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_2Eordinal_2Edclose_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Edclose_2E1(s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),c_2Eordinal_2Edclose_2E0),s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Eordinal_2Epreds_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Epreds_2E1(s(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool)),c_2Eordinal_2Epreds_2E0),s(tyop_2Eordinal_2Eordinal(A_27a),X0_2E0))))).
fof(arityeq1_2Ec_2Eordinal_2Esup_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Esup_2E1(s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eordinal_2Eordinal(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Eordinal_2Eordinal(A_27a)),c_2Eordinal_2Esup_2E0),s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ecardinal_2Ecardleq_2E0),s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X1_2E0))))).
fof(ordinalTheory_2Epreds__sup,axiom,![A_27a]: ![V0s_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) => (s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Epreds_2E1(s(tyop_2Eordinal_2Eordinal(A_27a),c_2Eordinal_2Esup_2E1(s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),c_2Eordinal_2Edclose_2E1(s(tyop_2Emin_2Efun(tyop_2Eordinal_2Eordinal(A_27a),tyop_2Emin_2Ebool),V0s_2E0)))))).
