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|
(my_list_induction
(less_wf 0
(less_wf-1 nil 3667405436
("" (expand "well_founded?")
(("" (skolem 1 P)
(("" (flatten)
(("" (skolem -1 Y)
(("" (expand "less")
(("" (lemma naturalnumbers.wf_nat)
(("" (expand "well_founded?")
((""
(inst -1 "(LAMBDA(n:nat):EXISTS(l:(P)):length(l)=n)")
(("" (split)
(("1" (skosimp*)
(("1" (typepred y!1)
(("1" (skolem -1 L)
(("1" (inst 1 L)
(("1" (skolem 1 G)
(("1"
(inst -2 "length(G)")
(("1" (assert) nil nil)
("2"
(typepred G)
(("2" (inst 1 G) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
("2" (grind)
(("2" (inst 1 "length(Y)")
(("2" (inst 1 Y) nil nil)) nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((well_founded? const-decl "bool" orders nil)
(less const-decl "bool" my_list_induction nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(P skolem-const-decl "pred[list[X]]" my_list_induction nil)
(G skolem-const-decl "(P)" my_list_induction nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(length def-decl "nat" list_props nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(list type-decl nil list_adt nil)
(X formal-type-decl nil my_list_induction nil)
(pred type-eq-decl nil defined_types 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)
(wf_nat formula-decl nil naturalnumbers nil))
shostak))
(list_length_induction 0
(list_length_induction-1 nil 3667403384
("" (lemma "wf_induction[list[X],less].wf_induction")
(("1" (propax) nil nil) ("2" (rewrite less_wf) nil nil)) nil)
((less_wf formula-decl nil my_list_induction nil)
(pred type-eq-decl nil defined_types nil)
(well_founded? const-decl "bool" orders nil)
(wf_induction formula-decl nil wf_induction nil)
(X formal-type-decl nil my_list_induction nil)
(list type-decl nil list_adt nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(less const-decl "bool" my_list_induction nil))
shostak)))
(my_list_props
(occ_TCC1 0
(occ_TCC1-1 nil 3667035231 ("" (termination-tcc) nil nil)
((real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(length def-decl "nat" list_props nil))
nil))
(occ_TCC2 0
(occ_TCC2-1 nil 3667035231 ("" (termination-tcc) nil nil)
((real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(length def-decl "nat" list_props nil))
nil))
(occ_nth 0
(occ_nth-1 nil 3667035247
("" (induct l)
(("1" (grind) nil nil)
("2" (skolem 1 (HD TL))
(("2" (flatten)
(("2" (expand nth 1)
(("2" (skeep)
(("2" (expand occ -2)
(("2" (lift-if)
(("2" (split -2)
(("1" (flatten)
(("1" (inst 1 0)
(("1" (assert) (("1" (grind) nil nil)) nil))
nil))
nil)
("2" (flatten)
(("2" (inst -2 x)
(("2" (assert)
(("2" (skolem -2 I)
(("2" (flatten)
(("2" (inst 2 "I+1")
(("2"
(assert)
(("2" (grind) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(list_induction formula-decl nil list_adt nil)
(X formal-type-decl nil my_list_props nil)
(nth def-decl "T" list_props nil)
(below type-eq-decl nil nat_types nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(length def-decl "nat" list_props nil)
(< const-decl "bool" reals nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(occ def-decl "nat" my_list_props 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)
(> const-decl "bool" reals 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)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(list type-decl nil list_adt nil))
shostak))
(nth_occ 0
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shostak))
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shostak))
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nil))
nil))
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nil))
nil))
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shostak))
(length_append 0
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((list type-decl nil list_adt nil)
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nil)
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(bool nonempty-type-eq-decl nil booleans nil)
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integers nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil))
shostak))
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("" (skeep)
(("" (lemma length_append)
(("" (inst? -1) (("" (assert) nil nil)) nil)) nil))
nil)
((length_append formula-decl nil my_list_props nil)
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"(strict_total_order?[real])" real_props nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(list type-decl nil list_adt nil)
(X formal-type-decl nil my_list_props nil))
nil))
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((boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
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nil)
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(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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nil))
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("" (induct l1)
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("2" (skolem 1 (H T))
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nil))
nil))
nil)
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(assert 1)
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nil))
nil))
nil)
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
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nil))
nil))
nil)
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integers nil)
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(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)
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(number nonempty-type-decl nil numbers nil)
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(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
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(= const-decl "[T, T -> boolean]" equalities nil)
(below type-eq-decl nil nat_types nil)
(nth def-decl "T" list_props nil)
(IF const-decl "[boolean, T, T -> T]" if_def nil)
(X formal-type-decl nil my_list_props nil)
(list_induction formula-decl nil list_adt nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(i skolem-const-decl "nat" my_list_props nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(length_append formula-decl nil my_list_props nil))
shostak)))
(SPLIT
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(split_TCC1-1 nil 3667407453 ("" (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)
(PRED type-eq-decl nil defined_types nil)
(list type-decl nil 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)
(>= const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
(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)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(length def-decl "nat" list_props nil))
nil))
(split_length 0
(split_length-1 nil 3667407485 ("" (induct-and-simplify l) nil nil)
((list type-decl nil list_adt nil)
(PRED type-eq-decl nil defined_types nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(length def-decl "nat" list_props nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(split def-decl "[list[nat], list[nat]]" SPLIT 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)
(list_induction formula-decl nil list_adt nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nnint_plus_posint_is_posint application-judgement "posint"
integers nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil))
shostak))
(split_occ 0
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((list type-decl nil list_adt nil)
(PRED type-eq-decl nil defined_types nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(occ def-decl "nat" my_list_props nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
(split def-decl "[list[nat], list[nat]]" SPLIT 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)
(list_induction formula-decl nil list_adt nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil))
shostak))
(split_lwb_upb 0
(split_lwb_upb-1 nil 3667407762
("" (assert)
(("" (induct l)
(("1" (grind) nil nil)
("2" (skolem 1 (H T))
(("2" (flatten) (("2" (postpone) nil nil)) nil)) nil))
nil))
nil)
((list type-decl nil list_adt nil)
(PRED type-eq-decl nil defined_types nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(upb const-decl "bool" SPLIT nil)
(split def-decl "[list[nat], list[nat]]" SPLIT nil)
(lwb const-decl "bool" SPLIT 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)
(list_induction formula-decl nil list_adt nil)
(length def-decl "nat" list_props nil)
(nth def-decl "T" list_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
shostak)))
(QS
(qs_TCC1 0
(qs_TCC1-1 nil 3329457968
("" (skosimp*)
(("" (lemma split_length)
(("" (inst? -1)
(("" (assert)
(("" (replace -2)
(("" (expand length 1 2) (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((split_length formula-decl nil SPLIT nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(length def-decl "nat" list_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(PRED type-eq-decl nil defined_types nil)
(list type-decl nil list_adt 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))
nil))
(qs_TCC2 0
(qs_TCC2-1 nil 3329457968
("" (skosimp*)
(("" (replace -1)
(("" (expand length 1 2)
(("" (lemma split_length)
(("" (inst? -1) (("" (assert) nil nil)) nil)) nil))
nil))
nil))
nil)
((split_length formula-decl nil SPLIT nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(PRED type-eq-decl nil defined_types nil)
(list type-decl nil list_adt 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)
(length def-decl "nat" list_props nil))
nil)))
(SORTED
(sorted?_TCC1 0
(sorted?_TCC1-1 nil 3667449016 ("" (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)
(PRED type-eq-decl nil defined_types nil)
(list type-decl nil 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)
(>= const-decl "bool" reals nil)
(int nonempty-type-eq-decl nil integers nil)
(nat nonempty-type-eq-decl nil naturalnumbers nil)
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(split_lwb_upb formula-decl nil SPLIT nil)
(cdr adt-accessor-decl "[(cons?) -> list]" list_adt nil)
(car adt-accessor-decl "[(cons?) -> T]" list_adt nil)
(cons? adt-recognizer-decl "[list -> boolean]" list_adt nil)
(split_length formula-decl nil SPLIT nil)
(sorted_append formula-decl nil SORTED nil)
(lwb_perm formula-decl nil QS_props nil)
(qs_perm formula-decl nil QS_props nil)
(perm_commutative formula-decl nil my_list_props nil)
(nth def-decl "T" list_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(posint_plus_nnint_is_posint application-judgement "posint"
integers nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(int_minus_int_is_int application-judgement "int" integers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(lwb const-decl "bool" SPLIT nil)
(upb_perm formula-decl nil QS_props nil)
(less const-decl "bool" my_list_induction nil)
(split def-decl "[list[nat], list[nat]]" SPLIT nil)
(cons adt-constructor-decl "[[T, list] -> (cons?)]" list_adt nil)
(nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
integers nil)
(length def-decl "nat" list_props nil)
(list_length_induction formula-decl nil my_list_induction 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))
shostak)))
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