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(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_2Eosyntax__CASE_2E3_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(A_27a,c_2EordinalNotation_2Eosyntax__CASE_2E3(s(tyop_2EordinalNotation_2Eosyntax,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,A_27a))),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,A_27a))),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,A_27a))),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,A_27a))),A_27a))),c_2EordinalNotation_2Eosyntax__CASE_2E0),s(tyop_2EordinalNotation_2Eosyntax,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,A_27a))),X2_2E0))))).
fof(ordinalNotationTheory_2Eosyntax__case__eq,axiom,![A_27a]: ![V0v_2E0, V1f1_2E0, V2f_2E0, V3x_2E0]: ((s(A_27a,c_2EordinalNotation_2Eosyntax__CASE_2E3(s(tyop_2EordinalNotation_2Eosyntax,V3x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,A_27a))),V1f1_2E0))) = s(A_27a,V0v_2E0)) <=> (?[V4n_2E0]: ((s(tyop_2EordinalNotation_2Eosyntax,V3x_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))) & (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))) = s(A_27a,V0v_2E0))) | ?[V5o_27_2E0, V6n_2E0, V7o0_2E0]: ((s(tyop_2EordinalNotation_2Eosyntax,V3x_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V5o_27_2E0),s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2EordinalNotation_2Eosyntax,V7o0_2E0)))) & (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2EordinalNotation_2Eosyntax,A_27a))),V1f1_2E0),s(tyop_2EordinalNotation_2Eosyntax,V5o_27_2E0))),s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V7o0_2E0))) = s(A_27a,V0v_2E0)))))).
