fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Enum_2Enum_29_20mono_2Etyop_2EordinalNotation_2Eosyntax,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),X1_2E0))))).
fof(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),X2_2E0))))).
fof(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Enum_2Enum_29,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)))),c_2Eind__type_2EFCONS_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),X1_2E0))))).
fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(ordinalNotationTheory_2Eosyntax__TY__DEF,axiom,![F2_2E0, F1_2E0, F0_2E0]: (![V9n_2E0]: (s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),F2_2E0),s(tyop_2Enum_2Enum,V9n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),c_2Eind__type_2EBOTTOM_2E0)) => (![V5n_2E0]: (s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),F1_2E0),s(tyop_2Enum_2Enum,V5n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),c_2Eind__type_2EBOTTOM_2E0)) => (![V1a0_27_2E0]: (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),V1a0_27_2E0)))) <=> ![V2_27osyntax_27_2E0]: (![V3a0_27_2E0]: ((?[V4a_2E0]: (s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),F1_2E0)))) | ?[V6a0_2E0, V7a1_2E0, V8a2_2E0]: ((s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Enum_2Enum,V7a1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),V6a0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),V8a2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),F2_2E0)))))))) & (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V2_27osyntax_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),V6a0_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V2_27osyntax_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),V8a2_2E0))))))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V2_27osyntax_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),V3a0_27_2E0))))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V2_27osyntax_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),V1a0_27_2E0)))))) => ?[V0rep_2E0]: p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Eind__type_2Erecspace(tyop_2Enum_2Enum)),V0rep_2E0)))))))).
