Quellcode-Bibliothek convex_functions.prf   Sprache: Lisp

(
 (java.lang.StringIndexOutOfBoundsException: Range [14, 10) out of bounds for length 18
  (composition_of_convex-1
number_field_pred [ -booleannumber_fields
    ((""nil nonempty-type-decl nil
java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 18
        (inst)
          (("(""()
            (              (""(hide-3
                                (
inst f( x -*y +)
                 "f(y) - t * f(y) + t * f(x)")
                ("composition_of_convex-1 nil 365424
                  (" (inst "f(x)" "(y)" "t)
                    ((""     (" "convex?")
                  nil)
                nil(" ( "" t)
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (java.lang.StringIndexOutOfBoundsException: Range [0, 27) out of bounds for length 18
    (convexf() -t (y  t*()
    (O const-decl "T3" function_props nil)
    (real_minus_real_is_real java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 49
    (real_le_is_total_order name-judgement "((("( n) )
     real_props nil
    (numfield nonempty-type-eq-decl nil number_fields nil)nil("1(" " java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 71
numfield> number_fields)
    (- const-decl(""(   (real_times_real_is_real realjava.lang.StringIndexOutOfBoundsException: Range [67, 65) out of bounds for length 68
d" java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
    (real nonempty-type-from-decl niljava.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for length 58
real_pred)
    (number_field(  number_fieldsjava.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
mult-by)
     nil)
                                  
tnil nil
   nil))
 (max_of_convex     real nonempty-type-from-decl
  real_predconst-decl"number_field- ] )
   (" skeepjava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
    (("" (expand "convex?")
      (("" (skeep)
        (( inst)nil)
java.lang.StringIndexOutOfBoundsException: Range [45, 22) out of bounds for length 22
((java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
              (("" (hide(("(expand ")
                ((        ("()
                  ((""
 ) =tx-   y) ft*x t* y+y  (   *y+y"
                    (("1"                                   )
                      (("1" (case "f(x) >=nil))
                        (("1" (prop)
                          (1 ""java.lang.StringIndexOutOfBoundsException: Range [48, 47) out of bounds for length 71
                             *                             java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
                           (" (1 case "x g(""
                            (("2" (assert)
                              (("2"
                                (("1" prop
                                ((2" ("" (expand((5"(assert nil)
( -3n)
                                  ((                            
                                  nil))
                               )
                              nil(  "java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
nil
( expand"
                            (("3" (assert)
                              3
                                (mult-by -2 "(1-t)")
                                (("3"
                                  (mult-by -3 "t")
""( ""java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
                                  nil)(("7( nil nil)java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
                                nil))
                              nil))
                            nil
                           ("4" (expand "max")
                            (("4" (assert)
                              (""
                                (mult-by -2                         " nil
nil
                                  )
                                  ((" nil)
                                 )
                                nil))
                              nil)
                            nil)
                           (((""
                            (("5" (assert)
                              (5
                                 -1)java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
                                6
                                  ((mult-byjava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
                                  (("5" (assertnil
                                  nil))
                                nil)                              (7
                              ( - t"java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
                            nil)
                           ("" "max")
                            (("nil)
                              (("6"
mult-by2 "1t))
                                (("6"
( 3")
                                  (("6" (assert) nil nil))
                                  ( (   
                                ))
                              nil))
                            nil)
                           ("7" (expand nil)
                            (("7" (assert)
                              ((2"(1 (2" ) )java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
                                nil
                                ((        )java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
                                  (mult-by -3  nil)
                                  (("7" (assert) nil nil))
                                  nil(number nilnumbersnil)
nil
                              nil))
                            nil)
                           ""( ")("8"(assert) niljava.lang.StringIndexOutOfBoundsException: Range [69, 66) out of bounds for length 71
                            nil)( "[ ->boolean"  java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
                          nil)
                         ""  il
                          (("2"     
                            (("2" (grindnil
                          nil)
                        nil)
                       ("2" (hide-all-but     real_ge_is_total_order name-judgement"(otal_order?real])"
                        nil))
    (maxconst-decl"{: real p> m AND p > n} niljava.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
                     ("2" (real_lt_is_strict_total_ordername-judgement
                )
                         nil)
                  ))
                     real_props nil
          )java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
    (bot formula-declnil( boolreals)
          nil    (  java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 9
        nil))
)
l
   ("strict_total_order?real)"real_props)
tion-judgement"" realsnil
java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 35
    (*"numfield,numfield->]"number_fieldsnil)
    ( nil    OR ,java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 55
    (number_field_pred const-decl "[ -> ]"number_fields
     nil)
    (number_field    (numfield nonempty-type-eq-decl il   shostak))
    (real_pred const-decl 1190
    (realeep)
    *"numfield - numfield]number_fields)
     real_props nil)
    (  nilextra_real_props
     nil)
     name-judgement
     real_minus_real_is_real    (real_minus_real_is_real 
    (real_ge_is_total_order name-judgement "(total_order?[real])"
      )
    (max const-decl "{p: real nil))
nonempty-type-eq-decl real_typesnil
    (both_sides_times_pos_ge1_imp formula-decl java.lang.StringIndexOutOfBoundsException: Range [0, 50) out of bounds for length 11
niljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    posreal  nil)
    (> const-decl "bool" reals(real_plus_real_is_real application-judgement ""  )
    (both_sides_times_pos_lt1 formula-decl nil real_props nilnil)
    (bool            nil nil numbersniljava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
    (OR    (  "number - ]" number_fields
    (=  " nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ ( "number_field >boolean"  ( realreals)
         nilrealsnil)
*"[is_real "realrealsnil
    (< (eal_le_is_total_order name-judgement( const-decl"" convex_functions niljava.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
    ))
   shostak))
 ( 0
  (sum_of_convex-1 nil 34  scal_convex-1 45143177
   ("" (skeep nonempty-type-from-decl nil nil
    (" ( " skeep)
      (((" expand "convex?")
        (("(inst - (""(skeepjava.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
          ( name-judgement"(?real)
            (""(ssert
              ((""     (+ const-decl"T - " java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
            nil))
          nil))
        ))
      nil))
    nil)
   ((   ( application-judgementreal reals)
    (real_plus_real_is_real application-judgement "real (("inst- x""y t)
    (?  "" convex_functionsnil
    (number nonempty-type-declconvex  bool   (")
    boolean( mult-by-aaa)((  il) )java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
    number_field_pred nil
nil)
    ((    nil)
    (real_pred const-decl "[number_field - application-judgement "nil
     real_propsnil)
    (  rreals nil
    (java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 9
real_propsnil)
(+[- eal real_fun_opsnil)
   shostak))
 scal_convex 00
  (scal_convex-1 nil 3465142    (bool nonempty-type-eq-declnil  )
   ("" (skeep)
" expand"convex( nonempty-type-decl nilbooleans)
      (""skeep
        (("" (inst -+ "numfield,n -]" umber_fields
      (" (expand*)
            (("" (assert)
(("factorjava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
                " mult-by 1 aaa" " (" (nil)
    real  nil realsniljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48

     nil
          nil))
nil)
      nil))
    nil
   ((real_times_real_is_real application-judgement     )
    (real_plus_real_is_real application-judgement "real reals nil) nonempty-type-from-decl number_fields nil)
    (    real_predconst-decl"number_field iljava.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
    (    bool nonempty-type-eq-declnilbooleans name-judgement
    (  booleans)
    (number_field_pred const-decl  -const-decl "numfield,numfield -numfield ( (convex? "")
     )
    (number_field nonempty-type-from-decl nil number_fields nil)
    ( const-decl "number_field >boolean ( application-judgement real reals nil)
    real  nil reals nil
    real_minus_real_is_real real=[T- "n
( "total_order[real)
     real_props nilconvex_function_right_lt-3nil 509java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
    (both_sides_times_pos_le1_imp(booleannonempty-type-decl nilbooleans   " """java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
     iljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (nnreal("" inst BAtt)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields                (1 ( " + numbers)
    (- const-decl "[numfield (number_field_pred const-decl ""()
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl( nonempty-type-from-declniljava.lang.StringIndexOutOfBoundsException: Range [46, 39) out of bounds for length 39
    =("java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
]  ))
   shostak))
(convex_function_right_lt_TCC1 
  (convex_function_right_lt_TCC1-1strict_total_orderrealreal_propsnil)
   ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool (""
    (NOT const-decl "[bool (replace "ttname"
( nonempty-type-decl numbersnil
    (number_field_pred const-decl [ -> boolean]"number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
il
    (real_minus_real_is_real application-judgement "real" reals nil)
    real_lt_is_strict_total_ordername-judgement
     "(strict_total_order?[real (convex_function_right_lt 0
    (convex?const-declnililjava.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
 niljava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
    real_times_real_is_realapplication-judgement  reals nil
    (real_plus_real_is_real application-judgement "real" reals("" labelottname -1)
   nil" cross-mult )
 (""(fieldnil nil) nil))
  ( nil3463
   ("" (skeep)
    (("" (name "tt" "(C-A)/(B-A)" ((2( "ttname" +rl
      (("1"                  (" ((2 cross-mult1)("2(assert)nil )
        (("1" (case "1-tt = (B-C)/(B-A)")
          (("1" (label "ottname" -1)
            (("1" (expand "convex?")
              (("1" (inst 3 ("ttname+java.lang.StringIndexOutOfBoundsException: Range [52, 51) out of bounds for length 53
(("1"nil)
                  (("1" (replace -1)
                    ("
                      (("1" (split)
                        (nil
                          (case-replace
                           ))nil
                          (("1"
                            ((""
                            ((()
                              (("1 nil)
(replace ttname+ l)
                                (("1"
                                  (cross-mult 1)
                                                     (        java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
                                  nil))
                                )
                              nil)
                             "" ((cross-mult1
                              (    (nznumnonempty-type-eq-declnil number_fieldsnil)
                            nil)
                           (( number_fields"(1nil )nil)
)nil))
     T  >] n(2replacettname +rl)
(2(nonempty-type-decl booleans niljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
                          (("2" (nil
                            nil))
                          nil)
                         " (replacettname rl
                          (("3" (cross-mult 1) (("3 (("3" (cross-multreal_times_real_is_realapplication-judgement "  )
                            nil))
))
                        nil))
                      nil)
                    nil)
                   ("2" (replace "ttname" + rl)
                    (("2" (field 1) nil nil)) nil))
                  )java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
                nil)nil)
              nil))
           niljava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
           ("2" (replace "ttname" + rl) (("2" (field 1) nil nil(" replace ttname" +rl ("2 (field 1) nil nil)) nil))
          nil))
        nil)
       ""(   nonzero_realnonempty-type-eq-declnileals)
      nil)
   nilnil(bool  nil booleansnil)
-nilreals niljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    - const-decl"numfield,numfield>numfield]"number_fieldsniljava.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
    (/ const-decl "[numfield, nznum ->(/= const-decl "boolean" notequal n)
    ( nonempty-type-from-decl nil number_fields nil)
(=const-decl "boolean" notequal nil
    (number_field nonempty-type-from-decl nil number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil
    (number_field_pred const-decl "[number -> boolean]" number_fields
     =const-decl [T  -boolean]"equalities ) (? ""functions java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
    =[ T- ]" equalities nil)
    booleannonempty-type-decl nil niljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
    ( nonempty-type-decl nilnumbersnil)
     (real_minus_real_is_real application-judgement "real"realsnil)
    (real_minus_real_is_real application-judgement ( application-judgementreal reals nil)
l  application-judgement"real realsn)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (convex? const-decl "bool" convex_functions nil)
    (+ const-decl    (convex  nonempty-type-eq-decl nil nil)
 "numfield numfield- numfield" number_fieldsnil
    real_le_is_total_ordername-judgement"total_order?real])java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
     real_props
real_propsnil)
     real_propsnil( name-judgement (total_order[eal]
    (real_lt_is_strict_total_order name-judgement
 real_props nil)
    (div_mult_pos_le1 formula-decl nil real_props nil)
    (div_mult_pos_le2 formula-decl nil real_props nil)
    (div_cancel3 formula-decl nil real_props nil)
    (    (div_mult_pos_le2( nil 3463054
    times_div2  nil real_props nil(""name tt"C-A)(B-A))
    (nonzero_real nonempty-type-eq-decl nil reals nil)
onst-decl"[ -bool] nil)
    (bool nonempty-type-eq-decl nil booleans nil)
( const-decl "" realsniljava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
    (both_sides_times_pos_ge1     NOT( "?java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
( nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
(  ""  niljava.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
    (=const-decl     (>= const-decl "bool()
    (AND const-decl ""[bool, bool - bool  )
                        (""
     "([real]) real_props )
    (bijective                           "(B java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
    (id const-decl "(bijective?[T, case-replace "(B -A)/ C- A =1/t")
    (TRUEconst-decl "bool booleans nil)
    (both_sides_times_neg_ge1                                replace    (both_sides_times_neg_ge1 formula-decl  eal_propsjava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
    (nonpos_real nonempty-type-eq-decl nil real_types nil)
    (negreal nonempty-type-eq-decl nil real_types nil)
    (s nil) (<=const-decl "" reals nil)
    ( formula-decl nilextra_real_propsnil)
    nzreal_div_nzreal_is_nzrealapplication-judgement "nzrealjava.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
     (both_sides_times1 formula-decl)java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
    (                         " convex_function_right_lt-2 nil 360546
    ( formula-decl nil real_props nil))
   nil)
  ( nil 36354java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
skeep)
    ("3 (( "1
( "ttname -1java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
        (("1" (case "1-tt = (B-C)/(B-A)")
          ("1" (label "ottname" -)
            (("1" (expand "convex?")
              (("1" (inst - "B" "A" "tt")
                (("1" (case "A + tt * B - tt * A = C")
                  ("1 (replace -1)
java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 34
                      (("1" (splitt)
                        (("1"
               case-replace
                           "( (convex_function_right_lt-1 nil 3465308java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
(1java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
                            (case-replace "(B - A) / (C ("1 expandconvex"
                            (("1" (field 1)
                              (1
                                (replace (("1" ()
                                ("
                                  (case-replace
                                  (1                      (" splitjava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
                             ("2" (                          ("1java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
                              (                              (1
                           ("2" (cross-mult 1) (                                (replace ttnamerl)
                         ("2" (replace "ttname" + rl)
                          (("2" (cross-mult 1) (("2" (assert) nil)))))
                         (3                             2" java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
                          (("3" (cross-mult 1 ("" (1 (2" )))
                            (("3" (assert) nil)))))))))))
ce" +rl
                    (("2" (field 1) nil)))))))))))
           ("2" (replace "ttname" +                            () ))))))
       ("(assert) )))
    nil)
   nil nil)
  (convex_function_right_lt-1 nil 3465305687
   ("" (skeep)
    (("" (name "t" "(C-A)/(B-A ("(ieldnil))))
      (" ( ((""assertnil))))
        (("1" (case "1-t = (B-C)/(B-A)")
          (("" replacetname" +rl)
            (1 java.lang.StringIndexOutOfBoundsException: Range [18, 8) out of bounds for length 8
  ("1"( -""""t)
                (("1" (case "A + t * B - t * A = C")
                  (("1" (replace -1)
                    (("1" (assert)
                      (("1" (split)
         (1
                          (case-replace "(B - C) / (C - A) = (( nil 345354
("1"
                            (case-replace "(B - A) / (C - A) = 1/t")
(1" ( 1java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
                              1
                                (replace "tname" + rl)
                                (("" splitnumbersjava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
                                  (cross-mult 1)
                                  (1 assert il))
                             (" ((" ( 1
("2 (() ))
                           ("2" (cross-mult 1) (("2" (field 1) nil)))))
                         ("2" (replace "real_lt_is_strict_total_order (replace"" )
                          (("2" (cross-mult 1) ((                                  cross-mult1
l"" )
                          (("3" (cross-mult 1)

                   ("2" (replace  application-judgement"( )))
                    (("2" (field 1) nil)))))))))))
                         (3 ((  69java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
""()        (""(assert(" )(("( ) nil nilnil))
    nil)
    )java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
  nil
  convex_function_left_lt_TCC1-1nil3465305984
   (    (real_times_real_is_real application-judgement ""  niljava.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
   ((boolean   " subtype-tcc) nil nil)
    (bool nonempty-type-eq-decl nil booleans nil)
   NOT( name-judgement
    numbernonempty-type-decl nilnumbers niljava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
ed "number "
     nil)
    (nonempty-type-from-declnumber_fields
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
application-judgement   java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (convex? const-decl "bool" convex_functions nil)
/""notequal)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   nil))
 (convex_function_left_lt 0
  ( nil 45058java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
   ("" (lemma "convex_function_right_lt")
    ("(keepjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
      java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
        (("" (assert) ((declreal_times_real_is_realapplication-judgement"eal reals java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
          nil))
        nil))
      ))
    )
   ("(java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
    real_times_real_is_real "real_propsnil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order
     "(strict_total_order?[real])" real_props nil)
boolnonempty-type-eq-decl )
    (NOT const-decl "[bool -> bool]" booleans    (times_div2 formula-declnilreal_props nil)
    (/= const-decl "boolean" notequal nil)
  number_fieldsnil
        realnonempty-type-from-decl nilreals niljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
    (= const-decl     real_props nil
    (* const-decl "[numfield, numfield"strict_total_order     il)
(   number_fields nil
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (TRUE bool"niljava.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
    (id const-decl "(bijective?[ (java.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bounds for length 69
(?  "bool" functionsfunctionsnil)
    (real_gt_is_strict_total_order name-judgement
     ([" niljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
    (>= const-decl "bool" reals nil)
   ( skolem-const-decl"" convex_functionsnil
    nonneg_real nonempty-type-eq-decl real_typesniljava.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
    (both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
     nil)
    (real_plus_real_is_realconst-decl[ -] number_fields)
(    TRUEconst-decl nil
     real_props nil)
    ( formula-decl real_propsnil
    (div_distributes_minus formula-decl           "3 (mult-by "())"" field nil) )
    (times_div2 formula-decl nil real_props nil)
    (> const-decl "bool" reals nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 49
( nonempty-type-from-decl number_fields nil
    (number_field_pred const-decl    (real_pred  "number_field -> boolean (FDX_69 " " niljava.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
nil)
    (boolean nonempty-type-decl nil booleans nil)
      ilnumbersniljava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
    ( formula-decl nilconvex_functions )
   shostak))
 
  (between_point_is_wtd_av-1(div_mult_pos_ge2  numbers)
   ("" (skeep)
(( case"
      (("1" (inst + 0) (("1" (assert) nil nil))    ( formula-decl nil real_props nil
       (2 inst    minus_odd_is_oddapplication-judgement"" integers nil
        (("1" (prop)
          ("1" (ross-mult 1)("" assertnilnil)) nil    real   nilreals java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
           (    (number_field_pred const-decl"numberjava.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
           ("3" (mult-by 1 "(y-x)") (("3" (field)     (numbernonempty-type-decl nil    real_ge_is_total_orderame-judgement "?"
          nil)
         ("2" (assert) nil nil)    >  (between_point_is_wtd_av-1 nil42721
        ))
      nil))
    nil      (" (+ 0)((1 ( nil)niljava.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
          ("1 cross-mult 1) ((java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 58
    (real_pred const-decl "[number_field -> boolean]" reals nil)
        (div_mult_pos_le1 formula-decl
    (number_field_pred const-decl "[number -> boolean]" number_fields
nil
    (= const-decl "[T, T -> boolean]" equalities    (bijective? const-decl "" functionsnil
type-decl booleans java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
    (number nonempty-type-decl nil numbers     nil( const-decl"bool >bool] niljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
(    nonempty-type-eq-declnilrealsnil)
     eal_propsniljava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
    real_times_real_is_realnil umber_fields)
    (  nil  niljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
     "(strict_total_order?[real])" real_props nil)
_order?[[])"
     real_props nil)
    (bool nonempty-type-eq-decl nil booleans nil)
AND "[ - bool]"booleans niljava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
    (>= const-decl "bool" reals nil) (> const-decl "bool" reals( name-judgement
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    div_mult_pos_le2 formula-declnilrnil
    (div_mult_pos_le1 formula-decl nilreal_props)
umfield" number_fields niljava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
    (bijective? const-decl "bool" functions nil)
    (id const-decl(= const-decl      ("(inst ""java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 31
    (TRUE const-decl "bool" booleans nil)
    (minus_odd_is_odd  "odd_int" integers nil)
    (NOT const-decl "[bool -> bool (("" (inst + "(1-t!1)"(div_mult_pos_le2 nilreal_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    +onst-declnumfield,numfield->numfield" number_fields niljava.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
    (nonzero_real nonempty-type-eq-decl nil     nil) const-decl"bijective[,T)"identityniljava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
    (both_sides_times1 formula-decl nil real_props nil)
    (  "numfield,, znum -> numfield]" number_fieldsnil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (  nil number_fieldsniljava.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    y  real"convex_functions nil)
    (x skolem-const-decl "real" convex_functions nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (    (real_div_nzreal_is_realapplication-judgement "real" reals nil)
  shostak)

  (between_point_is_wtd_av2-1 nil 3462897482
   (" (skeep)
    (""    (both_sides_times1 formula-declnil  nilnil)
      ("(inst -x "y" "    (-  [,numfield>numfield" nil)
         nonempty-type-eq-declnil  nil)
          (("(skosimp)
            (("" (inst + "(1-t!1)") (("" (assert) nil nil)) nil)) nil))
          nil))
        nil))
      )
    nil)
   ((between_point_is_wtd_av formula-decl nil convex_functions nil)
    real_minus_real_is_real"" eals)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_propsniljava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
    (- const-decl "[numfield, numfield - number nil numbersnilshostak)
    (numfield nonempty-type-eq-decl nil number_fields
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    ( nonempty-type-from-declnil nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    y-type-decl nil numbers nil))
   shostak))
 (convex_const_on_connected_min 0
  (convex_const_on_connected_min-1 nil 3462807489
   ("" (skosimp*)
(""case =y"java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28

           umfield nnumber_fields)
          (1  tname1java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
"java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
java.lang.StringIndexOutOfBoundsException: Range [30, 26) out of bounds for length 35
                (("1" (cancel-by- "java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
                  (""( -1)
                (""( "yname -)
                      (""( - y!"
                        ((" convex_const_on_connected_min 0
                          (nil)
                            (("1"
(both-sides- f1x1+tt!(1"
                               -2)
                              (("1 (("1 namettt "y1- nil))
                                (assert)
                                "( tname -)
                                   -"ttt)
                                  "
                                    (replace "tname" + rl)
               (1
                (1 case!    w1 ttt!  !)
  (1assert  ))
                                      nil))
                                     )
                                  nil))
                                )
                              nil))
                            nil)
                          nil))
                        nil)
                      nil))
                    -2
                   ("2"((""
                    ("(hide-all-but 1
                      (("2(("1
((2 assert
                          (""
                          ))
                        nilnil)
                      nil((""
                    nil))
                  nil)
                 )
                  (("2" (cross-mult 1) (("2" (assert) nil nil)) nil)       ("2" (case "w!1 < x!1")
                  nil)
                 " replacetame +rl
                  (("3" (cross-mult 1) (("3" (assert) nil nil)) nil))
                  nil))
                nil)
              nil))
            nil)
                   ("( " rl
          nil))
        nil)
       (2" "!  x1)
        (("1" (expand "convex?")
((" assert)
            ("assert
              (("1" (inst - "y!1" "w!1" "ttt" ((2" ( ( -"*1x)-
                nil)
(1 case "! * y1 -tt * w! x!"
                    (("1" (replace -1)
                      nil)
                  )
                          (1 assert
                            ""replace-6 -rljava.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
(1
                                (both-sides "-" "ttt*f!1(x!1)" -2)
                                (("1"
                                  (assert)
                                  "
                        factor2
                                    ""
                                      name"" (ttt"java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
                                      (("1"
                                        (1namettt (!-1/y1w!)java.lang.StringIndexOutOfBoundsException: Range [50, 51) out of bounds for length 50
                                        
                                            - ")
                                          (("1"
                                            (case "ttt < 1"                  (""(java.lang.StringIndexOutOfBoundsException: Range [49, 48) out of bounds for length 53
                                            (("1" (assert) nil nil)
                                                  ("
                                              (replace "tname" + rl
                                              (2
                                                (cross-mult 1)
                                                (("2"
                                                  (""
                                                  nil))
                                                                            nil)
                                                nil)                                      )
                                              
                                             1
                                        
                                        
                                      nil))
                                    nil))
                                  nil))
                                ("2"
                              ( "tname"  rl)
                            )
                          (cross-mult)
                        nil)
java.lang.StringIndexOutOfBoundsException: Range [53, 22) out of bounds for length 26
                     ("2" (replace "tname" 1 rl)
                      (("2" niljava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
                        "( 1 ) )java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
                     )
                    nil)
                   (2 ( "" +rl
                    (" cross-mult1 (2( nilnil)))java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
                    nil)
                   ("3" (replace "java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 18
                    (("3
                    )
                  )
                nilnil)
              niljava.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
             ("2" number_field_pred" (""( (2 ssert ilnil)nil))
            nil)
          nil)
l )
        nil))

    nil)
   ((>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    realnonempty-type-from-decl nil ealsjava.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 25
    ( const-decl" - ] realsjava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
    (number_field nonempty-type-from-decl nil number_fields nil)
number_field_pred[ ->booleannumber_fields
     nil)
    (boolean(nznum nonempty-type-eq-decl nilnumber_fields nil)
    ( nonempty-type-declnilnumbers niljava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
( pplication-judgementreal realsnil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
realnonempty-type-from-declnil  )
    (/    (eal_predconst-decl" - ] )
    x1skolem-const-decl "convex_functions nil)
    (div_mult_pos_le1 formula-decl nil real_props nil)
    (    (number_field_pred const-decl "number -boolean number_fields
     niljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
(x! skolem-const-decl  niljava.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
     formula-declnilrealniljava.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
    (    numfield nilnumber_fields)
    ( const-decl [numfield  >] number_fields nil)
    (real_lt_is_strict_total_order java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 36
      [, >]number_fieldsjava.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
    (real_ge_is_total_order name-judgement "(real_gt_is_strict_total_ordername-judgement
     real_propsdiv_mult_pos_le1  nil niljava.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
    (real_le_is_total_ordernzreal_div_nzreal_is_nzrealapplication-judgementnzreal
     real_props nil)
    (<= const-decl "bool" reals nil)
    (NOT const-decl "[ (niljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
(formula-declreal_props)
    (both_sides_plus_le2 formula-decl nil     *const-decl"numfield, >numfield"    bijectiveconst-decl" functionsniljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
real_gt_is_strict_total_orderion-judgement "nzint" integers nil)
     "(strict_total_order?[real])" real_props nil)
( ""reals
    (nzreal_div_nzreal_is_nzrealreal_props)
         (real_le_is_total_order  "total_orderreal"
    ( formula-declnil
     nil    <=const-decl" reals nil
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    - const-decl[numfield- ] number_fields)
    (    (real_g name-judgement
    (ijective?const-decl "bool"functions)
( (minus_real_is_realapplication-judgement real realsnil
    (TRUE application-judgementnzreal
    _s_even  even_int  nil
    ((osrealnonempty-type-eq-decl    both_sides_times_pos_le1_imp nil
    (zero_times1 formula-decl nil real_props nil)
    (    ( const-decl[numfield>]number_fields
    ( nonempty-type-eq-decl(oth_sides_times1 formula-decl  real_propsnil
    both_sides_times_neg_le1_imp nilextra_real_props
     nil)
    (div_mult_neg_le1 formula-decl nil real_props nil)
    (minus_real_is_real application-judgement "real" reals "bijective[,T]"identity
    (eg_one_times nile nil
    (div_mult_pos_gt1"integers nil)
 nilreal_types)
    (minus_odd_is_odd application-judgementtimes_div_cancel2  nil  nil
    nonzero_realnonempty-type-eq-decl nilrealsnil)( formula-declnilreal_props)
    (both_sides_times1 formula-decl nil real_props nil)
    (convex? const-declboth_sides_times_neg_le1_imp  
    ( application-judgement" )
    (eal_times_real_is_real convex_min_is_connectedjava.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
    both_sides_div_pos_le1 nil real_propsnil
    GEE skolem-const-decl ""convex_functions)
    formula-decl  extra_real_props
ty-type-eq-decl   nil)
    (y!1 skolem-const-decl("" (inst - x "y t1)
    (<     nonzero_real   nil
            (("(java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
 (convex_min_is_connected 0
  ( nil342707
   ("" (skeep)
    (" ()
      (("" (lemma "between_point_is_wtd_av")
        (("" (inst - "x" "y" "w")
          (("" (assert)
            (" ((skosimp*java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
              (("nil)
                (("" (inst - "x" "y ( application-judgement "real" reals nil)
                  )
(("(replace - -rl)
                      (("" (inst - "nil))
                        ((""
                          numbernonempty-type-decl numbersnil
                           "f(y)-t!*f(y) 1t1*fy"java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
                          ""grindnil" grind )
niljava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
                        )
          ))
                    nil))
                    (onvex_min_is_connected-1 nil 3462871047
                nil)    (- const-decl    (numfield nonempty-type-eq-decl nil number_fields nil)
                  (convex? const-decl "bool" convex_functions nil)
            nil))
          nil))
        nil))
      nil))
    nil)
   ((number nonempty-type-decl     (real_le_is_total_order name-judgement "(total_order?[real])"
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl " (real_minus_real_is_real application-judgement "real" reals nil)
     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)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (convex? const-decl "bool" convex_functions nil)
    (real_plus_real_is_real application-judgement "real" reals 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)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (between_point_is_wtd_av formula-decl nil convex_functions nil))
   shostak))
 (loc_convex_min_is_connected 0
  (loc_convex_min_is_connected-1 nil 3462873854
   ("" (skeep)
    (("" (skeep)
      (("" (lemma "between_point_is_wtd_av")
        (("" (inst - "x" "y" "w")
          (("" (assert)
            (("" (skosimp*)
java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
                nil
                  )
                    (("" (replace -3 - rl)
                      ((""nil)java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
          nil))
        nil)
      nil))
    nil)
   (     )
    (boolean nonempty-type-decl nil booleans    (number_field nonempty-type-from-decl nilnumber_fieldsnil)
    number_field_predconst-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)
       (realnonempty-type-from-declrealsnil
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (? const-decl "bool"  nil
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_propsreal_le_is_total_order "(total_order?[])"
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    between_point_is_wtd_avformula-decl nil convex_functions nil))
   shostak))
 (convex_btw_pt_left_lt 0
  (convex_btw_pt_left_lt-1 nil 3465122 nil  nil)
   (""))
    (("" (label "convexf" -1)
      ((""(label "ft_lt-1 6512224java.lang.StringIndexOutOfBoundsException: Range [42, 41) out of bounds for length 41
        (("" (label      (" ( nonempty-type-decl booleans nil)
          (" label "" -4)
            ("" java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 9
              (("" (label "fxc" 1)
                (("" (lemma "between_point_is_wtd_av2")
                  (("" (label "bpwa" -1)
                    (("" (inst - "A" "B" "x")
                      (("" (assert)
                        (("" (skosimp*)
                          (""(expand"?")
                            (("" (inst - "B" " (("" (assert)
                              ((""
                                (assert)
                                ("
                                  (copy "fac")
                                  ((""
                                    (mult-by -                                )
                                    ((""
                                      (copy "fbc")
                                      ((""
                                        (mult-by -1 "t!1")
                                        ((""
                                          (add-formulas -1 -2)
                                          nil
                                          )
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              ))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((between_point_is_wtd_av2 formula-decl  convex_functions nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans 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))
    (<    (number_fieldnonempty-type-from-declnilnumber_fields nil
(  [  > ] nil
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)  nilreals )
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (both_sides_times_pos_le1_imp formula-decl nil extra_real_props
     nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (convex? const-decl "bool" convex_functions 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)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   shostak))
 (convex_btw_pt_right_lt 0
  (convex_btw_pt_right_lt-1 nil 3465122644
   ("" (skeep)
    (("" (label "convexf" -1)
      (("" (label "Ax" -2)
        (("" (label "Bx" -3)
          (("" (label "fac" -4)
            (("" (label "fbc" -5)
              (("" (label "fxc" 1)
                (("" (lemma "between_point_is_wtd_av2")
                  (("" (label "bpwa" -1)
                    (("" (inst - "A" "B" "x")
                      (("" (assert)
                        (("" (skosimp*)
("(inst-")( assert )) nil))
                            (("" (inst - "B" "A" "t!1")
                              ((""
                                                      nil))
                                
                                  (copy "fac")
                                  ((""
                                    (mult-by -1 "1-t!1")
                                    ((""
                                      (copy "fbc")
                                      ((""
                                        )
                                        (( nonempty-type-declnilnumbersnil
                                          )
                                          
                                          )
                                        nil))
                                      nil))
                                   )
                                  nil))
                                nil))
                              ))
                            )java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
                          nil))
                        nil))
                      ))
                    nil))
                          (("" (label "Bx" -3)
                nil))
              nil))
            nil))
          nil))
        nil                    (("" (inst - "A" "B" "x")
nil)
    nil)
   ((between_point_is_wtd_av2  nilconvex_functions nil)
    (number                          ("" (expand   shostak))
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    Ax2
    (real_pred const-decl "[number_field -> boolean]" reals nil        (""(label "Bx" 3 ("
    (real nonempty-type-from-decl nil reals nil)
    (< const-decl "bool" reals           ("" (label"fac -44)
    (+ const-decl "[numfield, numfield -> ( "fac)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)label fxc" )
    (both_sides_times_pos_le1_imp formula-decl nil extra_real_props
     nil)
    (real_gt_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)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (convex? const-decl "bool" convex_functions nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   nil))
 (convex_wtd_av_lt 0
  (convex_wtd_av_lt-1 nil 3466357784
   ("" (skeep)
    (("" (skeep)
      (("" (expand "convex?")
        (("" (inst - "x" "y" "t")
          (("" (assert)
            (("" (mult-by -2 "t")
              (("" (mult-by -3 "1-t")
                (("" (add-formulas -2 -3) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans 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)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (< const-decl "bool" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (convex? const-decl "bool" convex_functions nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil))
   nil))
 (convex_increasing 0
  (convex_increasing-1 nil 3487678404
   ("" (skeep)
    (("" (lemma "convex_btw_pt_left_lt")
      (("" (inst - "x" "w" "f(w) + (f(v)-f(w))/2" "f" "v")
        (("" (assert)
          (("" (split)
            (("1" (case "x = v")
              (("1" (replace -1) (("1" (inst - "w") nil nil)) nil)
               ("2" (assert) nil nil))
              nil)
             ("2" (inst - "w") (("2" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((convex_btw_pt_left_lt formula-decl nil convex_functions nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(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)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   shostak))
 (convex_decreasing 0
  (convex_decreasing-1 nil 3487678783
   ("" (skeep)
    (("" (lemma "convex_btw_pt_left_lt")
      (("" (inst - "w" "x" "(f(v)-f(w))/2 + f(w)" "f" "v")
        (("" (assert) (("" (inst - "w") (("" (assert) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((convex_btw_pt_left_lt formula-decl nil convex_functions nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals 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)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   shostak))
 (strictly_convex_implies_convex 0
  (strictly_convex_implies_convex-1 nil 3466438530
   ("" (skeep)
    (("" (expand "strictly_convex?")
      (("" (expand "convex?")
        (("" (skeep)
          (("" (case "t = 0")
            (("1" (replace -1) (("1" (assert) nil nil)) nil)
             ("2" (case "t = 1")
              (("1" (replace -1) (("1" (assert) nil nil)) nil)
               ("2" (inst - "x" "y" "t") (("2" (assert) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (strictly_convex? const-decl "bool" convex_functions 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)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (convex? const-decl "bool" convex_functions nil))
   shostak))
 (strictly_convex_unique_min 0
  (strictly_convex_unique_min-1 nil 3462701259
   ("" (skosimp*)
java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 36
      (    (real_ge_is_total_order name-judgement "(total_order?[real])"     nil)
        (("" (assert)
          (("" (inst - "1 / 2 * x!1 (posreal nonempty-type-eq-decl (real_plus_real_is_real application-judgement "real" reals nil))
            ( (convex_decreasing 0
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (strictly_convex? const-decl "bool" convex_functions nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real]) nil))
    (real_lt_is_strict_total_order name-judgement
     real_props nil    (("" (skeep)
    (        (("" (inst - "x" "y" "t")
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
        (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil))
   shostak))
 (strictly_conv_uniq_intv_min 0
  (strictly_conv_uniq_intv_min-1 nil 3462701814
   ("" (skosimp*)
    (("" (expand            (nonneg_real nonempty-type-eq-decl nil real_types nil)
      ((""  (("1" (replace -1) (("1" (assert) nil nil)) nil)
        (("" (inst - "x!1" "y!1" "1/2")
          ((" real_props nil)
            (("" (inst - "1 / 2 * x!1 - 1 / 2 * y!1 + y!1")
                  (< const-decl "bool" reals             nil))
                nil))
    (- const-decl "[numfield, numfield
            nil))
          nil))
        nil))
      nil     "(strict_total_order?[real])" real_props nil)
    nil)
   ((real_times_real_is_real     "(strict_total_order?[real])" real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (strictly_convex? const-decl "bool" convex_functions nil)
    (real_lt_is_strict_total_order
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_minus_real_is_real application-judgement "real (("" (split)
    (    (real_pred const-decl "[number_field -> boolean]" reals nil)
        (real nonempty-type-from-decl nil reals nil)
            nil   (
     java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 8
    (nznum nonempty-type-eq-decl nil number_fields    (real_lt_is_strict_total_order name-judgement
                ((""  ))
     real_props nil)
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    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl " (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
     nil)
    booleannonempty-type-decl nilbooleansnil
    (number nonempty-type-decl nil numbers nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil))
   ))
 (? const-decl "bool" convex_functions nil
  (composition_of_strictly_convex-1 nil 34    (real_lt_is_strict_total_order
   " skeep)
    (("" (expand "strictly_convex?")
      (("" (expand "convex?")
        (("" (skeep)
          (("" (expand "o nil))
            (("" (inst -2 "x" "y" "t")
              ( const-decl [,numfield    convex_btw_pt_left_ltformula-declnil convex_functionsnil
                (
                  (inst-"f( * (real_lt_is_strict_total_order name-judgement
                   "f(y) - t * f(y) + t * f(x)")
                  (("" (assert)
                    (("" (inst - "f(x)" "f(y)" "t")
                      (("" (assert) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
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   ((real_times_real_is_real application-judgement "real" reals nil)
        (number_field nonempty-type-from-decl nil number_fields nil)
    (strictly_convex? const-decl "bool" convex_functions nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans 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 "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (O const-decl "T3" function_props nil)
    (convex? const-decl "bool" convex_functions nil))
   nil))
 (max_of_strictly_convex 0
  (max_of_strictly_convex-1 nil 3462703577
   ("" (skeep)
    (("" (expand "strictly_convex?")
      (("" (skeep)
        (("" (inst?)
          (("" (inst?)
            (("" (assert)
              (("" (hide -3)
                (("" (hide -3)
                  ((""
                    (case "f(t * x - t * y + y) >= g(t * x - t * y + y) or f(t * x - t * y + y) < g(t * x - t * y + y)")
                    (("1" (case "f(y) >= g(y) or f(y) < g(y)")
                      (("1" (case "f(x) >= g(x) or f(x) < g(x)")
                        (("1" (prop)
                          (("1" (expand "max") (("1" (assert) nil nil))
                            nil)
                           ("2" (expand "max")
                            (("2" (assert)
                              (("2"
                                (mult-by -2 "(1-t)")
                                (("2"
                                  (mult-by -3 "t")
                                  (("2" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("3" (expand "max")
                            (("3" (assert)
                              (("3"
                                (mult-by -2 "(1-t)")
                                (("3"
                                  (mult-by -3 "t")
                                  (("3" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("4" (expand "max")
                            (("4" (assert)
                              (("4"
                                (mult-by -2 "(1-t)")
                                (("4"
                                  (mult-by -3 "t")
                                  (("4" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("5" (expand "max")
                            (("5" (assert)
                              (("5"
                                (mult-by -2 "(1-t)")
                                (("5"
                                  (mult-by -3 "t")
                                  (("5" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("6" (expand "max")
                            (("6" (assert)
                              (("6"
                                (mult-by -2 "(1-t)")
                                (("6"
                                  (mult-by -3 "t")
                                  (("6" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("7" (expand "max")
                            (("7" (assert)
                              (("7"
                                (mult-by -2 "(1-t)")
                                (("7"
                                  (mult-by -3 "t")
                                  (("7" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("8" (expand "max") (("8" (assert) nil nil))
                            nil))
                          nil)
                         ("2" (mult-by -3 "t")
                          (("2" (hide-all-but 1)
                            (("2" (grind) nil nil)) nil))
                          nil))
                        nil)
                       ("2" (hide-all-but 1) (("2" (grind) nil nil))
                        nil))
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                     ("2" (hide-all-but 1) (("2" (grind) nil nil))
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        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (strictly_convex? const-decl "bool" convex_functions nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans 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)
    (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)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
     nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (bool nonempty-type-eq-decl nil booleans nil)
--> --------------------

--> maximum size reached

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

quality100%

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