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_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_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(arityeq3_2Ec_2EordinalNotation_2Ecf2_2E3,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Enum_2Enum,c_2EordinalNotation_2Ecf2_2E3(s(tyop_2EordinalNotation_2Eosyntax,X0_2E0),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2EordinalNotation_2Ecf2_2E0),s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))),s(tyop_2EordinalNotation_2Eosyntax,X1_2E0))),s(tyop_2Enum_2Enum,X2_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(ordinalNotationTheory_2Epmult__ind,axiom,![V0P_2E0]: (![V1a_2E0, V2b_2E0, V3n_2E0]: (![V4v_2E0, V5v1_2E0, V6e2_2E0, V7c2_2E0, V8k2_2E0, V9m_2E0]: ((~ (((s(tyop_2EordinalNotation_2Eosyntax,V1a_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) | (s(tyop_2EordinalNotation_2Eosyntax,V2b_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) & ((s(tyop_2Epair_2Eprod(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),c_2Epair_2E_2C_2E2(s(tyop_2EordinalNotation_2Eosyntax,V1a_2E0),s(tyop_2EordinalNotation_2Eosyntax,V2b_2E0))) = s(tyop_2Epair_2Eprod(tyop_2EordinalNotation_2Eosyntax,tyop_2EordinalNotation_2Eosyntax),c_2Epair_2E_2C_2E2(s(tyop_2EordinalNotation_2Eosyntax,V4v_2E0),s(tyop_2EordinalNotation_2Eosyntax,V5v1_2E0)))) & ((s(tyop_2EordinalNotation_2Eosyntax,V5v1_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V6e2_2E0),s(tyop_2Enum_2Enum,V7c2_2E0),s(tyop_2EordinalNotation_2Eosyntax,V8k2_2E0)))) & (s(tyop_2Enum_2Enum,V9m_2E0) = s(tyop_2Enum_2Enum,c_2EordinalNotation_2Ecf2_2E3(s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2Eexpt_2E1(s(tyop_2EordinalNotation_2Eosyntax,V1a_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V6e2_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2EordinalNotation_2Eosyntax,V1a_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V8k2_2E0))),s(tyop_2Enum_2Enum,V9m_2E0))))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2EordinalNotation_2Eosyntax,V1a_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V2b_2E0))),s(tyop_2Enum_2Enum,V3n_2E0))))) => ![V10v_2E0, V11v1_2E0, V12v2_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2EordinalNotation_2Eosyntax,V10v_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V11v1_2E0))),s(tyop_2Enum_2Enum,V12v2_2E0)))))).
