Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/Tarski/   (Beweissystem der NASA Version 6.0.9©)  Datei vom 7.10.2014 mit Größe 745 kB image not shown  

Impressum poly_system_strategy.prf

  Interaktion und
PortierbarkeitLisp
 

(poly_system_strategy
 (first_eq_TCC1 0
  (first_eq_TCC1-1 nil 3621331936 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil))
   nil))
 (first_eq_TCC2 0
  (first_eq_TCC2-1 nil 3621331936 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil))
 (first_eq_TCC3 0
  (first_eq_TCC3-1 nil 3621331936 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (< const-decl "bool" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (subrange type-eq-decl nil integers nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (> const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil))
   nil))
 (first_eq_TCC4 0
  (first_eq_TCC4-1 nil 3621331936 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (< const-decl "bool" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (subrange type-eq-decl nil integers nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (> const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil))
   nil))
 (first_eq_TCC5 0
  (first_eq_TCC5-1 nil 3621331936 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (< const-decl "bool" reals nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (subrange type-eq-decl nil integers nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (> const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil))
   nil))
 (first_eq_TCC6 0
  (first_eq_TCC6-1 nil 3621331936 ("" (termination-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (first_eq_TCC7 0
  (first_eq_TCC7-1 nil 3621341858 ("" (termination-tcc) nil nilnil
   nil))
 (greatify_poly_TCC1 0
  (greatify_poly_TCC1-1 nil 3622457802 ("" (subtype-tcc) nil nil)
   ((minus_odd_is_odd application-judgement "odd_int" integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/"))
   nil))
 (greatify_rel_TCC1 0
  (greatify_rel_TCC1-1 nil 3621333990 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil))
   nil))
 (greatify_def_TCC1 0
  (greatify_def_TCC1-1 nil 3621333990
   ("" (skeep)
    (("" (skeep)
      (("" (expand "greatify_poly_rel")
        (("" (expand "greatify_poly")
          (("" (expand "*")
            (("" (inst - "j")
              (("" (lift-if) (("" (ground) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((greatify_poly const-decl "[nat -> int]" poly_system_strategy 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)
    (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)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (greatify_poly_rel const-decl "[nat -> int]" poly_system_strategy
     nil))
   nil))
 (greatify_def 0
  (greatify_def-1 nil 3621333996
   ("" (skeep)
    (("" (expand "solvable?")
      (("" (expand "solvable_at?")
        (("" (expand "rel5")
          (("" (ground)
            (("1" (skeep)
              (("1" (inst + "x")
                (("1" (skeep)
                  (("1" (inst - "i")
                    (("1" (assert)
                      (("1" (typepred "greatify_rel(RelF6)(i)")
                        (("1" (assert)
                          (("1" (split -)
                            (("1" (flatten)
                              (("1"
                                (expand "greatify_rel" 3 1)
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "greatify_poly_rel" +)
                                    (("1"
                                      (expand "greatify_poly")
                                      (("1" (propax) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (flatten)
                              (("2"
                                (split -)
                                (("1"
                                  (flatten)
                                  (("1"
                                    (assert)
                                    (("1"
                                      (expand "greatify_rel" 4)
                                      (("1"
                                        (expand "greatify_poly_rel" +)
                                        (("1"
                                          (expand "greatify_poly")
                                          (("1" (propax) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (flatten)
                                  (("2"
                                    (split -)
                                    (("1"
                                      (flatten)
                                      (("1"
                                        (expand "greatify_rel" 5)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (expand
                                             "greatify_poly_rel"
                                             +)
                                            (("1"
                                              (expand "greatify_poly")
                                              (("1"
                                                (rewrite
                                                 "scal_polynomial2")
                                                (("1"
                                                  (assert)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (flatten)
                                      (("2"
                                        (split -)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (flatten)
                                            (("1"
                                              (expand "greatify_rel" 7)
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (expand
                                                   "greatify_poly_rel"
                                                   +)
                                                  (("1"
                                                    (expand
                                                     "greatify_poly")
                                                    (("1"
                                                      (propax)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (flatten)
                                          (("2"
                                            (split -)
                                            (("1"
                                              (flatten)
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (expand
                                                   "greatify_rel"
                                                   7)
                                                  (("1"
                                                    (assert)
                                                    (("1"
                                                      (expand
                                                       "greatify_poly_rel"
                                                       +)
                                                      (("1"
                                                        (expand
                                                         "greatify_poly")
                                                        (("1"
                                                          (propax)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (flatten)
                                              (("2"
                                                (expand
                                                 "greatify_rel"
                                                 8)
                                                (("2"
                                                  (assert)
                                                  (("2"
                                                    (expand
                                                     "greatify_poly_rel"
                                                     +)
                                                    (("2"
                                                      (expand
                                                       "greatify_poly")
                                                      (("2"
                                                        (rewrite
                                                         "scal_polynomial2")
                                                        (("2"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (skeep)
              (("2" (inst + "x")
                (("2" (skeep)
                  (("2" (inst - "i")
                    (("2" (split 1)
                      (("1" (flatten)
                        (("1" (expand "greatify_rel" -)
                          (("1" (assert)
                            (("1" (expand "greatify_poly_rel")
                              (("1"
                                (expand "greatify_poly")
                                (("1" (propax) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (flatten)
                        (("2" (expand "greatify_rel" -)
                          (("2" (assert)
                            (("2" (split +)
                              (("1"
                                (flatten)
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "greatify_poly_rel")
                                    (("1"
                                      (expand "greatify_poly")
                                      (("1" (propax) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (flatten)
                                (("2"
                                  (split +)
                                  (("1"
                                    (flatten)
                                    (("1"
                                      (assert)
                                      (("1"
                                        (expand "greatify_poly_rel")
                                        (("1"
                                          (expand "greatify_poly")
                                          (("1"
                                            (rewrite
                                             "scal_polynomial2")
                                            (("1" (assertnil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (flatten)
                                    (("2"
                                      (split +)
                                      (("1"
                                        (flatten)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (expand
                                             "greatify_poly_rel")
                                            (("1"
                                              (expand "greatify_poly")
                                              (("1" (propax) nil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (flatten)
                                        (("2"
                                          (assert)
                                          (("2"
                                            (split +)
                                            (("1"
                                              (flatten)
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (expand
                                                   "greatify_poly_rel")
                                                  (("1"
                                                    (expand
                                                     "greatify_poly")
                                                    (("1"
                                                      (propax)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (flatten)
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (expand
                                                   "greatify_poly_rel")
                                                  (("2"
                                                    (expand
                                                     "greatify_poly")
                                                    (("2"
                                                      (rewrite
                                                       "scal_polynomial2")
                                                      (("2"
                                                        (assert)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((solvable? const-decl "bool" poly_system_strategy nil)
    (rel5 const-decl "bool" poly_system_strategy nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_ge_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)
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (scal_polynomial2 formula-decl nil polynomials "reals/")
    (sequence type-eq-decl nil sequences nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (greatify_poly const-decl "[nat -> int]" poly_system_strategy nil)
    (greatify_poly_rel const-decl "[nat -> int]" poly_system_strategy
     nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (/= const-decl "boolean" notequal nil)
    (greatify_rel const-decl
     "{pz: subrange(0, 5) | pz /= 2 AND pz /= 5}" poly_system_strategy
     nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real 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)
    (solvable_at? const-decl "bool" poly_system_strategy nil))
   shostak))
 (compute_solvable_single_TCC1 0
  (compute_solvable_single_TCC1-1 nil 3621353314
   ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (<= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (/= const-decl "boolean" notequal nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (compute_solvable_single_TCC2 0
  (compute_solvable_single_TCC2-1 nil 3621353314
   ("" (subtype-tcc) nil nil)
   ((/= const-decl "boolean" notequal nil)
    (array2list const-decl
                "{l: listn(n) | FORALL (i: below(n)): a(i) = nth(l, i)}"
                array2list "structures/")
    (base_list const-decl "listn[below(n)](digits)" base_repr "reals/")
    (sturm_tarski_faster const-decl "{r: real |
         r = NSol_all(k, a, m, p, n, RelF6) AND
          rational_pred(r) AND integer_pred(r)}" system_solvers nil)
    (odd? const-decl "bool" integers nil)
    (poly_deriv const-decl "real" polynomials "reals/")
    (int_plus_int_is_int application-judgement "int" integers nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil))
   nil))
 (compute_solvable_single_TCC3 0
  (compute_solvable_single_TCC3-1 nil 3621353314
   ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (<= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (subrange type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (rel5 const-decl "bool" poly_system_strategy nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (/= const-decl "boolean" notequal nil)
    (array2list const-decl
                "{l: listn(n) | FORALL (i: below(n)): a(i) = nth(l, i)}"
                array2list "structures/")
    (base_list const-decl "listn[below(n)](digits)" base_repr "reals/")
    (sturm_tarski_faster const-decl "{r: real |
         r = NSol_all(k, a, m, p, n, RelF6) AND
          rational_pred(r) AND integer_pred(r)}" system_solvers nil)
    (odd? const-decl "bool" integers nil)
    (poly_deriv const-decl "real" polynomials "reals/")
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil))
   nil))
 (compute_solvable_single_TCC4 0
  (compute_solvable_single_TCC4-1 nil 3621354679
   ("" (skosimp*)
    (("" (lift-if)
      (("" (split -)
        (("1" (flatten)
          (("1" (replaces -2) (("1" (assertnil nil)) nil)) nil)
         ("2" (flatten)
          (("2" (replaces -1)
            (("2" (expand "*") (("2" (propax) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((minus_odd_is_odd application-judgement "odd_int" integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (compute_solvable_single_TCC5 0
  (compute_solvable_single_TCC5-1 nil 3621354679
   ("" (skosimp*)
    (("" (lift-if)
      (("" (split -)
        (("1" (flatten)
          (("1" (replaces -2) (("1" (assertnil nil)) nil)) nil)
         ("2" (flatten)
          (("2" (replaces -1)
            (("2" (expand "*") (("2" (assertnil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((minus_odd_is_odd application-judgement "odd_int" integers nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (compute_solvable_single_def 0
  (compute_solvable_single_def-1 nil 3621354856
   ("" (skeep)
    (("" (skeep)
      (("" (expand "compute_solvable_single")
        (("" (lift-if)
          (("" (split +)
            (("1" (flatten)
              (("1" (replace -1)
                (("1" (assert) (("1" (grind) nil nil)) nil)) nil))
              nil)
             ("2" (flatten)
              (("2" (assert)
                (("2" (split +)
                  (("1" (flatten)
                    (("1" (assert)
                      (("1" (replace -1)
                        (("1" (name "x1" "-a(0)/a(1)-1")
                          (("1" (name "x2" "-a(0)/a(1)+1")
                            (("1"
                              (case "(polynomial(a,1)(x1)>0 AND polynomial(a,1)(x2)<0) OR (polynomial(a,1)(x1)<0 AND polynomial(a,1)(x2)>0)")
                              (("1"
                                (inst-cp + "x1")
                                (("1"
                                  (inst-cp + "x2")
                                  (("1"
                                    (inst + "-a(0)/a(1)")
                                    (("1" (grind) nil nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (hide 2)
                                (("2"
                                  (flatten)
                                  (("2" (grind) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (flatten)
                    (("2" (assert)
                      (("2" (split +)
                        (("1" (flatten)
                          (("1" (lemma "system_roots_enum")
                            (("1"
                              (inst - "0" "LAMBDA (k): d"
                               "LAMBDa (k): a")
                              (("1"
                                (assert)
                                (("1"
                                  (skeep -)
                                  (("1"
                                    (case "K = 0")
                                    (("1"
                                      (inst + "0")
                                      (("1"
                                        (inst -4 "0" "0")
                                        (("1"
                                          (assert)
                                          (("1"
                                            (replace -5 +)
                                            (("1"
                                              (expand "rel5")
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (skosimp*)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (inst + "enum(K-1)+2")
                                      (("1"
                                        (replace -4 +)
                                        (("1"
                                          (expand "rel5")
                                          (("1"
                                            (inst -3 "2+enum(K-1)" "0")
                                            (("1"
                                              (assert)
                                              (("1"
                                                (skosimp*)
                                                (("1"
                                                  (inst - "i!1" "K-1")
                                                  (("1"
                                                    (ground)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2" (assertnil nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2" (assertnil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (flatten)
                          (("2"
                            (case "NOT ((sturm_tarski_faster(1,
                                                                                           a,
                                                                                           d,
                                                                                           LAMBDA (k): LAMBDA (j): 1,
                                                                                           LAMBDA (k): 0,
                                                                                           LAMBDA (j): 1)
                                                             /= 0) IFF (EXISTS (x:real): polynomial(a,d)(x)=0))")
                            (("1" (hide 3)
                              (("1"
                                (typepred
                                 "sturm_tarski_faster(1,
                                       a,
                                       d,
                                       LAMBDA (k): LAMBDA (j): 1,
                                       LAMBDA (k): 0,
                                       LAMBDA (j): 1)")
                                (("1"
                                  (replaces -1)
                                  (("1"
                                    (hide -)
                                    (("1"
                                      (expand "NSol_all")
                                      (("1"
                                        (lemma "empty_card[real]")
                                        (("1"
                                          (inst?)
                                          (("1"
                                            (assert)
                                            (("1"
                                              (expand "empty?")
                                              (("1"
                                                (expand "member")
                                                (("1"
                                                  (ground)
                                                  (("1"
                                                    (skosimp*)
                                                    (("1"
                                                      (inst - "x!1")
                                                      (("1"
                                                        (expand
                                                         "Sol_all"
                                                         +)
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (hide -)
                                                            (("1"
                                                              (grind)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (skosimp*)
                                                    (("2"
                                                      (inst + "x!1")
                                                      (("2"
                                                        (expand
                                                         "Sol_all"
                                                         -)
                                                        (("2"
                                                          (flatten)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (replace -1)
                              (("2"
                                (case "i = 0")
                                (("1"
                                  (replaces -1)
                                  (("1"
                                    (expand "rel5")
                                    (("1" (propax) nil nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (assert)
                                  (("2"
                                    (label "izero" 1)
                                    (("2"
                                      (hide "izero")
                                      (("2"
                                        (split +)
                                        (("1"
                                          (flatten)
                                          (("1"
                                            (assert)
                                            (("1"
                                              (hide -2)
                                              (("1"
                                                (skosimp*)
                                                (("1"
                                                  (inst + "x!1")
                                                  (("1"
                                                    (expand "rel5")
                                                    (("1"
                                                      (ground)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (flatten +)
                                          (("2"
                                            (split 2)
                                            (("1"
                                              (flatten)
                                              (("1"
                                                (case
                                                 "NOT (i = 0 OR i = 1 OR i=2 OR i=3 OR i=4 OR i=5)")
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (assert)
                                                  (("2"
                                                    (split -)
                                                    (("1"
                                                      (replace -1)
                                                      (("1"
                                                        (expand "rel5")
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (replace
                                                             -1)
                                                            (("1"
                                                              (case
                                                               "NOT greatify_rel(LAMBDA (j): 1) = (LAMBDA (j): 1)")
                                                              (("1"
                                                                (hide-all-but
                                                                 1)
                                                                (("1"
                                                                  (decompose-equality
                                                                   1)
                                                                  (("1"
                                                                    (expand
                                                                     "greatify_rel")
                                                                    (("1"
                                                                      (propax)
                                                                      nil
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (replaces
                                                                 -1)
                                                                (("2"
                                                                  (assert)
                                                                  (("2"
                                                                    (split
                                                                     1)
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (lemma
                                                                         "strict_poly_system_solvable")
                                                                        (("1"
                                                                          (inst
                                                                           -
                                                                           "0"
                                                                           "LAMBDA (ii:nat): d"
                                                                           "LAMBDA (ii:nat): a")
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (flatten
                                                                               -1)
                                                                              (("1"
                                                                                (hide
                                                                                 -2)
                                                                                (("1"
                                                                                  (split
                                                                                   -1)
                                                                                  (("1"
                                                                                    (inst
                                                                                     -
                                                                                     "0")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (inst
                                                                                     -1
                                                                                     "0")
                                                                                    (("2"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil)
                                                                                   ("3"
                                                                                    (hide
                                                                                     3)
                                                                                    (("3"
                                                                                      (skosimp*)
                                                                                      (("3"
                                                                                        (expand
                                                                                         "sigma")
                                                                                        (("3"
                                                                                          (expand
                                                                                           "sigma")
                                                                                          (("3"
                                                                                            (assert)
                                                                                            (("3"
                                                                                              (typepred
                                                                                               "sturm_tarski_faster(1,
                                                                                                         poly_deriv(a),
                                                                                                         d - 1,
                                                                                                         LAMBDA (j): a,
                                                                                                         LAMBDA (j): d,
                                                                                                         LAMBDA (j): 1)")
                                                                                              (("3"
                                                                                                (hide
                                                                                                 (-2
                                                                                                  -3))
                                                                                                (("3"
                                                                                                  (replaces
                                                                                                   -1)
                                                                                                  (("3"
                                                                                                    (assert)
                                                                                                    (("3"
                                                                                                      (expand
                                                                                                       "NSol_all"
                                                                                                       -)
                                                                                                      (("3"
                                                                                                        (lemma
                                                                                                         "empty_card[real]")
                                                                                                        (("3"
                                                                                                          (inst?)
                                                                                                          (("3"
                                                                                                            (assert)
                                                                                                            (("3"
                                                                                                              (expand
                                                                                                               "empty?")
                                                                                                              (("3"
                                                                                                                (inst
                                                                                                                 -
                                                                                                                 "x!1")
                                                                                                                (("3"
                                                                                                                  (expand
                                                                                                                   "member")
                                                                                                                  (("3"
                                                                                                                    (expand
                                                                                                                     "Sol_all"
                                                                                                                     +)
                                                                                                                    (("3"
                                                                                                                      (assert)
                                                                                                                      (("3"
                                                                                                                        (split)
                                                                                                                        (("1"
                                                                                                                          (replace
                                                                                                                           -2
                                                                                                                           1
                                                                                                                           :dir
                                                                                                                           rl)
                                                                                                                          (("1"
                                                                                                                            (rewrite
                                                                                                                             "poly_eq_le_degree")
                                                                                                                            (("1"
                                                                                                                              (hide
                                                                                                                               2)
                                                                                                                              (("1"
                                                                                                                                (skosimp*)
                                                                                                                                (("1"
                                                                                                                                  (expand
                                                                                                                                   "poly_deriv"
                                                                                                                                   +)
                                                                                                                                  (("1"
                                                                                                                                    (expand
                                                                                                                                     "prod_polynomials")
                                                                                                                                    (("1"
                                                                                                                                      (lift-if)
                                                                                                                                      (("1"
                                                                                                                                        (ground)
                                                                                                                                        nil
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil)
                                                                                                                         ("2"
                                                                                                                          (skosimp*)
                                                                                                                          (("2"
                                                                                                                            (inst
                                                                                                                             -
                                                                                                                             "0")
                                                                                                                            (("2"
                                                                                                                              (assert)
                                                                                                                              nil
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("4"
                                                                                    (skosimp*)
                                                                                    (("4"
                                                                                      (inst
                                                                                       +
                                                                                       "x!1")
                                                                                      (("4"
                                                                                        (skosimp*)
                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (flatten)
                                                                      (("2"
                                                                        (lemma
                                                                         "strict_poly_system_solvable")
                                                                        (("2"
                                                                          (inst
                                                                           -
                                                                           "0"
                                                                           "LAMBDA (ii:nat): d"
                                                                           "LAMBDA (ii:nat): a")
                                                                          (("2"
                                                                            (assert)
                                                                            (("2"
                                                                              (flatten)
                                                                              (("2"
                                                                                (hide
                                                                                 -1)
                                                                                (("2"
                                                                                  (split
                                                                                   -1)
                                                                                  (("1"
                                                                                    (skosimp*)
                                                                                    (("1"
                                                                                      (inst
                                                                                       -
                                                                                       "0")
                                                                                      (("1"
                                                                                        (inst
                                                                                         +
                                                                                         "x!1")
                                                                                        (("1"
                                                                                          (assert)
                                                                                          nil
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (flatten)
                                                                                    (("2"
                                                                                      (split
                                                                                       -1)
                                                                                      (("1"
                                                                                        (skosimp
                                                                                         1)
                                                                                        nil
                                                                                        nil)
                                                                                       ("2"
                                                                                        (flatten)
                                                                                        (("2"
                                                                                          (hide
                                                                                           1)
                                                                                          (("2"
                                                                                            (skosimp
                                                                                             1)
                                                                                            (("2"
                                                                                              (assert)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("3"
                                                                                        (typepred
                                                                                         "sturm_tarski_faster(1,
                                                                                                               poly_deriv(a),
                                                                                                               d - 1,
                                                                                                               LAMBDA (j): a,
                                                                                                               LAMBDA (j): d,
                                                                                                               LAMBDA (j): 1)")
                                                                                        (("3"
                                                                                          (hide
                                                                                           (-2
                                                                                            -3))
                                                                                          (("3"
                                                                                            (replaces
                                                                                             -1)
                                                                                            (("3"
                                                                                              (expand
                                                                                               "NSol_all"
                                                                                               -1)
                                                                                              (("3"
                                                                                                (lemma
                                                                                                 "empty_card[real]")
                                                                                                (("3"
                                                                                                  (inst?)
                                                                                                  (("3"
                                                                                                    (assert)
                                                                                                    (("3"
                                                                                                      (expand
                                                                                                       "empty?")
                                                                                                      (("3"
                                                                                                        (expand
                                                                                                         "member")
                                                                                                        (("3"
                                                                                                          (skosimp*)
                                                                                                          (("3"
                                                                                                            (inst
                                                                                                             4
                                                                                                             "x!1")
                                                                                                            (("3"
                                                                                                              (expand
                                                                                                               "Sol_all"
                                                                                                               -1)
                                                                                                              (("3"
                                                                                                                (flatten)
                                                                                                                (("3"
                                                                                                                  (split
                                                                                                                   4)
                                                                                                                  (("1"
                                                                                                                    (expand
                                                                                                                     "sigma"
                                                                                                                     1)
                                                                                                                    (("1"
                                                                                                                      (expand
                                                                                                                       "sigma"
                                                                                                                       1)
                                                                                                                      (("1"
                                                                                                                        (assert)
                                                                                                                        nil
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil)
                                                                                                                   ("2"
                                                                                                                    (expand
                                                                                                                     "sigma"
                                                                                                                     1)
                                                                                                                    (("2"
                                                                                                                      (expand
                                                                                                                       "sigma"
                                                                                                                       1)
                                                                                                                      (("2"
                                                                                                                        (invoke
                                                                                                                         (case
                                                                                                                          "%1 = %2")
                                                                                                                         (!
                                                                                                                          -1
                                                                                                                          1)
                                                                                                                         (!
                                                                                                                          1
                                                                                                                          1))
                                                                                                                        (("1"
                                                                                                                          (assert)
                                                                                                                          nil
                                                                                                                          nil)
                                                                                                                         ("2"
                                                                                                                          (hide
                                                                                                                           (-1
                                                                                                                            2))
                                                                                                                          (("2"
                                                                                                                            (rewrite
                                                                                                                             "poly_eq_le_degree")
                                                                                                                            (("2"
                                                                                                                              (hide
                                                                                                                               2)
                                                                                                                              (("2"
                                                                                                                                (skosimp*)
                                                                                                                                (("2"
                                                                                                                                  (expand
                                                                                                                                   "poly_deriv")
                                                                                                                                  (("2"
                                                                                                                                    (expand
                                                                                                                                     "prod_polynomials")
                                                                                                                                    (("2"
                                                                                                                                      (lift-if)
                                                                                                                                      (("2"
                                                                                                                                        (ground)
                                                                                                                                        nil
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil)
                                                                                                                   ("3"
                                                                                                                    (skosimp*)
                                                                                                                    (("3"
                                                                                                                      (inst
                                                                                                                       -
                                                                                                                       "0")
                                                                                                                      (("3"
                                                                                                                        (assert)
                                                                                                                        nil
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("2"
                                                      (replace -1)
                                                      (("2"
                                                        (expand "rel5")
                                                        (("2"
                                                          (propax)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("3"
                                                      (replace -1)
                                                      (("3"
                                                        (expand "rel5")
                                                        (("3"
                                                          (case
                                                           "NOT greatify_rel(LAMBDA (j): 4) = (LAMBDA (j): 4)")
                                                          (("1"
                                                            (decompose-equality
                                                             1)
                                                            (("1"
                                                              (expand
                                                               "greatify_rel")
                                                              (("1"
                                                                (propax)
                                                                nil
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (replaces
                                                             -1)
                                                            (("2"
                                                              (assert)
                                                              (("2"
                                                                (hide
                                                                 -2)
                                                                (("2"
                                                                  (split
                                                                   +)
                                                                  (("1"
                                                                    (flatten)
                                                                    (("1"
                                                                      (case
                                                                       "NOT EXISTS (x): polynomial(a, d)(x) > 0")
                                                                      (("1"
                                                                        (skeep)
                                                                        (("1"
                                                                          (inst
                                                                           +
                                                                           "x")
                                                                          (("1"
                                                                            (inst
                                                                             +
                                                                             "x")
                                                                            (("1"
                                                                              (assert)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (hide
                                                                         -2)
                                                                        (("2"
                                                                          (replace
                                                                           3)
                                                                          (("2"
                                                                            (typepred
                                                                             "sturm_tarski_faster(1,
                                                                                                         poly_deriv(a),
                                                                                                         d - 1,
                                                                                                         LAMBDA (j): a,
                                                                                                         LAMBDA (j): d,
                                                                                                         LAMBDA (j): 4)")
                                                                            (("2"
                                                                              (hide
                                                                               (-2
                                                                                -3))
                                                                              (("2"
                                                                                (replaces
                                                                                 -1)
                                                                                (("2"
                                                                                  (skosimp*)
                                                                                  (("2"
                                                                                    (lemma
                                                                                     "strict_poly_system_solvable")
                                                                                    (("2"
                                                                                      (inst
                                                                                       -
                                                                                       "0"
                                                                                       "LAMBDA (ii:nat): d"
                                                                                       "LAMBDA (ii:nat): a")
                                                                                      (("2"
                                                                                        (assert)
                                                                                        (("2"
                                                                                          (flatten
                                                                                           -1)
                                                                                          (("2"
                                                                                            (hide
                                                                                             -2)
                                                                                            (("2"
                                                                                              (split
                                                                                               -1)
                                                                                              (("1"
                                                                                                (inst
                                                                                                 -
                                                                                                 "0")
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil)
                                                                                               ("2"
                                                                                                (inst
                                                                                                 -1
                                                                                                 "0")
                                                                                                (("2"
                                                                                                  (assert)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil)
                                                                                               ("3"
                                                                                                (hide
                                                                                                 3)
                                                                                                (("3"
                                                                                                  (skosimp*)
                                                                                                  (("3"
                                                                                                    (expand
                                                                                                     "sigma")
                                                                                                    (("3"
                                                                                                      (expand
                                                                                                       "sigma")
                                                                                                      (("3"
                                                                                                        (assert)
                                                                                                        (("3"
                                                                                                          (typepred
                                                                                                           "sturm_tarski_faster(1,
                                                                                                                                     poly_deriv(a),
                                                                                                                                     d - 1,
                                                                                                                                     LAMBDA (j): a,
                                                                                                                                     LAMBDA (j): d,
                                                                                                                                     LAMBDA (j): 4)")
                                                                                                          (("3"
                                                                                                            (hide
                                                                                                             (-2
                                                                                                              -3))
                                                                                                            (("3"
                                                                                                              (replaces
                                                                                                               -1)
                                                                                                              (("3"
                                                                                                                (expand
                                                                                                                 "NSol_all"
                                                                                                                 -)
                                                                                                                (("3"
                                                                                                                  (lemma
                                                                                                                   "empty_card[real]")
                                                                                                                  (("3"
                                                                                                                    (inst?)
                                                                                                                    (("3"
                                                                                                                      (assert)
                                                                                                                      (("3"
                                                                                                                        (expand
                                                                                                                         "empty?")
                                                                                                                        (("3"
                                                                                                                          (inst
                                                                                                                           -
                                                                                                                           "x!2")
                                                                                                                          (("3"
                                                                                                                            (expand
                                                                                                                             "member")
                                                                                                                            (("3"
                                                                                                                              (expand
                                                                                                                               "Sol_all"
                                                                                                                               +)
                                                                                                                              (("3"
                                                                                                                                (assert)
                                                                                                                                (("3"
                                                                                                                                  (split
                                                                                                                                   +)
                                                                                                                                  (("1"
                                                                                                                                    (replace
                                                                                                                                     -3
                                                                                                                                     1
                                                                                                                                     :dir
                                                                                                                                     rl)
                                                                                                                                    (("1"
                                                                                                                                      (rewrite
                                                                                                                                       "poly_eq_le_degree"
                                                                                                                                       1
                                                                                                                                       :dir
                                                                                                                                       rl)
                                                                                                                                      (("1"
                                                                                                                                        (hide
                                                                                                                                         2)
                                                                                                                                        (("1"
                                                                                                                                          (skosimp*)
                                                                                                                                          (("1"
                                                                                                                                            (expand
                                                                                                                                             "poly_deriv")
                                                                                                                                            (("1"
                                                                                                                                              (expand
                                                                                                                                               "prod_polynomials")
                                                                                                                                              (("1"
                                                                                                                                                (lift-if)
                                                                                                                                                (("1"
                                                                                                                                                  (ground)
                                                                                                                                                  nil
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil)
                                                                                                                                   ("2"
                                                                                                                                    (inst
                                                                                                                                     -
                                                                                                                                     "0")
                                                                                                                                    (("2"
                                                                                                                                      (skosimp*)
                                                                                                                                      (("2"
                                                                                                                                        (assert)
                                                                                                                                        nil
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil)
                                                                                               ("4"
                                                                                                (inst
                                                                                                 +
                                                                                                 "x!1")
                                                                                                (("4"
                                                                                                  (assert)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (flatten)
                                                                    (("2"
                                                                      (split
                                                                       -1)
                                                                      (("1"
                                                                        (lemma
                                                                         "poly_sign_near_infinity")
                                                                        (("1"
                                                                          (inst?)
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (skosimp*)
                                                                              (("1"
                                                                                (inst
                                                                                 -
                                                                                 "M!1")
                                                                                (("1"
                                                                                  (inst
                                                                                   +
                                                                                   "M!1")
                                                                                  (("1"
                                                                                    (assert)
                                                                                    (("1"
                                                                                      (expand
                                                                                       "sign_ext")
                                                                                      (("1"
                                                                                        (assert)
                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (split
                                                                         -)
                                                                        (("1"
                                                                          (propax)
                                                                          nil
                                                                          nil)
                                                                         ("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (lemma
                                                                             "poly_sign_near_negative_infinity")
                                                                            (("2"
                                                                              (inst?)
                                                                              (("2"
                                                                                (assert)
                                                                                (("2"
                                                                                  (skosimp*)
                                                                                  (("2"
                                                                                    (inst
                                                                                     -
                                                                                     "-M!1")
                                                                                    (("2"
                                                                                      (assert)
                                                                                      (("2"
                                                                                        (lemma
                                                                                         "even_or_odd")
                                                                                        (("2"
                                                                                          (inst?)
                                                                                          (("2"
                                                                                            (assert)
                                                                                            (("2"
                                                                                              (inst
                                                                                               +
                                                                                               "-M!1")
                                                                                              (("2"
                                                                                                (expand
                                                                                                 "sign_ext")
                                                                                                (("2"
                                                                                                  (lift-if)
                                                                                                  (("2"
                                                                                                    (ground)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("3"
                                                                        (typepred
                                                                         "sturm_tarski_faster(1,
                                                                                                         poly_deriv(a),
                                                                                                         d - 1,
                                                                                                         LAMBDA (j): a,
                                                                                                         LAMBDA (j): d,
                                                                                                         LAMBDA (j): 4)")
                                                                        (("3"
                                                                          (hide
                                                                           (-2
                                                                            -3))
                                                                          (("3"
                                                                            (flatten)
                                                                            (("3"
                                                                              (replaces
                                                                               -1)
                                                                              (("3"
                                                                                (expand
                                                                                 "NSol_all"
                                                                                 +)
                                                                                (("3"
                                                                                  (lemma
                                                                                   "empty_card[real]")
                                                                                  (("3"
                                                                                    (inst?)
                                                                                    (("3"
                                                                                      (assert)
                                                                                      (("3"
                                                                                        (expand
                                                                                         "empty?"
                                                                                         1)
                                                                                        (("3"
                                                                                          (skosimp*)
                                                                                          (("3"
                                                                                            (inst
                                                                                             +
                                                                                             "x!1")
                                                                                            (("3"
                                                                                              (expand
                                                                                               "member")
                                                                                              (("3"
                                                                                                (expand
                                                                                                 "Sol_all")
                                                                                                (("3"
                                                                                                  (flatten)
                                                                                                  (("3"
                                                                                                    (inst
                                                                                                     -
                                                                                                     "0")
                                                                                                    (("3"
                                                                                                      (assert)
                                                                                                      nil
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("4"
                                                      (replace -1)
                                                      (("4"
                                                        (expand "rel5")
                                                        (("4"
                                                          (propax)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (flatten)
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (case
                                                   "NOT (i=2 OR i=5 )")
                                                  (("1"
                                                    (reveal "izero")
                                                    (("1"
                                                      (flatten)
                                                      (("1"
                                                        (expand
                                                         "rel5"
                                                         4)
                                                        (("1"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (split -1)
                                                    (("1"
                                                      (assert)
                                                      (("1"
                                                        (replace -1)
                                                        (("1"
                                                          (expand
                                                           "rel5")
                                                          (("1"
                                                            (case
                                                             "NOT greatify_rel(LAMBDA (j): 2) = (LAMBDA (j): 1)")
                                                            (("1"
                                                              (decompose-equality
                                                               1)
                                                              (("1"
                                                                (expand
                                                                 "greatify_rel")
                                                                (("1"
                                                                  (propax)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil)
                                                             ("2"
                                                              (replaces
                                                               -1)
                                                              (("2"
                                                                (assert)
                                                                (("2"
                                                                  (expand
                                                                   "*")
                                                                  (("2"
                                                                    (split
                                                                     +)
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (lemma
                                                                           "strict_poly_system_solvable")
                                                                          (("1"
                                                                            (inst
                                                                             -
                                                                             "0"
                                                                             "LAMBDA (ii:nat): d"
                                                                             "LAMBDA (ii:nat): (-1)*a")
                                                                            (("1"
                                                                              (assert)
                                                                              (("1"
                                                                                (expand
                                                                                 "*")
                                                                                (("1"
                                                                                  (flatten
                                                                                   -1)
                                                                                  (("1"
                                                                                    (hide
                                                                                     -2)
                                                                                    (("1"
                                                                                      (split
                                                                                       -1)
                                                                                      (("1"
                                                                                        (inst
                                                                                         -
                                                                                         "0")
                                                                                        (("1"
                                                                                          (assert)
                                                                                          nil
                                                                                          nil))
                                                                                        nil)
                                                                                       ("2"
                                                                                        (inst
                                                                                         -1
                                                                                         "0")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          nil
                                                                                          nil))
                                                                                        nil)
                                                                                       ("3"
                                                                                        (hide
                                                                                         3)
                                                                                        (("3"
                                                                                          (skosimp*)
                                                                                          (("3"
                                                                                            (expand
                                                                                             "sigma")
                                                                                            (("3"
                                                                                              (expand
                                                                                               "sigma")
                                                                                              (("3"
                                                                                                (assert)
                                                                                                (("3"
                                                                                                  (typepred
                                                                                                   "sturm_tarski_faster(1,
                                                               poly_deriv(a),
                                                               d - 1,
                                                               LAMBDA
                                                               (j):
                                                               LAMBDA (x: nat): (-1) * a(x),
                                                               LAMBDA (j): d,
                                                               (LAMBDA (j): 1))")
                                                                                                  (("3"
                                                                                                    (hide
                                                                                                     (-2
                                                                                                      -3))
                                                                                                    (("3"
                                                                                                      (replaces
                                                                                                       -1)
                                                                                                      (("3"
                                                                                                        (assert)
                                                                                                        (("3"
                                                                                                          (expand
                                                                                                           "NSol_all"
                                                                                                           -)
                                                                                                          (("3"
                                                                                                            (lemma
                                                                                                             "empty_card[real]")
                                                                                                            (("3"
                                                                                                              (inst?)
                                                                                                              (("3"
                                                                                                                (assert)
                                                                                                                (("3"
                                                                                                                  (expand
                                                                                                                   "empty?")
                                                                                                                  (("3"
                                                                                                                    (inst
                                                                                                                     -
                                                                                                                     "x!1")
                                                                                                                    (("3"
                                                                                                                      (expand
                                                                                                                       "member")
                                                                                                                      (("3"
                                                                                                                        (expand
                                                                                                                         "Sol_all"
                                                                                                                         +)
                                                                                                                        (("3"
                                                                                                                          (assert)
                                                                                                                          (("3"
                                                                                                                            (split)
                                                                                                                            (("1"
                                                                                                                              (case
                                                                                                                               "polynomial(poly_deriv(prod_polynomials(LAMBDA
                                                                              (ii: nat):
                                                                              LAMBDA (x: nat): (-1) * a(x),
                                                                              LAMBDA (ii: nat): d,
                                                                              (LAMBDA (i: nat): 1),
                                                                              0)),
                                                  d - 1)
                                                 (x!1)=(-1)*polynomial(poly_deriv(a), d - 1)(x!1)")
                                                                                                                              (("1"
                                                                                                                                (assert)
                                                                                                                                nil
                                                                                                                                nil)
                                                                                                                               ("2"
                                                                                                                                (rewrite
                                                                                                                                 "scal_polynomial2"
                                                                                                                                 :dir
                                                                                                                                 rl)
                                                                                                                                (("2"
                                                                                                                                  (rewrite
                                                                                                                                   "poly_eq_le_degree")
                                                                                                                                  (("2"
                                                                                                                                    (hide
                                                                                                                                     2)
                                                                                                                                    (("2"
                                                                                                                                      (skosimp*)
                                                                                                                                      (("2"
                                                                                                                                        (expand
                                                                                                                                         "poly_deriv"
                                                                                                                                         +)
                                                                                                                                        (("2"
                                                                                                                                          (expand
                                                                                                                                           "prod_polynomials")
                                                                                                                                          (("2"
                                                                                                                                            (expand
                                                                                                                                             "*")
                                                                                                                                            (("2"
                                                                                                                                              (lift-if)
                                                                                                                                              (("2"
                                                                                                                                                (ground)
                                                                                                                                                nil
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil)
                                                                                                                             ("2"
                                                                                                                              (skosimp*)
                                                                                                                              (("2"
                                                                                                                                (inst
                                                                                                                                 -
                                                                                                                                 "0")
                                                                                                                                (("2"
                                                                                                                                  (assert)
                                                                                                                                  nil
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("4"
                                                                                        (skosimp*)
                                                                                        (("4"
                                                                                          (inst
                                                                                           +
                                                                                           "x!1")
                                                                                          (("4"
                                                                                            (skosimp*)
                                                                                            (("4"
                                                                                              (lemma
                                                                                               "scal_polynomial2")
                                                                                              (("4"
                                                                                                (expand
                                                                                                 "*"
                                                                                                 -)
                                                                                                (("4"
                                                                                                  (rewrite
                                                                                                   -1
                                                                                                   +)
                                                                                                  (("4"
                                                                                                    (assert)
                                                                                                    (("4"
                                                                                                      (lemma
                                                                                                       "sigma_tolambda")
                                                                                                      (("4"
                                                                                                        (expand
                                                                                                         "polynomial"
                                                                                                         (-4
                                                                                                          1))
                                                                                                        (("4"
                                                                                                          (assert)
                                                                                                          nil
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil)
                                                                             ("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (expand
                                                                                 "*"
                                                                                 1)
                                                                                (("2"
                                                                                  (propax)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (flatten)
                                                                      (("2"
                                                                        (lemma
                                                                         "strict_poly_system_solvable")
                                                                        (("2"
                                                                          (inst
                                                                           -
                                                                           "0"
                                                                           "LAMBDA (ii:nat): d"
                                                                           "LAMBDA (ii:nat): (-1)*a")
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (expand
                                                                               "*"
                                                                               -1
                                                                               1)
                                                                              (("1"
                                                                                (flatten)
                                                                                (("1"
                                                                                  (hide
                                                                                   -1)
                                                                                  (("1"
                                                                                    (split
                                                                                     -1)
                                                                                    (("1"
                                                                                      (skosimp*)
                                                                                      (("1"
                                                                                        (inst
                                                                                         -
                                                                                         "0")
                                                                                        (("1"
                                                                                          (assert)
                                                                                          (("1"
                                                                                            (inst
                                                                                             +
                                                                                             "x!1")
                                                                                            (("1"
                                                                                              (rewrite
                                                                                               "scal_polynomial2")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                nil
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil)
                                                                                     ("2"
                                                                                      (flatten)
                                                                                      (("2"
                                                                                        (split
                                                                                         -1)
                                                                                        (("1"
                                                                                          (skosimp
                                                                                           1)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "*"
                                                                                             1)
                                                                                            (("1"
                                                                                              (propax)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (assert)
                                                                                          (("2"
                                                                                            (flatten)
                                                                                            (("2"
                                                                                              (hide
                                                                                               1)
                                                                                              (("2"
                                                                                                (skosimp
                                                                                                 1)
                                                                                                (("2"
                                                                                                  (assert)
                                                                                                  (("2"
                                                                                                    (expand
                                                                                                     "*"
                                                                                                     1)
                                                                                                    (("2"
                                                                                                      (assert)
                                                                                                      nil
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("3"
                                                                                          (typepred
                                                                                           "sturm_tarski_faster(1,
                                                                 poly_deriv(a),
                                                                 d - 1,
                                                                 LAMBDA
                                                                 (j):
                                                                 LAMBDA (zz: nat): (-1) * a(zz),
                                                                 LAMBDA (j): d,
                                                                 (LAMBDA (j): 1))")
                                                                                          (("3"
                                                                                            (hide
                                                                                             (-2
                                                                                              -3))
                                                                                            (("3"
                                                                                              (replaces
                                                                                               -1)
                                                                                              (("3"
                                                                                                (expand
                                                                                                 "NSol_all"
                                                                                                 -1)
                                                                                                (("3"
                                                                                                  (lemma
                                                                                                   "empty_card[real]")
                                                                                                  (("3"
                                                                                                    (inst?)
                                                                                                    (("3"
                                                                                                      (assert)
                                                                                                      (("3"
                                                                                                        (expand
                                                                                                         "empty?")
                                                                                                        (("3"
                                                                                                          (expand
                                                                                                           "member")
                                                                                                          (("3"
                                                                                                            (skosimp*)
                                                                                                            (("3"
                                                                                                              (inst
                                                                                                               5
                                                                                                               "x!1")
                                                                                                              (("3"
                                                                                                                (expand
                                                                                                                 "Sol_all"
                                                                                                                 -1)
                                                                                                                (("3"
                                                                                                                  (flatten)
                                                                                                                  (("3"
                                                                                                                    (inst
                                                                                                                     -
                                                                                                                     "0")
                                                                                                                    (("3"
                                                                                                                      (assert)
                                                                                                                      (("3"
                                                                                                                        (lemma
                                                                                                                         "scal_polynomial2")
                                                                                                                        (("3"
                                                                                                                          (expand
                                                                                                                           "*"
                                                                                                                           -1)
                                                                                                                          (("3"
                                                                                                                            (rewrite
                                                                                                                             -1)
                                                                                                                            (("3"
                                                                                                                              (assert)
                                                                                                                              (("3"
                                                                                                                                (hide-all-but
                                                                                                                                 (-3
                                                                                                                                  5))
                                                                                                                                (("3"
                                                                                                                                  (invoke
                                                                                                                                   (case
                                                                                                                                    "NOT %1 = %2")
                                                                                                                                   (!
                                                                                                                                    -1
                                                                                                                                    1
                                                                                                                                    2)
                                                                                                                                   (!
                                                                                                                                    1
                                                                                                                                    1))
                                                                                                                                  (("1"
                                                                                                                                    (rewrite
                                                                                                                                     "poly_eq_le_degree")
                                                                                                                                    nil
                                                                                                                                    nil)
                                                                                                                                   ("2"
                                                                                                                                    (assert)
                                                                                                                                    nil
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (skosimp*)
                                                                            (("2"
                                                                              (expand
                                                                               "*"
                                                                               1)
                                                                              (("2"
                                                                                (propax)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("2"
                                                      (replace -1)
                                                      (("2"
                                                        (expand "rel5")
                                                        (("2"
                                                          (assert)
                                                          (("2"
                                                            (hide -2)
                                                            (("2"
                                                              (split +)
                                                              (("1"
                                                                (flatten)
                                                                (("1"
                                                                  (case
                                                                   "NOT EXISTS (x): polynomial(a, d)(x) < 0")
                                                                  (("1"
                                                                    (skeep)
                                                                    (("1"
                                                                      (inst
                                                                       +
                                                                       "x")
                                                                      (("1"
                                                                        (inst
                                                                         +
                                                                         "x")
                                                                        (("1"
                                                                          (assert)
                                                                          nil
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (hide
                                                                     -2)
                                                                    (("2"
                                                                      (replace
                                                                       3)
                                                                      (("2"
                                                                        (case
                                                                         "NOT greatify_rel(LAMBDA (j): 5) = (LAMBDA (j): 4)")
                                                                        (("1"
                                                                          (decompose-equality
                                                                           1)
                                                                          (("1"
                                                                            (expand
                                                                             "greatify_rel"
                                                                             1)
                                                                            (("1"
                                                                              (propax)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (replaces
                                                                           -1)
                                                                          (("2"
                                                                            (typepred
                                                                             "sturm_tarski_faster(1,
                                                             poly_deriv(a),
                                                             d - 1,
                                                             LAMBDA (j): (-1) * a,
                                                             LAMBDA (j): d,
                                                             (LAMBDA (j): 4))")
                                                                            (("1"
                                                                              (hide
                                                                               (-2
                                                                                -3))
                                                                              (("1"
                                                                                (replaces
                                                                                 -1)
                                                                                (("1"
                                                                                  (skosimp*)
                                                                                  (("1"
                                                                                    (lemma
                                                                                     "strict_poly_system_solvable")
                                                                                    (("1"
                                                                                      (inst
                                                                                       -
                                                                                       "0"
                                                                                       "LAMBDA (ii:nat): d"
                                                                                       "LAMBDA (ii:nat): (-1)*a")
                                                                                      (("1"
                                                                                        (assert)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "*"
                                                                                           -1
                                                                                           1)
                                                                                          (("1"
                                                                                            (flatten
                                                                                             -1)
                                                                                            (("1"
                                                                                              (hide
                                                                                               -2)
                                                                                              (("1"
                                                                                                (split
                                                                                                 -1)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   -
                                                                                                   "0")
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (inst
                                                                                                   -1
                                                                                                   "0")
                                                                                                  (("2"
                                                                                                    (assert)
                                                                                                    (("2"
                                                                                                      (expand
                                                                                                       "*"
                                                                                                       1)
                                                                                                      (("2"
                                                                                                        (assert)
                                                                                                        (("2"
                                                                                                          (expand
                                                                                                           "*")
                                                                                                          (("2"
                                                                                                            (lift-if)
                                                                                                            (("2"
                                                                                                              (assert)
                                                                                                              nil
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("3"
                                                                                                  (hide
                                                                                                   3)
                                                                                                  (("3"
                                                                                                    (expand
                                                                                                     "*")
                                                                                                    (("3"
                                                                                                      (assert)
                                                                                                      (("3"
                                                                                                        (skosimp*)
                                                                                                        (("3"
                                                                                                          (expand
                                                                                                           "sigma")
                                                                                                          (("3"
                                                                                                            (expand
                                                                                                             "sigma")
                                                                                                            (("3"
                                                                                                              (assert)
                                                                                                              (("3"
                                                                                                                (expand
                                                                                                                 "NSol_all"
                                                                                                                 -)
                                                                                                                (("3"
                                                                                                                  (lemma
                                                                                                                   "empty_card[real]")
                                                                                                                  (("3"
                                                                                                                    (inst?)
                                                                                                                    (("3"
                                                                                                                      (assert)
                                                                                                                      (("3"
                                                                                                                        (expand
                                                                                                                         "empty?")
                                                                                                                        (("3"
                                                                                                                          (inst
                                                                                                                           -
                                                                                                                           "x!2")
                                                                                                                          (("3"
                                                                                                                            (expand
                                                                                                                             "member")
                                                                                                                            (("3"
                                                                                                                              (expand
                                                                                                                               "Sol_all"
                                                                                                                               +)
                                                                                                                              (("3"
                                                                                                                                (assert)
                                                                                                                                (("3"
                                                                                                                                  (split
                                                                                                                                   +)
                                                                                                                                  (("1"
                                                                                                                                    (case
                                                                                                                                     "polynomial(poly_deriv(prod_polynomials(LAMBDA
                                                                             (ii: nat):
                                                                             LAMBDA (x: nat): (-1) * a(x),
                                                                             LAMBDA (ii: nat): d,
                                                                             (LAMBDA (i: nat): 1),
                                                                             0)),
                                                 d - 1)
                                                (x!2)=(-1)*polynomial(poly_deriv(a), d - 1)(x!2)")
                                                                                                                                    (("1"
                                                                                                                                      (assert)
                                                                                                                                      nil
                                                                                                                                      nil)
                                                                                                                                     ("2"
                                                                                                                                      (rewrite
                                                                                                                                       "scal_polynomial2"
                                                                                                                                       :dir
                                                                                                                                       rl)
                                                                                                                                      (("2"
                                                                                                                                        (rewrite
                                                                                                                                         "poly_eq_le_degree"
                                                                                                                                         1
                                                                                                                                         :dir
                                                                                                                                         rl)
                                                                                                                                        (("2"
                                                                                                                                          (hide
                                                                                                                                           2)
                                                                                                                                          (("2"
                                                                                                                                            (skosimp*)
                                                                                                                                            (("2"
                                                                                                                                              (expand
                                                                                                                                               "poly_deriv")
                                                                                                                                              (("2"
                                                                                                                                                (expand
                                                                                                                                                 "prod_polynomials")
                                                                                                                                                (("2"
                                                                                                                                                  (expand
                                                                                                                                                   "*")
                                                                                                                                                  (("2"
                                                                                                                                                    (lift-if)
                                                                                                                                                    (("2"
                                                                                                                                                      (ground)
                                                                                                                                                      nil
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil)
                                                                                                                                   ("2"
                                                                                                                                    (skosimp*)
                                                                                                                                    (("2"
                                                                                                                                      (inst
                                                                                                                                       -
                                                                                                                                       "0")
                                                                                                                                      (("2"
                                                                                                                                        (assert)
                                                                                                                                        nil
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("4"
                                                                                                  (inst
                                                                                                   +
                                                                                                   "x!1")
                                                                                                  (("4"
                                                                                                    (skosimp*)
                                                                                                    (("4"
                                                                                                      (rewrite
                                                                                                       "scal_polynomial2")
                                                                                                      (("4"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("2"
                                                                                        (skosimp*)
                                                                                        (("2"
                                                                                          (expand
                                                                                           "*"
                                                                                           1)
                                                                                          (("2"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil)
                                                                             ("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (expand
                                                                                 "*"
                                                                                 1)
                                                                                (("2"
                                                                                  (expand
                                                                                   "*"
                                                                                   -1)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil)
                                                                             ("3"
                                                                              (skosimp*)
                                                                              (("3"
                                                                                (expand
                                                                                 "*"
                                                                                 1)
                                                                                (("3"
                                                                                  (propax)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (flatten)
                                                                (("2"
                                                                  (split
                                                                   -1)
                                                                  (("1"
                                                                    (lemma
                                                                     "poly_sign_near_infinity")
                                                                    (("1"
                                                                      (inst
                                                                       -
                                                                       "(-1)*a"
                                                                       "d")
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (skosimp*)
                                                                          (("1"
                                                                            (inst
                                                                             -
                                                                             "M!1")
                                                                            (("1"
                                                                              (inst
                                                                               +
                                                                               "M!1")
                                                                              (("1"
                                                                                (assert)
                                                                                (("1"
                                                                                  (rewrite
                                                                                   "scal_polynomial2")
                                                                                  (("1"
                                                                                    (expand
                                                                                     "*")
                                                                                    (("1"
                                                                                      (expand
                                                                                       "sign_ext")
                                                                                      (("1"
                                                                                        (assert)
                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (flatten)
                                                                    (("2"
                                                                      (assert)
                                                                      (("2"
                                                                        (lemma
                                                                         "poly_sign_near_negative_infinity")
                                                                        (("2"
                                                                          (inst?)
                                                                          (("2"
                                                                            (assert)
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (inst
                                                                                 -
                                                                                 "-M!1")
                                                                                (("2"
                                                                                  (assert)
                                                                                  (("2"
                                                                                    (lemma
                                                                                     "even_or_odd")
                                                                                    (("2"
                                                                                      (inst?)
                                                                                      (("2"
                                                                                        (assert)
                                                                                        (("2"
                                                                                          (expand
                                                                                           "*"
                                                                                           -3)
                                                                                          (("2"
                                                                                            (inst
                                                                                             +
                                                                                             "-M!1")
                                                                                            (("2"
                                                                                              (expand
                                                                                               "sign_ext")
                                                                                              (("2"
                                                                                                (lift-if)
                                                                                                (("2"
                                                                                                  (ground)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("3"
                                                                    (case
                                                                     "NOT greatify_rel(LAMBDA (j): 5) = (LAMBDA (j): 4)")
                                                                    (("1"
                                                                      (decompose-equality
                                                                       1)
                                                                      (("1"
                                                                        (expand
                                                                         "greatify_rel"
                                                                         1)
                                                                        (("1"
                                                                          (propax)
                                                                          nil
                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (replaces
                                                                       -1)
                                                                      (("2"
                                                                        (typepred
                                                                         "sturm_tarski_faster(1,
                                                             poly_deriv(a),
                                                             d - 1,
                                                             LAMBDA (j): (-1) * a,
                                                             LAMBDA (j): d,
                                                             (LAMBDA (j): 4))")
                                                                        (("1"
                                                                          (hide
                                                                           (-2
                                                                            -3))
                                                                          (("1"
                                                                            (replaces
                                                                             -1)
                                                                            (("1"
                                                                              (assert)
                                                                              (("1"
                                                                                (flatten)
                                                                                (("1"
                                                                                  (expand
                                                                                   "NSol_all"
                                                                                   +)
                                                                                  (("1"
                                                                                    (lemma
                                                                                     "empty_card[real]")
                                                                                    (("1"
                                                                                      (inst?)
                                                                                      (("1"
                                                                                        (assert)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "empty?"
                                                                                           1)
                                                                                          (("1"
                                                                                            (skosimp*)
                                                                                            (("1"
                                                                                              (inst
                                                                                               +
                                                                                               "x!1")
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "member")
                                                                                                (("1"
                                                                                                  (expand
                                                                                                   "Sol_all")
                                                                                                  (("1"
                                                                                                    (flatten)
                                                                                                    (("1"
                                                                                                      (inst
                                                                                                       -
                                                                                                       "0")
                                                                                                      (("1"
                                                                                                        (assert)
                                                                                                        (("1"
                                                                                                          (rewrite
                                                                                                           "scal_polynomial2")
                                                                                                          (("1"
                                                                                                            (assert)
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("2"
                                                                                        (skosimp*)
                                                                                        (("2"
                                                                                          (expand
                                                                                           "*"
                                                                                           1)
                                                                                          (("2"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (skosimp*)
                                                                          (("2"
                                                                            (expand
                                                                             "*"
                                                                             -1)
                                                                            (("2"
                                                                              (assert)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("3"
                                                                          (skosimp*)
                                                                          (("3"
                                                                            (expand
                                                                             "*"
                                                                             1)
                                                                            (("3"
                                                                              (propax)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((rat nonempty-type-eq-decl nil rationals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (- const-decl "[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)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (rat_minus_rat_is_rat application-judgement "rat" rationals nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (> const-decl "bool" reals nil)
    (sequence type-eq-decl nil sequences nil)
    (< const-decl "bool" reals nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (rat_times_rat_is_rat application-judgement "rat" rationals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (rat_expt application-judgement "rat" exponentiation nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (minus_int_is_int application-judgement "int" integers nil)
    (rat_div_nzrat_is_rat application-judgement "rat" rationals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (rat_plus_rat_is_rat application-judgement "rat" rationals nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (scal_polynomial2 formula-decl nil polynomials "reals/")
    (sigma_tolambda formula-decl nil sigma_nat "reals/")
    (a skolem-const-decl "[nat -> int]" poly_system_strategy nil)
    (sign_ext const-decl
     "{sig: real | (sig = -1 OR sig = 1 OR sig = 0) AND sig * x = abs(x)}"
     sign "reals/")
    (poly_sign_near_infinity formula-decl nil more_polynomial_props
     "reals/")
    (even_or_odd formula-decl nil naturalnumbers nil)
    (minus_nzint_is_nzint application-judgement "nzint" integers nil)
    (poly_sign_near_negative_infinity formula-decl nil
     more_polynomial_props "reals/")
    (greatify_rel const-decl
     "{pz: subrange(0, 5) | pz /= 2 AND pz /= 5}" poly_system_strategy
     nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (poly_deriv const-decl "real" polynomials "reals/")
    (int_plus_int_is_int application-judgement "int" integers nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (even_plus_even_is_even application-judgement "even_int" integers
     nil)
    (nnint_times_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (poly_eq_le_degree formula-decl nil polynomials "reals/")
    (T_low type-eq-decl nil sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (T_low type-eq-decl nil product "reals/")
    (T_high type-eq-decl nil product "reals/")
    (product def-decl "real" product "reals/")
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (prod_polynomials def-decl "{a |
         (FORALL (x):
            polynomial(a, sigma(0, k, KF * GP))(x) =
             product(0, k,
                     LAMBDA (j): polynomial(GF(j), KF(j))(x) ^ GP(j)))
          AND
          ((FORALL (i): i <= k AND GP(i) /= 0 IMPLIES GF(i)(KF(i)) /= 0)
            IMPLIES a(sigma(0, k, KF * GP)) /= 0)
           AND (FORALL (i): i > sigma(0, k, KF * GP) IMPLIES a(i) = 0)}"
     poly_families nil)
    (sigma_nnreal application-judgement "nnreal" sigma_nat "reals/")
    (sigma_nat application-judgement "nat" sigma_nat "reals/")
    (strict_poly_system_solvable formula-decl nil poly_systems nil)
    (Sol_all const-decl "finite_set[real]" poly_families nil)
    (finite_set type-eq-decl nil finite_sets nil)
    (is_finite const-decl "bool" finite_sets nil)
    (set type-eq-decl nil sets nil) (empty? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (empty_card formula-decl nil finite_sets nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (IFF const-decl "[bool, bool -> bool]" booleans nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (<= const-decl "bool" reals nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (subrange type-eq-decl nil integers nil)
    (NSol_all const-decl "nat" poly_families nil)
    (sturm_tarski_faster const-decl "{r: real |
         r = NSol_all(k, a, m, p, n, RelF6) AND
          rational_pred(r) AND integer_pred(r)}" system_solvers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (K skolem-const-decl "nat" poly_system_strategy nil)
    (below type-eq-decl nil naturalnumbers nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (system_roots_enum formula-decl nil poly_systems nil)
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (sigma def-decl "real" sigma "reals/")
    (^ const-decl "real" exponentiation nil)
    (expt def-decl "real" exponentiation nil)
    (rel5 const-decl "bool" poly_system_strategy nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (compute_solvable_single const-decl "bool" poly_system_strategy
     nil))
   shostak))
 (poly_deriv_integer 0
  (poly_deriv_integer-1 nil 3621599183
   ("" (skeep) (("" (expand "poly_deriv") (("" (propax) nil nil)) nil))
    nil)
   ((mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (poly_deriv const-decl "real" polynomials "reals/"))
   shostak))
 (compute_solvable_TCC1 0
  (compute_solvable_TCC1-1 nil 3621339345 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (> const-decl "bool" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (/= const-decl "boolean" notequal nil))
   nil))
 (compute_solvable_TCC2 0
  (compute_solvable_TCC2-3 nil 3622460405
   ("" (skeep)
    (("" (skeep*)
      (("" (split)
        (("1" (typepred "n")
          (("1" (inst - "fe")
            (("1" (assertnil nil)
             ("2" (assert)
              (("2" (typepred "fe")
                (("2" (assert)
                  (("2" (inst - "i") (("2" (assertnil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (replaces -1)
          (("2" (expand "greatify_poly_rel")
            (("2" (expand "greatify_poly")
              (("2" (lift-if)
                (("2" (expand "*")
                  (("2" (typepred "n")
                    (("2" (inst - "fe")
                      (("1" (assert) (("1" (ground) nil nil)) nil)
                       ("2" (typepred "fe")
                        (("2" (assert)
                          (("2" (hide -2)
                            (("2" (inst - "i") (("2" (assertnil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((greatify_poly const-decl "[nat -> int]" poly_system_strategy nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (greatify_poly_rel const-decl "[nat -> int]" poly_system_strategy
     nil)
    (> const-decl "bool" reals nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (k skolem-const-decl "nat" poly_system_strategy nil)
    (subrange type-eq-decl nil integers nil)
    (newRel skolem-const-decl
     "[nat -> {pz: subrange(0, 5) | pz /= 2 AND pz /= 5}]"
     poly_system_strategy nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (< const-decl "bool" reals nil)
    (fe skolem-const-decl "{i |
         (i > k IMPLIES (FORALL (j: upto(k)): newRel(j) > 0)) AND
          (i <= k IMPLIES
            newRel(i) = 0 AND (FORALL (j): j < i IMPLIES newRel(j) > 0))}"
     poly_system_strategy nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   nil)
  (compute_solvable_TCC2-2 nil 3621608685
   ("" (skeep*)
    (("" (typepred "n")
      (("" (typepred "fe")
        (("" (assert)
          (("" (case "fe <=k")
            (("1" (assert)
              (("1" (inst - "fe")
                (("1" (assert)
                  (("1" (flatten)
                    (("1" (assert)
                      (("1" (replace -6 +)
                        (("1" (expand "greatify_poly_rel" +)
                          (("1" (expand "*")
                            (("1" (lift-if)
                              (("1"
                                (typepred "n")
                                (("1"
                                  (inst - "fe")
                                  (("1"
                                    (flatten)
                                    (("1" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (assert)
              (("2" (inst - "i") (("2" (assertnil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((ge_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil)
  (compute_solvable_TCC2-1 nil 3621339345 ("" (subtype-tcc) nil nil)
   ((le_realorder name-judgement "RealOrder" real_orders "reals/")
    (ge_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (compute_solvable_TCC3 0
  (compute_solvable_TCC3-3 nil 3622460555
   ("" (skeep*)
    (("" (lift-if)
      (("" (assert)
        (("" (replaces -1)
          (("" (expand "greatify_poly_rel" -)
            (("" (expand "greatify_poly")
              (("" (lift-if)
                (("" (lift-if)
                  (("" (expand "*")
                    (("" (typepred "n")
                      (("" (inst-cp - "1+i_1")
                        (("" (inst - "i_1") (("" (ground) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((greatify_poly const-decl "[nat -> int]" poly_system_strategy nil)
    (> const-decl "bool" reals nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (greatify_poly_rel const-decl "[nat -> int]" poly_system_strategy
     nil)
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   nil)
  (compute_solvable_TCC3-2 nil 3621608859
   ("" (skeep)
    (("" (skeep*)
      (("" (split)
        (("1" (typepred "n")
          (("1" (inst - "fe")
            (("1" (assertnil nil)
             ("2" (assert)
              (("2" (typepred "fe")
                (("2" (assert)
                  (("2" (inst - "i") (("2" (assertnil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (replaces -1)
          (("2" (expand "greatify_poly_rel")
            (("2" (expand "greatify_poly")
              (("2" (lift-if)
                (("2" (expand "*")
                  (("2" (typepred "n")
                    (("2" (inst - "fe")
                      (("1" (assert) (("1" (ground) nil nil)) nil)
                       ("2" (typepred "fe")
                        (("2" (assert)
                          (("2" (hide -2)
                            (("2" (inst - "i") (("2" (assertnil nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (le_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil)
  (compute_solvable_TCC3-1 nil 3621339345
   ("" (skeep*)
    (("" (typepred "fe")
      (("" (assert)
        (("" (case "fe <=k")
          (("1" (assert)
            (("1" (hide -2)
              (("1" (flatten)
                (("1" (inst + "fe")
                  (("1" (replace -6 -2)
                    (("1" (expand "greatify_rel" -2)
                      (("1" (lift-if)
                        (("1" (ground)
                          (("1" (replace -5 -1)
                            (("1" (expand "greatify_poly_rel" -1)
                              (("1"
                                (typepred "n")
                                (("1"
                                  (inst?)
                                  (("1" (assertnil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (assert)
            (("2" (inst - "i") (("2" (assertnil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (le_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (compute_solvable_TCC4 0
  (compute_solvable_TCC4-4 nil 3622460572
   ("" (skeep*)
    (("" (assert)
      (("" (typepred "Qprodlist")
        (("" (replace -9 :dir rl)
          (("" (replace -3 + :dir rl)
            (("" (typepred "prod_polynomials(newp, n, LAMBDA i: 1, k)")
              (("" (assert)
                (("" (skosimp*)
                  (("" (replace -8 -3)
                    (("" (expand "greatify_poly_rel" -)
                      (("" (expand "greatify_poly")
                        (("" (assert)
                          (("" (expand "*")
                            (("" (lift-if)
                              ((""
                                (assert)
                                ((""
                                  (typepred "n")
                                  ((""
                                    (inst - "i!1")
                                    (("" (ground) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (int_minus_int_is_int application-judgement "int" integers nil)
    (greatify_poly_rel const-decl "[nat -> int]" poly_system_strategy
     nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (greatify_poly const-decl "[nat -> int]" poly_system_strategy nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (PRED type-eq-decl nil defined_types nil)
    (list type-decl nil list_adt nil)
    (every adt-def-decl "boolean" list_adt nil)
    (AND const-decl "[bool, bool -> bool]" 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)
    (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 "[T, T -> boolean]" equalities nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (length def-decl "nat" list_props nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (T_low type-eq-decl nil sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (sigma def-decl "real" sigma "reals/")
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil)
    (> const-decl "bool" reals nil)
    (subrange type-eq-decl nil integers nil)
    (sequence type-eq-decl nil sequences nil)
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (T_low type-eq-decl nil product "reals/")
    (T_high type-eq-decl nil product "reals/")
    (product def-decl "real" product "reals/")
    (^ const-decl "real" exponentiation nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (prod_polynomials def-decl "{a |
         (FORALL (x):
            polynomial(a, sigma(0, k, KF * GP))(x) =
             product(0, k,
                     LAMBDA (j): polynomial(GF(j), KF(j))(x) ^ GP(j)))
          AND
          ((FORALL (i): i <= k AND GP(i) /= 0 IMPLIES GF(i)(KF(i)) /= 0)
            IMPLIES a(sigma(0, k, KF * GP)) /= 0)
           AND (FORALL (i): i > sigma(0, k, KF * GP) IMPLIES a(i) = 0)}"
     poly_families nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil)
    (nth def-decl "T" list_props nil)
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/"))
   nil)
  (compute_solvable_TCC4-3 nil 3622459343
   ("" (skeep*)
    (("" (lift-if)
      (("" (assert)
        (("" (replaces -1)
          (("" (expand "greatify_poly_rel" -)
            (("" (expand "greatify_poly")
              (("" (lift-if)
                (("" (lift-if)
                  (("" (expand "*")
                    (("" (typepred "n")
                      (("" (inst-cp - "1+i_1")
                        (("" (inst - "i_1") (("" (ground) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (gt_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil)
  (compute_solvable_TCC4-2 nil 3621608892
   ("" (skeep*)
    (("" (assert)
      (("" (typepred "Qprodlist")
        (("" (replace -9 :dir rl)
          (("" (replace -3 + :dir rl)
            (("" (typepred "prod_polynomials(newp, n, LAMBDA i: 1, k)")
              (("" (assert)
                (("" (skosimp*)
                  (("" (replace -8 -3)
                    (("" (expand "greatify_poly_rel" -)
                      (("" (assert)
                        (("" (expand "*")
                          (("" (lift-if)
                            (("" (assert)
                              ((""
                                (typepred "n")
                                ((""
                                  (inst - "i!1")
                                  (("" (ground) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (list type-decl nil list_adt nil)
    (T_low type-eq-decl nil sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (sigma def-decl "real" sigma "reals/")
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (T_low type-eq-decl nil product "reals/")
    (T_high type-eq-decl nil product "reals/")
    (product def-decl "real" product "reals/")
    (prod_polynomials def-decl "{a |
         (FORALL (x):
            polynomial(a, sigma(0, k, KF * GP))(x) =
             product(0, k,
                     LAMBDA (j): polynomial(GF(j), KF(j))(x) ^ GP(j)))
          AND
          ((FORALL (i): i <= k AND GP(i) /= 0 IMPLIES GF(i)(KF(i)) /= 0)
            IMPLIES a(sigma(0, k, KF * GP)) /= 0)
           AND (FORALL (i): i > sigma(0, k, KF * GP) IMPLIES a(i) = 0)}"
     poly_families nil)
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/"))
   nil)
  (compute_solvable_TCC4-1 nil 3621339345
   ("" (skeep*)
    (("" (lift-if)
      (("" (assert)
        (("" (replaces -1)
          (("" (expand "greatify_poly_rel" -)
            (("" (lift-if)
              (("" (lift-if)
                (("" (expand "*")
                  (("" (typepred "n")
                    (("" (inst-cp - "1+i_1")
                      (("" (inst - "i_1") (("" (ground) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((le_realorder name-judgement "RealOrder" real_orders "reals/")
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (lt_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil))
 (compute_solvable_TCC5 0
  (compute_solvable_TCC5-4 nil 3622460592
   ("" (skeep*)
    (("" (replaces -1)
      (("" (expand "greatify_poly_rel" -6)
        (("" (expand "greatify_poly")
          (("" (lift-if)
            (("" (expand "*")
              (("" (typepred "n")
                (("" (inst - "i") (("" (ground) nil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((greatify_poly const-decl "[nat -> int]" poly_system_strategy nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (/= const-decl "boolean" notequal nil)
    (> const-decl "bool" reals nil)
    (greatify_poly_rel const-decl "[nat -> int]" poly_system_strategy
     nil)
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/"))
   nil)
  (compute_solvable_TCC5-3 nil 3622459303
   ("" (skeep*)
    (("" (assert)
      (("" (typepred "Qprodlist")
        (("" (replace -9 :dir rl)
          (("" (replace -3 + :dir rl)
            (("" (typepred "prod_polynomials(newp, n, LAMBDA i: 1, k)")
              (("" (assert)
                (("" (skosimp*)
                  (("" (replace -8 -3)
                    (("" (expand "greatify_poly_rel" -)
                      (("" (expand "greatify_poly")
                        (("" (assert)
                          (("" (expand "*")
                            (("" (lift-if)
                              ((""
                                (assert)
                                ((""
                                  (typepred "n")
                                  ((""
                                    (inst - "i!1")
                                    (("" (ground) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (prod_polynomials def-decl "{a |
         (FORALL (x):
            polynomial(a, sigma(0, k, KF * GP))(x) =
             product(0, k,
                     LAMBDA (j): polynomial(GF(j), KF(j))(x) ^ GP(j)))
          AND
          ((FORALL (i): i <= k AND GP(i) /= 0 IMPLIES GF(i)(KF(i)) /= 0)
            IMPLIES a(sigma(0, k, KF * GP)) /= 0)
           AND (FORALL (i): i > sigma(0, k, KF * GP) IMPLIES a(i) = 0)}"
     poly_families nil)
    (product def-decl "real" product "reals/")
    (T_high type-eq-decl nil product "reals/")
    (T_low type-eq-decl nil product "reals/")
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (sigma def-decl "real" sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (T_low type-eq-decl nil sigma "reals/")
    (list type-decl nil list_adt nil)
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (ge_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil)
  (compute_solvable_TCC5-2 nil 3621608908
   ("" (skeep*)
    (("" (replaces -1)
      (("" (expand "greatify_poly_rel" -6)
        (("" (lift-if)
          (("" (expand "*")
            (("" (typepred "n")
              (("" (inst - "i") (("" (ground) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/"))
   nil)
  (compute_solvable_TCC5-1 nil 3621339345
   ("" (skeep*)
    (("" (assert)
      (("" (typepred "Qprodlist")
        (("" (replace -9 :dir rl)
          (("" (replace -3 + :dir rl)
            (("" (typepred "prod_polynomials(newp, n, LAMBDA i: 1, k)")
              (("" (assert)
                (("" (skosimp*)
                  (("" (replace -8 -3)
                    (("" (expand "greatify_poly_rel" -)
                      (("" (assert)
                        (("" (expand "*")
                          (("" (lift-if)
                            (("" (assert)
                              ((""
                                (typepred "n")
                                ((""
                                  (inst - "i!1")
                                  (("" (ground) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (list type-decl nil list_adt nil)
    (T_low type-eq-decl nil sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (sigma def-decl "real" sigma "reals/")
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (T_low type-eq-decl nil product "reals/")
    (T_high type-eq-decl nil product "reals/")
    (product def-decl "real" product "reals/")
    (prod_polynomials def-decl "{a |
         (FORALL (x):
            polynomial(a, sigma(0, k, KF * GP))(x) =
             product(0, k,
                     LAMBDA (j): polynomial(GF(j), KF(j))(x) ^ GP(j)))
          AND
          ((FORALL (i): i <= k AND GP(i) /= 0 IMPLIES GF(i)(KF(i)) /= 0)
            IMPLIES a(sigma(0, k, KF * GP)) /= 0)
           AND (FORALL (i): i > sigma(0, k, KF * GP) IMPLIES a(i) = 0)}"
     poly_families nil)
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/"))
   nil))
 (compute_solvable_TCC6 0
  (compute_solvable_TCC6-4 nil 3622460611
   ("" (skeep*)
    (("" (assert) (("" (rewrite "poly_deriv_integer" +) nil nil)) nil))
    nil)
   ((real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (int_minus_int_is_int application-judgement "int" integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real 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)
    (poly_deriv_integer formula-decl nil poly_system_strategy nil)
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/"))
   nil)
  (compute_solvable_TCC6-3 nil 3622459268
   ("" (skeep*)
    (("" (replaces -1)
      (("" (expand "greatify_poly_rel" -6)
        (("" (expand "greatify_poly")
          (("" (lift-if)
            (("" (expand "*")
              (("" (typepred "n")
                (("" (inst - "i") (("" (ground) nil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/"))
   nil)
  (compute_solvable_TCC6-2 nil 3621608920
   ("" (skeep*)
    (("" (assert) (("" (rewrite "poly_deriv_integer" +) nil nil)) nil))
    nil)
   ((gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/"))
   nil)
  (compute_solvable_TCC6-1 nil 3621339345
   ("" (skeep*)
    (("" (replaces -1)
      (("" (expand "greatify_poly_rel" -6)
        (("" (lift-if)
          (("" (expand "*")
            (("" (typepred "n")
              (("" (inst - "i") (("" (ground) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/"))
   nil))
 (compute_solvable_TCC7 0
  (compute_solvable_TCC7-4 nil 3622460629
   ("" (skeep*)
    (("" (assert)
      (("" (label "igz" 6)
        (("" (expand "poly_deriv" +)
          (("" (copy "igz")
            (("" (case "NOT Qprod(Qdeg)=0")
              (("1" (assert)
                (("1" (mult-by 1 "Qdeg") (("1" (assertnil nil)) nil))
                nil)
               ("2" (replace -8 -1)
                (("2" (assert)
                  (("2" (typepred "Qprodlist")
                    (("2" (decompose-equality -3)
                      (("2" (inst - "Qdeg")
                        (("2" (assert)
                          (("2" (replaces -1 :dir rl)
                            (("2" (hide -1)
                              (("2"
                                (typepred
                                 "prod_polynomials(newp, n, LAMBDA i: 1, k)")
                                (("2"
                                  (hide -1)
                                  (("2"
                                    (split -)
                                    (("1" (assertnil nil)
                                     ("2"
                                      (replaces -5 1)
                                      (("2"
                                        (hide-all-but 1)
                                        (("2"
                                          (expand "greatify_poly_rel")
                                          (("2"
                                            (expand "greatify_poly")
                                            (("2"
                                              (skosimp*)
                                              (("2"
                                                (expand "*")
                                                (("2"
                                                  (typepred "n")
                                                  (("2"
                                                    (inst - "i!1")
                                                    (("2"
                                                      (lift-if)
                                                      (("2"
                                                        (ground)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (minus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (int_minus_int_is_int application-judgement "int" integers nil)
    (poly_deriv const-decl "real" polynomials "reals/")
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real 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)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (both_sides_times1 formula-decl nil real_props nil)
    (/= const-decl "boolean" notequal nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (even_times_int_is_even application-judgement "even_int" integers
     nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (lt_realorder name-judgement "RealOrder" real_orders "reals/")
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (greatify_poly_rel const-decl "[nat -> int]" poly_system_strategy
     nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (k skolem-const-decl "nat" poly_system_strategy nil)
    (i!1 skolem-const-decl "nat" poly_system_strategy nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (greatify_poly const-decl "[nat -> int]" poly_system_strategy nil)
    (PRED type-eq-decl nil defined_types nil)
    (list type-decl nil list_adt nil)
    (every adt-def-decl "boolean" list_adt nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (length def-decl "nat" list_props nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (T_low type-eq-decl nil sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (sigma def-decl "real" sigma "reals/")
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (> const-decl "bool" reals nil)
    (subrange type-eq-decl nil integers nil)
    (sequence type-eq-decl nil sequences nil)
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (T_low type-eq-decl nil product "reals/")
    (T_high type-eq-decl nil product "reals/")
    (product def-decl "real" product "reals/")
    (^ const-decl "real" exponentiation nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (prod_polynomials def-decl "{a |
         (FORALL (x):
            polynomial(a, sigma(0, k, KF * GP))(x) =
             product(0, k,
                     LAMBDA (j): polynomial(GF(j), KF(j))(x) ^ GP(j)))
          AND
          ((FORALL (i): i <= k AND GP(i) /= 0 IMPLIES GF(i)(KF(i)) /= 0)
            IMPLIES a(sigma(0, k, KF * GP)) /= 0)
           AND (FORALL (i): i > sigma(0, k, KF * GP) IMPLIES a(i) = 0)}"
     poly_families nil)
    (IF const-decl "[boolean, T, T -> T]" if_def nil)
    (< const-decl "bool" reals nil)
    (below type-eq-decl nil nat_types nil)
    (nth def-decl "T" list_props nil)
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/"))
   nil)
  (compute_solvable_TCC7-3 nil 3622459250
   ("" (skeep*)
    (("" (assert) (("" (rewrite "poly_deriv_integer" +) nil nil)) nil))
    nil)
   ((listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (gt_realorder name-judgement "RealOrder" real_orders "reals/"))
   nil)
  (compute_solvable_TCC7-2 nil 3621608951
   ("" (skeep*)
    (("" (assert)
      (("" (case "NOT Qdeg>=2")
        (("1" (typepred "Qprodlist")
          (("1" (replace -7 :dir rl)
            (("1" (replace -2)
              (("1" (expand "sigma" 1)
                (("1" (expand "sigma" 1)
                  (("1" (expand "*" 1 1)
                    (("1" (expand "*" 1 1)
                      (("1" (typepred "n")
                        (("1" (inst-cp - "k-1")
                          (("1" (inst - "k")
                            (("1" (flatten)
                              (("1"
                                (assert)
                                (("1"
                                  (case
                                   "sigma(0, k - 2, n * (LAMBDA i: 1)) >=0")
                                  (("1" (assertnil nil)
                                   ("2"
                                    (rewrite "sigma_ge_0")
                                    (("2"
                                      (skosimp*)
                                      (("2"
                                        (expand "*" 1)
                                        (("2" (assertnil nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (assert)
          (("2" (case "Qprod(Qdeg)/=0")
            (("1" (expand "poly_deriv" +)
              (("1" (assert)
                (("1" (flatten)
                  (("1" (mult-by 1 "Qdeg") (("1" (assertnil nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (flatten)
              (("2" (assert)
                (("2" (typepred "Qprodlist")
                  (("2" (replace -13 :dir rl)
                    (("2" (replace -3 :dir rl)
                      (("2" (replace -9 -4)
                        (("2" (replace -2)
                          (("2" (assert)
                            (("2"
                              (typepred
                               "prod_polynomials(newp, n, LAMBDA i: 1, k)")
                              (("2"
                                (assert)
                                (("2"
                                  (label "hp" 1)
                                  (("2"
                                    (skosimp*)
                                    (("2"
                                      (replace -10 -3)
                                      (("2"
                                        (expand "greatify_poly_rel" -3)
                                        (("2"
                                          (expand "*")
                                          (("2"
                                            (typepred "n")
                                            (("2"
                                              (inst - "i!1")
                                              (("2"
                                                (flatten)
                                                (("2"
                                                  (assert)
                                                  (("2"
                                                    (lift-if)
                                                    (("2"
                                                      (ground)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (prod_polynomials def-decl "{a |
         (FORALL (x):
            polynomial(a, sigma(0, k, KF * GP))(x) =
             product(0, k,
                     LAMBDA (j): polynomial(GF(j), KF(j))(x) ^ GP(j)))
          AND
          ((FORALL (i): i <= k AND GP(i) /= 0 IMPLIES GF(i)(KF(i)) /= 0)
            IMPLIES a(sigma(0, k, KF * GP)) /= 0)
           AND (FORALL (i): i > sigma(0, k, KF * GP) IMPLIES a(i) = 0)}"
     poly_families nil)
    (product def-decl "real" product "reals/")
    (T_high type-eq-decl nil product "reals/")
    (T_low type-eq-decl nil product "reals/")
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (sigma def-decl "real" sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (T_low type-eq-decl nil sigma "reals/")
    (list type-decl nil list_adt nil)
    (le_realorder name-judgement "RealOrder" real_orders "reals/")
    (poly_deriv const-decl "real" polynomials "reals/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/"))
   nil)
  (compute_solvable_TCC7-1 nil 3621339345
   ("" (skeep*) (("" (rewrite "poly_deriv_integer" 5) nil nil)) nil)
   ((listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/"))
   nil))
 (compute_solvable_TCC8 0
  (compute_solvable_TCC8-2 nil 3622459232
   ("" (skeep*)
    (("" (replaces -1 -7)
      (("" (copy -6)
        (("" (expand "greatify_poly_rel" -1)
          (("" (expand "greatify_poly")
            (("" (lift-if)
              (("" (expand "*" -1)
                (("" (typepred "n")
                  (("" (inst - "i") (("" (ground) nil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((greatify_poly_rel const-decl "[nat -> int]" poly_system_strategy
     nil)
    (> const-decl "bool" reals nil)
    (/= const-decl "boolean" notequal nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (upto nonempty-type-eq-decl nil naturalnumbers nil)
    (<= const-decl "bool" reals nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (minus_int_is_int application-judgement "int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (* const-decl "[T -> real]" real_fun_ops "reals/")
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (greatify_poly const-decl "[nat -> int]" poly_system_strategy nil)
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/"))
   nil)
  (compute_solvable_TCC8-1 nil 3621340773
   ("" (skeep*)
    (("" (assert)
      (("" (copy -7)
        (("" (replace -2 -1)
          (("" (expand "greatify_poly_rel" -1)
            (("" (expand "*")
              (("" (lift-if)
                (("" (typepred "n")
                  (("" (inst - "i") (("" (ground) nil nil)) nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((gt_realorder name-judgement "RealOrder" real_orders "reals/")
    (ge_realorder name-judgement "RealOrder" real_orders "reals/")
    (listn_0 name-judgement "listn[real](0)" polynomial_division
     "Sturm/")
    (listn_0 name-judgement "listn[int](0)" gcd_coeff "Sturm/"))
   nil))
 (compute_solvable_def 0
  (compute_solvable_def-2 nil 3621611318
   ("" (skeep)
    (("" (label "ndef" -1)
      (("" (case "k = 0")
        (("1" (replace -1)
          (("1" (expand "compute_solvable")
            (("1" (lemma "compute_solvable_single_def")
              (("1" (inst - "p(0)" "n(0)")
                (("1" (assert)
                  (("1" (split -)
                    (("1" (inst - "RelF6(0)")
                      (("1" (replaces -1 :dir rl)
                        (("1" (ground)
                          (("1" (skosimp*)
                            (("1" (inst + "x!1")
                              (("1" (inst - "0"nil nil)) nil))
                            nil)
                           ("2" (skosimp*)
                            (("2" (inst + "x!1")
                              (("2"
                                (skosimp*)
                                (("2" (assertnil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil)
                     ("2" (inst - "0") (("2" (assertnil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (expand "compute_solvable" :assert? none)
          (("2" (name "newp" "greatify_poly_rel(p, RelF6)")
            (("2" (replace -1)
              (("2" (name "newRel" "greatify_rel(RelF6)")
                (("2" (replace -1)
                  (("2" (replace 1)
                    (("2" (case "(EXISTS (i:upto(k)): newRel(i)=0)")
                      (("1" (name "fe" "first_eq(newRel, k)")
                        (("1" (assert)
                          (("1" (replace -2)
                            (("1" (replace -1)
                              (("1"
                                (case "NOT fe<=k")
                                (("1"
                                  (typepred "fe")
                                  (("1"
                                    (assert)
                                    (("1"
                                      (skosimp*)
                                      (("1"
                                        (inst - "i!1")
                                        (("1" (assertnil nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (assert)
                                  (("2"
                                    (typepred "fe")
                                    (("2"
                                      (hide -1)
                                      (("2"
                                        (assert)
                                        (("2"
                                          (flatten)
                                          (("2"
                                            (typepred
                                             "sturm_tarski_faster(k - 1,
                                                                                           newp(fe),
                                                                                           n(fe),
                                                                                           LAMBDA
                                                                                           (i):
                                                                                           IF i < fe
                                                                                           THEN newp(i)
                                                                                           ELSE newp(1 + i)
                                                                                           ENDIF,
                                                                                           LAMBDA
                                                                                           (i):
                                                                                           IF i < fe
                                                                                           THEN n(i)
                                                                                           ELSE n(1 + i)
                                                                                           ENDIF,
                                                                                           LAMBDA
                                                                                           (i):
                                                                                           IF i < fe
                                                                                           THEN newRel(i)
                                                                                           ELSE newRel(1 + i)
                                                                                           ENDIF)")
                                            (("1"
                                              (hide (-2 -3))
                                              (("1"
                                                (replaces -1)
                                                (("1"
                                                  (expand "NSol_all" +)
                                                  (("1"
                                                    (lemma
                                                     "empty_card[real]")
                                                    (("1"
                                                      (inst?)
                                                      (("1"
                                                        (replaces
                                                         -1
                                                         :dir
                                                         rl)
                                                        (("1"
                                                          (expand
                                                           "empty?")
                                                          (("1"
                                                            (expand
                                                             "member")
                                                            (("1"
                                                              (ground)
                                                              (("1"
                                                                (skosimp*)
                                                                (("1"
                                                                  (inst
                                                                   -2
                                                                   "x!1")
                                                                  (("1"
                                                                    (expand
                                                                     "Sol_all")
                                                                    (("1"
                                                                      (split
                                                                       1)
                                                                      (("1"
                                                                        (inst
                                                                         -
                                                                         "fe")
                                                                        (("1"
                                                                          (expand
                                                                           "newRel"
                                                                           -2)
                                                                          (("1"
                                                                            (expand
                                                                             "greatify_rel"
                                                                             -2)
                                                                            (("1"
                                                                              (lift-if)
                                                                              (("1"
                                                                                (ground)
                                                                                (("1"
                                                                                  (replace
                                                                                   -1)
                                                                                  (("1"
                                                                                    (expand
                                                                                     "rel5"
                                                                                     -2)
                                                                                    (("1"
                                                                                      (expand
                                                                                       "newp"
                                                                                       +)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "greatify_poly_rel"
                                                                                         +)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "greatify_poly")
                                                                                          (("1"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (skosimp*)
                                                                        (("2"
                                                                          (case
                                                                           "i!2 < fe")
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (inst
                                                                               -
                                                                               "i!2")
                                                                              (("1"
                                                                                (expand
                                                                                 "rel5"
                                                                                 -3)
                                                                                (("1"
                                                                                  (expand
                                                                                   "newRel"
                                                                                   +)
                                                                                  (("1"
                                                                                    (expand
                                                                                     "greatify_rel"
                                                                                     +)
                                                                                    (("1"
                                                                                      (expand
                                                                                       "newp"
                                                                                       +)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "greatify_poly_rel"
                                                                                         +)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "greatify_poly")
                                                                                          (("1"
                                                                                            (lift-if)
                                                                                            (("1"
                                                                                              (lift-if)
                                                                                              (("1"
                                                                                                (lift-if)
                                                                                                (("1"
                                                                                                  (lift-if)
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    (("1"
                                                                                                      (ground)
                                                                                                      (("1"
                                                                                                        (rewrite
                                                                                                         "scal_polynomial2")
                                                                                                        (("1"
                                                                                                          (assert)
                                                                                                          nil
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (rewrite
                                                                                                         "scal_polynomial2")
                                                                                                        (("2"
                                                                                                          (assert)
                                                                                                          nil
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (assert)
                                                                            (("2"
                                                                              (inst
                                                                               -
                                                                               "1+i!2")
                                                                              (("2"
                                                                                (assert)
                                                                                (("2"
                                                                                  (expand
                                                                                   "rel5"
                                                                                   -2)
                                                                                  (("2"
                                                                                    (expand
                                                                                     "newRel"
                                                                                     +)
                                                                                    (("2"
                                                                                      (expand
                                                                                       "newp"
                                                                                       +)
                                                                                      (("2"
                                                                                        (expand
                                                                                         "greatify_rel"
                                                                                         +)
                                                                                        (("2"
                                                                                          (expand
                                                                                           "greatify_poly_rel"
                                                                                           +)
                                                                                          (("2"
                                                                                            (expand
                                                                                             "greatify_poly")
                                                                                            (("2"
                                                                                              (lift-if)
                                                                                              (("2"
                                                                                                (assert)
                                                                                                (("2"
                                                                                                  (rewrite
                                                                                                   "scal_polynomial2")
                                                                                                  (("2"
                                                                                                    (ground)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (skosimp*)
                                                                (("2"
                                                                  (inst
                                                                   +
                                                                   "x!1")
                                                                  (("2"
                                                                    (case
                                                                     "NOT RelF6(fe) = 0")
                                                                    (("1"
                                                                      (expand
                                                                       "newRel"
                                                                       -2)
                                                                      (("1"
                                                                        (expand
                                                                         "greatify_rel"
                                                                         -2)
                                                                        (("1"
                                                                          (lift-if)
                                                                          (("1"
                                                                            (ground)
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (skeep)
                                                                      (("2"
                                                                        (case
                                                                         "j = fe")
                                                                        (("1"
                                                                          (replace
                                                                           -1)
                                                                          (("1"
                                                                            (replace
                                                                             -2)
                                                                            (("1"
                                                                              (expand
                                                                               "rel5"
                                                                               1)
                                                                              (("1"
                                                                                (expand
                                                                                 "Sol_all"
                                                                                 -3)
                                                                                (("1"
                                                                                  (flatten)
                                                                                  (("1"
                                                                                    (expand
                                                                                     "newp"
                                                                                     -3)
                                                                                    (("1"
                                                                                      (expand
                                                                                       "greatify_poly_rel"
                                                                                       -3)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "greatify_poly")
                                                                                        (("1"
                                                                                          (assert)
                                                                                          nil
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (case
                                                                           "j < fe")
                                                                          (("1"
                                                                            (expand
                                                                             "Sol_all")
                                                                            (("1"
                                                                              (flatten)
                                                                              (("1"
                                                                                (inst
                                                                                 -
                                                                                 "j")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (expand
                                                                                     "newp"
                                                                                     -4)
                                                                                    (("1"
                                                                                      (expand
                                                                                       "newRel"
                                                                                       -4)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "greatify_poly_rel"
                                                                                         -4)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "greatify_poly")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "greatify_rel"
                                                                                             -4)
                                                                                            (("1"
                                                                                              (assert)
                                                                                              (("1"
                                                                                                (lift-if)
                                                                                                (("1"
                                                                                                  (lift-if)
                                                                                                  (("1"
                                                                                                    (lift-if)
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "rel5"
                                                                                                         +)
                                                                                                        (("1"
                                                                                                          (rewrite
                                                                                                           "scal_polynomial2")
                                                                                                          (("1"
                                                                                                            (ground)
                                                                                                            nil
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (expand
                                                                             "Sol_all")
                                                                            (("2"
                                                                              (flatten)
                                                                              (("2"
                                                                                (inst
                                                                                 -
                                                                                 "j-1")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (expand
                                                                                     "newp"
                                                                                     -3)
                                                                                    (("1"
                                                                                      (expand
                                                                                       "newRel"
                                                                                       -3)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "greatify_rel"
                                                                                         -3)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "greatify_poly_rel"
                                                                                           -3)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "greatify_poly")
                                                                                            (("1"
                                                                                              (assert)
                                                                                              (("1"
                                                                                                (lift-if)
                                                                                                (("1"
                                                                                                  (lift-if)
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    (("1"
                                                                                                      (expand
                                                                                                       "rel5"
                                                                                                       +)
                                                                                                      (("1"
                                                                                                        (rewrite
                                                                                                         "scal_polynomial2")
                                                                                                        (("1"
                                                                                                          (ground)
                                                                                                          nil
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (assert)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("2"
                                              (hide 3)
                                              (("2"
                                                (skosimp*)
                                                (("2"
                                                  (inst-cp - "i!1")
                                                  (("2"
                                                    (inst - "1+i!1")
                                                    (("2"
                                                      (lift-if)
                                                      (("2"
                                                        (expand
                                                         "newp"
                                                         -1)
                                                        (("2"
                                                          (expand
                                                           "greatify_poly_rel"
                                                           -1)
                                                          (("2"
                                                            (expand
                                                             "greatify_poly")
                                                            (("2"
                                                              (expand
                                                               "*"
                                                               -1)
                                                              (("2"
                                                                (lift-if)
                                                                (("2"
                                                                  (lift-if)
                                                                  (("2"
                                                                    (assert)
                                                                    (("2"
                                                                      (inst-cp
                                                                       -
                                                                       "i!1")
                                                                      (("2"
                                                                        (flatten)
                                                                        (("2"
                                                                          (inst
                                                                           -
                                                                           "1+i!1")
                                                                          (("2"
                                                                            (flatten)
                                                                            (("2"
                                                                              (ground)
                                                                              nil
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2"
                        (name "Qprodlist"
                              "prod_polynomials_list(newp, n, LAMBDA i: 1, k)")
                        (("2" (name "Qdeg" "length(Qprodlist) - 1")
                          (("2"
                            (name "Qprod" "LAMBDA (i):
                                                                                         IF i < length(Qprodlist) THEN nth(Qprodlist, i)
                                                                                         ELSE 0
                                                                                         ENDIF")
                            (("2" (assert)
                              (("2"
                                (replace -3)
                                (("2"
                                  (replace -2)
                                  (("2"
                                    (replace -1)
                                    (("2"
                                      (case
                                       "NOT length(Qprodlist) - 2 = Qdeg -1")
                                      (("1" (assertnil nil)
                                       ("2"
                                        (replace -1)
                                        (("2"
                                          (assert)
                                          (("2"
                                            (lift-if)
                                            (("2"
                                              (replace 1)
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (split +)
                                                  (("1"
                                                    (flatten)
                                                    (("1"
                                                      (case
                                                       "NOT Qdeg>=2")
                                                      (("1"
                                                        (assert)
                                                        (("1"
                                                          (typepred
                                                           "Qprodlist")
                                                          (("1"
                                                            (replace
                                                             -2)
                                                            (("1"
                                                              (replace
                                                               -7
                                                               1
                                                               :dir
                                                               rl)
                                                              (("1"
                                                                (expand
                                                                 "sigma")
                                                                (("1"
                                                                  (expand
                                                                   "sigma")
                                                                  (("1"
                                                                    (expand
                                                                     "*"
                                                                     1
                                                                     1)
                                                                    (("1"
                                                                      (expand
                                                                       "*"
                                                                       1
                                                                       1)
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (copy
                                                                           "ndef")
                                                                          (("1"
                                                                            (inst-cp
                                                                             -
                                                                             "k")
                                                                            (("1"
                                                                              (inst
                                                                               -
                                                                               "k-1")
                                                                              (("1"
                                                                                (flatten)
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (lemma
                                                                                     "sigma_ge_0")
                                                                                    (("1"
                                                                                      (inst?)
                                                                                      (("1"
                                                                                        (assert)
                                                                                        (("1"
                                                                                          (skosimp*)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "*")
                                                                                            (("1"
                                                                                              (assert)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (assert)
                                                        (("2"
                                                          (skeep)
                                                          (("2"
                                                            (case
                                                             "EXISTS (pz:upto(k)): polynomial(p(pz),n(pz))(x) = 0")
                                                            (("1"
                                                              (skeep -)
                                                              (("1"
                                                                (case
                                                                 "NOT newRel(pz)=4")
                                                                (("1"
                                                                  (expand
                                                                   "newRel"
                                                                   1)
                                                                  (("1"
                                                                    (inst
                                                                     -
                                                                     "pz")
                                                                    (("1"
                                                                      (inst
                                                                       +
                                                                       "pz")
                                                                      (("1"
                                                                        (expand
                                                                         "rel5"
                                                                         -3)
                                                                        (("1"
                                                                          (expand
                                                                           "greatify_rel"
                                                                           1)
                                                                          (("1"
                                                                            (lift-if)
                                                                            (("1"
                                                                              (ground)
                                                                              (("1"
                                                                                (expand
                                                                                 "newRel"
                                                                                 6)
                                                                                (("1"
                                                                                  (expand
                                                                                   "greatify_rel"
                                                                                   6)
                                                                                  (("1"
                                                                                    (propax)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil)
                                                                 ("2"
                                                                  (typepred
                                                                   "sturm_tarski_faster(k, Qprod, Qdeg, newp, n, newRel)")
                                                                  (("2"
                                                                    (hide
                                                                     (-2
                                                                      -3))
                                                                    (("2"
                                                                      (replaces
                                                                       -1)
                                                                      (("2"
                                                                        (expand
                                                                         "NSol_all"
                                                                         -)
                                                                        (("2"
                                                                          (lemma
                                                                           "empty_card[real]")
                                                                          (("2"
                                                                            (inst?)
                                                                            (("2"
                                                                              (assert)
                                                                              (("2"
                                                                                (expand
                                                                                 "empty?"
                                                                                 -1)
                                                                                (("2"
                                                                                  (expand
                                                                                   "member")
                                                                                  (("2"
                                                                                    (inst
                                                                                     -
                                                                                     "x")
                                                                                    (("2"
                                                                                      (expand
                                                                                       "Sol_all"
                                                                                       +)
                                                                                      (("2"
                                                                                        (split
                                                                                         1)
                                                                                        (("1"
                                                                                          (typepred
                                                                                           "Qprodlist")
                                                                                          (("1"
                                                                                            (replace
                                                                                             -11)
                                                                                            (("1"
                                                                                              (typepred
                                                                                               "prod_polynomials(newp, n, LAMBDA i: 1, k)")
                                                                                              (("1"
                                                                                                (inst
                                                                                                 -
                                                                                                 "x")
                                                                                                (("1"
                                                                                                  (replace
                                                                                                   -6)
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -5
                                                                                                     :dir
                                                                                                     rl)
                                                                                                    (("1"
                                                                                                      (lemma
                                                                                                       "Qdeg")
                                                                                                      (("1"
                                                                                                        (replaces
                                                                                                         -1
                                                                                                         -2
                                                                                                         :dir
                                                                                                         rl)
                                                                                                        (("1"
                                                                                                          (replaces
                                                                                                           -1
                                                                                                           +)
                                                                                                          (("1"
                                                                                                            (lemma
                                                                                                             "product_eq_zero[nat]")
                                                                                                            (("1"
                                                                                                              (inst?)
                                                                                                              (("1"
                                                                                                                (assert)
                                                                                                                (("1"
                                                                                                                  (inst
                                                                                                                   +
                                                                                                                   "pz")
                                                                                                                  (("1"
                                                                                                                    (expand
                                                                                                                     "^"
                                                                                                                     1)
                                                                                                                    (("1"
                                                                                                                      (expand
                                                                                                                       "expt")
                                                                                                                      (("1"
                                                                                                                        (expand
                                                                                                                         "expt")
                                                                                                                        (("1"
                                                                                                                          (expand
                                                                                                                           "newp"
                                                                                                                           +)
                                                                                                                          (("1"
                                                                                                                            (expand
                                                                                                                             "greatify_poly_rel"
                                                                                                                             1)
                                                                                                                            (("1"
                                                                                                                              (expand
                                                                                                                               "greatify_poly")
                                                                                                                              (("1"
                                                                                                                                (lift-if)
                                                                                                                                (("1"
                                                                                                                                  (split
                                                                                                                                   1)
                                                                                                                                  (("1"
                                                                                                                                    (flatten)
                                                                                                                                    (("1"
                                                                                                                                      (rewrite
                                                                                                                                       "scal_polynomial2")
                                                                                                                                      (("1"
                                                                                                                                        (assert)
                                                                                                                                        nil
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil)
                                                                                                                                   ("2"
                                                                                                                                    (flatten)
                                                                                                                                    nil
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (skosimp*)
                                                                                          (("2"
                                                                                            (inst
                                                                                             -
                                                                                             "i!1")
                                                                                            (("2"
                                                                                              (hide
                                                                                               (2
                                                                                                3))
                                                                                              (("2"
                                                                                                (expand
                                                                                                 "rel5")
                                                                                                (("2"
                                                                                                  (expand
                                                                                                   "newp"
                                                                                                   +)
                                                                                                  (("2"
                                                                                                    (expand
                                                                                                     "newRel"
                                                                                                     +)
                                                                                                    (("2"
                                                                                                      (expand
                                                                                                       "greatify_poly_rel"
                                                                                                       +)
                                                                                                      (("2"
                                                                                                        (expand
                                                                                                         "greatify_poly")
                                                                                                        (("2"
                                                                                                          (expand
                                                                                                           "greatify_rel"
                                                                                                           +)
                                                                                                          (("2"
                                                                                                            (hide
                                                                                                             2)
                                                                                                            (("2"
                                                                                                              (lift-if)
                                                                                                              (("2"
                                                                                                                (assert)
                                                                                                                (("2"
                                                                                                                  (ground)
                                                                                                                  (("1"
                                                                                                                    (rewrite
                                                                                                                     "scal_polynomial2")
                                                                                                                    (("1"
                                                                                                                      (assert)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil)
                                                                                                                   ("2"
                                                                                                                    (rewrite
                                                                                                                     "scal_polynomial2")
                                                                                                                    (("2"
                                                                                                                      (assert)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil)
                                                             ("2"
                                                              (name
                                                               "SS"
                                                               "LAMBDA (i:nat): IF newRel(i)/=3 OR (newRel(i)=3 AND polynomial(newp(i),n(i))(x)>=0) THEN 1 ELSE (-1) ENDIF")
                                                              (("2"
                                                                (name
                                                                 "NP"
                                                                 "LAMBDA (i:nat): SS(i)*newp(i)")
                                                                (("2"
                                                                  (lemma
                                                                   "strict_poly_system_solvable")
                                                                  (("2"
                                                                    (inst
                                                                     -
                                                                     "k"
                                                                     "n"
                                                                     "NP")
                                                                    (("1"
                                                                      (assert)
                                                                      (("1"
                                                                        (split
                                                                         -1)
                                                                        (("1"
                                                                          (flatten)
                                                                          (("1"
                                                                            (hide
                                                                             -2)
                                                                            (("1"
                                                                              (split
                                                                               -1)
                                                                              (("1"
                                                                                (hide
                                                                                 (1
                                                                                  3))
                                                                                (("1"
                                                                                  (skeep)
                                                                                  (("1"
                                                                                    (inst
                                                                                     -
                                                                                     "j")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "NP"
                                                                                         -1)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "*"
                                                                                           -1)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "SS"
                                                                                             -1)
                                                                                            (("1"
                                                                                              (lift-if)
                                                                                              (("1"
                                                                                                (split
                                                                                                 -1)
                                                                                                (("1"
                                                                                                  (flatten)
                                                                                                  (("1"
                                                                                                    (expand
                                                                                                     "newRel"
                                                                                                     1)
                                                                                                    (("1"
                                                                                                      (expand
                                                                                                       "greatify_rel"
                                                                                                       1)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "rel5"
                                                                                                         1)
                                                                                                        (("1"
                                                                                                          (inst
                                                                                                           +
                                                                                                           "j")
                                                                                                          (("1"
                                                                                                            (copy
                                                                                                             2)
                                                                                                            (("1"
                                                                                                              (expand
                                                                                                               "newRel"
                                                                                                               1)
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "greatify_rel"
                                                                                                                 1)
                                                                                                                (("1"
                                                                                                                  (lift-if)
                                                                                                                  (("1"
                                                                                                                    (ground)
                                                                                                                    nil
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (flatten)
                                                                                                  (("2"
                                                                                                    (replace
                                                                                                     -1
                                                                                                     2)
                                                                                                    (("2"
                                                                                                      (expand
                                                                                                       "rel5"
                                                                                                       2)
                                                                                                      (("2"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil)
                                                                               ("2"
                                                                                (hide
                                                                                 (1
                                                                                  2))
                                                                                (("2"
                                                                                  (skeep)
                                                                                  (("2"
                                                                                    (inst
                                                                                     -
                                                                                     "j")
                                                                                    (("2"
                                                                                      (inst
                                                                                       +
                                                                                       "j")
                                                                                      (("2"
                                                                                        (lemma
                                                                                         "even_or_odd")
                                                                                        (("2"
                                                                                          (inst?)
                                                                                          (("2"
                                                                                            (assert)
                                                                                            (("2"
                                                                                              (assert)
                                                                                              (("2"
                                                                                                (lift-if)
                                                                                                (("2"
                                                                                                  (expand
                                                                                                   "NP"
                                                                                                   -2)
                                                                                                  (("2"
                                                                                                    (expand
                                                                                                     "SS"
                                                                                                     -2)
                                                                                                    (("2"
                                                                                                      (lift-if)
                                                                                                      (("2"
                                                                                                        (lift-if)
                                                                                                        (("2"
                                                                                                          (expand
                                                                                                           "*")
                                                                                                          (("2"
                                                                                                            (split
                                                                                                             -2)
                                                                                                            (("1"
                                                                                                              (flatten)
                                                                                                              (("1"
                                                                                                                (assert)
                                                                                                                (("1"
                                                                                                                  (hide
                                                                                                                   -3)
                                                                                                                  (("1"
                                                                                                                    (split
                                                                                                                     -)
                                                                                                                    (("1"
                                                                                                                      (flatten)
                                                                                                                      (("1"
                                                                                                                        (expand
                                                                                                                         "newRel"
                                                                                                                         2)
                                                                                                                        (("1"
                                                                                                                          (expand
                                                                                                                           "greatify_rel"
                                                                                                                           2)
                                                                                                                          (("1"
                                                                                                                            (expand
                                                                                                                             "rel5"
                                                                                                                             +)
                                                                                                                            (("1"
                                                                                                                              (ground)
                                                                                                                              (("1"
                                                                                                                                (expand
                                                                                                                                 "newRel"
                                                                                                                                 +)
                                                                                                                                (("1"
                                                                                                                                  (expand
                                                                                                                                   "greatify_rel"
                                                                                                                                   +)
                                                                                                                                  (("1"
                                                                                                                                    (propax)
                                                                                                                                    nil
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil)
                                                                                                                               ("2"
                                                                                                                                (expand
                                                                                                                                 "newRel"
                                                                                                                                 +)
                                                                                                                                (("2"
                                                                                                                                  (expand
                                                                                                                                   "greatify_rel"
                                                                                                                                   +)
                                                                                                                                  (("2"
                                                                                                                                    (propax)
                                                                                                                                    nil
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil)
                                                                                                                     ("2"
                                                                                                                      (flatten)
                                                                                                                      (("2"
                                                                                                                        (assert)
                                                                                                                        (("2"
                                                                                                                          (replace
                                                                                                                           -1
                                                                                                                           +)
                                                                                                                          (("2"
                                                                                                                            (expand
                                                                                                                             "rel5"
                                                                                                                             +)
                                                                                                                            (("2"
                                                                                                                              (propax)
                                                                                                                              nil
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil)
                                                                                                             ("2"
                                                                                                              (flatten)
                                                                                                              (("2"
                                                                                                                (assert)
                                                                                                                (("2"
                                                                                                                  (hide
                                                                                                                   -2)
                                                                                                                  (("2"
                                                                                                                    (split
                                                                                                                     -)
                                                                                                                    (("1"
                                                                                                                      (flatten)
                                                                                                                      (("1"
                                                                                                                        (expand
                                                                                                                         "newRel"
                                                                                                                         +)
                                                                                                                        (("1"
                                                                                                                          (expand
                                                                                                                           "greatify_rel"
                                                                                                                           +)
                                                                                                                          (("1"
                                                                                                                            (lift-if)
                                                                                                                            (("1"
                                                                                                                              (expand
                                                                                                                               "rel5"
                                                                                                                               +)
                                                                                                                              (("1"
                                                                                                                                (assert)
                                                                                                                                (("1"
                                                                                                                                  (ground)
                                                                                                                                  nil
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil)
                                                                                                                     ("2"
                                                                                                                      (flatten)
                                                                                                                      (("2"
                                                                                                                        (replace
                                                                                                                         -1)
                                                                                                                        (("2"
                                                                                                                          (assert)
                                                                                                                          (("2"
                                                                                                                            (expand
                                                                                                                             "rel5"
                                                                                                                             +)
                                                                                                                            (("2"
                                                                                                                              (propax)
                                                                                                                              nil
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil)
                                                                               ("3"
                                                                                (skosimp
                                                                                 -1)
                                                                                (("3"
                                                                                  (typepred
                                                                                   "sturm_tarski_faster(k,
                                                         poly_deriv(Qprod),
                                                         Qdeg - 1,
                                                         newp,
                                                         n,
                                                         newRel)")
                                                                                  (("3"
                                                                                    (hide
                                                                                     (-2
                                                                                      -3))
                                                                                    (("3"
                                                                                      (replaces
                                                                                       -1)
                                                                                      (("3"
                                                                                        (expand
                                                                                         "NSol_all"
                                                                                         -9)
                                                                                        (("3"
                                                                                          (lemma
                                                                                           "empty_card[real]")
                                                                                          (("3"
                                                                                            (inst?)
                                                                                            (("3"
                                                                                              (assert)
                                                                                              (("3"
                                                                                                (expand
                                                                                                 "empty?"
                                                                                                 -1)
                                                                                                (("3"
                                                                                                  (expand
                                                                                                   "member")
                                                                                                  (("3"
                                                                                                    (inst
                                                                                                     -
                                                                                                     "x!1")
                                                                                                    (("3"
                                                                                                      (expand
                                                                                                       "Sol_all"
                                                                                                       1)
                                                                                                      (("3"
                                                                                                        (assert)
                                                                                                        (("3"
                                                                                                          (split
                                                                                                           1)
                                                                                                          (("1"
                                                                                                            (case
                                                                                                             "EXISTS (nzr: nzreal): nzr*prod_polynomials(NP,
                                                                        n,
                                                                        (LAMBDA (i: nat): 1),
                                                                        k) = Qprod")
                                                                                                            (("1"
                                                                                                              (skeep
                                                                                                               -1)
                                                                                                              (("1"
                                                                                                                (replace
                                                                                                                 -1
                                                                                                                 1
                                                                                                                 :dir
                                                                                                                 rl)
                                                                                                                (("1"
                                                                                                                  (case
                                                                                                                   "Qdeg-1 = sigma(0, k, n) - 1")
                                                                                                                  (("1"
                                                                                                                    (replace
                                                                                                                     -1
                                                                                                                     :dir
                                                                                                                     rl)
                                                                                                                    (("1"
                                                                                                                      (rewrite
                                                                                                                       "poly_deriv_scal")
                                                                                                                      (("1"
                                                                                                                        (rewrite
                                                                                                                         "scal_polynomial2")
                                                                                                                        (("1"
                                                                                                                          (assert)
                                                                                                                          nil
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil)
                                                                                                                   ("2"
                                                                                                                    (hide
                                                                                                                     2)
                                                                                                                    (("2"
                                                                                                                      (typepred
                                                                                                                       "Qprodlist")
                                                                                                                      (("2"
                                                                                                                        (assert)
                                                                                                                        (("2"
                                                                                                                          (case
                                                                                                                           "n = n*(LAMBDA (i): 1)")
                                                                                                                          (("1"
                                                                                                                            (assert)
                                                                                                                            nil
                                                                                                                            nil)
                                                                                                                           ("2"
                                                                                                                            (decompose-equality
                                                                                                                             1)
                                                                                                                            (("1"
                                                                                                                              (expand
                                                                                                                               "*"
                                                                                                                               1)
                                                                                                                              (("1"
                                                                                                                                (propax)
                                                                                                                                nil
                                                                                                                                nil))
                                                                                                                              nil)
                                                                                                                             ("2"
                                                                                                                              (skosimp*)
                                                                                                                              (("2"
                                                                                                                                (expand
                                                                                                                                 "*"
                                                                                                                                 1)
                                                                                                                                (("2"
                                                                                                                                  (assert)
                                                                                                                                  nil
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil)
                                                                                                             ("2"
                                                                                                              (typepred
                                                                                                               "Qprodlist")
                                                                                                              (("2"
                                                                                                                (replace
                                                                                                                 -14)
                                                                                                                (("2"
                                                                                                                  (replace
                                                                                                                   -3
                                                                                                                   1
                                                                                                                   :dir
                                                                                                                   rl)
                                                                                                                  (("2"
                                                                                                                    (case
                                                                                                                     "FORALL (dd:nat): dd<=k IMPLIES EXISTS (nzr: nzreal):
                                     nzr * prod_polynomials(NP, n, (LAMBDA (i: nat): 1), dd) =
                                      prod_polynomials(newp, n, LAMBDA i: 1, dd)")
                                                                                                                    (("1"
                                                                                                                      (inst
                                                                                                                       -
                                                                                                                       "k")
                                                                                                                      (("1"
                                                                                                                        (assert)
                                                                                                                        nil
                                                                                                                        nil))
                                                                                                                      nil)
                                                                                                                     ("2"
                                                                                                                      (hide
                                                                                                                       2)
                                                                                                                      (("2"
                                                                                                                        (induct
                                                                                                                         "dd")
                                                                                                                        (("1"
                                                                                                                          (assert)
                                                                                                                          (("1"
                                                                                                                            (inst
                                                                                                                             +
                                                                                                                             "SS(0)")
                                                                                                                            (("1"
                                                                                                                              (decompose-equality
                                                                                                                               1)
                                                                                                                              (("1"
                                                                                                                                (expand
                                                                                                                                 "*"
                                                                                                                                 1)
                                                                                                                                (("1"
                                                                                                                                  (expand
                                                                                                                                   "prod_polynomials"
                                                                                                                                   1)
                                                                                                                                  (("1"
                                                                                                                                    (expand
                                                                                                                                     "NP"
                                                                                                                                     1)
                                                                                                                                    (("1"
                                                                                                                                      (expand
                                                                                                                                       "*"
                                                                                                                                       1)
                                                                                                                                      (("1"
                                                                                                                                        (expand
                                                                                                                                         "SS"
                                                                                                                                         1)
                                                                                                                                        (("1"
                                                                                                                                          (lift-if)
                                                                                                                                          (("1"
                                                                                                                                            (lift-if)
                                                                                                                                            (("1"
                                                                                                                                              (lift-if)
                                                                                                                                              (("1"
                                                                                                                                                (assert)
                                                                                                                                                nil
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil)
                                                                                                                         ("2"
                                                                                                                          (skolem
                                                                                                                           1
                                                                                                                           "d")
                                                                                                                          (("2"
                                                                                                                            (assert)
                                                                                                                            (("2"
                                                                                                                              (flatten)
                                                                                                                              (("2"
                                                                                                                                (assert)
                                                                                                                                (("2"
                                                                                                                                  (skeep
                                                                                                                                   -)
                                                                                                                                  (("2"
                                                                                                                                    (inst
                                                                                                                                     +
                                                                                                                                     "SS(1+d)*nzr")
                                                                                                                                    (("2"
                                                                                                                                      (decompose-equality
                                                                                                                                       +)
                                                                                                                                      (("2"
                                                                                                                                        (expand
                                                                                                                                         "prod_polynomials"
                                                                                                                                         +)
                                                                                                                                        (("2"
                                                                                                                                          (expand
                                                                                                                                           "*"
                                                                                                                                           1)
                                                                                                                                          (("2"
                                                                                                                                            (replace
                                                                                                                                             -1
                                                                                                                                             +
                                                                                                                                             :dir
                                                                                                                                             rl)
                                                                                                                                            (("2"
                                                                                                                                              (expand
                                                                                                                                               "polynomial_prod"
                                                                                                                                               1)
                                                                                                                                              (("2"
                                                                                                                                                (rewrite
                                                                                                                                                 "sigma_scal"
                                                                                                                                                 :dir
                                                                                                                                                 rl)
                                                                                                                                                (("1"
                                                                                                                                                  (rewrite
                                                                                                                                                   "sigma_scal_right"
                                                                                                                                                   :dir
                                                                                                                                                   rl)
                                                                                                                                                  (("1"
                                                                                                                                                    (rewrite
                                                                                                                                                     "sigma_eq")
                                                                                                                                                    (("1"
                                                                                                                                                      (hide
                                                                                                                                                       2)
                                                                                                                                                      (("1"
                                                                                                                                                        (skosimp*)
                                                                                                                                                        (("1"
                                                                                                                                                          (expand
                                                                                                                                                           "NP"
                                                                                                                                                           +
                                                                                                                                                           2)
                                                                                                                                                          (("1"
                                                                                                                                                            (lift-if)
                                                                                                                                                            (("1"
                                                                                                                                                              (assert)
                                                                                                                                                              (("1"
                                                                                                                                                                (expand
                                                                                                                                                                 "SS"
                                                                                                                                                                 1)
                                                                                                                                                                (("1"
                                                                                                                                                                  (lift-if)
                                                                                                                                                                  (("1"
                                                                                                                                                                    (assert)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (expand
                                                                                                                                                                       "*"
                                                                                                                                                                       1)
                                                                                                                                                                      (("1"
                                                                                                                                                                        (propax)
                                                                                                                                                                        nil
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil)
                                                                                                                                                     ("2"
                                                                                                                                                      (hide
                                                                                                                                                       2)
                                                                                                                                                      (("2"
                                                                                                                                                        (hide-all-but
                                                                                                                                                         1)
                                                                                                                                                        (("2"
                                                                                                                                                          (case
                                                                                                                                                           "FORALL (gg:nat): rational_pred(sigma[nat](0, gg, LAMBDA (x: nat): n(x))) AND
                                         integer_pred(sigma[nat](0, gg, LAMBDA (x: nat): n(x)))")
                                                                                                                                                          (("1"
                                                                                                                                                            (inst
                                                                                                                                                             -
                                                                                                                                                             "d")
                                                                                                                                                            nil
                                                                                                                                                            nil)
                                                                                                                                                           ("2"
                                                                                                                                                            (hide
                                                                                                                                                             2)
                                                                                                                                                            (("2"
                                                                                                                                                              (induct
                                                                                                                                                               "gg")
                                                                                                                                                              (("1"
                                                                                                                                                                (grind)
                                                                                                                                                                nil
                                                                                                                                                                nil)
                                                                                                                                                               ("2"
                                                                                                                                                                (grind)
                                                                                                                                                                nil
                                                                                                                                                                nil)
                                                                                                                                                               ("3"
                                                                                                                                                                (skosimp*)
                                                                                                                                                                (("3"
                                                                                                                                                                  (assert)
                                                                                                                                                                  nil
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil)
                                                                                                                                                     ("3"
                                                                                                                                                      (hide
                                                                                                                                                       2)
                                                                                                                                                      (("3"
                                                                                                                                                        (skosimp*)
                                                                                                                                                        (("3"
                                                                                                                                                          (assert)
                                                                                                                                                          nil
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil)
                                                                                                                                                   ("2"
                                                                                                                                                    (hide
                                                                                                                                                     2)
                                                                                                                                                    (("2"
                                                                                                                                                      (hide-all-but
                                                                                                                                                       1)
                                                                                                                                                      (("2"
                                                                                                                                                        (case
                                                                                                                                                         "FORALL (gg:nat): rational_pred(sigma[nat](0, gg, LAMBDA (x: nat): n(x))) AND
                                       integer_pred(sigma[nat](0, gg, LAMBDA (x: nat): n(x)))")
                                                                                                                                                        (("1"
                                                                                                                                                          (inst
                                                                                                                                                           -
                                                                                                                                                           "d")
                                                                                                                                                          nil
                                                                                                                                                          nil)
                                                                                                                                                         ("2"
                                                                                                                                                          (hide
                                                                                                                                                           2)
                                                                                                                                                          (("2"
                                                                                                                                                            (induct
                                                                                                                                                             "gg")
                                                                                                                                                            (("1"
                                                                                                                                                              (grind)
                                                                                                                                                              nil
                                                                                                                                                              nil)
                                                                                                                                                             ("2"
                                                                                                                                                              (grind)
                                                                                                                                                              nil
                                                                                                                                                              nil)
                                                                                                                                                             ("3"
                                                                                                                                                              (skosimp*)
                                                                                                                                                              (("3"
                                                                                                                                                                (assert)
                                                                                                                                                                nil
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil)
                                                                                                                                                   ("3"
                                                                                                                                                    (hide
                                                                                                                                                     2)
                                                                                                                                                    (("3"
                                                                                                                                                      (skosimp*)
                                                                                                                                                      (("3"
                                                                                                                                                        (assert)
                                                                                                                                                        nil
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil)
                                                                                                                                                 ("2"
                                                                                                                                                  (hide-all-but
                                                                                                                                                   1)
                                                                                                                                                  (("2"
                                                                                                                                                    (case
                                                                                                                                                     "FORALL (gg:nat): rational_pred(sigma[nat](0, gg, LAMBDA (x: nat): n(x))) AND
                                          integer_pred(sigma[nat](0, gg, LAMBDA (x: nat): n(x)))")
                                                                                                                                                    (("1"
                                                                                                                                                      (inst
                                                                                                                                                       -
                                                                                                                                                       "d")
                                                                                                                                                      nil
                                                                                                                                                      nil)
                                                                                                                                                     ("2"
                                                                                                                                                      (hide
                                                                                                                                                       2)
                                                                                                                                                      (("2"
                                                                                                                                                        (induct
                                                                                                                                                         "gg")
                                                                                                                                                        (("1"
                                                                                                                                                          (grind)
                                                                                                                                                          nil
                                                                                                                                                          nil)
                                                                                                                                                         ("2"
                                                                                                                                                          (grind)
                                                                                                                                                          nil
                                                                                                                                                          nil)
                                                                                                                                                         ("3"
                                                                                                                                                          (grind)
                                                                                                                                                          nil
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil)
                                                                                                                                                 ("3"
                                                                                                                                                  (hide
                                                                                                                                                   2)
                                                                                                                                                  (("3"
                                                                                                                                                    (skeep)
                                                                                                                                                    (("3"
                                                                                                                                                      (assert)
                                                                                                                                                      nil
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil)
                                                                                                           ("2"
                                                                                                            (skeep)
                                                                                                            (("2"
                                                                                                              (inst
                                                                                                               -
                                                                                                               "i")
                                                                                                              (("2"
                                                                                                                (assert)
                                                                                                                (("2"
                                                                                                                  (inst
                                                                                                                   5
                                                                                                                   "i")
                                                                                                                  (("2"
                                                                                                                    (assert)
                                                                                                                    (("2"
                                                                                                                      (expand
                                                                                                                       "NP"
                                                                                                                       -4)
                                                                                                                      (("2"
                                                                                                                        (rewrite
                                                                                                                         "scal_polynomial2")
                                                                                                                        (("2"
                                                                                                                          (expand
                                                                                                                           "SS"
                                                                                                                           -4)
                                                                                                                          (("2"
                                                                                                                            (lift-if)
                                                                                                                            (("2"
                                                                                                                              (split
                                                                                                                               -)
                                                                                                                              (("1"
                                                                                                                                (flatten)
                                                                                                                                (("1"
                                                                                                                                  (assert)
                                                                                                                                  nil
                                                                                                                                  nil))
                                                                                                                                nil)
                                                                                                                               ("2"
                                                                                                                                (flatten)
                                                                                                                                (("2"
                                                                                                                                  (assert)
                                                                                                                                  nil
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil)
                                                                               ("4"
                                                                                (inst
                                                                                 +
                                                                                 "x")
                                                                                (("4"
                                                                                  (skeep)
                                                                                  (("4"
                                                                                    (expand
                                                                                     "NP"
                                                                                     1)
                                                                                    (("4"
                                                                                      (rewrite
                                                                                       "scal_polynomial2")
                                                                                      (("4"
                                                                                        (expand
                                                                                         "SS"
                                                                                         1)
                                                                                        (("4"
                                                                                          (lift-if)
                                                                                          (("4"
                                                                                            (split
                                                                                             1)
                                                                                            (("1"
                                                                                              (flatten)
                                                                                              (("1"
                                                                                                (case
                                                                                                 "newRel(i)/=3")
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (hide
                                                                                                     -2)
                                                                                                    (("1"
                                                                                                      (inst
                                                                                                       5
                                                                                                       "i")
                                                                                                      (("1"
                                                                                                        (inst
                                                                                                         +
                                                                                                         "i")
                                                                                                        (("1"
                                                                                                          (assert)
                                                                                                          (("1"
                                                                                                            (expand
                                                                                                             "newp"
                                                                                                             1)
                                                                                                            (("1"
                                                                                                              (expand
                                                                                                               "newRel"
                                                                                                               5)
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "greatify_poly_rel"
                                                                                                                 1)
                                                                                                                (("1"
                                                                                                                  (expand
                                                                                                                   "greatify_poly")
                                                                                                                  (("1"
                                                                                                                    (expand
                                                                                                                     "greatify_rel"
                                                                                                                     +)
                                                                                                                    (("1"
                                                                                                                      (inst
                                                                                                                       -
                                                                                                                       "i")
                                                                                                                      (("1"
                                                                                                                        (expand
                                                                                                                         "rel5"
                                                                                                                         -6)
                                                                                                                        (("1"
                                                                                                                          (lift-if)
                                                                                                                          (("1"
                                                                                                                            (expand
                                                                                                                             "newRel"
                                                                                                                             -1)
                                                                                                                            (("1"
                                                                                                                              (expand
                                                                                                                               "greatify_rel"
                                                                                                                               -1)
                                                                                                                              (("1"
                                                                                                                                (lift-if)
                                                                                                                                (("1"
                                                                                                                                  (rewrite
                                                                                                                                   "scal_polynomial2")
                                                                                                                                  (("1"
                                                                                                                                    (ground)
                                                                                                                                    nil
--> --------------------

--> maximum size reached

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

Messung V0.5 in Prozent
C=100 H=97 G=98

¤ Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.0.785Bemerkung:  (vorverarbeitet am  2026-04-27) ¤

*Bot Zugriff






Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung und die Messung sind noch experimentell.