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_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(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(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(ordinalNotationTheory_2Eoless__def,axiom,![V0x_2E0, V1x_27_2E0]: (p(s(tyop_2Emin_2Ebool,c_2EordinalNotation_2Eoless_2E2(s(tyop_2EordinalNotation_2Eosyntax,V0x_2E0),s(tyop_2EordinalNotation_2Eosyntax,V1x_27_2E0)))) <=> ![V2oless_27_2E0]: (![V3a0_2E0, V4a1_2E0]: ((?[V5k1_2E0, V6k2_2E0]: ((s(tyop_2EordinalNotation_2Eosyntax,V3a0_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,V5k1_2E0)))) & ((s(tyop_2EordinalNotation_2Eosyntax,V4a1_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,V6k2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V5k1_2E0),s(tyop_2Enum_2Enum,V6k2_2E0)))))) | (?[V7k1_2E0, V8e2_2E0, V9k2_2E0, V10t2_2E0]: ((s(tyop_2EordinalNotation_2Eosyntax,V3a0_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EEnd_2E1(s(tyop_2Enum_2Enum,V7k1_2E0)))) & (s(tyop_2EordinalNotation_2Eosyntax,V4a1_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V8e2_2E0),s(tyop_2Enum_2Enum,V9k2_2E0),s(tyop_2EordinalNotation_2Eosyntax,V10t2_2E0))))) | (?[V11e1_2E0, V12k1_2E0, V13t1_2E0, V14e2_2E0, V15k2_2E0, V16t2_2E0]: ((s(tyop_2EordinalNotation_2Eosyntax,V3a0_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V11e1_2E0),s(tyop_2Enum_2Enum,V12k1_2E0),s(tyop_2EordinalNotation_2Eosyntax,V13t1_2E0)))) & ((s(tyop_2EordinalNotation_2Eosyntax,V4a1_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V14e2_2E0),s(tyop_2Enum_2Enum,V15k2_2E0),s(tyop_2EordinalNotation_2Eosyntax,V16t2_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)),V2oless_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,V11e1_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V14e2_2E0)))))) | (?[V17e1_2E0, V18k1_2E0, V19t1_2E0, V20e2_2E0, V21k2_2E0, V22t2_2E0]: ((s(tyop_2EordinalNotation_2Eosyntax,V3a0_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V17e1_2E0),s(tyop_2Enum_2Enum,V18k1_2E0),s(tyop_2EordinalNotation_2Eosyntax,V19t1_2E0)))) & ((s(tyop_2EordinalNotation_2Eosyntax,V4a1_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V20e2_2E0),s(tyop_2Enum_2Enum,V21k2_2E0),s(tyop_2EordinalNotation_2Eosyntax,V22t2_2E0)))) & ((s(tyop_2EordinalNotation_2Eosyntax,V17e1_2E0) = s(tyop_2EordinalNotation_2Eosyntax,V20e2_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V18k1_2E0),s(tyop_2Enum_2Enum,V21k2_2E0))))))) | ?[V23e1_2E0, V24k1_2E0, V25t1_2E0, V26e2_2E0, V27k2_2E0, V28t2_2E0]: ((s(tyop_2EordinalNotation_2Eosyntax,V3a0_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V23e1_2E0),s(tyop_2Enum_2Enum,V24k1_2E0),s(tyop_2EordinalNotation_2Eosyntax,V25t1_2E0)))) & ((s(tyop_2EordinalNotation_2Eosyntax,V4a1_2E0) = s(tyop_2EordinalNotation_2Eosyntax,c_2EordinalNotation_2EPlus_2E3(s(tyop_2EordinalNotation_2Eosyntax,V26e2_2E0),s(tyop_2Enum_2Enum,V27k2_2E0),s(tyop_2EordinalNotation_2Eosyntax,V28t2_2E0)))) & ((s(tyop_2EordinalNotation_2Eosyntax,V23e1_2E0) = s(tyop_2EordinalNotation_2Eosyntax,V26e2_2E0)) & ((s(tyop_2Enum_2Enum,V24k1_2E0) = s(tyop_2Enum_2Enum,V27k2_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)),V2oless_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,V25t1_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V28t2_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)),V2oless_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,V3a0_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V4a1_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)),V2oless_27_2E0),s(tyop_2EordinalNotation_2Eosyntax,V0x_2E0))),s(tyop_2EordinalNotation_2Eosyntax,V1x_27_2E0))))))).
