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(arityeq1_2Ec_2EordinalNotation_2EEnd_2E1,axiom,![X0_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),c_2EordinalNotation_2EEnd_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq1_2Ec_2EordinalNotation_2Eis__ord_2E1,axiom,![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2EordinalNotation_2Eis__ord_2E1(s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Ebool),c_2EordinalNotation_2Eis__ord_2E0),s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))))).
fof(arityeq3_2Ec_2EordinalNotation_2EPlus_2E3,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2EordinalNotation_2Eosyntax,X2_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax))),c_2EordinalNotation_2EPlus_2E0),s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2EordinalNotation_2Eosyntax,X2_2E0))))).
fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))))).
fof(arityeq1_2Ec_2EordinalNotation_2Eexpt_2E1,axiom,![X0_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eexpt_2E1(s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),c_2EordinalNotation_2Eexpt_2E0),s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))))).
fof(arityeq2_2Ec_2EordinalNotation_2Eoless_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2EordinalNotation_2Eoless_2E2(s(tyop_2EordinalNotation_2Eosyntax,X0_2E0),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Ebool)),c_2EordinalNotation_2Eoless_2E0),s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0))))).
fof(ordinalNotationTheory_2Eis__ord__strongind,axiom,![V0is__ord_27_2E0]: ((![V1k_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Ebool),V0is__ord_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,V1k_2E0)))))) & ![V2e_2E0, V3k_2E0, V4t_2E0]: ((p(s(tyop_2Emin_2Ebool,c_2EordinalNotation_2Eis__ord_2E1(s(tyop_2EordinalNotation_2Eosyntax,V2e_2E0)))) & (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Ebool),V0is__ord_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,V2e_2E0)))) & (~ ((s(tyop_2EordinalNotation_2Eosyntax,V2e_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V3k_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2EordinalNotation_2Eis__ord_2E1(s(tyop_2EordinalNotation_2Eosyntax,V4t_2E0)))) & (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Ebool),V0is__ord_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,V4t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2EordinalNotation_2Eoless_2E2(s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eexpt_2E1(s(tyop_2EordinalNotation_2Eosyntax,V4t_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V2e_2E0)))))))))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Ebool),V0is__ord_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V2e_2E0),s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2EordinalNotation_2Eosyntax,V4t_2E0)))))))) => ![V5a0_2E0]: (p(s(tyop_2Emin_2Ebool,c_2EordinalNotation_2Eis__ord_2E1(s(tyop_2EordinalNotation_2Eosyntax,V5a0_2E0)))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Ebool),V0is__ord_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,V5a0_2E0))))))).
