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(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))))).
fof(arityeq2_2Ec_2EordinalNotation_2Eord__mult_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eord__mult_2E2(s(tyop_2EordinalNotation_2Eosyntax,X0_2E0),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),c_2EordinalNotation_2Eord__mult_2E0),s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2EordinalNotation_2Eosyntax_20mono_2Etyop_2EordinalNotation_2Eosyntax,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),c_2Epair_2E_2C_2E2(s(tyop_2EordinalNotation_2Eosyntax,X0_2E0),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Epair_2Eprod(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Epair_2Eprod(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax))),c_2Epair_2E_2C_2E0),s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0))))).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2EordinalNotation_2Eosyntax,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2EordinalNotation_2Eosyntax,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_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0))),s(tyop_2EordinalNotation_2Eosyntax,X2_2E0))))).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2EordinalNotation_2Eosyntax_20mono_2Etyop_2EordinalNotation_2Eosyntax_20mono_2Etyop_2EordinalNotation_2Eosyntax,axiom,![X0_2E0, X1_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),X0_2E0),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),X1_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),tyop_2EordinalNotation_2Eosyntax)),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),X1_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_2EordinalNotation_2Eord__add_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eord__add_2E2(s(tyop_2EordinalNotation_2Eosyntax,X0_2E0),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),c_2EordinalNotation_2Eord__add_2E0),s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0))))).
fof(arityeq3_2Ec_2EordinalNotation_2Eosyntax__CASE_2E3_2Emono_2Etyop_2EordinalNotation_2Eosyntax,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eosyntax__CASE_2E3(s(tyop_2EordinalNotation_2Eosyntax,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),X1_2E0),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax))),X2_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax))),tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax))),tyop_2EordinalNotation_2Eosyntax)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax))),tyop_2EordinalNotation_2Eosyntax))),c_2EordinalNotation_2Eosyntax__CASE_2E0),s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax))),X2_2E0))))).
fof(ordinalNotationTheory_2Eord__mult__def,axiom,![F7_2E0, F6_2E0, F3_2E0, F5_2E0, F4_2E0, F2_2E0, F1_2E0, F0_2E0]: (![V9e_27_2E0, V10k_27_2E0, V11t_27_2E0, V13e2_2E0, V14k2_2E0, V15t2_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))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,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_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)))))),F7_2E0),s(tyop_2EordinalNotation_2Eosyntax,V9e_27_2E0))),s(tyop_2Enum_2Enum,V10k_27_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V11t_27_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V13e2_2E0))),s(tyop_2Enum_2Enum,V14k2_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V15t2_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eord__add_2E2(s(tyop_2EordinalNotation_2Eosyntax,V9e_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,V13e2_2E0))),s(tyop_2Enum_2Enum,V14k2_2E0),s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eord__mult_2E2(s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V9e_27_2E0),s(tyop_2Enum_2Enum,V10k_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,V11t_27_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V15t2_2E0)))))) => (![V9e_27_2E0, V10k_27_2E0, V11t_27_2E0, V12n_27_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax)))),F6_2E0),s(tyop_2EordinalNotation_2Eosyntax,V9e_27_2E0))),s(tyop_2Enum_2Enum,V10k_27_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V11t_27_2E0))),s(tyop_2Enum_2Enum,V12n_27_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V9e_27_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V10k_27_2E0),s(tyop_2Enum_2Enum,V12n_27_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V11t_27_2E0)))) => (![V3v1_2E0, V9e_27_2E0, V10k_27_2E0, V11t_27_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))),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)))),F3_2E0),s(tyop_2EordinalNotation_2Eosyntax,V3v1_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V9e_27_2E0))),s(tyop_2Enum_2Enum,V10k_27_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V11t_27_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eosyntax__CASE_2E3(s(tyop_2EordinalNotation_2Eosyntax,V3v1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax)))),F6_2E0),s(tyop_2EordinalNotation_2Eosyntax,V9e_27_2E0))),s(tyop_2Enum_2Enum,V10k_27_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V11t_27_2E0))),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,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_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,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_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)))))),F7_2E0),s(tyop_2EordinalNotation_2Eosyntax,V9e_27_2E0))),s(tyop_2Enum_2Enum,V10k_27_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V11t_27_2E0)))))) => (![V4m_2E0, V6e_2E0, V7k_2E0, V8t_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))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)))),F5_2E0),s(tyop_2Enum_2Enum,V4m_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V6e_2E0))),s(tyop_2Enum_2Enum,V7k_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V8t_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eord__add_2E2(s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V6e_2E0))),s(tyop_2Enum_2Enum,V7k_2E0),s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eord__mult_2E2(s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,V4m_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V8t_2E0)))))) => (![V4m_2E0, V5n_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax)),F4_2E0),s(tyop_2Enum_2Enum,V4m_2E0))),s(tyop_2Enum_2Enum,V5n_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V4m_2E0),s(tyop_2Enum_2Enum,V5n_2E0)))))) => (![V3v1_2E0, V4m_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax)),F2_2E0),s(tyop_2EordinalNotation_2Eosyntax,V3v1_2E0))),s(tyop_2Enum_2Enum,V4m_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eosyntax__CASE_2E3(s(tyop_2EordinalNotation_2Eosyntax,V3v1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax)),F4_2E0),s(tyop_2Enum_2Enum,V4m_2E0))),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)))),F5_2E0),s(tyop_2Enum_2Enum,V4m_2E0)))))) => (![V2v_2E0, V3v1_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),F1_2E0),s(tyop_2EordinalNotation_2Eosyntax,V2v_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V3v1_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eosyntax__CASE_2E3(s(tyop_2EordinalNotation_2Eosyntax,V2v_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2EordinalNotation_2Eosyntax)),F2_2E0),s(tyop_2EordinalNotation_2Eosyntax,V3v1_2E0))),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,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_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)))),F3_2E0),s(tyop_2EordinalNotation_2Eosyntax,V3v1_2E0)))))) => (![V1x_2E0, V0y_2E0]: (p(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)),F0_2E0),s(tyop_2EordinalNotation_2Eosyntax,V1x_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V0y_2E0)))) <=> ((s(tyop_2EordinalNotation_2Eosyntax,V1x_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) | (s(tyop_2EordinalNotation_2Eosyntax,V0y_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) => ![V0y_2E0, V1x_2E0]: (s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eord__mult_2E2(s(tyop_2EordinalNotation_2Eosyntax,V1x_2E0),s(tyop_2EordinalNotation_2Eosyntax,V0y_2E0))) = s(tyop_2EordinalNotation_2Eosyntax,c_2Ebool_2ECOND_2E3(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)),F0_2E0),s(tyop_2EordinalNotation_2Eosyntax,V1x_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V0y_2E0))),s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2EordinalNotation_2Eosyntax,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),c_2Epair_2E_2C_2E2(s(tyop_2EordinalNotation_2Eosyntax,V1x_2E0),s(tyop_2EordinalNotation_2Eosyntax,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax)),F1_2E0))))))))))))))).
