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Datei: skolemization.prf   Sprache: Lisp

Original von: PVS©

(well_ordering
 (ordered_set_order_TCC1 0
  (ordered_set_order_TCC1-1 nil 3315836233 ("" (subtype-tcc) nil nil)
   ((ordered_set type-eq-decl nil well_ordering nil)
    (well_ordered? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil well_ordering 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)
    (subset? const-decl "bool" sets nil))
   nil))
 (ordered_set_order_TCC2 0
  (ordered_set_order_TCC2-1 nil 3315836233 ("" (subtype-tcc) nil nil)
   ((ordered_set type-eq-decl nil well_ordering nil)
    (well_ordered? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil well_ordering 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)
    (subset? const-decl "bool" sets nil))
   nil))
 (ordered_set_order_TCC3 0
  (ordered_set_order_TCC3-1 nil 3315836233 ("" (subtype-tcc) nil nil)
   ((ordered_set type-eq-decl nil well_ordering nil)
    (well_ordered? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (difference const-decl "set" sets nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil well_ordering 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)
    (subset? const-decl "bool" sets nil))
   nil))
 (partial_ordered_set 0
  (partial_ordered_set-1 nil 3315836233
   ("" (grind :if-match nil)
    (("1" (grind-with-ext) nil nil)
     ("2" (inst - "r!1")
      (("2" (assert)
        (("2" (inst -9 "t!1")
          (("1" (inst -9 "r!1"nil nil)
           ("2" (inst -7 "t!1")
            (("2" (inst -7 "r!1")
              (("2" (inst -9 "r!1" "t!1") (("2" (assertnil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("3" (inst-cp - "r!1")
      (("3" (inst - "t!1")
        (("3" (assert)
          (("3" (inst - "t!1" "r!1")
            (("3" (inst -8 "t!1" "r!1") (("3" (assertnil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("4" (inst-cp - "r!1")
      (("4" (inst - "t!1")
        (("4" (assert)
          (("4" (inst - "t!1" "r!1")
            (("4" (inst -8 "t!1" "r!1") (("4" (assertnil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     ("5" (inst - "x!2")
      (("5" (inst -4 "x!2") (("5" (assertnil nil)) nil)) nil))
    nil)
   ((y!1 skolem-const-decl "ordered_set" well_ordering nil)
    (z!1 skolem-const-decl "ordered_set" well_ordering nil)
    (x!1 skolem-const-decl "ordered_set" well_ordering nil)
    (t!1 skolem-const-decl "(difference(z!1`1, x!1`1))" well_ordering
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (T formal-type-decl nil well_ordering nil)
    (set type-eq-decl nil sets nil)
    (difference const-decl "set" sets nil)
    (pred type-eq-decl nil defined_types nil)
    (well_ordered? const-decl "bool" orders nil)
    (ordered_set type-eq-decl nil well_ordering nil)
    (restrict const-decl "R" restrict nil)
    (partial_order? const-decl "bool" orders nil)
    (antisymmetric? const-decl "bool" relations nil)
    (preorder? const-decl "bool" orders nil)
    (transitive? const-decl "bool" relations nil)
    (reflexive? const-decl "bool" relations nil)
    (ordered_set_order const-decl "bool" well_ordering nil)
    (upper_bound? const-decl "bool" bounded_orders nil)
    (subset? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil))
   nil))
 (ordered_set_union_TCC1 0
  (ordered_set_union_TCC1-1 nil 3315836233
   ("" (skolem-typepred)
    ((""
      (expand"well_ordered?" "strict_total_order?" "strict_order?")
      (("" (split)
        (("1" (expand "irreflexive?")
          (("1" (skosimp* t)
            (("1" (typepred "ord!1`2")
              (("1"
                (expand"well_ordered?" "strict_total_order?"
                 "strict_order?" "irreflexive?")
                (("1" (flatten) (("1" (inst - "x!1"nil nil)) nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (expand "transitive?")
          (("2" (skosimp* t)
            (("2"
              (expand"chain?" "restrict" "total_order?"
               "dichotomous?")
              (("2" (flatten)
                (("2" (inst - "ord!1" "ord!2")
                  (("2" (split)
                    (("1" (expand "ordered_set_order" -1)
                      (("1" (flatten)
                        (("1" (expand"subset?" "member")
                          (("1" (inst - "x!1")
                            (("1" (assert)
                              (("1"
                                (inst + "ord!2")
                                (("1"
                                  (typepred "ord!2`2")
                                  (("1"
                                    (expand*
                                     "well_ordered?"
                                     "strict_total_order?"
                                     "strict_order?"
                                     "transitive?")
                                    (("1"
                                      (flatten)
                                      (("1"
                                        (inst - "x!1" "y!1" "z!1")
                                        (("1"
                                          (inst - "x!1" "y!1")
                                          (("1" (ground) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (expand "ordered_set_order" -1)
                      (("2" (flatten)
                        (("2" (expand"subset?" "member")
                          (("2" (inst - "z!1")
                            (("2" (assert)
                              (("2"
                                (inst + "ord!1")
                                (("2"
                                  (typepred "ord!1`2")
                                  (("2"
                                    (expand*
                                     "well_ordered?"
                                     "strict_total_order?"
                                     "strict_order?"
                                     "transitive?")
                                    (("2"
                                      (flatten)
                                      (("2"
                                        (inst - "x!1" "y!1" "z!1")
                                        (("2"
                                          (inst - "y!1" "z!1")
                                          (("2" (ground) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("3" (expand "trichotomous?")
          (("3" (skosimp* t)
            (("3"
              (expand"chain?" "restrict" "total_order?"
               "dichotomous?")
              (("3" (flatten)
                (("3" (inst - "S!1" "S!2")
                  (("3" (split)
                    (("1" (expand "ordered_set_order" -1)
                      (("1" (flatten)
                        (("1" (expand"subset?" "member")
                          (("1" (inst - "x!1")
                            (("1" (assert)
                              (("1"
                                (typepred "S!2`2")
                                (("1"
                                  (expand*
                                   "well_ordered?"
                                   "strict_total_order?"
                                   "trichotomous?")
                                  (("1"
                                    (flatten)
                                    (("1"
                                      (inst - "x!1" "y!1")
                                      (("1"
                                        (inst + "S!2")
                                        (("1"
                                          (inst + "S!2")
                                          (("1" (ground) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (expand "ordered_set_order" -1)
                      (("2" (flatten)
                        (("2" (expand"subset?" "member")
                          (("2" (inst - "y!1")
                            (("2" (assert)
                              (("2"
                                (typepred "S!1`2")
                                (("2"
                                  (expand*
                                   "well_ordered?"
                                   "strict_total_order?"
                                   "trichotomous?")
                                  (("2"
                                    (flatten)
                                    (("2"
                                      (inst - "x!1" "y!1")
                                      (("2"
                                        (inst + "S!1")
                                        (("2"
                                          (inst + "S!1")
                                          (("2" (ground) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("4" (expand "well_founded?")
          (("4" (skosimp* t)
            (("4" (typepred "S!1`2")
              (("4" (expand"well_ordered?" "well_founded?")
                (("4" (flatten)
                  (("4" (inst - "{t: (S!1`1) | p!1(t)}")
                    (("1" (split)
                      (("1" (skolem-typepred)
                        (("1" (inst + "y!2")
                          (("1" (skosimp* t)
                            (("1"
                              (expand"chain?" "restrict"
                               "total_order?" "dichotomous?")
                              (("1"
                                (flatten)
                                (("1"
                                  (inst - "S!1" "ord!1")
                                  (("1"
                                    (split)
                                    (("1"
                                      (expand "ordered_set_order" -1)
                                      (("1"
                                        (flatten)
                                        (("1"
                                          (inst - "x!1" "y!2")
                                          (("1"
                                            (assert)
                                            (("1"
                                              (inst -10 "x!1")
                                              nil
                                              nil))
                                            nil)
                                           ("2"
                                            (inst - "x!1")
                                            (("1"
                                              (expand*
                                               "restrict"
                                               "upper_bound?")
                                              (("1"
                                                (inst - "y!2")
                                                (("1"
                                                  (typepred "ord!1`2")
                                                  (("1"
                                                    (expand*
                                                     "well_ordered?"
                                                     "strict_total_order?"
                                                     "strict_order?"
                                                     "irreflexive?"
                                                     "transitive?")
                                                    (("1"
                                                      (flatten)
                                                      (("1"
                                                        (inst - "x!1")
                                                        (("1"
                                                          (inst
                                                           -
                                                           "x!1"
                                                           "y!2"
                                                           "x!1")
                                                          (("1"
                                                            (assert)
                                                            nil
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (expand*
                                               "difference"
                                               "member")
                                              (("2" (assertnil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (expand "ordered_set_order" -1)
                                      (("2"
                                        (flatten)
                                        (("2"
                                          (expand"subset?" "member")
                                          (("2"
                                            (inst - "x!1")
                                            (("2"
                                              (assert)
                                              (("2"
                                                (inst - "x!1" "y!2")
                                                (("2"
                                                  (inst -10 "x!1")
                                                  (("2"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (inst + "y!1"nil nil))
                      nil)
                     ("2" (skolem-typepred)
                      (("2" (inst + "S!1"nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((strict_total_order? const-decl "bool" orders nil)
    (strict_order? const-decl "bool" orders nil)
    (well_founded? const-decl "bool" orders nil)
    (p!1 skolem-const-decl "pred[({t | EXISTS (S: (C!1)): S`1(t)})]"
     well_ordering nil)
    (x!1 skolem-const-decl "(p!1)" well_ordering nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (upper_bound? const-decl "bool" bounded_orders nil)
    (ord!1 skolem-const-decl "(C!1)" well_ordering nil)
    (difference const-decl "set" sets nil)
    (y!1 skolem-const-decl "({t | EXISTS (S: (C!1)): S`1(t)})"
     well_ordering nil)
    (S!1 skolem-const-decl "(C!1)" well_ordering nil)
    (C!1 skolem-const-decl "chain[ordered_set, ordered_set_order]"
     well_ordering nil)
    (trichotomous? const-decl "bool" orders nil)
    (transitive? const-decl "bool" relations nil)
    (restrict const-decl "R" restrict nil)
    (dichotomous? const-decl "bool" orders nil)
    (total_order? const-decl "bool" orders nil)
    (member const-decl "bool" sets nil)
    (subset? const-decl "bool" sets nil)
    (irreflexive? const-decl "bool" relations nil)
    (chain nonempty-type-eq-decl nil chain nil)
    (chain? const-decl "bool" chain nil)
    (ordered_set_order const-decl "bool" well_ordering nil)
    (ordered_set type-eq-decl nil well_ordering nil)
    (well_ordered? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil well_ordering nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 (chain_upper_bound 0
  (chain_upper_bound-1 nil 3315837585
   ("" (skolem-typepred)
    (("" (expand"bounded_above?" "upper_bound?")
      (("" (inst + "ordered_set_union(C!1)")
        (("" (skolem!)
          (("" (expand "ordered_set_order")
            (("" (split)
              (("1" (expand"subset?" "member" "ordered_set_union")
                (("1" (skosimp) (("1" (inst?) nil nil)) nil)) nil)
               ("2" (skolem!)
                (("2" (prop)
                  (("1" (expand "ordered_set_union")
                    (("1" (inst?) (("1" (assertnil nil)) nil)) nil)
                   ("2"
                    (expand"ordered_set_union" "chain?"
                     "total_order?" "dichotomous?" "restrict")
                    (("2" (skosimp)
                      (("2" (inst - "r!1" "ord!1")
                        (("2" (expand "ordered_set_order")
                          (("2" (prop)
                            (("1" (inst - "t!1" "r!2")
                              (("1" (assertnil nil)) nil)
                             ("2" (inst - "t!1" "r!2")
                              (("2" (assertnil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("3" (skolem-typepred)
                (("3"
                  (expand"restrict" "difference" "member"
                   "upper_bound?")
                  (("3" (skosimp :preds? t)
                    (("3"
                      (expand"ordered_set_union" "chain?"
                       "total_order?" "dichotomous?" "restrict")
                      (("3" (skosimp*)
                        (("3" (inst - "S!2" "r!1")
                          (("3"
                            (expand"ordered_set_order" "subset?"
                             "member")
                            (("3" (prop)
                              (("1"
                                (inst - "t!1")
                                (("1" (assertnil nil))
                                nil)
                               ("2"
                                (inst - "r!2")
                                (("2"
                                  (assert)
                                  (("2"
                                    (inst - "t!1")
                                    (("1"
                                      (expand*
                                       "restrict"
                                       "upper_bound?")
                                      (("1"
                                        (inst - "r!2")
                                        (("1"
                                          (inst + "S!2")
                                          (("1" (assertnil nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (expand"difference" "member")
                                      nil
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((upper_bound? const-decl "bool" bounded_orders nil)
    (bounded_above? const-decl "bool" bounded_orders nil)
    (subset? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (total_order? const-decl "bool" orders nil)
    (reflexive_restrict application-judgement "(reflexive?[S])"
     restrict_order_props nil)
    (antisymmetric_restrict application-judgement "(antisymmetric?[S])"
     restrict_order_props nil)
    (transitive_restrict application-judgement "(transitive?[S])"
     restrict_order_props nil)
    (preorder_restrict application-judgement "(preorder?[S])"
     restrict_order_props nil)
    (partial_order_restrict application-judgement "(partial_order?[S])"
     restrict_order_props nil)
    (restrict const-decl "R" restrict nil)
    (dichotomous? const-decl "bool" orders nil)
    (t!1 skolem-const-decl
     "(difference(ordered_set_union(C!1)`1, r!1`1))" well_ordering nil)
    (r!1 skolem-const-decl "(C!1)" well_ordering nil)
    (S!2 skolem-const-decl "(C!1)" well_ordering nil)
    (C!1 skolem-const-decl "chain[ordered_set, ordered_set_order]"
     well_ordering nil)
    (difference const-decl "set" sets nil)
    (ordered_set_union const-decl "ordered_set" well_ordering nil)
    (chain nonempty-type-eq-decl nil chain nil)
    (chain? const-decl "bool" chain nil)
    (ordered_set_order const-decl "bool" well_ordering nil)
    (ordered_set type-eq-decl nil well_ordering nil)
    (well_ordered? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (set type-eq-decl nil sets nil)
    (T formal-type-decl nil well_ordering nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   shostak))
 (well_ordering 0
  (well_ordering-1 nil 3315837896
   ("" (lemma "chain_upper_bound")
    (("" (forward-chain "zorn")
      (("" (expand "bounded_above?")
        (("" (skolem!)
          (("" (expand"fullset" "maximal?")
            (("" (typepred "t!1`2")
              (("" (case "full?(t!1`1)")
                (("1" (expand"full?" "member")
                  (("1"
                    (inst 2
                     "LAMBDA (t, r: T): IF t!1`1(t) AND t!1`1(r) THEN t!1`2(t, r) ELSE FALSE ENDIF")
                    (("1"
                      (expand"well_ordered?" "strict_total_order?"
                       "strict_order?")
                      (("1" (prop)
                        (("1" (expand "irreflexive?")
                          (("1" (skolem!)
                            (("1" (prop)
                              (("1" (inst -5 "x!1"nil nil)) nil))
                            nil))
                          nil)
                         ("2" (expand "transitive?")
                          (("2" (skosimp)
                            (("2" (prop)
                              (("2"
                                (inst - "x!1" "y!1" "z!1")
                                (("2" (assertnil nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("3" (expand "trichotomous?")
                          (("3" (skosimp)
                            (("3" (inst-cp - "y!1")
                              (("3"
                                (inst - "x!1")
                                (("3"
                                  (inst - "x!1" "y!1")
                                  (("3" (assertnil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("4" (expand "well_founded?")
                          (("4" (skosimp*)
                            (("4" (inst - "y!1")
                              (("4"
                                (inst - "{t: (t!1`1) | p!1(t)}")
                                (("4"
                                  (split)
                                  (("1"
                                    (skolem-typepred)
                                    (("1"
                                      (inst + "y!2")
                                      (("1"
                                        (skolem-typepred)
                                        (("1"
                                          (prop)
                                          (("1"
                                            (inst - "x!1")
                                            nil
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2" (inst + "y!1"nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (hide 3)
                  (("2" (expand"full?" "member")
                    (("2" (skolem!)
                      (("2"
                        (inst +
                         "(add(x!1, t!1`1), LAMBDA (t, r: (add(x!1, t!1`1))): IF t = x!1 THEN FALSE ELSIF r = x!1 THEN TRUE ELSE t!1`2(t, r) ENDIF)")
                        (("1" (expand "ordered_set_order")
                          (("1" (prop)
                            (("1" (use "subset_add[T]"nil nil)
                             ("2" (skolem!)
                              (("2"
                                (lift-if)
                                (("2" (ground) nil nil))
                                nil))
                              nil)
                             ("3" (expand"restrict" "upper_bound?")
                              (("3"
                                (skosimp* t)
                                (("3"
                                  (expand"add" "difference" "member")
                                  (("3" (ground) nil nil))
                                  nil))
                                nil))
                              nil)
                             ("4" (replace -1 1)
                              (("4"
                                (beta)
                                (("4"
                                  (expand"add" "member")
                                  nil
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2"
                          (expand"well_ordered?"
                           "strict_total_order?" "strict_order?")
                          (("2" (prop)
                            (("1" (expand "irreflexive?")
                              (("1"
                                (skolem-typepred)
                                (("1"
                                  (expand"add" "member")
                                  (("1"
                                    (ground)
                                    (("1" (inst - "x!2"nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (expand "transitive?")
                              (("2"
                                (skosimp :preds? t)
                                (("2"
                                  (expand"add" "member")
                                  (("2"
                                    (ground)
                                    (("2"
                                      (inst - "x!2" "y!1" "z!1")
                                      (("2" (assertnil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("3" (expand "trichotomous?")
                              (("3"
                                (skosimp :preds? t)
                                (("3"
                                  (expand"add" "member")
                                  (("3"
                                    (ground)
                                    (("3"
                                      (inst - "x!2" "y!1")
                                      (("3" (assertnil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("4" (expand "well_founded?")
                              (("4"
                                (skosimp* t)
                                (("4"
                                  (expand"add" "member")
                                  (("4"
                                    (inst - "{t: (t!1`1) | p!1(t)}")
                                    (("1"
                                      (split)
                                      (("1"
                                        (split)
                                        (("1"
                                          (skolem-typepred)
                                          (("1"
                                            (inst + "y!2")
                                            (("1"
                                              (skolem-typepred)
                                              (("1"
                                                (expand*
                                                 "add"
                                                 "member")
                                                (("1"
                                                  (ground)
                                                  (("1"
                                                    (inst - "x!2")
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (inst 2 "y!1")
                                          (("2"
                                            (skolem-typepred)
                                            (("2"
                                              (expand"add" "member")
                                              (("2"
                                                (ground)
                                                (("2"
                                                  (inst + "x!2")
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (split)
                                        (("1"
                                          (skolem-typepred)
                                          (("1"
                                            (inst + "y!2")
                                            (("1"
                                              (skolem-typepred)
                                              (("1"
                                                (expand*
                                                 "add"
                                                 "member")
                                                (("1"
                                                  (ground)
                                                  (("1"
                                                    (inst - "x!2")
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2" (inst + "y!1"nil nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (skolem-typepred)
                                      (("2"
                                        (expand"add" "member")
                                        nil
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("3" (skosimp :preds? t)
                          (("3" (expand"add" "member")
                            (("3" (ground) nil nil)) nil))
                          nil)
                         ("4" (skosimp :preds? t)
                          (("4" (expand"add" "member")
                            (("4" (ground) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((zorn formula-decl nil zorn nil)
    (T formal-type-decl nil well_ordering nil)
    (set type-eq-decl nil sets nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (pred type-eq-decl nil defined_types nil)
    (well_ordered? const-decl "bool" orders nil)
    (ordered_set type-eq-decl nil well_ordering nil)
    (ordered_set_order const-decl "bool" well_ordering nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (p!1 skolem-const-decl "pred[(add(x!1, t!1`1))]" well_ordering nil)
    (y!1 skolem-const-decl "(add(x!1, t!1`1))" well_ordering nil)
    (upper_bound? const-decl "bool" bounded_orders nil)
    (restrict const-decl "R" restrict nil)
    (difference const-decl "set" sets nil)
    (subset_add formula-decl nil sets_lemmas nil)
    (TRUE const-decl "bool" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (x!1 skolem-const-decl "T" well_ordering nil)
    (add const-decl "(nonempty?)" sets nil)
    (nonempty? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (strict_total_order? const-decl "bool" orders nil)
    (strict_order? const-decl "bool" orders nil)
    (well_founded? const-decl "bool" orders nil)
    (y!1 skolem-const-decl "T" well_ordering nil)
    (trichotomous? const-decl "bool" orders nil)
    (t!1 skolem-const-decl "ordered_set" well_ordering nil)
    (x!1 skolem-const-decl "T" well_ordering nil)
    (y!1 skolem-const-decl "T" well_ordering nil)
    (transitive? const-decl "bool" relations nil)
    (irreflexive? const-decl "bool" relations nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (FALSE const-decl "bool" booleans nil)
    (full? const-decl "bool" sets nil)
    (fullset const-decl "set" sets nil)
    (maximal? const-decl "bool" minmax_orders nil)
    (bounded_above? const-decl "bool" bounded_orders nil)
    (chain_upper_bound formula-decl nil well_ordering nil))
   shostak)))


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