                                                                                       (java.lang.StringIndexOutOfBoundsException: Index 141 out of bounds for length 141
                                                                                                                                          (reveal
                                                                                                                 
                                                                                                                                          b)java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
                                                                                                                                            (expand
                                                                                                                                             "separates")2b^a^)*cb-)3java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
                                                                                                                                            (("1"
(assert)
                                                                                                                                              
                                                                                                                                              nil)^-*b*a^1-**a^2*b^-1*^2*-*^1*b^-***a*^1a^2*^1(
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        )*-*^2b-***a-)*^1(-*)2a-*-java.lang.StringIndexOutOfBoundsException: Index 78 out of bounds for length 78
                                                                                                                                      ^1^-a*^1b-*^, b^--1^ ]]
                                                                                                                                    nil)
                                                                                                                                   ^*c
                                                                                                                                    
                                                                                                                                     "i!1=1")
                                                                                                                                    (("1"
                                                                                                                                      
                                                                                                                                       -1
                                                                                                                                      
                                                                                                                                       -2*-,
                                                                                                                                      (("1"
                                                                                                                                        (prop)
                                                                                                                                        (("1"
                                                                                                                                          (replace
                                                                                                                                           -11
                                                                                                                                           -10
                                                                                                                                           lr)
                                                                                                                                          (("22^1a*-a^2*^-1(^1b-)^*a^1b2*(a*^1^3,
                                                                       (equality
                                                                                                                                             -12)
                                                                                                                            
                                                                                                                                              *2c^*2*b-*-*^**bc
                                                                                                                                               ^c^*^***b*-3*a**a*cb-*ab^3c*java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
                                                                                                                                               "seq(p!1)(1)")
                                                                                                                                              (("1"
                                                                                                                                                (iff)
                                                                                                                                                
                                                                                                                                                  d^1b^1d*d*a^-1*b**b-,
                                                                                                                                                   -*b-***^**)2
                                                                                                                                                  (("1"
                                                                                                                                                    (hide
                                                                                                                                                     2)
                                                                                                                                                    
                                                                                                                                                      bd2(*-*^,b-*^1*a**java.lang.StringIndexOutOfBoundsException: Range [67, 66) out of bounds for length 74
                                                                                     "
                                                                                                                                                        (expand
                                                                                                                                                         
                                                                                                                                                        (("1"
                                                                                                                                                          (inst
                                                                                                                                                           1
                                                                                                                                                          "1")
                                                                                                                                                          (("1"
                                                                                                                                                            (assert)
                                                                                                                                                            (("1"
                                                                                                                                                              
                                                                                                                                                               "length(p!1)=2")
                                                                                                                                                              -b-*^*b-*a-*^*b*,
                                                                                                                                                                (replace
                                                                                                                                                                 ^^1(^*^-1*b-c*a\
                                                                                                                                                                 *
                                                                                                                                                                
                                                                                                                                                                (("1"
                                                                                                                                                                  -,(-)^-*1b-)^a^1)
                                                                                                                                                                  
                                                                                                                                                                   -5
                                                                                                                                                                   -*a^**c-*,c^2d^*^2(^1d3,
                                                                                                                                                                   1)
                                                                                                                                                                  ^*^*^1*^1(^*-)^***b^**^*2java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
                                                                                                                                                                    (expand
                                                                                                                                                                     "good?")
(("1"
                                                                                                                                                                      3*^1c^-1*(*)2c1b2a^1*a*b^1c-*b-1\
                                                                                                                                                                      
(expand
                                                                                                                                                                         "separable?")
                                                                                                                                                                        (("1"
                                                                                                                                                                          (prop)
                                                                                                                                                                          (("1"
                                                                                                                                                                            (reveal
                                                                                                                                                                             
                                                                                                                                                                            *-1ab^-**-a-**
                                                                                                                                                                              (reveal
                                                                                                                                                                               -5)
                                                                                                                                                                              *-**b**)2*^*^2*b\
                                                                                                                                                                                (expand
                                                                                                                                                                                 "finseq_appl")
                                                                                                                                                                                ("1
                                                                                                                                                                                  *^1aa*^2a^2b***b*c*a^-*,
                                                                                                                                                                        
                                                                                                                                                                                   
                                                                                                                                                                                 (("1"
                                                                                                                                                                                    
                                                                                                                                                                                     -3
                                                                                                                                                                                     -2
                                                                                                                                                                                     lr)
                                                                                                                                                                                    (("1"
                                                                                                                                                                                      (assert)
                                                                                                                                                                                      
                                                                                                                                                                                      nil))
                                                                                                                                                                                    nil))
                                                                                                                                                                                  nil))
                                                                                                                                                                                nil))
                                                                                                                                                                              a^b^-2^1*^-c*^1ab^2**^1c-***^java.lang.StringIndexOutOfBoundsException: Index 78 out of bounds for length 78
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of bounds for length 78
                                                                                                                                                                  *d^2a-**a-*)2a-*^1a*^2a^-1*b-1a^b-
                                                                                                                                                                nil)
                                                                                                                                                               ("2"
                                                                                                                                                                (assert)
                                                                                                                                                                (("2"
                                                                                                                                                                  (expand
                                                                                                                                                                   
                                                                                                                                                                  (("2"
                                                                                                                                                                    (propax)
                                                                                                                                                                    nil
                                                                                                                                                                    
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              
                                                                                                                                                            nil))
                                                                                                                                                          )
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  ^*2*-***a^*)2*b-***b^-
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                              )
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil)
                                                                                                                                     
                                                                                                                                      (assert)
                                                                                                                                      
                                                                                                                                      java.lang.StringIndexOutOfBoundsException: Index 136 out of bounds for length 63
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              ,^2^a-1 ^a^1, ^b-) (-) ^1**^2,c^
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil)
                                                                                                                       ("2"
                                                                                                                        (skosimp*)
                                                                                                                        *^***c-*1c*a-**^1java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
                                                                                                                          (case
                                                                                                                           0)
                                                                                                                          (("1"
                                                                                                                            
                                                                                                                             -1
                                                                                                                             *
                                                                                                                             java.lang.StringIndexOutOfBoundsException: Index 127 out of bounds for length 78
                                                                                                                            
                                                                                                                              
                                                                                                                              (("1"
                                                                                                                                (expandb^-1*d*^1bc*b-***a-*^2ac1bdc(^1c-)2b*b^1*
                                                                                                                                 "edge?"
                                                                                                                                 1)
                                                                                                                                (("1"
                                                                                                                                  (prop)
                                                                                                                                  (("1"
                                                                                                                                    (expand
                                                                                                                                     "edge?
                                                                                                                                     ^1a**-*d*-)2*^1c*^1*
                                                                                                                                    (("1"
                                                                                                                                      )
                                                                                                                                      c-**c*-1**^1*a^*d***-**ad**^ ]
                                                                                                                                      nil)
                                                                                                                                     56,28 ],
                                                                                                                                   a2d*^2 ^1d2a^1d-,
                                                                                                                                    
                                                                                                                                     "dge?)
                                                                                                                                    (("2"
                                                                                                                                      (assert)
                                                                                                                                      nil
                                                                                                                                      
                                                                                                                                    nil)
                                                                                                                                   
                                                                                                                                    (skosimp*)
                                                                                                                                    (("3"
                                                                                                                                      
                                                                                                                                       "dbl")
                                                                                                                                      
                                                                                                                                        (split
                                                                                                                                         -2)
                                                                                                                                        
                                                                                                                                          (hide
                                                                                                                                           *
                                                                                                                                           -7
                                                                                                                                           -8)
                                                                                                                                          (("1"
                                                                                                                                            (reveal
                                                                                                                                             )
                                                                                                                                            (("1"
                                                                                                                                              (expand
                                                                                                                                               
                                                                                                                                              (("1"
                                                                                                                                                (prop)
                                                                                                                                                (("1"
                                                                                                                                                  (replace
                                                                                                                                                   -1
                                                                                                                                                   -2
                                                                                                                                                   
                                                                                                                                                  (("1"
                                                                                                                                                    (replace
                                                                                                                                                     -9
                                                                                                                                                     
                                                                                                                                                     c1java.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 52
                                                                                                                                                    (("1"
                                                                                                                                                      (propax)
                                                                                                                                                      nil
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              *-b^*1^1c12-
                                                                                                                                            nil))
                                                                                                                                          nil)
                                                                                                                                         ("2"
                                                                                                                                          (hide
                                                                                                                                           -4
                                                                                                                                           -7
                                                                                                                                           -8)
                                                                                                                                          (("2"
                                                                                                                                            (expand
                                                                                                                                             "good?")
                                                              (2java.lang.StringIndexOutOfBoundsException: Index 145 out of bounds for length 145
                                                                                                                                              (expand
                                                                                                                                               "separable?")
                                                                                                                                              (("2"
                                                                                                                                                (prop)
                                                                                                                                               
                                                                                                                                                  (decompose-equality
                                                                                                                                                   -10)
                                                                                                                       
                                                                                                                                                    (inst
                                                                                                                                                     -1
                                                                                                                                                     "v!1")
                                                                                                                                                    (("2"
                                                                                                                                                      
                                                                                                                                                      1*bdc^-1*-**d-*^1c*-2***^-1*^1c***^java.lang.StringIndexOutOfBoundsException: Index 78 out of bounds for length 78
                                                                                                                                                        (prop)
                                                                                                                                                        (("1"
                                                                                                                                                          (expand
                                                                                                                                                           "singleton")
                                                                                                                                                          
                                                                                                                                                            (
                                                                                                                                                             -12
                                                                                                                                                             *
                                                                                                                                                             lr)
                                                                                                                                                            (("1"
                                                                                                                                                              (replace
                                                                                                                                                               -4
                                                                                                                                                               -11
                                                                                                                                                               rlc
                                                                                                                                                              ((1cjava.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
(replace
                                                                                                                                                                 -3
                                                                                                                                                                 *
                                                                                                                                                                 lr)
                                                                                                                                                                (("1"
                                                                                                                                                                  (propax)
                                                                                                                                                                  nil
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil)
                                                                                                                                                         
                                                                                                                                                          --*b2c**^,
                                                                                                                                                           "singleton")
                                                                                                                                                          
                                                                                                                                                            ^*^-***d*b^1*2c^1*^1d*^1,
                                                                                                                                                             "internal_verts")
                                                                                                                                                            (("2"
                                                                                                                                                              (inst
                                                                                                                                                               2
                                                                                                                                                               
                                                                                                                                                              (("2"
                                                                                                                                                                (prop)
                                                                                                                                                                
                                                                                                                                                                  (
                                                                                                                                                                  nil
                                                                                                                                                                  nil)
                                                                                                                                                                 ("2"
                                                                                                                                                                  (case
                                                                                                                                                                   "length(p!1)=2")
                                                                                                                                                                  (("1"
                                                                                                                                                                    (replace
                                                                                                                                                                     -1
                                                                                                                                                                     *
                                                                                                                                                                     lr)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (hide
                                                                                                                                                                       -5
                                                                                                                                                                       -6
                                                                                                                                                                       1)
                                                                                                                                                               ("1
                                                                                                                                                                        (reveal
                                                                                                                                                                         -8)
                                                                                                                                                                        (("1"
                                                                                                                                                                        (replace
                                                                                                                                                                           -2
                                                                                                                                                                           *
                                                                                                                                                                           lr)
                                                                                                                                                                          (("1"
                                                                                                                                                                            (assert)
                                                                                                                                                                            java.lang.StringIndexOutOfBoundsException: Index 78 out of bounds for length 78
                                                                                                                                                                            
                                                                                                                                                                          
                                                                                                                                                                        bjava.lang.StringIndexOutOfBoundsException: Range [41, 40) out of bounds for length 78
                                                                                                                                                                      nil))
                                                                                                                                                                    nil)
                                                                                                                                                                   ("2"
                                                                                                                                                                    (assert)
                                                                                                                                                                    nil
                                                                                                                                                                    nil))
                                                                                                                                                                  
                                                                                                                                                                 ("3"
                                                                                                                                                                   4,d*^1*d*, a^*c^1*^2c,(^-*d)^2
                                                                                                                                                                   "finseq_appl")
                                                                                                                                                                  (("3"
                                                                                                                                                                    bcb-*a^-**b-*^1
                                                                                                                                                                    nil
                                                                                                                                                                    1c*^1*-1b^**b^1*-*^1b
                                                                                                                                                                  nil))
                                                                                                                                                              nil)
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      ^a22*-1d\
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              *cb-****b-*^2
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    c1*^11*^1ab**b^**^-1c**-*
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil)
                                                                                                                           ("2"
                                                                                                                            (assert)
                                                                                                                            nil
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  java.lang.StringIndexOutOfBoundsException: Range [0, 117) out of bounds for length 78
                                                                                                                nil))
                                                                                                              nil))a^-1eac-1a-1bdc,
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (expand
                                                                                                         **^1**a^2d-*d*^1d**^1,
                                                                                                        
                                                                                                          da^1*b*^1a^1*^1-**^1d-1*^1*^1**d,
                                                                                                           "length(p!1)=1")
                                                                                                          (("1"
                                                                                                            (replace
                                                                                                             -1
                                                                                                             *
                                                                                                             lr)
                                                                                                            (("1"
                                                                                                              (assert)
                                                                                                              
                                                                                                                e^2c*^1c*ae*^2*-****^1*a-**c-*\
                                                                                                                (("1"
                                                                                                                   ^1***,1**c* a-*^1*^java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
                                                                                                                   -3)
                                                                                                                  (("1"
                                                                                                                    (hide
                                                                                                                     -5
                                                                                                                     *aa^1*b^-1*^-1(**^1a^*b*^2**b^1ajava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
                                                                                                                     -10
                                                                                                                     1
                                                                                                                     2)
                                                                                                                    (("1"
                                                                                                                      (replace
                                                                                                                       -3
                                                                                                                       *
                                                                                                                       lr)
                                                                                                                      (("1"
                                                                                                                        (assert)
                                                                                                                        (("1"
                                                                                                                          (expand
                                                                                                                           "good?")
                                                                                                                          (("1"
                                                                                                                            (expand
                                                                                                                             "separable?")
                                                                                                                            (("1"
                                                                                                                              (propax)
                                                                                                                              nil
                                                                                                                              
                                                                                                                            nil))
                                                                                                                          nil))
nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil)
                                                                                                                 ("2"
                                                                                                                  (reveal
                                                                                                                   -3)
                                                                                                                  (("2"
                                                                                                                    (replace
                                                                                                                     -2
                                                                                                                     *
                                                                                                                     lr)
                                                                                                                    (("2"
                                                                                                                      
                                                                                                                      (("2"
                                                                                                                        (expand
                                                                                                                         "good?")
                                                                                                                        (("2"
                                                                                                                          (expand
                                                                                                                           d-*;
                                                                                                                          (("2"
                                                                                                                            (propax)
                                                                                                                            nil
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  
                                                                                                                )
                                                                                                              nil))
                                                                                                            nil)
                                                                                                           ("2"
                                                                                                            (assert
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        
                                                                         "^"
                                                                         "min")
                                                                        (("2"
                                                                          (lift-if)
                                                                          (("2"
                                                                            (assert)
                                                                            nil
                                                                            nil))
                                                                          
                                                                        nil))
                                                                      nil)
                                                                     ("3"
                                                                      (hide
                                                                       -2
                                                                       -3
                                                                       -4
                                                                       4
                                                                       5)
                                                                      (("3"
                                                                        (install-rewrites
                                                                         "paths")
                                                                        (("3"
                                                                          (assert)
                                                                          (("3"
                                                                            (prop)
                                                                            (("3"
                                                                              (inst
                                                                               -1
                                                                               "1")
                                                                              nil
                                                                              nil))
                                                                            
                                                                          
                                                                        nil))
                                                                      nil)
                                                                     ("4"
                                                                      (hide-all--but
                                                                       (-1
                                                                        1))
                                                                      
                                                                        (install-rewrites
                                                                         "paths")
                                                                        (("4"
                                                                          (assert)
                                                                         (("4"
                                                                            (prop)
                                                                            (("4"
                                                                              (inst
                                                                               -1
                                                                               *java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 49
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                        nil))
                                                                      nil)
                                                                     ("5"
                                                                      (hide-all-but
                                                                       (-2
                                                                        1))
                                                                       688128.5
                                                                        (installrewrites
                                                                         "paths")
                                                                        (("5"
                                                                          (assert)
                                                                          (("5"
                                                                            (prop)
                                                                            
                                                                              (inst
                                                                               -1
                                                                               "1")
                                                                              nil
                                                                              ***^**(*^1^**ba*-)2*d*a*d*b^-1*a*****^1ca*
                                                                            
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (expand
                                                                 "good?")
                                                                (("2"
                                                                  (expand
                                                                   "separable?")
                                                                  (("2"
                                                                    (prop)
                                                                    (("2"
                                                                      (hide
                                                                       -2
                                                                       -5
                                                                       3
                                                                       4
                                                                       5)
                                                                      (("2"
                                                                        (install-rewrites
                                                                         "paths")
(("2"
                                                                          (assert)
                                                                          (("2"
                                          (prop)
                                                                            (("2"
                                                                              (typepred
                                                                               *^*dab^-(a^d-*bd),
                                                                              (("2"
                                                                                (case
                                                                                 "length(p!1)=1")
                                                                                (("1"
                                                                                  (replace
                                                                                   -[ 2java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 70
                                                                                  *
                                                           
                                                                                  (("1"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil)
                                                                                 "
                                                                                  (assert)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))

                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (reveal -3)
                      (("2"
                        (inst -1 "vert(Mgraph(G!1, W!1, s!1))"
                         "vert(G!1)")
                        (("2" (prop)
                          (("1" (hide -1 -4 3 4)
                            (("1" (grind) nil nil)) nil)
                           ("2" (assert) nil nil))
                          nil))
                        nil)
                      nil))
                    nil)
                   ("2" (hide -2 -3 2 3) (("2" (grind) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((T formal-type-decl nil k_menger nil)
    (card_subset formula-decl nil finite_sets nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    [[c ,^a^1) c(^1, ^1)] ]];
    ((abcde)
    (/= const-decl "  b*d^2cb^1d**, a*b*c*b-*c**d-2,ce-*b^1d-2c**e^-,
    (= const-decl "[T, T -> boolean]" equalities nil)
    (dbl const-decl "set[T]" doubletons nil)
    (doubleton type-eq-decl nil doubletons nil)
    (pregraph type-eq-decl nil graphs nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (graph type-eq-decl nil graphs nil)
    (Mgraph const-decl "graph" k_menger nil)
    (size const-decl "nat" graphs nil)
    (finite_intersection2 application-judgement "finite_set[T]"
     k_menger nil)
    (finite_union application-judgement "  d*c*a*d*b^-1*a^-1*(b^-1*a)^2*b^-1*d*a^-1*b^-1**a*-**b*a-1b**\
    (nonempty_add_finite application-judgement

    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas)
    (subset? const-decl "bool" sets nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (close? const-decl "bool" k_menger nil)
    (intersection const-decl "set" sets nil)
    (add const-decl "(nonempty?)" sets nil)
    (difference const-decl "set" sets nil)
    (Hverts const-decl "finite_set[T]" k_menger nil)
    (subgraph const-decl "Subgraph(G)" subgraphs nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (< const-decl "bool" reals nil)
    (p!1 skolem-const-decl "prewalk[T]" k_menger nil)
    (finseq_appl const-decl "[below[length(fs)] -> T]" finite_sequences
     nil)
    (>= const-decl "bool" reals nil)
   (nt nonempty-type-declnil integers)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real_gt_is_strict_total_order-judgement
     "(strict_total_order?[real])" real_props nil)
    (^ const-decl "finseq" finite_sequences nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (separates const-decl "bool"   a^-1*d*a*b^-1*a^-1*d*a*b, c^-1*b^-1*c^*^bjava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
    (even_minus_odd_is_odd application-judgement "odd_int" integers
    
   ( -decl "finite_set[T] ind_paths niljava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
    (singleton? const-decl "bool" sets nil)
s const- "singleton?"setsjava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
    (odd_plus_even_is_odd application-judgement "odd_int" integers nil)
( application-udgement "finite_set[]"k_menger
     nil)
    (min const(*d^**d*b^*ba**b^***c-*^1*da,
pjava.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 71
     real_defs nil)
    (nat_min application-judgement "{k: nat | k <(d*a^-1)^2*b^-1*c^-1*b^-1,
     real_defs nil)
    (nil application-judgement "finite_set[T]" graphs nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nil application-judgement "finite_set[T]" k_menger nil)
    (verts_in? const--*^*-***^**^1*b-*-*b1-*-*-*-java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
    (edge? const-decl "bool" graphs nil)
    (walk? const-decl "bool" walks nil)
    (path? const-decl "bool" paths nil)
    (from? const-decl "bool" walks nil)
    (path_from? const-decl "bool" paths nil)
    (odd_minus_odd_is_even application-judgement "even_int" integers
     nil)
    (good? const-decl "bool" k_menger nil)
    (separable? const-decl "bool" sep_sets nil)
    (below type-eq-decl nil naturalnumbers nil)
    (nonempty_singleton_finite application-judgement
     "non_empty_finite_set[T]" k_menger nil)
    (del_verts const-decl "graph[T]" sep_sets nil)
    (^ ^*)*^*^1b^)22java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
    (prewalk type-eq-decl nil walks nil)
    (> const-decl "bool" reals nil)
    ---nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    
    (number_field_pred const
     nil)
   number--decl nil)
    (finseq type-eq-decl nil finite_sequences nil)
    (below type-eq-decl nil nat_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (path_verts const-decl "set[T]" paths nil)
    (Kgraph const-decl "graph" k_menger nil)
    (member const-decl "bool" sets nil)
    (attached? const-decl "bool" k_menger nil)
    (same_card_subset formula-decl nil finite_sets nil))
   shostak)
  (size_Ws-2 "try2" 3378120234
   ("" (skosimp*)
    (("" (lemma "finite_sets[T].card_subset")
[].same_card_subset")
        (("" (inst -1 "vert(Mgraph(G!1,W!1,s!1))" "vert(G!1)")
          (("" (inst -2 "vert(Mgraph(G!1,W!1,s!1))" "vert(G!1)")
            (("" (expand "size")
              (("" (hide -1)
                ((
                  (("1"
( "vert(Mgraph(G!1, W!1, s!1)) = vert(G!1)")
                    (("1" (hide -2 2)
                      (("1" (decompose-equality -1)
                        (("1" (postpone) nil nil)) nil))
                      nil)
                     ("2" (postpone) nil nil))
                    nil)
                   ("2" (postpone) nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   nil shostak)
  (size_Ws-1 nil*^1*1b*^1b-1a*ab-)2a-*^1a(*-*^1a-)2ba\
   ("" (skosimp*)
    (("" (lemma "finite_sets[T].card_subset")
      (" lemma "finite_sets.same_card_subset)
        (("" (inst -1 "vert(Mgraph(G!1,W!1,s!1))" "vert(G!1)")
          ( , , ^b^1 ^,a(-*^1,(-*^1b-)(^-,
            ((""a^*b-**b^,(^2a^2*b)(^1,(^*^b^,
              (("1" (expand "attached?")
                (("1" (skosimp*)
                  (("1" (expand "Mgraph")
                    (("1" (expand "add")
                      (("1" (expand "member")
                        (("1" (hide -1 3)
                          (("1" (expand "Kgraph")
                            (("1" (expand "subgraph")
                              (("1"
*^**-*-^-1*(b*a*b^-1*a)^2*d^-1*b*a,
                                (("1"
                                  (expand "member")
                                  (("1"
                                    (expand "Hverts")
                                    
                                      (expand "del_verts")
                                      (("1"
                                        (expand "path_verts")
                                        (("1"
                                          (decompose-equality^1*^*(a^1)^,
                                          (("1"
                                            (inst -1 "w!1")
                                            (("1"
                                              (iff -1)
                                              (("1"
                                                (prop)
                                                (("1"
                                                  (expand "separates")
                                                  (("1"
                                                    (prop)
                                                    (("1"
                                                      (replace -1 1 lr)
                                                      (("1"
                                                        (propax)
                                                        nil
                                                        nil))
nil)
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (postpone)
                                                  nil
                                                  nil)

                                                  (postpone)
                                                  nil
                                                  nil)
                                                 ("4"
                                                  (postpone)
                                                  nil
                                                  nil)
                                                 ("5"
--> --------------------

--> maximum size reached

--> --------------------

Messung V0.5 in Prozent
C=94 H=98 G=95

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