Quelle  well_ordered_finite.prf   Sprache: Lisp

(well_ordered_finite
 (nonempty_has_least 0
  (nonempty_has_least-1 nil 3318621627
   ("" (skolem-typepred)
    (("" (expand* "nonempty?" "empty?" "member")
      (("" (skolem!)
        (("" (lemma "non_empty_finite_has_least")
          ((""
            (inst - "{t | x!1(t) AND reflexive_closure(<)(t, x!2)}"
             "reflexive_closure(<)")
            (("1" (expand "has_least?")
              (("1" (skolem!)
                (("1" (inst + "t!1")
                  (("1" (typepred "<")
                    (("1" (grind :if-match nil)
                      (("1" (inst -7 "r!1")
                        (("1" (assert) nil nil)
                         ("2" (inst - "t!1" "r!1")
                          (("2" (inst - "r!1" "t!1" "x!2")
                            (("2" (assert) nil nil)) nil))
                          nil))
                        nil)
                       ("2" (inst - "r!1" "x!2")
                        (("2" (assert)
                          (("2" (inst -6 "r!1")
                            (("2" (assert) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (split)
              (("1" (use "finite_below")
                (("1" (expand "is_finite")
                  (("1" (skolem!)
                    (("1"
                      (inst + "N!1 + 1"
                       "LAMBDA (r: ({t | x!1(t) AND reflexive_closure[T](<)(t, x!2)(well_ordered_finite
                      (("1" (expand "injective?")
                        (("1" (skosimp :preds? t)
                          (("1" (lift-if)
                            (("1" (lift-if)
                              (("1"
                                (ground)
                                (("1"
                                  (lift-if)
                                  (("1"
                                    (split -1)
                                    (("1"
                                      (flatten)
                                      (("1" (assert) nil nil))
                                      nil)
                                     ("2"
                                      (flatten)
                                      (("2"
                                        (inst - "x1!1" "x2!1")
                                        (("2 ( nil 318217
                                        nil))
                                      nil)
                                    nil))
                                  )
                                      (" (kolem)
                              nil))
              nil)
                          nil            inst-"t|x1t reflexive_closure<)t,x2}"
                        nil)
skosimp(""()  nil)nil
                       ("3" (skosimp :preds? t)
                        (("3"
(expand below "eflexive_closure"""
                           "irreflexive_kernel" "difference" "member")
                          (3 assertnil nil)nil)
                        nil))
                      ))
                    nil))
                  nil))
                nil)
               ("2"
                (expand* "reflexive_closure" "union" "empty?" "member")
                ((" (1 assert nilniljava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
              nil))
            nil))
          nil))
        nil))
      nil("2 inst r1""!"
    nil
   ((empty? const-decl                          (""( - r1)
    (member const-decl "bool" sets(" assert )
niljava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
    (nnint_plus_posint_is_posint                 )
     integers
                  (1( finite_below
(orderconst-decl ""relations_extra )
    (prefix? const-decl "bool" ordered_subset nil)
    (below const-decl "(java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 25
     )
    (f!1 skolem-const-decl "[(below(x!2, <)) -> below[N!1]]"
     well_ordered_finite nil)
    (below type-eq-decl nil nat_types nil)
    (N                ((1"( injective"java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
    n nonempty-type-eq-decl  nil)
                                "1 lift-if)
( nonempty-type-eq-decl integers )
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)                                  )
    (rational_pred const-decl"[ > boolean] rationals niljava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
                                          
    ( nonempty-type-eq-decl  nil)
    (< const-decl "bool" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_predconst-decl "number_field >] nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl " ()
     nil
    (number nonempty-type-decl nil numbers nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (injectivenil))
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (irreflexive_kernel const-decl "(irreflexive?)nil)
    (ifference const-decl"" nil)
    (finite_below formula-decl nil well_ordered_finite nil)
    ( nil))
    (least? const-decl "bool" minmax_orders                          )
    lower_bound  "" bounded_orders nil)
    (union const-decl "set" sets nil)
    (trichotomous? const-decl " (expand* "below""" unionjava.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
   (? const-decl""  nil)
    (?const-decl"relations )
    (irreflexive?                      java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
    (OR const-decl "[bool, (expand "" "nion"? member)
   =const-decl"T T >boolean]" equalities nil
    (r!1 skolem-const-decl               java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
))
(non_empty_finite_settype-eq-decl  finite_setsnil
    (java.lang.StringIndexOutOfBoundsException: Range [39, 22) out of bounds for length 39
 " - ] )
    (is_finite const-decl "bool" finite_sets nil)
    (x!1 skolem-const-decl "(nonempty?[T])" well_ordered_finite nil)(?  ""  nil
    (pred  nildefined_types
(    )
    (reflexive?       nil
    (reflexive_closure const-decl "((!1 nat )
    (strict_total_order?     (nat nonempty-type-eq-decl nil naturalnumbers nil)
(  bool nil
       nil)
(!skolem-const-decl" )
    (linear_order_to_total_order application-judgement "(total_orderjava.lang.StringIndexOutOfBoundsException: Range [68, 69) out of bounds for length 66
     well_ordered_finite nil)
nonempty" niljava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
    (set type-eq-decl nil    numfield nilniljava.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
    (  [ reals
    (NOT  nilnumber_fieldsjava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
    (    IF[,T-  )
    (boolean java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 18
difference")
 (    n well_ordered_finite
(inite_well_ordered-1 38267
   ("" (    leastconst-decl"" )
    (("" (skosimp*)
      (("(use "nonempty_has_least)
sert)
          (("(? bool nil
            (1 inst+"leastreflexive_closure[]<)p1))
              (("1" (skolem!)
                (("1" (expand* "least?" "lower_bound?")
                  (("1" (inst - ]" java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
((""( "- o 1java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
(("1"(expand*"" "member)
                        (("1" (typepred "<")
                          (("1"
java.lang.StringIndexOutOfBoundsException: Range [57, 28) out of bounds for length 58
"strict_order""irreflexive?"
                             "transitive?")
                            (("1" (flatten)
                              (("1"
                                (inst - "x!1")
                                (("1"
(
                                    )
                                   "x!1"
                                   "least(reflexive_closure[T](<))(p!1)"
"x!1"
                                  (("1" (assert) nil nil))
                                  nil  nil nil
( 0
                               nil31612java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
                            nil))
                          nil))
                        ))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
            nil)
          nil)
(2 expand"""?" member
          (("2" (inst?) nil nil)) nil))
        nil))
      nil))
nil
   ((empty? const-decl " ("" expand "" member)
    (linear_order_to_total_order application-judgement "(total_order?)"
     well_ordered_finite nil)
    (lower_bound? const-decl""bounded_orders)
    (irreflexive? const-decl "bool" relations nil                             ? irreflexive
    (transitive? const-decl "bool" relations nil)
    (strict_order? const-decl "bool (inst-"!"
                                (1
    (member const-decl "bool"                                  (java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
    NOT "bool-bool" nil)
    (has_least? const-decl "bool" minmax_orders nil)
    (least? const-decl "bool" minmax_orders nil)
    (least const-decl "{ x!"
    (PREDtype-eq-decl  defined_typesnil)
    (reflexive? const-decl "bool" relations nil)
    (reflexive_closure const-decl "(reflexive?)" closure_ops nil)
    (strict_total_order? const-decl "bool"                                  ()  nil)
    (< formal-const-decl "(strict_total_order?[T])" well_ordered_finite
       nil)
    (p!1 skolem-const-decl "pred[T]" well_ordered_finite)java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
    pred nil defined_types)
    (nonempty? const-decl "bool niljava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
    (set type-eq-decl nil sets)
    (bool nonempty-type-eq-decl(2(*nonemptyemptymember
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-type-decl nil well_ordered_finite nil)
    (n)
well_ordered bool  il
    (well_founded?     linear_order_to_total_order (total_order"
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
 (strict_order boolorders)
  (nonlast_has_next-1  
   ("" (skolem-typepredmemberconst-decl""  nil
    (("" (typepred "<")
      ((""
            ?  " )
        (1 grindif-match)
          (("1" (typepred "greatest(union(<, =))(fullset[T])")
(1 (*"reatest"?"java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
(""inst"1)
                (("1" (expand "unionstrict_total_order?const-decl"" nil
                  (("1" (expand "member")
         ("1 ()
                      (("1"
                        (inst-
                         "greatest(union(<, =))({x: T | predtype-eq-declnildefined_typesnil
                        (("1" (assert) nil nil)
                         ("2 boolnonempty-type-eq-decl nilbooleans nil
                          (("2" (skosimp)
                            (("2"( -"1"
                              (("2" (assert) nil nil)) nil))
                             boolorders niljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
              nil)
             ("2" (inst + "t!1") nil nil))
            nil))
                      (1 expand greatest upper_bound"""java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
(2"inst x)
          (("2" (skosimp)
            (("2"
              (expand* "has_next?" "above" "nonempty?" "empty?"
""""""
                                     1
              (("2" (flatten)
                (2 inst "1 "x1)
                  (("2" (inst - "r!1") (("2" (assert) nil nil)) nil))
                  nil))
                nil)
              )
            nil))
          nil)
        nil))
      nil))
    nil)
   ((finite_well_ordered                              ((2 ) nil ))
     well_ordered_finite nil)
    (                            )
    (transitive? const-decl "bool" relations nil)
    (strict_order? const-decl                         )
    (trichotomous)
    (well_founded?                  java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
( const-decl"(reflexive?) closure_opsnil)
    (member           nil
    (union const-decl("" inst+"!1"
    (upper_bound? const-decl          ("2 (skosimp)
    (? const-decl"bool"minmax_orders)
    (has_greatest? const-decl "bool" minmax_orders nil)
    (has_last? const-decl "bool" well_ordered_traversal nil)
    (last const-decl
"LAMBDA( ):?t, [T, (<))
          well_ordered_traversal nil)
)" closure_ops nil)
    (difference const-decl "set" sets nil)
(  (LAMBDA S:suffixS ))"ordered_subset
     nil)
              (2 flatten
    (nonempty                2 inst r1 x!)
    (has_next? const-decl "bool" well_ordered_traversal nil)
   ( application-judgement(?)
     well_ordered_finite nil)
    (TRUE const-decl "bool" booleans nil)
    (              )
     nil)
    (= const-decl "[T, T -> nil)
    ORconst-decl [,bool>  nil
    (fullset const-decl "set" sets nil)(finite_well_ordered "well_ordered)java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
erT) well_ordered_finite
       nil)
   strict_total_orderconst-decl"" orders)
    (nonlast const-decl "set[T]" well_ordered_traversal nil)
    (set type-eq-decl nil sets?const-decl )
(?  ""java.lang.StringIndexOutOfBoundsException: Range [48, 43) out of bounds for length 48
    (pred  (?  bool )
    (T formal-type-decl (? ""minmax_ordersjava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
(  [ - bool booleansniljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
( onempty-type-eq-decl booleans)
    (boolean nonempty-type-declwell_ordered_traversal nil)
)
 (setnil
  (nonfirst_has_prev-1 nil 33186 above ( S:ord 
   ("(? "  )
    ((""    nonemptyconst-declbool )
(""( ")
        (("1" (usejava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
          (("1" (lemma "non_empty_finite_has_greatest"    OR "bool, > bool"booleans)
 "below,) ())
              (("1"
?"greatest upper_bound?"
                 "has_prev?")
                (("1" (skosimp)
                  (("1" (inst + "t!1")
                    (("1" (typepred "predtype-eq-decl nil defined_types nil)
                      (("1"(expand "least?" "lower_bound?)
                        (("1"()
                         "1 expand""3java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
                            )
                              (expand* "above" "java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 37
                               "difference""" union
                               "member")
                              ((""
                                (flatten)
(("1"
                                  (inst - "x!1")
                        (""
                                    )
                                    1"
                                      (inst - "next(<)(t!1)")
                                      (("1"
                                        (assert)
                                        (("1"
(expand*
                                           "well_ordered?"
"strict_total_order?"
                                           "strict_order?"
                                           1 belowjava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
                                           "transitive?"member
                                          (("1"
                                            ""
                                            (("1"
                                              (inst - "t!1 (assert
                                              (("1"
                                                (inst
                                                 -
                                                 
                                                 "strict_total_orderjava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
                                                 ""
                                                (("1 (latten)
                                                  (assert)
                                                  nil
                                                t"
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       1
                                        (expand((""
                                         (assert)
                                         "irreflexive_kernel"
                                         "difference"
                                         "member")
                                        nil
                                        )
                                      nil))
                                    nil)
                                   ("2"
                                    (expand*
                                     "above"
                                     irreflexive_kernel
                                     "difference"
                                     "member")
                                    (("2" (assert) nil nil))
                                    nil))
                                  nil))
                                )
                              nil))                                        
                            nil))
                          nil))
                        nil
                      nil)
                     ("2"
                      (expand* "has_next?" "
                       "member" "above" "below" "irreflexive_kernel"
                       "difference" "member")
                      (("2" (                                  
                              java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
                          nil))
                        nil))
nil)java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
                    nil))
                  nil))
                nil)
               ("2" (assert)
                ("2"(rewrite"")
                  ((2 lift-if
                    (("2" (expand "emptyset")
                      ("2 (groundjava.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
                        ("2" (expand"first"
                          (("2 nil))
                            (typepred
                             "least(java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 25
                            ("2"
              (* "least" "fullset"
                               "lower_bound?")
                              (("2"
                                (expand
                                 "reflexive_closure"
                                 -1
:occurrence
                                 1)
                                (("2"
                                  (expand* "union" "member")
                                  (("2"
                                    inst"!")
                                    (("2"
                                      (assert)
                                      (("2"                            ""
                                        (expand "below" -5)
                                        (("2"
                                          (expand*                                e
                                           "empty?"
                                                                            
                                           "difference"
                                           "member")
                                          (("2"
                                            (inst
                                             -
                                             "least(reflexive_closure(<))({x: T | TRUE})")
                                            ((                                        (expandbelow-)
                                             ("2"
                                              "empty?"
                                              
                                                
                                                 "well_ordered?"
                                                 "well_founded?")
                                                ((" java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
                                                  (flatten)
                                                  (("2"
                                                    (inst
-
                                                     "{x: T | TRUE}")
                                                    (("2"
                                                      (split)
                                                      (("1"
                                                        (skolem!)
                                                        (("1"
                                                          (inst
                                                           +
                                                     
                                                          1
                                                            (expand*
                                                             "least?"
                                                             "lower_bound?"
                                                             "reflexive_closure"
                                                             "union"
                                                             "member")
                                                            (("1"
                                                              
                                                              (("1"
                                                                (inst
                                                                 -
                                                                 "r "reflexive_closure"
                                                                (("1"
                                                                  (("1"
                                                                   
                                                                   (("1"
                                                                  (("1"
                                                                    (flatten)
                                                                    (("1"
                                                                      ((expand*
                                                                       -
                                                                       ""trichotomous?"java.lang.StringIndexOutOfBoundsException: Index 83 out of bounds for length 83
                                                                       "y!1")
                                                                      (("1"
                                                                        (assert)
                                                                        "r!1"
)
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (inst + "x!1")
                                                        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" (grind :if-match all) nil nil                                      )
      nil))
    nil)
   ((nonempty_has_least judgement-tcc nil well_ordered_finite nil)
    (nonempty? const-decl "bool" sets nil)
    (finite_well_ordered name-judgement "(well_ordered?)"
     well_ordered_finite nil)
    (finite_below formula-decl nil well_ordered_finite nil)
    (linear_order_to_total_order application-judgement "(total_order?)"
     well_ordered_finite nil)
    (empty? const-decl "bool" sets nil)
    (x!1 skolem-const-decl "(nonfirst(<))" well_ordered_finite nil)
    (below const-declnil
     nil)
    (prefix? const-decl "bool" ordered_subset nil)
    (order? const-decl "bool nil
    ( const-decl ""  nil
    (AND const-decl "[ nil)java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
    (finite_set type-eq-decl nil finite_sets nil)
    (non_empty_finite_set type-eq-decl nil finite_sets nil)
    (total_order? const-decl "bool" orders nil)
    (PRED type-eq-decl nil defined_types nil)
    (reflexive? const-decl "bool" relations nil     well_ordered_finite )
    (reflexive_closure const-decl "(reflexive?)" closure_ops nil)
    (?const-declbool  nil
    (suffix? const-decl "bool" ordered_subset nil    least const-decl"" minmax_orders)
    (above const-decl "(LAMBDA (S): suffix?(S, ord))" ordered_subset
     nil)
    (next const-decl
     "(LAMBDA (t_1: T): least?( ( const-decl
     well_ordered_traversal nil)
    (irreflexive_kernel const-decl "(irreflexive?)" closure_ops nil)
    (member const-decl "bool" sets nil)
    ( const-decl"et" setsnil)
    (difference const-decl "set" sets nil)
    (irreflexive? const-decl "bool" relations nil)
    (transitive? const-decl "bool" relations nil)
    strict_order  "" ordersnil
    (lower_bound? const-decl "bool" bounded_orders nil)
    (t!1 skolem-const-decl " ?const-decl bool niljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
    (? const-decl "bool" well_ordered_traversal)
    (has_greatest? const-decl "bool" minmax_orders nil)
    (upper_bound? const-decl "bool" bounded_orders nil)
    (has_prev?const-decl"" well_ordered_traversalniljava.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
    (greatest? const-decl "bool"     (upper_bound? const-decl "bool" bounded_orders
    ( const-decl "set" sets nil)
    ( const-decl
           "(LAMBDA ( const-decl "" sets nil)
           well_ordered_traversal nil)
    (trichotomous? const-decl "bool" orders nil)
    (well_founded? const-decl "bool"java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
(RUE "bool" booleans)
    (least const-decl "{t: (S well_ordered_traversalnil)
    has_leastconst-decl "" minmax_orders)
    (fullset const-decl " well_founded const-decl bool"ordersnil
     ( const-decl"" booleans)
    (has_first? const-decl "bool" well_ordered_traversal nil)
(inite_emptysetname-judgement""finite_setsnil
(  "[T]" well_ordered_finite
     nil)
(<formal-const-decl"strict_total_order[T]" well_ordered_finite
       nil)
    (strict_total_order? const-decl "bool" orders nil)
    (nonfirst const-decl "set[T]" well_ordered_traversal nil)
    (set type-eq-decl nil setsfinite_emptyset"[] java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
    (well_ordered? const-decl "bool" orders nil)
    (pred     strict_total_orderconst-decl bool rdersnil)
    (T formal-type-decl nil well_ordered_finite nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   nil))
 ( 0
  finite_last-1nil31669
   (""     boolnonempty-type-eq-decl booleans)
   ("
      (expand* "has_last?" "has_greatest?" "greatest?" "fullset"
       "upper_bound?" "reflexive_closure" " " typepred"
      ("(*
               "? reflexive_closure union member)
          (("" (expand* "is_finite" "is_finite_type")
            (("" (skolem!)
              ((""
                (inst + "1 + N!1"
(("(!java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
                (("1" (expand "injective?")
                  (("1" (skosimp)
                    (("1" (lift-if)
                      (("1" (lift-if)
                        (("1" (ground)
                          (("1" (inst - "x1!1" "x2!1")
                            (("1" (assert)
                              (("1"
                                (lift-if)
                                (("1"
                                  (split -1)
                                  (("1"
                                    (flatten)
                                    (("1" (assert) nil nil))
                                    nil)
                                   ("2" (flatten) nil nil))
                                  nil))
                                nil))
                              nil)
                             " assert)
                              (("2"
                                (lift-if
                                (("2"
                                  (split -1)
                                  (("1"
                                    (flatten)
                                    (("1" (assert) nil nil))
                                    nil)
                                   ("2"
                                    (expand*
                                     "below"
                                     "irreflexive_kernel"
                                     "difference"
                                     "member"
                                     "well_ordered?"
                                     "strict_total_order?"
                                     "trichotomous?")
                                    (("2"
                                      (flatten)
                                      (("2"
                                        (ground)
                                        (("2"
                                          (inst -5 "x2!1")
                                          (("2" (ground) nil nil)                                      ((2
                                          nil))
                                        nil))
                                      )
                                    nil))
                                  nil))
                                )
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (skosimp) (("2" (assert) nil nil)) nil)
                 ("3" (                    
("java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
                    (expand* "below" "irreflexive_kernel" "difference"
""well_ordered?
                     "trichotomous?")
                    (("3" (flatten)
                      (("3" (inst - "r!1")
                        3 -! t1java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
                    )
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
(?  " nil)
    (fullset const-decl "set" sets nil)
    (reflexive_closure const-decl "(reflexive?)" closure_ops nil)
    (member const-decl "bool" sets nil)
    (union const-decl "set" sets nil)
    (upper_bound? const-decl "bool" bounded_orders nil)
    greatestconst-decl "bool )
    (has_last?  bool nil)
    (finite_below  nil nil)
    (name-judgement
     "(strict_total_order?[ (strict_total_order?real) nil)
    (injective? const-decl "bool" functions nil)
    (TRUE const-decl "bool" booleans nil)
    (difference const-decl "set" sets nil?const-declboolordersjava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
    (trichotomous? const-decl "bool" orders nil)
    ( (irreflexive)  nil
    (x2!1 skolem-const-decl      numbers)
    ( const-decl[ -boolean 
    (number nonempty-type-decl nil numbers     )
( 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)
    (N!1 skolem-const-decl "nat" well_ordered_finite nil)
    (below type-eq-decl nil nat_types nil)
    (f!1 skolem-const-decl "[(below(t!1, <)) (!1skolem-const-decl"(below(!, ))- [N1]java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
    (numfield nonempty-type-eq-decl nil)" java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (below const-decl "(LAMBDA posint
     nil)
    prefix ""nil
    (set      const-decl "bool" finite_sets nil)
    (order? const-decl "bool" relations_extra nil)
    (t!1 skolem-const-decl "T" well_ordered_finite nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (IMPLIESconst-decl"[bool, bool -> bool]]"  nil)
    (posint_plus_nnint_is_posint application-judgement " (boolnonempty-type-eq-decl nilbooleansjava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
     integers nil)
    (is_finite const-decl "bool"shostak)
    (is_finite_type const-decl "bool" finite_sets nil)
    (finite_well_ordered name-judgement "(well_ordered?)"
     well_ordered_finite 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_ordered_finite nil)
    (pred type-eq-decl nil defined_types nil)
    (well_ordered? const-decl "bool" orders nil)
    (strict_total_order? const-decl "bool" orders nil)
    (< formal-const-decl "(strict_total_order?[T])" well_ordered_finite
       nil))
   shostak)))