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Datei: trig_values.prf   Sprache: Lisp

Original von: PVS©
(strat_util
 (multipoly_minmax_sound 0
  (multipoly_minmax_sound-1 nil 3509989257
   ("" (skeep)
    (("" (expand "multipoly_minmax")
      ((""
        (typepred "multipolynomial_minmax(mp`mpoly,
                                                   mp`mdeg,
                                                   mv`numvars,
                                                   mp`terms,
                                                   mp`mcoeff,
                                                   mv`vars_lb,
                                                   mv`vars_ub,
                                                   depth,
                                                   eps_localexit(precision),
                                                   false_globalexit,
                                                   mv`iepts,
                                                   LAMBDA (i: nat): (TRUE, TRUE),
                                                   varselect)")
        ((""
          (name-replace "SPF" "multipolynomial_minmax(mp`mpoly,
                                                   mp`mdeg,
                                                   mv`numvars,
                                                   mp`terms,
                                                   mp`mcoeff,
                                                   mv`vars_lb,
                                                   mv`vars_ub,
                                                   depth,
                                                   eps_localexit(precision),
                                                   false_globalexit,
                                                   mv`iepts,
                                                   LAMBDA (i: nat): (TRUE, TRUE),
                                                   varselect)")
          (("" (expand "sound_poly?")
            (("" (assert)
              (("" (split -1)
                (("1" (flatten)
                  (("1" (hide-all-but 1) (("1" (grind) nil nil)) nil))
                  nil)
                 ("2" (hide-all-but 1) (("2" (grind) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((multipoly_minmax const-decl "Outminmax" strat_util nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (bounded_points_exclusive? const-decl "bool" util nil)
    (bounded_points_true? const-decl "bool" util 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)
    (Polynomial type-eq-decl nil util nil)
    (Polyproduct type-eq-decl nil util nil)
    (MultiPolynomial type-eq-decl nil util nil)
    (DegreeMono type-eq-decl nil util nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (Coeff type-eq-decl nil util nil) (Vars type-eq-decl nil util nil)
    (IntervalEndpoints type-eq-decl nil util nil)
    (list type-decl nil list_adt nil)
    (Outminmax type-eq-decl nil minmax nil)
    (sound_poly? const-decl "bool" poly_minmax nil)
    (MPoly type-eq-decl nil MPoly nil)
    (MVars type-eq-decl nil MPoly nil)
    (TRUE const-decl "bool" booleans nil)
    (MultiBernstein type-eq-decl nil util nil)
    (VarSelector type-eq-decl nil vardirselector nil)
    (multipolynomial_minmax const-decl
     "(sound_poly?(mpoly, polydegmono, nvars, terms, cf, Avars, Bvars,
             boundedpts, intendpts))" poly_minmax nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (eps_localexit const-decl "bool" minmax nil)
    (false_globalexit const-decl "bool" minmax nil))
   shostak))
 (multipoly_strategy_TCC1 0
  (multipoly_strategy_TCC1-1 nil 3509445920 ("" (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)
    (Polynomial type-eq-decl nil util nil)
    (Polyproduct type-eq-decl nil util nil)
    (MultiPolynomial type-eq-decl nil util nil)
    (DegreeMono type-eq-decl nil util nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (Coeff type-eq-decl nil util nil) (Vars type-eq-decl nil util nil)
    (IntervalEndpoints type-eq-decl nil util nil)
    (list type-decl nil list_adt nil)
    (Outminmax type-eq-decl nil minmax nil)
    (sound_poly? const-decl "bool" poly_minmax nil)
    (RealOrder type-eq-decl nil util nil)
    (MPolyRel type-eq-decl nil MPoly nil)
    (MVars type-eq-decl nil MPoly nil)
    (rel_localexit const-decl "bool" minmax nil)
    (rel_counterex const-decl "bool" minmax nil)
    (sound_poly_inf? const-decl "bool" poly_minmax nil)
    (inf_box_poly_ub? const-decl "bool" poly_minmax nil)
    (inf_box_poly_lb? const-decl "bool" poly_minmax nil)
    (forall_X_poly_rel const-decl "bool" multi_polynomial nil)
    (sound_poly_fin? const-decl "bool" poly_minmax nil)
    (length_eq? const-decl "bool" minmax nil)
    (box_poly_ub? const-decl "bool" poly_minmax nil)
    (box_poly_lb? const-decl "bool" poly_minmax nil)
    (forall_X_poly_between const-decl "bool" multi_polynomial nil)
    (multipoly_eval const-decl "real" multi_polynomial nil)
    (polyproduct_eval const-decl "real" multi_polynomial nil)
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (^ const-decl "real" exponentiation nil)
    (boxbetween? const-decl "bool" util nil)
    (interval_between? const-decl "bool" util nil)
    (bounded_points_true? const-decl "bool" util nil)
    (bounded_points_exclusive? const-decl "bool" util nil)
    (lt_below? const-decl "bool" util nil)
    (ge_realorder name-judgement "RealOrder" util nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (rel_localexit_inv application-judgement "(localexit_inv?)" minmax
     nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (le_realorder name-judgement "RealOrder" util nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (lt_realorder name-judgement "RealOrder" util nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (single_outminmax const-decl "Outminmax" minmax nil)
    (empty_minmax const-decl "Outminmax" minmax nil)
    (Bernstein_minmax const-decl
     "(sound?(bspoly, bsdegmono, nvars, terms, cf, intendpts))"
     bernstein_minmax nil)
    (denormalize_listreal const-decl "listn[real](length(l))" util nil)
    (multipolynomial_minmax const-decl
     "(sound_poly?(mpoly, polydegmono, nvars, terms, cf, Avars, Bvars,
             boundedpts, intendpts))" poly_minmax nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (minus_real_is_real application-judgement "real" reals nil))
   nil))
 (multipoly_strategy_TCC2 0
  (multipoly_strategy_TCC2-1 nil 3509445920 ("" (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)
    (Polynomial type-eq-decl nil util nil)
    (Polyproduct type-eq-decl nil util nil)
    (MultiPolynomial type-eq-decl nil util nil)
    (DegreeMono type-eq-decl nil util nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (Coeff type-eq-decl nil util nil) (Vars type-eq-decl nil util nil)
    (IntervalEndpoints type-eq-decl nil util nil)
    (list type-decl nil list_adt nil)
    (Outminmax type-eq-decl nil minmax nil)
    (sound_poly? const-decl "bool" poly_minmax nil)
    (RealOrder type-eq-decl nil util nil)
    (MPolyRel type-eq-decl nil MPoly nil)
    (MVars type-eq-decl nil MPoly nil)
    (rel_localexit const-decl "bool" minmax nil)
    (rel_counterex const-decl "bool" minmax nil)
    (sound_poly_inf? const-decl "bool" poly_minmax nil)
    (inf_box_poly_ub? const-decl "bool" poly_minmax nil)
    (inf_box_poly_lb? const-decl "bool" poly_minmax nil)
    (forall_X_poly_rel const-decl "bool" multi_polynomial nil)
    (sound_poly_fin? const-decl "bool" poly_minmax nil)
    (length_eq? const-decl "bool" minmax nil)
    (box_poly_ub? const-decl "bool" poly_minmax nil)
    (box_poly_lb? const-decl "bool" poly_minmax nil)
    (forall_X_poly_between const-decl "bool" multi_polynomial nil)
    (multipoly_eval const-decl "real" multi_polynomial nil)
    (polyproduct_eval const-decl "real" multi_polynomial nil)
    (polynomial const-decl "[real -> real]" polynomials "reals/")
    (^ const-decl "real" exponentiation nil)
    (boxbetween? const-decl "bool" util nil)
    (interval_between? const-decl "bool" util nil)
    (bounded_points_true? const-decl "bool" util nil)
    (bounded_points_exclusive? const-decl "bool" util nil)
    (lt_below? const-decl "bool" util nil)
    (ge_realorder name-judgement "RealOrder" util nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (rel_localexit_inv application-judgement "(localexit_inv?)" minmax
     nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (le_realorder name-judgement "RealOrder" util nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (lt_realorder name-judgement "RealOrder" util nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (single_outminmax const-decl "Outminmax" minmax nil)
    (empty_minmax const-decl "Outminmax" minmax nil)
    (Bernstein_minmax const-decl
     "(sound?(bspoly, bsdegmono, nvars, terms, cf, intendpts))"
     bernstein_minmax nil)
    (denormalize_listreal const-decl "listn[real](length(l))" util nil)
    (multipolynomial_minmax const-decl
     "(sound_poly?(mpoly, polydegmono, nvars, terms, cf, Avars, Bvars,
             boundedpts, intendpts))" poly_minmax nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (minus_real_is_real application-judgement "real" reals nil))
   nil))
 (multipoly_strategy_true 0
  (multipoly_strategy_true-1 nil 3509487957
   ("" (skeep)
    (("" (expand "multipoly_strategy" :assert? none)
      (("" (beta)
        ((""
          (name-replace "mm" "multipolynomial_minmax(mpr`mpoly,
                                                             mpr`mdeg,
                                                             mv`numvars,
                                                             mpr`terms,
                                                             mpr`mcoeff,
                                                             mv`vars_lb,
                                                             mv`vars_ub,
                                                             depth,
                                                             rel_localexit(mpr`rel),
                                                             rel_globalexit(mpr`rel,depth,true),
                                                             mv`iepts,
                                                             mv`bdpts,
                                                             varselect)")
          (("" (lift-if)
            (("" (assert)
              (("" (split -3)
                (("1" (typepred "mm")
                  (("1" (expand "rel_localexit")
                    (("1" (lemma "sound_poly_lb_le_ub")
                      (("1" (inst?)
                        (("1" (assert)
                          (("1" (label "lbleub" -1)
                            (("1" (hide "lbleub")
                              (("1"
                                (expand "sound_poly?")
                                (("1"
                                  (split -1)
                                  (("1"
                                    (flatten)
                                    (("1"
                                      (expand "sound_poly_fin?")
                                      (("1"
                                        (flatten)
                                        (("1"
                                          (expand
                                           "forall_X_poly_interval")
                                          (("1"
                                            (expand
                                             "forall_X_poly_between")
                                            (("1"
                                              (skeep)
                                              (("1"
                                                (inst? -)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (flatten)
                                                    (("1"
                                                      (name-replace
                                                       "meval"
                                                       "multipoly_eval(mpr`mpoly, mpr`mdeg, mpr`mcoeff, mv`numvars,
                                                                                mpr`terms)
                                                                               (X)")
                                                      (("1"
                                                        (hide-all-but
                                                         (-2 -3 -7 1))
                                                        (("1"
                                                          (typepred
                                                           "mpr`rel")
                                                          (("1"
                                                            (expand
                                                             "realorder?")
                                                            (("1"
                                                              (grind)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (flatten)
                                    (("2"
                                      (expand "sound_poly_inf?")
                                      (("2"
                                        (inst? -1)
                                        (("2"
                                          (flatten)
                                          (("2"
                                            (hide -2 -3)
                                            (("2"
                                              (typepred "mpr`rel")
                                              (("2"
                                                (expand "realorder?")
                                                (("2"
                                                  (split -2)
                                                  (("1"
                                                    (expand
                                                     "forall_X_poly_interval")
                                                    (("1"
                                                      (expand
                                                       "forall_X_poly_rel")
                                                      (("1"
                                                        (propax)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (reveal "lbleub")
                                                    (("2"
                                                      (expand
                                                       "lb_le_ub?")
                                                      (("2"
                                                        (hide-all-but
                                                         (-1
                                                          -2
                                                          -4
                                                          -5
                                                          1))
                                                        (("2"
                                                          (grind)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil)
                                                   ("3"
                                                    (reveal "lbleub")
                                                    (("3"
                                                      (expand
                                                       "lb_le_ub?")
                                                      (("3"
                                                        (hide-all-but
                                                         (-1
                                                          -2
                                                          -4
                                                          -5
                                                          1))
                                                        (("3"
                                                          (grind)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (propax) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((multipoly_strategy const-decl "Outcome" strat_util nil)
    (real nonempty-type-from-decl nil reals 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)
    (list type-decl nil list_adt nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (Outminmax type-eq-decl nil minmax nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (Polynomial type-eq-decl nil util nil)
    (Polyproduct type-eq-decl nil util nil)
    (MultiPolynomial type-eq-decl nil util nil)
    (DegreeMono type-eq-decl nil util nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (Coeff type-eq-decl nil util nil) (Vars type-eq-decl nil util nil)
    (IntervalEndpoints type-eq-decl nil util nil)
    (MultiBernstein type-eq-decl nil util nil)
    (VarSelector type-eq-decl nil vardirselector nil)
    (sound_poly? const-decl "bool" poly_minmax nil)
    (multipolynomial_minmax const-decl
     "(sound_poly?(mpoly, polydegmono, nvars, terms, cf, Avars, Bvars,
             boundedpts, intendpts))" poly_minmax nil)
    (RealOrder type-eq-decl nil util nil)
    (MPolyRel type-eq-decl nil MPoly nil)
    (MVars type-eq-decl nil MPoly nil)
    (realorder? const-decl "bool" util nil)
    (rel_localexit const-decl "bool" minmax nil)
    (rel_globalexit const-decl "bool" minmax nil)
    (TRUE const-decl "bool" booleans nil)
    (rel_localexit_inv application-judgement "(localexit_inv?)" minmax
     nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (sound_poly_lb_le_ub formula-decl nil poly_minmax nil)
    (sound_poly_fin? const-decl "bool" poly_minmax nil)
    (forall_X_poly_interval const-decl "bool" multi_polynomial nil)
    (multipoly_eval const-decl "real" multi_polynomial nil)
    (le_realorder name-judgement "RealOrder" util nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (ge_realorder name-judgement "RealOrder" util nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (lt_realorder name-judgement "RealOrder" util nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (gt_realorder name-judgement "RealOrder" util nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (forall_X_poly_between const-decl "bool" multi_polynomial nil)
    (sound_poly_inf? const-decl "bool" poly_minmax nil)
    (forall_X_poly_rel const-decl "bool" multi_polynomial nil)
    (lb_le_ub? const-decl "bool" minmax nil))
   shostak))
 (multipoly_strategy_false 0
  (multipoly_strategy_false-2 nil 3509800905
   ("" (skeep)
    (("" (expand "multipoly_strategy" :assert? none)
      (("" (beta)
        ((""
          (name-replace "mm" "multipolynomial_minmax
                                                              (mpr`mpoly,
                                                               mpr`mdeg,
                                                               mv`numvars,
                                                               mpr`terms,
                                                               mpr`mcoeff,
                                                               mv`vars_lb,
                                                               mv`vars_ub,
                                                               depth,
                                                               rel_localexit(mpr`rel),
                                                               rel_globalexit
                                                               (mpr`rel, depth, FALSE),
                                                               mv`iepts,
                                                               mv`bdpts,
                                                               varselect)")
          (("" (lift-if)
            (("" (assert)
              (("" (ground)
                (("" (expand "forall_X_poly_interval")
                  (("" (expand "rel_counterex")
                    (("" (ground)
                      (("1" (inst - "list2array(0)(mm`ub_var)")
                        (("1" (split -)
                          (("1" (typepred "mm")
                            (("1" (expand "sound_poly?")
                              (("1"
                                (split -)
                                (("1"
                                  (flatten)
                                  (("1"
                                    (expand "sound_poly_fin?")
                                    (("1"
                                      (flatten)
                                      (("1"
                                        (expand "box_poly_ub?")
                                        (("1" (ground) nil nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (flatten)
                                  (("2"
                                    (expand "sound_poly_inf?")
                                    (("2"
                                      (inst - "mpr`rel")
                                      (("2"
                                        (flatten)
                                        (("2"
                                          (expand "inf_box_poly_ub?")
                                          (("2" (ground) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (typepred "mm")
                            (("2" (expand "sound_poly?")
                              (("2"
                                (expand "sound_poly_fin?")
                                (("2"
                                  (expand "sound_poly_inf?")
                                  (("2"
                                    (expand "boxbetween?")
                                    (("2"
                                      (expand "box_poly_ub?")
                                      (("2"
                                        (expand "inf_box_poly_ub?")
                                        (("2"
                                          (ground)
                                          (("2"
                                            (inst - "<")
                                            (("2" (ground) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (inst - "list2array(0)(mm`lb_var)")
                        (("2" (split -)
                          (("1" (typepred "mm")
                            (("1" (expand "sound_poly?")
                              (("1"
                                (split -)
                                (("1"
                                  (flatten)
                                  (("1"
                                    (expand "sound_poly_fin?")
                                    (("1"
                                      (flatten)
                                      (("1"
                                        (expand "box_poly_lb?")
                                        (("1" (ground) nil nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (flatten)
                                  (("2"
                                    (expand "sound_poly_inf?")
                                    (("2"
                                      (inst - "mpr`rel")
                                      (("2"
                                        (flatten)
                                        (("2"
                                          (expand "inf_box_poly_lb?")
                                          (("2" (ground) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (typepred "mm")
                            (("2" (expand "sound_poly?")
                              (("2"
                                (expand "sound_poly_fin?")
                                (("2"
                                  (expand "sound_poly_inf?")
                                  (("2"
                                    (expand "boxbetween?")
                                    (("2"
                                      (expand "box_poly_lb?")
                                      (("2"
                                        (expand "inf_box_poly_lb?")
                                        (("2"
                                          (ground)
                                          (("2"
                                            (inst - ">")
                                            (("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)
   ((multipoly_strategy const-decl "Outcome" strat_util nil)
    (real nonempty-type-from-decl nil reals 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)
    (list type-decl nil list_adt nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (Outminmax type-eq-decl nil minmax nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (Polynomial type-eq-decl nil util nil)
    (Polyproduct type-eq-decl nil util nil)
    (MultiPolynomial type-eq-decl nil util nil)
    (DegreeMono type-eq-decl nil util nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (Coeff type-eq-decl nil util nil) (Vars type-eq-decl nil util nil)
    (IntervalEndpoints type-eq-decl nil util nil)
    (MultiBernstein type-eq-decl nil util nil)
    (VarSelector type-eq-decl nil vardirselector nil)
    (sound_poly? const-decl "bool" poly_minmax nil)
    (multipolynomial_minmax const-decl
     "(sound_poly?(mpoly, polydegmono, nvars, terms, cf, Avars, Bvars,
             boundedpts, intendpts))" poly_minmax nil)
    (RealOrder type-eq-decl nil util nil)
    (MPolyRel type-eq-decl nil MPoly nil)
    (MVars type-eq-decl nil MPoly nil)
    (realorder? const-decl "bool" util nil)
    (rel_localexit const-decl "bool" minmax nil)
    (rel_globalexit const-decl "bool" minmax nil)
    (FALSE const-decl "bool" booleans nil)
    (rel_localexit_inv application-judgement "(localexit_inv?)" minmax
     nil)
    (forall_X_poly_interval const-decl "bool" multi_polynomial nil)
    (inf_box_poly_ub? const-decl "bool" poly_minmax nil)
    (sound_poly_inf? const-decl "bool" poly_minmax nil)
    (box_poly_ub? const-decl "bool" poly_minmax nil)
    (sound_poly_fin? const-decl "bool" poly_minmax nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (< const-decl "bool" reals nil)
    (lt_realorder name-judgement "RealOrder" util nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (boxbetween? const-decl "bool" util nil)
    (PRED type-eq-decl nil defined_types nil)
    (every adt-def-decl "boolean" list_adt nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (list2array def-decl "T" array2list "structures/")
    (inf_box_poly_lb? const-decl "bool" poly_minmax nil)
    (box_poly_lb? const-decl "bool" poly_minmax nil)
    (gt_realorder name-judgement "RealOrder" util nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (rel_counterex const-decl "bool" minmax nil))
   nil)
  (multipoly_strategy_false-1 nil 3509798902 ("" (postpone) nil nil)
   nil shostak))
 (multipoly_strategy_counterexample 0
  (multipoly_strategy_counterexample-1 nil 3509877763
   ("" (skeep)
    (("" (expand "multipoly_strategy" :assert? none)
      (("" (beta)
        ((""
          (name-replace "mm" "multipolynomial_minmax
                                                                            (mpr`mpoly,
                                                                             mpr`mdeg,
                                                                             mv`numvars,
                                                                             mpr`terms,
                                                                             mpr`mcoeff,
                                                                             mv`vars_lb,
                                                                             mv`vars_ub,
                                                                             depth,
                                                                             rel_localexit(mpr`rel),
                                                                             rel_globalexit
                                                                             (mpr`rel, depth, FALSE),
                                                                             mv`iepts,
                                                                             mv`bdpts,
                                                                             varselect)")
          (("" (flatten)
            (("" (lift-if)
              (("" (ground)
                (("1" (expand "rel_counterex")
                  (("1" (flatten)
                    (("1" (typepred "mm")
                      (("1" (expand "sound_poly?")
                        (("1" (split -)
                          (("1" (flatten)
                            (("1" (expand "sound_poly_fin?")
                              (("1"
                                (flatten)
                                (("1"
                                  (expand "box_poly_ub?")
                                  (("1" (ground) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (flatten)
                            (("2" (expand "sound_poly_inf?")
                              (("2"
                                (inst - "mpr`rel")
                                (("2"
                                  (flatten)
                                  (("2"
                                    (expand "inf_box_poly_ub?")
                                    (("2" (ground) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (typepred "mm")
                  (("2" (expand "sound_poly?")
                    (("2" (expand "sound_poly_fin?")
                      (("2" (expand "sound_poly_inf?")
                        (("2" (expand "boxbetween?")
                          (("2" (expand "box_poly_ub?")
                            (("2" (expand "inf_box_poly_ub?")
                              (("2"
                                (expand "rel_counterex")
                                (("2"
                                  (ground)
                                  (("2"
                                    (inst - "<")
                                    (("2" (ground) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("3" (expand "rel_counterex")
                  (("3" (flatten)
                    (("3" (typepred "mm")
                      (("3" (expand "sound_poly?")
                        (("3" (split -)
                          (("1" (flatten)
                            (("1" (expand "sound_poly_fin?")
                              (("1"
                                (flatten)
                                (("1"
                                  (expand "box_poly_lb?")
                                  (("1" (ground) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (flatten)
                            (("2" (expand "sound_poly_inf?")
                              (("2"
                                (inst - "mpr`rel")
                                (("2"
                                  (flatten)
                                  (("2"
                                    (expand "inf_box_poly_lb?")
                                    (("2" (ground) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("4" (typepred "mm")
                  (("4" (expand "sound_poly?")
                    (("4" (expand "sound_poly_fin?")
                      (("4" (expand "sound_poly_inf?")
                        (("4" (expand "boxbetween?")
                          (("4" (expand "box_poly_lb?")
                            (("4" (expand "inf_box_poly_lb?")
                              (("4"
                                (expand "rel_counterex")
                                (("4"
                                  (ground)
                                  (("4"
                                    (inst - ">")
                                    (("4" (ground) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((multipoly_strategy const-decl "Outcome" strat_util nil)
    (real nonempty-type-from-decl nil reals 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)
    (list type-decl nil list_adt nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (Outminmax type-eq-decl nil minmax nil)
    (= const-decl "[T, T -> boolean]" equalities 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)
    (Polynomial type-eq-decl nil util nil)
    (Polyproduct type-eq-decl nil util nil)
    (MultiPolynomial type-eq-decl nil util nil)
    (DegreeMono type-eq-decl nil util nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (Coeff type-eq-decl nil util nil) (Vars type-eq-decl nil util nil)
    (IntervalEndpoints type-eq-decl nil util nil)
    (MultiBernstein type-eq-decl nil util nil)
    (VarSelector type-eq-decl nil vardirselector nil)
    (sound_poly? const-decl "bool" poly_minmax nil)
    (multipolynomial_minmax const-decl
     "(sound_poly?(mpoly, polydegmono, nvars, terms, cf, Avars, Bvars,
             boundedpts, intendpts))" poly_minmax nil)
    (RealOrder type-eq-decl nil util nil)
    (MPolyRel type-eq-decl nil MPoly nil)
    (MVars type-eq-decl nil MPoly nil)
    (realorder? const-decl "bool" util nil)
    (rel_localexit const-decl "bool" minmax nil)
    (rel_globalexit const-decl "bool" minmax nil)
    (FALSE const-decl "bool" booleans nil)
    (gt_realorder name-judgement "RealOrder" util nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (box_poly_lb? const-decl "bool" poly_minmax nil)
    (inf_box_poly_lb? const-decl "bool" poly_minmax nil)
    (boxbetween? const-decl "bool" util nil)
    (< const-decl "bool" reals nil)
    (lt_realorder name-judgement "RealOrder" util nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (rel_counterex const-decl "bool" minmax nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (sound_poly_fin? const-decl "bool" poly_minmax nil)
    (box_poly_ub? const-decl "bool" poly_minmax nil)
    (sound_poly_inf? const-decl "bool" poly_minmax nil)
    (inf_box_poly_ub? const-decl "bool" poly_minmax nil)
    (rel_localexit_inv application-judgement "(localexit_inv?)" minmax
     nil))
   nil)))


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