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("2"
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((R_subset_RTC formula-decl nil relations_closure nil)
(member const-decl "bool" sets nil)
(subset? const-decl "bool" sets nil)
(PRED type-eq-decl nil defined_types nil)
(pred type-eq-decl nil defined_types nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil)
(T formal-type-decl nil newman_yokouchi nil)
(confluent? const-decl "bool" ars_terminology nil)
(locally_confluent? const-decl "bool" ars_terminology nil)
(noetherian_induction formula-decl nil noetherian nil)
(IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(reflexive_transitive? const-decl "bool" relations_closure nil)
(reflexive_transitive type-eq-decl nil relations_closure nil)
(RTC const-decl "reflexive_transitive" relations_closure nil)
(joinable? const-decl "bool" ars_terminology nil)
(IUnion const-decl "set[T]" indexed_sets nil)
(int_plus_int_is_int application-judgement "int" integers nil)
(j skolem-const-decl "nat" newman_yokouchi nil)
(O const-decl "bool" relation_props nil)
(iterate_RTC formula-decl nil relations_closure nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(transitive? const-decl "bool" relations nil)
(R_subset_TC formula-decl nil relations_closure nil)
(i skolem-const-decl "nat" newman_yokouchi nil)
(- const-decl "[numfield, numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil 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)
(iterate_add_one formula-decl nil relation_iterate "orders/")
(iterate def-decl "pred[[T, T]]" relation_iterate "orders/")
(number nonempty-type-decl nil numbers nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(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)
(noetherian type-eq-decl nil noetherian nil)
(noetherian? const-decl "bool" noetherian nil)
(R skolem-const-decl "PRED[[T, T]]" newman_yokouchi nil))
shostak))
(Yokouchi_lemma_ax1 0
(Yokouchi_lemma_ax1-1 nil 3374070253
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--> --------------------
--> maximum size reached
--> --------------------
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