cocATP---0.2.0.THM-Prf.s

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SCT171^2 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n089.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:29:46 EDT 2014

% Result   : Theorem 7.59s
% Output   : Proof 7.59s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SCT171^2 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n089.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:29:36 CDT 2014
% % CPUTime  : 7.59 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x115c098>, <kernel.Type object at 0x115b950>) of role type named ty_ty_tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt
% Using role type
% Declaring arrow_475358991le_alt:Type
% FOF formula (<kernel.Constant object at 0x115c9e0>, <kernel.Type object at 0x115b950>) of role type named ty_ty_tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring arrow_1429601828e_indi:Type
% FOF formula (<kernel.Constant object at 0x115c1b8>, <kernel.Type object at 0x115b0e0>) of role type named ty_ty_tc__Nat__Onat
% Using role type
% Declaring nat:Type
% FOF formula (<kernel.Constant object at 0x115c2d8>, <kernel.Type object at 0x115b950>) of role type named ty_ty_tc__Product____Type__Ounit
% Using role type
% Declaring product_unit:Type
% FOF formula (<kernel.Constant object at 0x115c9e0>, <kernel.Type object at 0x115b908>) of role type named ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_Mtc__Arrow__
% Using role type
% Declaring produc1501160679le_alt:Type
% FOF formula (<kernel.Constant object at 0x115c9e0>, <kernel.DependentProduct object at 0x115bd40>) of role type named sy_c_All
% Using role type
% Declaring all:((produc1501160679le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x115c9e0>, <kernel.DependentProduct object at 0x115b4d0>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_OIIA
% Using role type
% Declaring arrow_797024463le_IIA:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x115bcf8>, <kernel.DependentProduct object at 0x115bf80>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_OLin
% Using role type
% Declaring arrow_823908191le_Lin:((produc1501160679le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x115b488>, <kernel.DependentProduct object at 0x115bd40>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_OProf
% Using role type
% Declaring arrow_734252939e_Prof:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x115bf38>, <kernel.DependentProduct object at 0x115b4d0>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Oabove
% Using role type
% Declaring arrow_789600939_above:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->(produc1501160679le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0x115bf80>, <kernel.DependentProduct object at 0x115b050>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Obelow
% Using role type
% Declaring arrow_2098199487_below:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->(produc1501160679le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0x115b518>, <kernel.DependentProduct object at 0x115b050>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Odictator
% Using role type
% Declaring arrow_1212662430ctator:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))
% FOF formula (<kernel.Constant object at 0x115be18>, <kernel.DependentProduct object at 0x115bd40>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Omkbot
% Using role type
% Declaring arrow_2054445623_mkbot:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(produc1501160679le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x115bc68>, <kernel.DependentProduct object at 0x115bcf8>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Omktop
% Using role type
% Declaring arrow_55669061_mktop:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(produc1501160679le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x115bf38>, <kernel.DependentProduct object at 0x115b050>) of role type named sy_c_Arrow__Order__Mirabelle__lcilvlkkzv_Ounanimity
% Using role type
% Declaring arrow_1706409458nimity:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x115b488>, <kernel.DependentProduct object at 0x115bab8>) of role type named sy_c_Finite__Set_Ocard_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O
% Using role type
% Declaring finite120663670_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x115bd40>, <kernel.DependentProduct object at 0x115b440>) of role type named sy_c_Finite__Set_Ocard_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lci
% Using role type
% Declaring finite28306938_alt_o:(((produc1501160679le_alt->Prop)->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x115b950>, <kernel.DependentProduct object at 0x115bb00>) of role type named sy_c_Finite__Set_Ocard_000_Eo
% Using role type
% Declaring finite_card_o:((Prop->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x115b518>, <kernel.DependentProduct object at 0x115b488>) of role type named sy_c_Finite__Set_Ocard_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring finite97476818e_indi:((arrow_1429601828e_indi->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x115b440>, <kernel.DependentProduct object at 0x115b128>) of role type named sy_c_Finite__Set_Ocard_000tc__Nat__Onat
% Using role type
% Declaring finite_card_nat:((nat->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x115b998>, <kernel.DependentProduct object at 0x115b9e0>) of role type named sy_c_Finite__Set_Ocard_000tc__Product____Type__Ounit
% Using role type
% Declaring finite1949902593t_unit:((product_unit->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x115bf38>, <kernel.DependentProduct object at 0x115bb48>) of role type named sy_c_Finite__Set_Ocard_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz
% Using role type
% Declaring finite537683861le_alt:((produc1501160679le_alt->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x115bb00>, <kernel.DependentProduct object at 0x115bb48>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% Using role type
% Declaring finite1956767223_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x115bd40>, <kernel.DependentProduct object at 0x115bb48>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____l
% Using role type
% Declaring finite2112685307_alt_o:(((produc1501160679le_alt->Prop)->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x115bc68>, <kernel.DependentProduct object at 0x115bb90>) of role type named sy_c_Finite__Set_Ofinite_000_Eo
% Using role type
% Declaring finite_finite_o:((Prop->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x115b638>, <kernel.DependentProduct object at 0x115b170>) of role type named sy_c_Finite__Set_Ofinite_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring finite664979089e_indi:((arrow_1429601828e_indi->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x115bb48>, <kernel.DependentProduct object at 0x115bc68>) of role type named sy_c_Finite__Set_Ofinite_000tc__Nat__Onat
% Using role type
% Declaring finite_finite_nat:((nat->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x115b440>, <kernel.DependentProduct object at 0x115b170>) of role type named sy_c_Finite__Set_Ofinite_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlk
% Using role type
% Declaring finite449174868le_alt:((produc1501160679le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x115b1b8>, <kernel.DependentProduct object at 0x115b3f8>) of role type named sy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_000t
% Using role type
% Declaring in_rel1252994498le_alt:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x115b680>, <kernel.DependentProduct object at 0x115bfc8>) of role type named sy_c_Fun_Oinj__on_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_
% Using role type
% Declaring inj_on1284293749_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x115b878>, <kernel.DependentProduct object at 0x115b1b8>) of role type named sy_c_Fun_Oinj__on_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring inj_on743426285_alt_o:(((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((produc1501160679le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x115b3f8>, <kernel.DependentProduct object at 0x115b440>) of role type named sy_c_Fun_Oinj__on_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk_001
% Using role type
% Declaring inj_on1877294875e_indi:(((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->(((produc1501160679le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x115b3b0>, <kernel.DependentProduct object at 0x115b830>) of role type named sy_c_Fun_Oinj__on_000_Eo_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlk
% Using role type
% Declaring inj_on867909093le_alt:((Prop->produc1501160679le_alt)->((Prop->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x115b878>, <kernel.DependentProduct object at 0x115b440>) of role type named sy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000_06
% Using role type
% Declaring inj_on1190919077_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((arrow_1429601828e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x115b680>, <kernel.DependentProduct object at 0x115ba28>) of role type named sy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000tc_
% Using role type
% Declaring inj_on978774663di_nat:((arrow_1429601828e_indi->nat)->((arrow_1429601828e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x115b8c0>, <kernel.DependentProduct object at 0x115bc20>) of role type named sy_c_Fun_Oinj__on_000tc__Nat__Onat_000tc__Nat__Onat
% Using role type
% Declaring inj_on_nat_nat:((nat->nat)->((nat->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x115bfc8>, <kernel.DependentProduct object at 0x115bbd8>) of role type named sy_c_Fun_Oinj__on_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa
% Using role type
% Declaring inj_on1911943593_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x115b3b0>, <kernel.DependentProduct object at 0x115b8c0>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O
% Using role type
% Declaring pi_Arr195212324lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x113acf8>, <kernel.DependentProduct object at 0x115b440>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O_002
% Using role type
% Declaring pi_Arr338314351e_indi:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x13a6200>, <kernel.DependentProduct object at 0x113d3b0>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O_003
% Using role type
% Declaring pi_Arr830584606t_unit:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(product_unit->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->product_unit)->Prop)))
% FOF formula (<kernel.Constant object at 0x113d368>, <kernel.DependentProduct object at 0x115ba28>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M
% Using role type
% Declaring pi_Arr1304755663_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x113d3b0>, <kernel.DependentProduct object at 0x115b998>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_004
% Using role type
% Declaring pi_Arr952516694lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x113d488>, <kernel.DependentProduct object at 0x115b8c0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_005
% Using role type
% Declaring pi_Arr1232280765e_indi:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x113d488>, <kernel.DependentProduct object at 0x115bfc8>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_006
% Using role type
% Declaring pi_Arr1963174508t_unit:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(product_unit->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->product_unit)->Prop)))
% FOF formula (<kernel.Constant object at 0x115bbd8>, <kernel.DependentProduct object at 0x115ba28>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz
% Using role type
% Declaring pi_Pro763888199_alt_o:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->(((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x115b3b0>, <kernel.DependentProduct object at 0x115b878>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz_007
% Using role type
% Declaring pi_Pro422690258lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(Prop->Prop))->(((produc1501160679le_alt->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x115b440>, <kernel.DependentProduct object at 0x115bbd8>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz_008
% Using role type
% Declaring pi_Pro468373057e_indi:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))->(((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x115bc20>, <kernel.DependentProduct object at 0x115d050>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz_009
% Using role type
% Declaring pi_Pro1306850800t_unit:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(product_unit->Prop))->(((produc1501160679le_alt->Prop)->product_unit)->Prop)))
% FOF formula (<kernel.Constant object at 0x115bbd8>, <kernel.DependentProduct object at 0x115d7e8>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvl
% Using role type
% Declaring pi_o_A1186128886_alt_o:((Prop->Prop)->((Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x115b440>, <kernel.DependentProduct object at 0x115d6c8>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring pi_o_A1182933120_alt_o:((Prop->Prop)->((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x115bbd8>, <kernel.DependentProduct object at 0x115dc68>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lc
% Using role type
% Declaring pi_o_P553196292_alt_o:((Prop->Prop)->((Prop->((produc1501160679le_alt->Prop)->Prop))->((Prop->(produc1501160679le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x115b440>, <kernel.DependentProduct object at 0x115d7e8>) of role type named sy_c_FuncSet_OPi_000_Eo_000tc__Nat__Onat
% Using role type
% Declaring pi_o_nat:((Prop->Prop)->((Prop->(nat->Prop))->((Prop->nat)->Prop)))
% FOF formula (<kernel.Constant object at 0x115bc20>, <kernel.DependentProduct object at 0x115d7e8>) of role type named sy_c_FuncSet_OPi_000_Eo_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring pi_o_P657324555le_alt:((Prop->Prop)->((Prop->(produc1501160679le_alt->Prop))->((Prop->produc1501160679le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x115bc20>, <kernel.DependentProduct object at 0x115d3f8>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000_062
% Using role type
% Declaring pi_Arr1564509167_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x115d908>, <kernel.DependentProduct object at 0x115d3f8>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000_062_010
% Using role type
% Declaring pi_Arr1060328391_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x115d950>, <kernel.DependentProduct object at 0x115d6c8>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000_062_011
% Using role type
% Declaring pi_Arr1929480907_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x115d368>, <kernel.DependentProduct object at 0x115d908>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000tc__
% Using role type
% Declaring pi_Arr251692973di_nat:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->(nat->Prop))->((arrow_1429601828e_indi->nat)->Prop)))
% FOF formula (<kernel.Constant object at 0x115dab8>, <kernel.DependentProduct object at 0x115d950>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000tc___012
% Using role type
% Declaring pi_Arr329216900le_alt:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((arrow_1429601828e_indi->produc1501160679le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x115db90>, <kernel.DependentProduct object at 0x115d7a0>) of role type named sy_c_FuncSet_OPi_000tc__Nat__Onat_000_Eo
% Using role type
% Declaring pi_nat_o:((nat->Prop)->((nat->(Prop->Prop))->((nat->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x115d4d0>, <kernel.DependentProduct object at 0x115dab8>) of role type named sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring pi_nat1219304995e_indi:((nat->Prop)->((nat->(arrow_1429601828e_indi->Prop))->((nat->arrow_1429601828e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x115d6c8>, <kernel.DependentProduct object at 0x115db90>) of role type named sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Nat__Onat
% Using role type
% Declaring pi_nat_nat:((nat->Prop)->((nat->(nat->Prop))->((nat->nat)->Prop)))
% FOF formula (<kernel.Constant object at 0x115d290>, <kernel.DependentProduct object at 0x115d4d0>) of role type named sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Product____Type__Ounit
% Using role type
% Declaring pi_nat_Product_unit:((nat->Prop)->((nat->(product_unit->Prop))->((nat->product_unit)->Prop)))
% FOF formula (<kernel.Constant object at 0x115d638>, <kernel.DependentProduct object at 0x115d680>) of role type named sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000_062_I_062_Itc__Arrow____Order
% Using role type
% Declaring pi_Pro1782982558_alt_o:((product_unit->Prop)->((product_unit->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x115da70>, <kernel.DependentProduct object at 0x115d4d0>) of role type named sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000_062_Itc__Arrow____Order____Mi
% Using role type
% Declaring pi_Pro1662176984_alt_o:((product_unit->Prop)->((product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((product_unit->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x115d7a0>, <kernel.DependentProduct object at 0x115d6c8>) of role type named sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000_062_Itc__prod_Itc__Arrow____O
% Using role type
% Declaring pi_Pro1312660828_alt_o:((product_unit->Prop)->((product_unit->((produc1501160679le_alt->Prop)->Prop))->((product_unit->(produc1501160679le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x115db90>, <kernel.DependentProduct object at 0x115d6c8>) of role type named sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__Nat__Onat
% Using role type
% Declaring pi_Product_unit_nat:((product_unit->Prop)->((product_unit->(nat->Prop))->((product_unit->nat)->Prop)))
% FOF formula (<kernel.Constant object at 0x115d680>, <kernel.DependentProduct object at 0x115d6c8>) of role type named sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__prod_Itc__Arrow____Order__
% Using role type
% Declaring pi_Pro701847987le_alt:((product_unit->Prop)->((product_unit->(produc1501160679le_alt->Prop))->((product_unit->produc1501160679le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x115d290>, <kernel.DependentProduct object at 0x115db90>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal
% Using role type
% Declaring pi_Pro1701359055_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(Prop->Prop))->((produc1501160679le_alt->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x115d7a0>, <kernel.DependentProduct object at 0x13a22d8>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal_013
% Using role type
% Declaring pi_Pro1767455108e_indi:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(arrow_1429601828e_indi->Prop))->((produc1501160679le_alt->arrow_1429601828e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x115db90>, <kernel.DependentProduct object at 0x13a22d8>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oal_014
% Using role type
% Declaring pi_Pro1475896499t_unit:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(product_unit->Prop))->((produc1501160679le_alt->product_unit)->Prop)))
% FOF formula (<kernel.Constant object at 0x115d290>, <kernel.Constant object at 0x13a2cb0>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat
% Using role type
% Declaring one_one_nat:nat
% FOF formula (<kernel.Constant object at 0x115db90>, <kernel.DependentProduct object at 0x13a2d88>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat
% Using role type
% Declaring plus_plus_nat:(nat->(nat->nat))
% FOF formula (<kernel.Constant object at 0x115d290>, <kernel.Constant object at 0x13a2290>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat
% Using role type
% Declaring zero_zero_nat:nat
% FOF formula (<kernel.Constant object at 0x115d7a0>, <kernel.DependentProduct object at 0x13a2d88>) of role type named sy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____lcilvlkkzv
% Using role type
% Declaring hilber598459244di_nat:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->nat)->(nat->arrow_1429601828e_indi)))
% FOF formula (<kernel.Constant object at 0x115d7a0>, <kernel.DependentProduct object at 0x13a22d8>) of role type named sy_c_Hilbert__Choice_Oinv__into_000tc__Nat__Onat_000tc__Nat__Onat
% Using role type
% Declaring hilber195283148at_nat:((nat->Prop)->((nat->nat)->(nat->nat)))
% FOF formula (<kernel.Constant object at 0x13a2d40>, <kernel.DependentProduct object at 0x13a2ea8>) of role type named sy_c_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_M
% Using role type
% Declaring if_Pro1561232536_alt_o:(Prop->((produc1501160679le_alt->Prop)->((produc1501160679le_alt->Prop)->(produc1501160679le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0x13a2f38>, <kernel.DependentProduct object at 0xf4f908>) of role type named sy_c_Nat_OSuc
% Using role type
% Declaring suc:(nat->nat)
% FOF formula (<kernel.Constant object at 0x13a2fc8>, <kernel.DependentProduct object at 0xf4f7e8>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_I_062_I_062_Itc__Arrow____Order____Mira
% Using role type
% Declaring ord_le1859604819lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x13a2290>, <kernel.DependentProduct object at 0xf4f950>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__Arrow____Order____Mirabelle_
% Using role type
% Declaring ord_le157835011lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x13a2f38>, <kernel.DependentProduct object at 0xf4f878>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__prod_Itc__Arrow____Order____
% Using role type
% Declaring ord_le910298367lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x13a2fc8>, <kernel.DependentProduct object at 0xf4f758>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_I_Eo_M_Eo_J
% Using role type
% Declaring ord_less_o_o:((Prop->Prop)->((Prop->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x13a2f80>, <kernel.DependentProduct object at 0xf4f7a0>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__Arrow____Order____Mirabelle____lci
% Using role type
% Declaring ord_le777687553indi_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x13a2fc8>, <kernel.DependentProduct object at 0xf4f6c8>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring ord_less_nat_o:((nat->Prop)->((nat->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x13a2290>, <kernel.DependentProduct object at 0xf4f710>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__Product____Type__Ounit_M_Eo_J
% Using role type
% Declaring ord_le232288914unit_o:((product_unit->Prop)->((product_unit->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x13a2290>, <kernel.DependentProduct object at 0xf4f638>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__prod_Itc__Arrow____Order____Mirabe
% Using role type
% Declaring ord_le988258430_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4f7a0>, <kernel.DependentProduct object at 0xf4f878>) of role type named sy_c_Orderings_Oord__class_Oless_000_Eo
% Using role type
% Declaring ord_less_o:(Prop->(Prop->Prop))
% FOF formula (<kernel.Constant object at 0xf4f6c8>, <kernel.DependentProduct object at 0xf4f7e8>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat
% Using role type
% Declaring ord_less_nat:(nat->(nat->Prop))
% FOF formula (<kernel.Constant object at 0xf4f638>, <kernel.DependentProduct object at 0xf4f5f0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Arrow____Order____
% Using role type
% Declaring ord_le134800455lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4f878>, <kernel.DependentProduct object at 0xf4f710>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Arrow____Order____Mirabe
% Using role type
% Declaring ord_le1992928527lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4f5a8>, <kernel.DependentProduct object at 0xf4f7a0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__prod_Itc__Arrow____Order
% Using role type
% Declaring ord_le1063113995lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4f6c8>, <kernel.DependentProduct object at 0xf4f488>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_Eo_M_Eo_J
% Using role type
% Declaring ord_less_eq_o_o:((Prop->Prop)->((Prop->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4f878>, <kernel.DependentProduct object at 0xf4f560>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Arrow____Order____Mirabelle___
% Using role type
% Declaring ord_le2080035663_alt_o:((arrow_475358991le_alt->(arrow_475358991le_alt->Prop))->((arrow_475358991le_alt->(arrow_475358991le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0xf4f638>, <kernel.DependentProduct object at 0xf4f440>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Arrow____Order____Mirabelle____015
% Using role type
% Declaring ord_le1799070453indi_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4f4d0>, <kernel.DependentProduct object at 0xf4f3f8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring ord_less_eq_nat_o:((nat->Prop)->((nat->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4f518>, <kernel.DependentProduct object at 0xf4f9e0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Product____Type__Ounit_M_Eo_J
% Using role type
% Declaring ord_le1511552390unit_o:((product_unit->Prop)->((product_unit->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4f7a0>, <kernel.DependentProduct object at 0xf4fa28>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__Arrow____Order____Mi
% Using role type
% Declaring ord_le97612146_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4f878>, <kernel.DependentProduct object at 0xf4f4d0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_Eo
% Using role type
% Declaring ord_less_eq_o:(Prop->(Prop->Prop))
% FOF formula (<kernel.Constant object at 0xf4f518>, <kernel.DependentProduct object at 0xf4f9e0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat
% Using role type
% Declaring ord_less_eq_nat:(nat->(nat->Prop))
% FOF formula (<kernel.Constant object at 0xf4fa28>, <kernel.DependentProduct object at 0xf4fab8>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_I_062_I_062_Itc__Arrow____Order____Mirab
% Using role type
% Declaring top_to1969627639lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0xf4f4d0>, <kernel.DependentProduct object at 0xf4f518>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__Arrow____Order____Mirabelle__
% Using role type
% Declaring top_to2122763103lt_o_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0xf4fa70>, <kernel.DependentProduct object at 0xf4f9e0>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__prod_Itc__Arrow____Order____M
% Using role type
% Declaring top_to1842727771lt_o_o:((produc1501160679le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0xf4fab8>, <kernel.DependentProduct object at 0xf4f518>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_I_Eo_M_Eo_J
% Using role type
% Declaring top_top_o_o:(Prop->Prop)
% FOF formula (<kernel.Constant object at 0xf4f4d0>, <kernel.DependentProduct object at 0xf4fb90>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____lcil
% Using role type
% Declaring top_to988227749indi_o:(arrow_1429601828e_indi->Prop)
% FOF formula (<kernel.Constant object at 0xf4fb48>, <kernel.DependentProduct object at 0xf4fbd8>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring top_top_nat_o:(nat->Prop)
% FOF formula (<kernel.Constant object at 0xf4f518>, <kernel.DependentProduct object at 0xf4fc20>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Product____Type__Ounit_M_Eo_J
% Using role type
% Declaring top_to1984820022unit_o:(product_unit->Prop)
% FOF formula (<kernel.Constant object at 0xf4fb90>, <kernel.DependentProduct object at 0xf4fc68>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__Arrow____Order____Mirabel
% Using role type
% Declaring top_to1841428258_alt_o:(produc1501160679le_alt->Prop)
% FOF formula (<kernel.Constant object at 0xf4fbd8>, <kernel.Sort object at 0xe2f998>) of role type named sy_c_Orderings_Otop__class_Otop_000_Eo
% Using role type
% Declaring top_top_o:Prop
% FOF formula (<kernel.Constant object at 0xf4f9e0>, <kernel.DependentProduct object at 0xf4f518>) of role type named sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_
% Using role type
% Declaring produc1347929815le_alt:(arrow_475358991le_alt->(arrow_475358991le_alt->produc1501160679le_alt))
% FOF formula (<kernel.Constant object at 0xf4fb00>, <kernel.DependentProduct object at 0xf4fd40>) of role type named sy_c_SetInterval_Oord__class_OatLeastLessThan_000tc__Nat__Onat
% Using role type
% Declaring ord_at4362885an_nat:(nat->(nat->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0xf4fb90>, <kernel.DependentProduct object at 0xf4fcb0>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring collec2009291517_alt_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0xf4f518>, <kernel.DependentProduct object at 0xf4f9e0>) of role type named sy_c_Set_OCollect_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_
% Using role type
% Declaring collec682858041_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0xf4fbd8>, <kernel.DependentProduct object at 0xf4fef0>) of role type named sy_c_Set_OCollect_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring collec94295101_alt_o:(((produc1501160679le_alt->Prop)->Prop)->((produc1501160679le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4fb00>, <kernel.DependentProduct object at 0xf4fd88>) of role type named sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring collec22405327e_indi:((arrow_1429601828e_indi->Prop)->(arrow_1429601828e_indi->Prop))
% FOF formula (<kernel.Constant object at 0xf4f8c0>, <kernel.DependentProduct object at 0xf4fb00>) of role type named sy_c_Set_OCollect_000tc__Nat__Onat
% Using role type
% Declaring collect_nat:((nat->Prop)->(nat->Prop))
% FOF formula (<kernel.Constant object at 0xf4fe60>, <kernel.DependentProduct object at 0xf4fef0>) of role type named sy_c_Set_OCollect_000tc__Product____Type__Ounit
% Using role type
% Declaring collect_Product_unit:((product_unit->Prop)->(product_unit->Prop))
% FOF formula (<kernel.Constant object at 0xf4fd88>, <kernel.DependentProduct object at 0xf4f8c0>) of role type named sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa
% Using role type
% Declaring collec869865362le_alt:((produc1501160679le_alt->Prop)->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0xf4fb90>, <kernel.DependentProduct object at 0xf4f8c0>) of role type named sy_c_Set_Oimage_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_000tc__N
% Using role type
% Declaring image_484224243di_nat:((arrow_1429601828e_indi->nat)->((arrow_1429601828e_indi->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0xf4fb00>, <kernel.DependentProduct object at 0xf4fd88>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__
% Using role type
% Declaring member1823529808lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4ff80>, <kernel.DependentProduct object at 0xf4fe60>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv___016
% Using role type
% Declaring member1452482393e_indi:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4ff38>, <kernel.DependentProduct object at 0x1155050>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv___017
% Using role type
% Declaring member1924666376t_unit:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->product_unit)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->product_unit)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4fb90>, <kernel.DependentProduct object at 0x1155128>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_
% Using role type
% Declaring member616898751_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4ff80>, <kernel.DependentProduct object at 0x11550e0>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__018
% Using role type
% Declaring member939334982lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4ff38>, <kernel.DependentProduct object at 0x11551b8>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__019
% Using role type
% Declaring member44294883e_indi:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4ff80>, <kernel.DependentProduct object at 0x1155248>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi__020
% Using role type
% Declaring member843528338t_unit:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->product_unit)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->product_unit)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4ff38>, <kernel.DependentProduct object at 0x1155320>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk
% Using role type
% Declaring member530241719_alt_o:(((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->((((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4fb90>, <kernel.DependentProduct object at 0x1155290>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk_021
% Using role type
% Declaring member1961363906lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->((((produc1501160679le_alt->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf4fb90>, <kernel.DependentProduct object at 0x1155170>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk_022
% Using role type
% Declaring member304866663e_indi:(((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->((((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155200>, <kernel.DependentProduct object at 0x1155128>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkk_023
% Using role type
% Declaring member221730070t_unit:(((produc1501160679le_alt->Prop)->product_unit)->((((produc1501160679le_alt->Prop)->product_unit)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11551b8>, <kernel.DependentProduct object at 0x1155170>) of role type named sy_c_member_000_062_I_Eo_M_062_I_062_Itc__Arrow____Order____Mirabelle____lcilvlk
% Using role type
% Declaring member1957863580_alt_o:((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155248>, <kernel.DependentProduct object at 0x1155050>) of role type named sy_c_member_000_062_I_Eo_M_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__O
% Using role type
% Declaring member1394214384_alt_o:((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155200>, <kernel.DependentProduct object at 0x11554d0>) of role type named sy_c_member_000_062_I_Eo_M_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lci
% Using role type
% Declaring member1862122484_alt_o:((Prop->(produc1501160679le_alt->Prop))->(((Prop->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11551b8>, <kernel.DependentProduct object at 0x11553b0>) of role type named sy_c_member_000_062_I_Eo_Mtc__Nat__Onat_J
% Using role type
% Declaring member_o_nat:((Prop->nat)->(((Prop->nat)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155248>, <kernel.DependentProduct object at 0x11554d0>) of role type named sy_c_member_000_062_I_Eo_Mtc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkz
% Using role type
% Declaring member492167345le_alt:((Prop->produc1501160679le_alt)->(((Prop->produc1501160679le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155200>, <kernel.DependentProduct object at 0x1155440>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062_
% Using role type
% Declaring member811956313_alt_o:((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11553f8>, <kernel.DependentProduct object at 0x11555f0>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062__024
% Using role type
% Declaring member1234151027_alt_o:((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11551b8>, <kernel.DependentProduct object at 0x11555f0>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_M_062__025
% Using role type
% Declaring member526088951_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155518>, <kernel.DependentProduct object at 0x1155680>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_Mtc__N
% Using role type
% Declaring member1315464153di_nat:((arrow_1429601828e_indi->nat)->(((arrow_1429601828e_indi->nat)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155488>, <kernel.DependentProduct object at 0x11554d0>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi_Mtc__p
% Using role type
% Declaring member351225838le_alt:((arrow_1429601828e_indi->produc1501160679le_alt)->(((arrow_1429601828e_indi->produc1501160679le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155170>, <kernel.DependentProduct object at 0x1155638>) of role type named sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring member_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155248>, <kernel.DependentProduct object at 0x11556c8>) of role type named sy_c_member_000_062_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle____lcilvlkkz
% Using role type
% Declaring member1391860553e_indi:((nat->arrow_1429601828e_indi)->(((nat->arrow_1429601828e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11551b8>, <kernel.DependentProduct object at 0x1155518>) of role type named sy_c_member_000_062_Itc__Nat__Onat_Mtc__Nat__Onat_J
% Using role type
% Declaring member_nat_nat:((nat->nat)->(((nat->nat)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11555f0>, <kernel.DependentProduct object at 0x1155638>) of role type named sy_c_member_000_062_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J
% Using role type
% Declaring member616671224t_unit:((nat->product_unit)->(((nat->product_unit)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155710>, <kernel.DependentProduct object at 0x1155248>) of role type named sy_c_member_000_062_Itc__Product____Type__Ounit_M_062_I_062_Itc__Arrow____Order_
% Using role type
% Declaring member1536989448_alt_o:((product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155170>, <kernel.DependentProduct object at 0x1155878>) of role type named sy_c_member_000_062_Itc__Product____Type__Ounit_M_062_Itc__Arrow____Order____Mir
% Using role type
% Declaring member283501700_alt_o:((product_unit->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((product_unit->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11551b8>, <kernel.DependentProduct object at 0x1155878>) of role type named sy_c_member_000_062_Itc__Product____Type__Ounit_M_062_Itc__prod_Itc__Arrow____Or
% Using role type
% Declaring member1661784200_alt_o:((product_unit->(produc1501160679le_alt->Prop))->(((product_unit->(produc1501160679le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11556c8>, <kernel.DependentProduct object at 0x1155908>) of role type named sy_c_member_000_062_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J
% Using role type
% Declaring member1827227242it_nat:((product_unit->nat)->(((product_unit->nat)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11557a0>, <kernel.DependentProduct object at 0x1155638>) of role type named sy_c_member_000_062_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow____Order___
% Using role type
% Declaring member495332125le_alt:((product_unit->produc1501160679le_alt)->(((product_unit->produc1501160679le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11557e8>, <kernel.DependentProduct object at 0x11558c0>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa
% Using role type
% Declaring member377231867_alt_o:((produc1501160679le_alt->Prop)->(((produc1501160679le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11555f0>, <kernel.DependentProduct object at 0x1155950>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa_026
% Using role type
% Declaring member1640632174e_indi:((produc1501160679le_alt->arrow_1429601828e_indi)->(((produc1501160679le_alt->arrow_1429601828e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11551b8>, <kernel.DependentProduct object at 0x11556c8>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oa_027
% Using role type
% Declaring member593902749t_unit:((produc1501160679le_alt->product_unit)->(((produc1501160679le_alt->product_unit)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155878>, <kernel.DependentProduct object at 0x11557e8>) of role type named sy_c_member_000_Eo
% Using role type
% Declaring member_o:(Prop->((Prop->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11555f0>, <kernel.DependentProduct object at 0x1155a28>) of role type named sy_c_member_000tc__Arrow____Order____Mirabelle____lcilvlkkzv__Oindi
% Using role type
% Declaring member2052026769e_indi:(arrow_1429601828e_indi->((arrow_1429601828e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155320>, <kernel.DependentProduct object at 0x1155ab8>) of role type named sy_c_member_000tc__Nat__Onat
% Using role type
% Declaring member_nat:(nat->((nat->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11551b8>, <kernel.DependentProduct object at 0x11555f0>) of role type named sy_c_member_000tc__Product____Type__Ounit
% Using role type
% Declaring member_Product_unit:(product_unit->((product_unit->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x1155a28>, <kernel.DependentProduct object at 0x1155b00>) of role type named sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv__Oalt_Mtc
% Using role type
% Declaring member214075476le_alt:(produc1501160679le_alt->((produc1501160679le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x11557e8>, <kernel.DependentProduct object at 0x11558c0>) of role type named sy_v_F
% Using role type
% Declaring f:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x11555f0>, <kernel.DependentProduct object at 0x1155878>) of role type named sy_v_Lab____
% Using role type
% Declaring lab:(produc1501160679le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x11551b8>, <kernel.DependentProduct object at 0x1155b48>) of role type named sy_v_Lba____
% Using role type
% Declaring lba:(produc1501160679le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x11558c0>, <kernel.DependentProduct object at 0x1155b00>) of role type named sy_v_P____
% Using role type
% Declaring p:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x1155878>, <kernel.Constant object at 0x1155b00>) of role type named sy_v_a____
% Using role type
% Declaring a:arrow_475358991le_alt
% FOF formula (<kernel.Constant object at 0x11551b8>, <kernel.Constant object at 0x1155b00>) of role type named sy_v_b____
% Using role type
% Declaring b:arrow_475358991le_alt
% FOF formula (<kernel.Constant object at 0x11558c0>, <kernel.Constant object at 0x1155b00>) of role type named sy_v_c____
% Using role type
% Declaring c:arrow_475358991le_alt
% FOF formula (<kernel.Constant object at 0x1155878>, <kernel.Constant object at 0x1155b00>) of role type named sy_v_d____
% Using role type
% Declaring d:arrow_475358991le_alt
% FOF formula (<kernel.Constant object at 0x11551b8>, <kernel.Constant object at 0x1155b00>) of role type named sy_v_e____
% Using role type
% Declaring e:arrow_475358991le_alt
% FOF formula (<kernel.Constant object at 0x11558c0>, <kernel.DependentProduct object at 0x1155d88>) of role type named sy_v_h____
% Using role type
% Declaring h:(arrow_1429601828e_indi->nat)
% FOF formula (<kernel.Constant object at 0x1155cb0>, <kernel.Constant object at 0x1155d88>) of role type named sy_v_n____
% Using role type
% Declaring n:nat
% FOF formula (arrow_797024463le_IIA f) of role axiom named fact_0_assms_I3_J
% A new axiom: (arrow_797024463le_IIA f)
% FOF formula (arrow_1706409458nimity f) of role axiom named fact_1_u
% A new axiom: (arrow_1706409458nimity f)
% FOF formula (not (((eq arrow_475358991le_alt) c) d)) of role axiom named fact_2__096c_A_126_061_Ad_096
% A new axiom: (not (((eq arrow_475358991le_alt) c) d))
% FOF formula ((member526088951_alt_o p) arrow_734252939e_Prof) of role axiom named fact_3__096P_A_058_AProf_096
% A new axiom: ((member526088951_alt_o p) arrow_734252939e_Prof)
% FOF formula (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (Z:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_2054445623_mkbot L_2) Z))) ((and ((and (not (((eq arrow_475358991le_alt) Y) Z))) ((((eq arrow_475358991le_alt) X) Z)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) X) Z))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2))))) of role axiom named fact_4_in__mkbot
% A new axiom: (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (Z:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_2054445623_mkbot L_2) Z))) ((and ((and (not (((eq arrow_475358991le_alt) Y) Z))) ((((eq arrow_475358991le_alt) X) Z)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) X) Z))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2)))))
% FOF formula (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (Z:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_55669061_mktop L_2) Z))) ((and ((and (not (((eq arrow_475358991le_alt) X) Z))) ((((eq arrow_475358991le_alt) Y) Z)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) Y) Z))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2))))) of role axiom named fact_5_in__mktop
% A new axiom: (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (Z:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_55669061_mktop L_2) Z))) ((and ((and (not (((eq arrow_475358991le_alt) X) Z))) ((((eq arrow_475358991le_alt) Y) Z)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) Y) Z))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2)))))
% FOF formula (forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_94:arrow_475358991le_alt) (B_73:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) A_94) B_73))->((not (((eq arrow_475358991le_alt) A_93) B_73))->((not (((eq arrow_475358991le_alt) B_72) A_94))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (f P_8))))))))))) of role axiom named fact_6__C2_C
% A new axiom: (forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_94:arrow_475358991le_alt) (B_73:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) A_94) B_73))->((not (((eq arrow_475358991le_alt) A_93) B_73))->((not (((eq arrow_475358991le_alt) B_72) A_94))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (f P_8)))))))))))
% FOF formula (forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_94:arrow_475358991le_alt) (B_73:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) A_94) B_73))->((not (((eq arrow_475358991le_alt) A_93) B_73))->((not (((eq arrow_475358991le_alt) B_72) A_94))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (P_8 I_1))))->(((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))->((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (f P_8))))))))))) of role axiom named fact_7__C1_C
% A new axiom: (forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_94:arrow_475358991le_alt) (B_73:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) A_94) B_73))->((not (((eq arrow_475358991le_alt) A_93) B_73))->((not (((eq arrow_475358991le_alt) B_72) A_94))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (P_8 I_1))))->(((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))->((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (f P_8)))))))))))
% FOF formula (forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (C_37:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) B_72) C_37))->((not (((eq arrow_475358991le_alt) A_93) C_37))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt B_72) C_37)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt B_72) C_37)) (f P_8)))))))))) of role axiom named fact_8__C4_C
% A new axiom: (forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (C_37:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) B_72) C_37))->((not (((eq arrow_475358991le_alt) A_93) C_37))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt B_72) C_37)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt B_72) C_37)) (f P_8))))))))))
% FOF formula (forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_94:arrow_475358991le_alt) (B_73:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) A_94) B_73))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (f P_8))))))))) of role axiom named fact_9_pairwise__neutrality
% A new axiom: (forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_94:arrow_475358991le_alt) (B_73:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) A_94) B_73))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (f P_8)))))))))
% FOF formula (forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt B_72) A_93)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt B_72) A_93)) (f P_8)))))))) of role axiom named fact_10__C3_C
% A new axiom: (forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt B_72) A_93)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt B_72) A_93)) (f P_8))))))))
% FOF formula (forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt c) d)) (p I_1))) ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) d)) ((arrow_55669061_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) d)) (((arrow_789600939_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member214075476le_alt ((produc1347929815le_alt c) d)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) of role axiom named fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J
% A new axiom: (forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt c) d)) (p I_1))) ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) d)) ((arrow_55669061_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) d)) (((arrow_789600939_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member214075476le_alt ((produc1347929815le_alt c) d)) ((arrow_2054445623_mkbot (p I_1)) e))))))))
% FOF formula ((member214075476le_alt ((produc1347929815le_alt c) d)) (p (((hilber598459244di_nat top_to988227749indi_o) h) n))) of role axiom named fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0
% A new axiom: ((member214075476le_alt ((produc1347929815le_alt c) d)) (p (((hilber598459244di_nat top_to988227749indi_o) h) n)))
% FOF formula ((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))) of role axiom named fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto
% A new axiom: ((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))
% FOF formula ((iff ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))) ((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))) of role axiom named fact_14_PW
% A new axiom: ((iff ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))) ((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))
% FOF formula (forall (P_6:(produc1501160679le_alt->Prop)), ((iff (all P_6)) (forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), (P_6 ((produc1347929815le_alt A_3) B_61))))) of role axiom named fact_15_split__paired__All
% A new axiom: (forall (P_6:(produc1501160679le_alt->Prop)), ((iff (all P_6)) (forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), (P_6 ((produc1347929815le_alt A_3) B_61)))))
% FOF formula ((member526088951_alt_o (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))) arrow_734252939e_Prof) of role axiom named fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai
% A new axiom: ((member526088951_alt_o (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))) arrow_734252939e_Prof)
% FOF formula ((member214075476le_alt ((produc1347929815le_alt c) e)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))) of role axiom named fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto
% A new axiom: ((member214075476le_alt ((produc1347929815le_alt c) e)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))
% FOF formula ((member214075476le_alt ((produc1347929815le_alt e) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))) of role axiom named fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto
% A new axiom: ((member214075476le_alt ((produc1347929815le_alt e) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))
% FOF formula ((ord_less_nat n) (finite97476818e_indi top_to988227749indi_o)) of role axiom named fact_19_n_I1_J
% A new axiom: ((ord_less_nat n) (finite97476818e_indi top_to988227749indi_o))
% FOF formula ((inj_on978774663di_nat h) top_to988227749indi_o) of role axiom named fact_20_injh
% A new axiom: ((inj_on978774663di_nat h) top_to988227749indi_o)
% FOF formula (forall (A_92:arrow_475358991le_alt) (B_71:arrow_475358991le_alt) (A_91:arrow_475358991le_alt) (B_70:arrow_475358991le_alt), ((((eq produc1501160679le_alt) ((produc1347929815le_alt A_92) B_71)) ((produc1347929815le_alt A_91) B_70))->(((((eq arrow_475358991le_alt) A_92) A_91)->(not (((eq arrow_475358991le_alt) B_71) B_70)))->False))) of role axiom named fact_21_Pair__inject
% A new axiom: (forall (A_92:arrow_475358991le_alt) (B_71:arrow_475358991le_alt) (A_91:arrow_475358991le_alt) (B_70:arrow_475358991le_alt), ((((eq produc1501160679le_alt) ((produc1347929815le_alt A_92) B_71)) ((produc1347929815le_alt A_91) B_70))->(((((eq arrow_475358991le_alt) A_92) A_91)->(not (((eq arrow_475358991le_alt) B_71) B_70)))->False)))
% FOF formula (forall (A_90:arrow_475358991le_alt) (B_69:arrow_475358991le_alt) (A_89:arrow_475358991le_alt) (B_68:arrow_475358991le_alt), ((iff (((eq produc1501160679le_alt) ((produc1347929815le_alt A_90) B_69)) ((produc1347929815le_alt A_89) B_68))) ((and (((eq arrow_475358991le_alt) A_90) A_89)) (((eq arrow_475358991le_alt) B_69) B_68)))) of role axiom named fact_22_Pair__eq
% A new axiom: (forall (A_90:arrow_475358991le_alt) (B_69:arrow_475358991le_alt) (A_89:arrow_475358991le_alt) (B_68:arrow_475358991le_alt), ((iff (((eq produc1501160679le_alt) ((produc1347929815le_alt A_90) B_69)) ((produc1347929815le_alt A_89) B_68))) ((and (((eq arrow_475358991le_alt) A_90) A_89)) (((eq arrow_475358991le_alt) B_69) B_68))))
% FOF formula (forall (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_797024463le_IIA F_18)) (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(forall (Xa:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o Xa) arrow_734252939e_Prof)->(forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), ((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (X_1 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (Xa I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 X_1))) ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 Xa))))))))))) of role axiom named fact_23_IIA__def
% A new axiom: (forall (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_797024463le_IIA F_18)) (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(forall (Xa:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o Xa) arrow_734252939e_Prof)->(forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), ((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (X_1 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (Xa I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 X_1))) ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 Xa)))))))))))
% FOF formula (forall (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_1706409458nimity F_18)) (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), ((forall (I_1:arrow_1429601828e_indi), ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (X_1 I_1)))->((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 X_1)))))))) of role axiom named fact_24_unanimity__def
% A new axiom: (forall (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_1706409458nimity F_18)) (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), ((forall (I_1:arrow_1429601828e_indi), ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (X_1 I_1)))->((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 X_1))))))))
% FOF formula (forall (X_70:(produc1501160679le_alt->Prop)), (top_to1842727771lt_o_o X_70)) of role axiom named fact_25_top1I
% A new axiom: (forall (X_70:(produc1501160679le_alt->Prop)), (top_to1842727771lt_o_o X_70))
% FOF formula (forall (X_70:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (top_to2122763103lt_o_o X_70)) of role axiom named fact_26_top1I
% A new axiom: (forall (X_70:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (top_to2122763103lt_o_o X_70))
% FOF formula (forall (X_70:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (top_to1969627639lt_o_o X_70)) of role axiom named fact_27_top1I
% A new axiom: (forall (X_70:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (top_to1969627639lt_o_o X_70))
% FOF formula (forall (X_70:produc1501160679le_alt), (top_to1841428258_alt_o X_70)) of role axiom named fact_28_top1I
% A new axiom: (forall (X_70:produc1501160679le_alt), (top_to1841428258_alt_o X_70))
% FOF formula (forall (X_70:arrow_1429601828e_indi), (top_to988227749indi_o X_70)) of role axiom named fact_29_top1I
% A new axiom: (forall (X_70:arrow_1429601828e_indi), (top_to988227749indi_o X_70))
% FOF formula (forall (X_70:product_unit), (top_to1984820022unit_o X_70)) of role axiom named fact_30_top1I
% A new axiom: (forall (X_70:product_unit), (top_to1984820022unit_o X_70))
% FOF formula (forall (X_70:nat), (top_top_nat_o X_70)) of role axiom named fact_31_top1I
% A new axiom: (forall (X_70:nat), (top_top_nat_o X_70))
% FOF formula (forall (X_69:Prop), ((member_o X_69) top_top_o_o)) of role axiom named fact_32_UNIV__I
% A new axiom: (forall (X_69:Prop), ((member_o X_69) top_top_o_o))
% FOF formula (forall (X_69:arrow_1429601828e_indi), ((member2052026769e_indi X_69) top_to988227749indi_o)) of role axiom named fact_33_UNIV__I
% A new axiom: (forall (X_69:arrow_1429601828e_indi), ((member2052026769e_indi X_69) top_to988227749indi_o))
% FOF formula (forall (X_69:product_unit), ((member_Product_unit X_69) top_to1984820022unit_o)) of role axiom named fact_34_UNIV__I
% A new axiom: (forall (X_69:product_unit), ((member_Product_unit X_69) top_to1984820022unit_o))
% FOF formula (forall (X_69:produc1501160679le_alt), ((member214075476le_alt X_69) top_to1841428258_alt_o)) of role axiom named fact_35_UNIV__I
% A new axiom: (forall (X_69:produc1501160679le_alt), ((member214075476le_alt X_69) top_to1841428258_alt_o))
% FOF formula (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_69) top_to2122763103lt_o_o)) of role axiom named fact_36_UNIV__I
% A new axiom: (forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_69) top_to2122763103lt_o_o))
% FOF formula (forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_69) top_to1969627639lt_o_o)) of role axiom named fact_37_UNIV__I
% A new axiom: (forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_69) top_to1969627639lt_o_o))
% FOF formula (forall (X_69:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_69) top_to1842727771lt_o_o)) of role axiom named fact_38_UNIV__I
% A new axiom: (forall (X_69:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_69) top_to1842727771lt_o_o))
% FOF formula (forall (X_69:nat), ((member_nat X_69) top_top_nat_o)) of role axiom named fact_39_UNIV__I
% A new axiom: (forall (X_69:nat), ((member_nat X_69) top_top_nat_o))
% FOF formula (forall (X_68:Prop), ((member_o X_68) top_top_o_o)) of role axiom named fact_40_iso__tuple__UNIV__I
% A new axiom: (forall (X_68:Prop), ((member_o X_68) top_top_o_o))
% FOF formula (forall (X_68:arrow_1429601828e_indi), ((member2052026769e_indi X_68) top_to988227749indi_o)) of role axiom named fact_41_iso__tuple__UNIV__I
% A new axiom: (forall (X_68:arrow_1429601828e_indi), ((member2052026769e_indi X_68) top_to988227749indi_o))
% FOF formula (forall (X_68:product_unit), ((member_Product_unit X_68) top_to1984820022unit_o)) of role axiom named fact_42_iso__tuple__UNIV__I
% A new axiom: (forall (X_68:product_unit), ((member_Product_unit X_68) top_to1984820022unit_o))
% FOF formula (forall (X_68:produc1501160679le_alt), ((member214075476le_alt X_68) top_to1841428258_alt_o)) of role axiom named fact_43_iso__tuple__UNIV__I
% A new axiom: (forall (X_68:produc1501160679le_alt), ((member214075476le_alt X_68) top_to1841428258_alt_o))
% FOF formula (forall (X_68:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_68) top_to2122763103lt_o_o)) of role axiom named fact_44_iso__tuple__UNIV__I
% A new axiom: (forall (X_68:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_68) top_to2122763103lt_o_o))
% FOF formula (forall (X_68:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_68) top_to1969627639lt_o_o)) of role axiom named fact_45_iso__tuple__UNIV__I
% A new axiom: (forall (X_68:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_68) top_to1969627639lt_o_o))
% FOF formula (forall (X_68:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_68) top_to1842727771lt_o_o)) of role axiom named fact_46_iso__tuple__UNIV__I
% A new axiom: (forall (X_68:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_68) top_to1842727771lt_o_o))
% FOF formula (forall (X_68:nat), ((member_nat X_68) top_top_nat_o)) of role axiom named fact_47_iso__tuple__UNIV__I
% A new axiom: (forall (X_68:nat), ((member_nat X_68) top_top_nat_o))
% FOF formula (forall (X_67:(produc1501160679le_alt->Prop)), ((iff (top_to1842727771lt_o_o X_67)) top_top_o)) of role axiom named fact_48_top__apply
% A new axiom: (forall (X_67:(produc1501160679le_alt->Prop)), ((iff (top_to1842727771lt_o_o X_67)) top_top_o))
% FOF formula (forall (X_67:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((iff (top_to2122763103lt_o_o X_67)) top_top_o)) of role axiom named fact_49_top__apply
% A new axiom: (forall (X_67:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((iff (top_to2122763103lt_o_o X_67)) top_top_o))
% FOF formula (forall (X_67:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (top_to1969627639lt_o_o X_67)) top_top_o)) of role axiom named fact_50_top__apply
% A new axiom: (forall (X_67:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (top_to1969627639lt_o_o X_67)) top_top_o))
% FOF formula (forall (X_67:produc1501160679le_alt), ((iff (top_to1841428258_alt_o X_67)) top_top_o)) of role axiom named fact_51_top__apply
% A new axiom: (forall (X_67:produc1501160679le_alt), ((iff (top_to1841428258_alt_o X_67)) top_top_o))
% FOF formula (forall (X_67:arrow_1429601828e_indi), ((iff (top_to988227749indi_o X_67)) top_top_o)) of role axiom named fact_52_top__apply
% A new axiom: (forall (X_67:arrow_1429601828e_indi), ((iff (top_to988227749indi_o X_67)) top_top_o))
% FOF formula (forall (X_67:product_unit), ((iff (top_to1984820022unit_o X_67)) top_top_o)) of role axiom named fact_53_top__apply
% A new axiom: (forall (X_67:product_unit), ((iff (top_to1984820022unit_o X_67)) top_top_o))
% FOF formula (forall (X_67:nat), ((iff (top_top_nat_o X_67)) top_top_o)) of role axiom named fact_54_top__apply
% A new axiom: (forall (X_67:nat), ((iff (top_top_nat_o X_67)) top_top_o))
% FOF formula (forall (A_88:((produc1501160679le_alt->Prop)->Prop)), (((ord_le910298367lt_o_o top_to1842727771lt_o_o) A_88)->False)) of role axiom named fact_55_not__top__less
% A new axiom: (forall (A_88:((produc1501160679le_alt->Prop)->Prop)), (((ord_le910298367lt_o_o top_to1842727771lt_o_o) A_88)->False))
% FOF formula (forall (A_88:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le157835011lt_o_o top_to2122763103lt_o_o) A_88)->False)) of role axiom named fact_56_not__top__less
% A new axiom: (forall (A_88:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le157835011lt_o_o top_to2122763103lt_o_o) A_88)->False))
% FOF formula (forall (A_88:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1859604819lt_o_o top_to1969627639lt_o_o) A_88)->False)) of role axiom named fact_57_not__top__less
% A new axiom: (forall (A_88:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1859604819lt_o_o top_to1969627639lt_o_o) A_88)->False))
% FOF formula (forall (A_88:Prop), (((ord_less_o top_top_o) A_88)->False)) of role axiom named fact_58_not__top__less
% A new axiom: (forall (A_88:Prop), (((ord_less_o top_top_o) A_88)->False))
% FOF formula (forall (A_88:(produc1501160679le_alt->Prop)), (((ord_le988258430_alt_o top_to1841428258_alt_o) A_88)->False)) of role axiom named fact_59_not__top__less
% A new axiom: (forall (A_88:(produc1501160679le_alt->Prop)), (((ord_le988258430_alt_o top_to1841428258_alt_o) A_88)->False))
% FOF formula (forall (A_88:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o top_to988227749indi_o) A_88)->False)) of role axiom named fact_60_not__top__less
% A new axiom: (forall (A_88:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o top_to988227749indi_o) A_88)->False))
% FOF formula (forall (A_88:(product_unit->Prop)), (((ord_le232288914unit_o top_to1984820022unit_o) A_88)->False)) of role axiom named fact_61_not__top__less
% A new axiom: (forall (A_88:(product_unit->Prop)), (((ord_le232288914unit_o top_to1984820022unit_o) A_88)->False))
% FOF formula (forall (A_88:(nat->Prop)), (((ord_less_nat_o top_top_nat_o) A_88)->False)) of role axiom named fact_62_not__top__less
% A new axiom: (forall (A_88:(nat->Prop)), (((ord_less_nat_o top_top_nat_o) A_88)->False))
% FOF formula (forall (A_87:((produc1501160679le_alt->Prop)->Prop)), ((iff (not (((eq ((produc1501160679le_alt->Prop)->Prop)) A_87) top_to1842727771lt_o_o))) ((ord_le910298367lt_o_o A_87) top_to1842727771lt_o_o))) of role axiom named fact_63_less__top
% A new axiom: (forall (A_87:((produc1501160679le_alt->Prop)->Prop)), ((iff (not (((eq ((produc1501160679le_alt->Prop)->Prop)) A_87) top_to1842727771lt_o_o))) ((ord_le910298367lt_o_o A_87) top_to1842727771lt_o_o)))
% FOF formula (forall (A_87:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) A_87) top_to2122763103lt_o_o))) ((ord_le157835011lt_o_o A_87) top_to2122763103lt_o_o))) of role axiom named fact_64_less__top
% A new axiom: (forall (A_87:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) A_87) top_to2122763103lt_o_o))) ((ord_le157835011lt_o_o A_87) top_to2122763103lt_o_o)))
% FOF formula (forall (A_87:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff (not (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) A_87) top_to1969627639lt_o_o))) ((ord_le1859604819lt_o_o A_87) top_to1969627639lt_o_o))) of role axiom named fact_65_less__top
% A new axiom: (forall (A_87:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff (not (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) A_87) top_to1969627639lt_o_o))) ((ord_le1859604819lt_o_o A_87) top_to1969627639lt_o_o)))
% FOF formula (forall (A_87:Prop), ((iff (((iff A_87) top_top_o)->False)) ((ord_less_o A_87) top_top_o))) of role axiom named fact_66_less__top
% A new axiom: (forall (A_87:Prop), ((iff (((iff A_87) top_top_o)->False)) ((ord_less_o A_87) top_top_o)))
% FOF formula (forall (A_87:(produc1501160679le_alt->Prop)), ((iff (not (((eq (produc1501160679le_alt->Prop)) A_87) top_to1841428258_alt_o))) ((ord_le988258430_alt_o A_87) top_to1841428258_alt_o))) of role axiom named fact_67_less__top
% A new axiom: (forall (A_87:(produc1501160679le_alt->Prop)), ((iff (not (((eq (produc1501160679le_alt->Prop)) A_87) top_to1841428258_alt_o))) ((ord_le988258430_alt_o A_87) top_to1841428258_alt_o)))
% FOF formula (forall (A_87:(arrow_1429601828e_indi->Prop)), ((iff (not (((eq (arrow_1429601828e_indi->Prop)) A_87) top_to988227749indi_o))) ((ord_le777687553indi_o A_87) top_to988227749indi_o))) of role axiom named fact_68_less__top
% A new axiom: (forall (A_87:(arrow_1429601828e_indi->Prop)), ((iff (not (((eq (arrow_1429601828e_indi->Prop)) A_87) top_to988227749indi_o))) ((ord_le777687553indi_o A_87) top_to988227749indi_o)))
% FOF formula (forall (A_87:(product_unit->Prop)), ((iff (not (((eq (product_unit->Prop)) A_87) top_to1984820022unit_o))) ((ord_le232288914unit_o A_87) top_to1984820022unit_o))) of role axiom named fact_69_less__top
% A new axiom: (forall (A_87:(product_unit->Prop)), ((iff (not (((eq (product_unit->Prop)) A_87) top_to1984820022unit_o))) ((ord_le232288914unit_o A_87) top_to1984820022unit_o)))
% FOF formula (forall (A_87:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_87) top_top_nat_o))) ((ord_less_nat_o A_87) top_top_nat_o))) of role axiom named fact_70_less__top
% A new axiom: (forall (A_87:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_87) top_top_nat_o))) ((ord_less_nat_o A_87) top_top_nat_o)))
% FOF formula ((member616898751_alt_o f) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin))) of role axiom named fact_71_assms_I1_J
% A new axiom: ((member616898751_alt_o f) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin)))
% FOF formula ((iff ((member214075476le_alt ((produc1347929815le_alt e) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) lab) lba))))) of role axiom named fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk
% A new axiom: ((iff ((member214075476le_alt ((produc1347929815le_alt e) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) lab) lba)))))
% FOF formula ((member377231867_alt_o lab) arrow_823908191le_Lin) of role axiom named fact_73__096Lab_A_058_ALin_096
% A new axiom: ((member377231867_alt_o lab) arrow_823908191le_Lin)
% FOF formula ((member377231867_alt_o lba) arrow_823908191le_Lin) of role axiom named fact_74__096Lba_A_058_ALin_096
% A new axiom: ((member377231867_alt_o lba) arrow_823908191le_Lin)
% FOF formula (not (((eq arrow_475358991le_alt) a) b)) of role axiom named fact_75__096a_A_126_061_Ab_096
% A new axiom: (not (((eq arrow_475358991le_alt) a) b))
% FOF formula ((member214075476le_alt ((produc1347929815le_alt a) b)) lab) of role axiom named fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096
% A new axiom: ((member214075476le_alt ((produc1347929815le_alt a) b)) lab)
% FOF formula ((member214075476le_alt ((produc1347929815le_alt b) a)) lba) of role axiom named fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096
% A new axiom: ((member214075476le_alt ((produc1347929815le_alt b) a)) lba)
% FOF formula (((member214075476le_alt ((produc1347929815le_alt a) b)) lba)->False) of role axiom named fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096
% A new axiom: (((member214075476le_alt ((produc1347929815le_alt a) b)) lba)->False)
% FOF formula (((member214075476le_alt ((produc1347929815le_alt b) a)) lab)->False) of role axiom named fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096
% A new axiom: (((member214075476le_alt ((produc1347929815le_alt b) a)) lab)->False)
% FOF formula (forall (N:nat), ((member526088951_alt_o (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) N)) lab) lba))) arrow_734252939e_Prof)) of role axiom named fact_80_PiProf
% A new axiom: (forall (N:nat), ((member526088951_alt_o (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) N)) lab) lba))) arrow_734252939e_Prof))
% FOF formula ((forall (Lab:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt a) b)) Lab)->(((member377231867_alt_o Lab) arrow_823908191le_Lin)->False)))->False) of role axiom named fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_
% A new axiom: ((forall (Lab:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt a) b)) Lab)->(((member377231867_alt_o Lab) arrow_823908191le_Lin)->False)))->False)
% FOF formula ((forall (Lba:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt b) a)) Lba)->(((member377231867_alt_o Lba) arrow_823908191le_Lin)->False)))->False) of role axiom named fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_
% A new axiom: ((forall (Lba:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt b) a)) Lba)->(((member377231867_alt_o Lba) arrow_823908191le_Lin)->False)))->False)
% FOF formula (forall (I_1:arrow_1429601828e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt e) d)) ((arrow_55669061_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt e) d)) (((arrow_789600939_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member214075476le_alt ((produc1347929815le_alt e) d)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt b) a)) lab))) ((((ord_less_nat (h I_1)) n)->False)->((member214075476le_alt ((produc1347929815le_alt b) a)) lba))))) of role axiom named fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk
% A new axiom: (forall (I_1:arrow_1429601828e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt e) d)) ((arrow_55669061_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt e) d)) (((arrow_789600939_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member214075476le_alt ((produc1347929815le_alt e) d)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt b) a)) lab))) ((((ord_less_nat (h I_1)) n)->False)->((member214075476le_alt ((produc1347929815le_alt b) a)) lba)))))
% FOF formula (forall (M:nat), (((ord_less_eq_nat M) n)->((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) M)) lab) lba)))))) of role axiom named fact_84_n_I2_J
% A new axiom: (forall (M:nat), (((ord_less_eq_nat M) n)->((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) M)) lab) lba))))))
% FOF formula (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((not (((eq arrow_475358991le_alt) X) Y))->((iff (((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2)->False)) ((member214075476le_alt ((produc1347929815le_alt Y) X)) L_2))))) of role axiom named fact_85_notin__Lin__iff
% A new axiom: (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((not (((eq arrow_475358991le_alt) X) Y))->((iff (((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2)->False)) ((member214075476le_alt ((produc1347929815le_alt Y) X)) L_2)))))
% FOF formula (forall (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->(((member214075476le_alt ((produc1347929815le_alt A_9) B_5)) L_2)->(((member214075476le_alt ((produc1347929815le_alt B_5) A_9)) L_2)->False)))) of role axiom named fact_86_Lin__irrefl
% A new axiom: (forall (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->(((member214075476le_alt ((produc1347929815le_alt A_9) B_5)) L_2)->(((member214075476le_alt ((produc1347929815le_alt B_5) A_9)) L_2)->False))))
% FOF formula (forall (X:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_55669061_mktop L_2) X)) arrow_823908191le_Lin))) of role axiom named fact_87_mktop__Lin
% A new axiom: (forall (X:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_55669061_mktop L_2) X)) arrow_823908191le_Lin)))
% FOF formula (forall (X:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_2054445623_mkbot L_2) X)) arrow_823908191le_Lin))) of role axiom named fact_88_mkbot__Lin
% A new axiom: (forall (X:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_2054445623_mkbot L_2) X)) arrow_823908191le_Lin)))
% FOF formula (forall (L_2:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_789600939_above L_2) X) Y)) arrow_823908191le_Lin)))) of role axiom named fact_89_above__Lin
% A new axiom: (forall (L_2:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_789600939_above L_2) X) Y)) arrow_823908191le_Lin))))
% FOF formula (forall (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member526088951_alt_o (fun (P_5:arrow_1429601828e_indi)=> L_2)) arrow_734252939e_Prof))) of role axiom named fact_90_const__Lin__Prof
% A new axiom: (forall (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member526088951_alt_o (fun (P_5:arrow_1429601828e_indi)=> L_2)) arrow_734252939e_Prof)))
% FOF formula (forall (X_66:nat) (Y_50:nat), ((((ord_less_nat X_66) Y_50)->False)->((not (((eq nat) X_66) Y_50))->((ord_less_nat Y_50) X_66)))) of role axiom named fact_91_linorder__cases
% A new axiom: (forall (X_66:nat) (Y_50:nat), ((((ord_less_nat X_66) Y_50)->False)->((not (((eq nat) X_66) Y_50))->((ord_less_nat Y_50) X_66))))
% FOF formula (forall (X_65:(nat->Prop)) (Y_49:(nat->Prop)), (((ord_less_nat_o X_65) Y_49)->(((ord_less_nat_o Y_49) X_65)->False))) of role axiom named fact_92_order__less__asym
% A new axiom: (forall (X_65:(nat->Prop)) (Y_49:(nat->Prop)), (((ord_less_nat_o X_65) Y_49)->(((ord_less_nat_o Y_49) X_65)->False)))
% FOF formula (forall (X_65:(product_unit->Prop)) (Y_49:(product_unit->Prop)), (((ord_le232288914unit_o X_65) Y_49)->(((ord_le232288914unit_o Y_49) X_65)->False))) of role axiom named fact_93_order__less__asym
% A new axiom: (forall (X_65:(product_unit->Prop)) (Y_49:(product_unit->Prop)), (((ord_le232288914unit_o X_65) Y_49)->(((ord_le232288914unit_o Y_49) X_65)->False)))
% FOF formula (forall (X_65:(arrow_1429601828e_indi->Prop)) (Y_49:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_65) Y_49)->(((ord_le777687553indi_o Y_49) X_65)->False))) of role axiom named fact_94_order__less__asym
% A new axiom: (forall (X_65:(arrow_1429601828e_indi->Prop)) (Y_49:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_65) Y_49)->(((ord_le777687553indi_o Y_49) X_65)->False)))
% FOF formula (forall (X_65:nat) (Y_49:nat), (((ord_less_nat X_65) Y_49)->(((ord_less_nat Y_49) X_65)->False))) of role axiom named fact_95_order__less__asym
% A new axiom: (forall (X_65:nat) (Y_49:nat), (((ord_less_nat X_65) Y_49)->(((ord_less_nat Y_49) X_65)->False)))
% FOF formula (forall (Z_8:(nat->Prop)) (Y_48:(nat->Prop)) (X_64:(nat->Prop)), (((ord_less_nat_o Y_48) X_64)->(((ord_less_nat_o Z_8) Y_48)->((ord_less_nat_o Z_8) X_64)))) of role axiom named fact_96_xt1_I10_J
% A new axiom: (forall (Z_8:(nat->Prop)) (Y_48:(nat->Prop)) (X_64:(nat->Prop)), (((ord_less_nat_o Y_48) X_64)->(((ord_less_nat_o Z_8) Y_48)->((ord_less_nat_o Z_8) X_64))))
% FOF formula (forall (Z_8:(product_unit->Prop)) (Y_48:(product_unit->Prop)) (X_64:(product_unit->Prop)), (((ord_le232288914unit_o Y_48) X_64)->(((ord_le232288914unit_o Z_8) Y_48)->((ord_le232288914unit_o Z_8) X_64)))) of role axiom named fact_97_xt1_I10_J
% A new axiom: (forall (Z_8:(product_unit->Prop)) (Y_48:(product_unit->Prop)) (X_64:(product_unit->Prop)), (((ord_le232288914unit_o Y_48) X_64)->(((ord_le232288914unit_o Z_8) Y_48)->((ord_le232288914unit_o Z_8) X_64))))
% FOF formula (forall (Z_8:(arrow_1429601828e_indi->Prop)) (Y_48:(arrow_1429601828e_indi->Prop)) (X_64:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o Y_48) X_64)->(((ord_le777687553indi_o Z_8) Y_48)->((ord_le777687553indi_o Z_8) X_64)))) of role axiom named fact_98_xt1_I10_J
% A new axiom: (forall (Z_8:(arrow_1429601828e_indi->Prop)) (Y_48:(arrow_1429601828e_indi->Prop)) (X_64:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o Y_48) X_64)->(((ord_le777687553indi_o Z_8) Y_48)->((ord_le777687553indi_o Z_8) X_64))))
% FOF formula (forall (Z_8:nat) (Y_48:nat) (X_64:nat), (((ord_less_nat Y_48) X_64)->(((ord_less_nat Z_8) Y_48)->((ord_less_nat Z_8) X_64)))) of role axiom named fact_99_xt1_I10_J
% A new axiom: (forall (Z_8:nat) (Y_48:nat) (X_64:nat), (((ord_less_nat Y_48) X_64)->(((ord_less_nat Z_8) Y_48)->((ord_less_nat Z_8) X_64))))
% FOF formula (forall (Z_7:(nat->Prop)) (X_63:(nat->Prop)) (Y_47:(nat->Prop)), (((ord_less_nat_o X_63) Y_47)->(((ord_less_nat_o Y_47) Z_7)->((ord_less_nat_o X_63) Z_7)))) of role axiom named fact_100_order__less__trans
% A new axiom: (forall (Z_7:(nat->Prop)) (X_63:(nat->Prop)) (Y_47:(nat->Prop)), (((ord_less_nat_o X_63) Y_47)->(((ord_less_nat_o Y_47) Z_7)->((ord_less_nat_o X_63) Z_7))))
% FOF formula (forall (Z_7:(product_unit->Prop)) (X_63:(product_unit->Prop)) (Y_47:(product_unit->Prop)), (((ord_le232288914unit_o X_63) Y_47)->(((ord_le232288914unit_o Y_47) Z_7)->((ord_le232288914unit_o X_63) Z_7)))) of role axiom named fact_101_order__less__trans
% A new axiom: (forall (Z_7:(product_unit->Prop)) (X_63:(product_unit->Prop)) (Y_47:(product_unit->Prop)), (((ord_le232288914unit_o X_63) Y_47)->(((ord_le232288914unit_o Y_47) Z_7)->((ord_le232288914unit_o X_63) Z_7))))
% FOF formula (forall (Z_7:(arrow_1429601828e_indi->Prop)) (X_63:(arrow_1429601828e_indi->Prop)) (Y_47:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_63) Y_47)->(((ord_le777687553indi_o Y_47) Z_7)->((ord_le777687553indi_o X_63) Z_7)))) of role axiom named fact_102_order__less__trans
% A new axiom: (forall (Z_7:(arrow_1429601828e_indi->Prop)) (X_63:(arrow_1429601828e_indi->Prop)) (Y_47:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_63) Y_47)->(((ord_le777687553indi_o Y_47) Z_7)->((ord_le777687553indi_o X_63) Z_7))))
% FOF formula (forall (Z_7:nat) (X_63:nat) (Y_47:nat), (((ord_less_nat X_63) Y_47)->(((ord_less_nat Y_47) Z_7)->((ord_less_nat X_63) Z_7)))) of role axiom named fact_103_order__less__trans
% A new axiom: (forall (Z_7:nat) (X_63:nat) (Y_47:nat), (((ord_less_nat X_63) Y_47)->(((ord_less_nat Y_47) Z_7)->((ord_less_nat X_63) Z_7))))
% FOF formula (forall (C_36:(nat->Prop)) (B_67:(nat->Prop)) (A_86:(nat->Prop)), (((ord_less_nat_o B_67) A_86)->((((eq (nat->Prop)) B_67) C_36)->((ord_less_nat_o C_36) A_86)))) of role axiom named fact_104_xt1_I2_J
% A new axiom: (forall (C_36:(nat->Prop)) (B_67:(nat->Prop)) (A_86:(nat->Prop)), (((ord_less_nat_o B_67) A_86)->((((eq (nat->Prop)) B_67) C_36)->((ord_less_nat_o C_36) A_86))))
% FOF formula (forall (C_36:(product_unit->Prop)) (B_67:(product_unit->Prop)) (A_86:(product_unit->Prop)), (((ord_le232288914unit_o B_67) A_86)->((((eq (product_unit->Prop)) B_67) C_36)->((ord_le232288914unit_o C_36) A_86)))) of role axiom named fact_105_xt1_I2_J
% A new axiom: (forall (C_36:(product_unit->Prop)) (B_67:(product_unit->Prop)) (A_86:(product_unit->Prop)), (((ord_le232288914unit_o B_67) A_86)->((((eq (product_unit->Prop)) B_67) C_36)->((ord_le232288914unit_o C_36) A_86))))
% FOF formula (forall (C_36:(arrow_1429601828e_indi->Prop)) (B_67:(arrow_1429601828e_indi->Prop)) (A_86:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o B_67) A_86)->((((eq (arrow_1429601828e_indi->Prop)) B_67) C_36)->((ord_le777687553indi_o C_36) A_86)))) of role axiom named fact_106_xt1_I2_J
% A new axiom: (forall (C_36:(arrow_1429601828e_indi->Prop)) (B_67:(arrow_1429601828e_indi->Prop)) (A_86:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o B_67) A_86)->((((eq (arrow_1429601828e_indi->Prop)) B_67) C_36)->((ord_le777687553indi_o C_36) A_86))))
% FOF formula (forall (C_36:nat) (B_67:nat) (A_86:nat), (((ord_less_nat B_67) A_86)->((((eq nat) B_67) C_36)->((ord_less_nat C_36) A_86)))) of role axiom named fact_107_xt1_I2_J
% A new axiom: (forall (C_36:nat) (B_67:nat) (A_86:nat), (((ord_less_nat B_67) A_86)->((((eq nat) B_67) C_36)->((ord_less_nat C_36) A_86))))
% FOF formula (forall (C_35:(nat->Prop)) (A_85:(nat->Prop)) (B_66:(nat->Prop)), (((ord_less_nat_o A_85) B_66)->((((eq (nat->Prop)) B_66) C_35)->((ord_less_nat_o A_85) C_35)))) of role axiom named fact_108_ord__less__eq__trans
% A new axiom: (forall (C_35:(nat->Prop)) (A_85:(nat->Prop)) (B_66:(nat->Prop)), (((ord_less_nat_o A_85) B_66)->((((eq (nat->Prop)) B_66) C_35)->((ord_less_nat_o A_85) C_35))))
% FOF formula (forall (C_35:(product_unit->Prop)) (A_85:(product_unit->Prop)) (B_66:(product_unit->Prop)), (((ord_le232288914unit_o A_85) B_66)->((((eq (product_unit->Prop)) B_66) C_35)->((ord_le232288914unit_o A_85) C_35)))) of role axiom named fact_109_ord__less__eq__trans
% A new axiom: (forall (C_35:(product_unit->Prop)) (A_85:(product_unit->Prop)) (B_66:(product_unit->Prop)), (((ord_le232288914unit_o A_85) B_66)->((((eq (product_unit->Prop)) B_66) C_35)->((ord_le232288914unit_o A_85) C_35))))
% FOF formula (forall (C_35:(arrow_1429601828e_indi->Prop)) (A_85:(arrow_1429601828e_indi->Prop)) (B_66:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_85) B_66)->((((eq (arrow_1429601828e_indi->Prop)) B_66) C_35)->((ord_le777687553indi_o A_85) C_35)))) of role axiom named fact_110_ord__less__eq__trans
% A new axiom: (forall (C_35:(arrow_1429601828e_indi->Prop)) (A_85:(arrow_1429601828e_indi->Prop)) (B_66:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_85) B_66)->((((eq (arrow_1429601828e_indi->Prop)) B_66) C_35)->((ord_le777687553indi_o A_85) C_35))))
% FOF formula (forall (C_35:nat) (A_85:nat) (B_66:nat), (((ord_less_nat A_85) B_66)->((((eq nat) B_66) C_35)->((ord_less_nat A_85) C_35)))) of role axiom named fact_111_ord__less__eq__trans
% A new axiom: (forall (C_35:nat) (A_85:nat) (B_66:nat), (((ord_less_nat A_85) B_66)->((((eq nat) B_66) C_35)->((ord_less_nat A_85) C_35))))
% FOF formula (forall (C_34:(nat->Prop)) (A_84:(nat->Prop)) (B_65:(nat->Prop)), ((((eq (nat->Prop)) A_84) B_65)->(((ord_less_nat_o C_34) B_65)->((ord_less_nat_o C_34) A_84)))) of role axiom named fact_112_xt1_I1_J
% A new axiom: (forall (C_34:(nat->Prop)) (A_84:(nat->Prop)) (B_65:(nat->Prop)), ((((eq (nat->Prop)) A_84) B_65)->(((ord_less_nat_o C_34) B_65)->((ord_less_nat_o C_34) A_84))))
% FOF formula (forall (C_34:(product_unit->Prop)) (A_84:(product_unit->Prop)) (B_65:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_84) B_65)->(((ord_le232288914unit_o C_34) B_65)->((ord_le232288914unit_o C_34) A_84)))) of role axiom named fact_113_xt1_I1_J
% A new axiom: (forall (C_34:(product_unit->Prop)) (A_84:(product_unit->Prop)) (B_65:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_84) B_65)->(((ord_le232288914unit_o C_34) B_65)->((ord_le232288914unit_o C_34) A_84))))
% FOF formula (forall (C_34:(arrow_1429601828e_indi->Prop)) (A_84:(arrow_1429601828e_indi->Prop)) (B_65:(arrow_1429601828e_indi->Prop)), ((((eq (arrow_1429601828e_indi->Prop)) A_84) B_65)->(((ord_le777687553indi_o C_34) B_65)->((ord_le777687553indi_o C_34) A_84)))) of role axiom named fact_114_xt1_I1_J
% A new axiom: (forall (C_34:(arrow_1429601828e_indi->Prop)) (A_84:(arrow_1429601828e_indi->Prop)) (B_65:(arrow_1429601828e_indi->Prop)), ((((eq (arrow_1429601828e_indi->Prop)) A_84) B_65)->(((ord_le777687553indi_o C_34) B_65)->((ord_le777687553indi_o C_34) A_84))))
% FOF formula (forall (C_34:nat) (A_84:nat) (B_65:nat), ((((eq nat) A_84) B_65)->(((ord_less_nat C_34) B_65)->((ord_less_nat C_34) A_84)))) of role axiom named fact_115_xt1_I1_J
% A new axiom: (forall (C_34:nat) (A_84:nat) (B_65:nat), ((((eq nat) A_84) B_65)->(((ord_less_nat C_34) B_65)->((ord_less_nat C_34) A_84))))
% FOF formula (forall (C_33:(nat->Prop)) (A_83:(nat->Prop)) (B_64:(nat->Prop)), ((((eq (nat->Prop)) A_83) B_64)->(((ord_less_nat_o B_64) C_33)->((ord_less_nat_o A_83) C_33)))) of role axiom named fact_116_ord__eq__less__trans
% A new axiom: (forall (C_33:(nat->Prop)) (A_83:(nat->Prop)) (B_64:(nat->Prop)), ((((eq (nat->Prop)) A_83) B_64)->(((ord_less_nat_o B_64) C_33)->((ord_less_nat_o A_83) C_33))))
% FOF formula (forall (C_33:(product_unit->Prop)) (A_83:(product_unit->Prop)) (B_64:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_83) B_64)->(((ord_le232288914unit_o B_64) C_33)->((ord_le232288914unit_o A_83) C_33)))) of role axiom named fact_117_ord__eq__less__trans
% A new axiom: (forall (C_33:(product_unit->Prop)) (A_83:(product_unit->Prop)) (B_64:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_83) B_64)->(((ord_le232288914unit_o B_64) C_33)->((ord_le232288914unit_o A_83) C_33))))
% FOF formula (forall (C_33:(arrow_1429601828e_indi->Prop)) (A_83:(arrow_1429601828e_indi->Prop)) (B_64:(arrow_1429601828e_indi->Prop)), ((((eq (arrow_1429601828e_indi->Prop)) A_83) B_64)->(((ord_le777687553indi_o B_64) C_33)->((ord_le777687553indi_o A_83) C_33)))) of role axiom named fact_118_ord__eq__less__trans
% A new axiom: (forall (C_33:(arrow_1429601828e_indi->Prop)) (A_83:(arrow_1429601828e_indi->Prop)) (B_64:(arrow_1429601828e_indi->Prop)), ((((eq (arrow_1429601828e_indi->Prop)) A_83) B_64)->(((ord_le777687553indi_o B_64) C_33)->((ord_le777687553indi_o A_83) C_33))))
% FOF formula (forall (C_33:nat) (A_83:nat) (B_64:nat), ((((eq nat) A_83) B_64)->(((ord_less_nat B_64) C_33)->((ord_less_nat A_83) C_33)))) of role axiom named fact_119_ord__eq__less__trans
% A new axiom: (forall (C_33:nat) (A_83:nat) (B_64:nat), ((((eq nat) A_83) B_64)->(((ord_less_nat B_64) C_33)->((ord_less_nat A_83) C_33))))
% FOF formula (forall (B_63:(nat->Prop)) (A_82:(nat->Prop)), (((ord_less_nat_o B_63) A_82)->(((ord_less_nat_o A_82) B_63)->False))) of role axiom named fact_120_xt1_I9_J
% A new axiom: (forall (B_63:(nat->Prop)) (A_82:(nat->Prop)), (((ord_less_nat_o B_63) A_82)->(((ord_less_nat_o A_82) B_63)->False)))
% FOF formula (forall (B_63:(product_unit->Prop)) (A_82:(product_unit->Prop)), (((ord_le232288914unit_o B_63) A_82)->(((ord_le232288914unit_o A_82) B_63)->False))) of role axiom named fact_121_xt1_I9_J
% A new axiom: (forall (B_63:(product_unit->Prop)) (A_82:(product_unit->Prop)), (((ord_le232288914unit_o B_63) A_82)->(((ord_le232288914unit_o A_82) B_63)->False)))
% FOF formula (forall (B_63:(arrow_1429601828e_indi->Prop)) (A_82:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o B_63) A_82)->(((ord_le777687553indi_o A_82) B_63)->False))) of role axiom named fact_122_xt1_I9_J
% A new axiom: (forall (B_63:(arrow_1429601828e_indi->Prop)) (A_82:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o B_63) A_82)->(((ord_le777687553indi_o A_82) B_63)->False)))
% FOF formula (forall (B_63:nat) (A_82:nat), (((ord_less_nat B_63) A_82)->(((ord_less_nat A_82) B_63)->False))) of role axiom named fact_123_xt1_I9_J
% A new axiom: (forall (B_63:nat) (A_82:nat), (((ord_less_nat B_63) A_82)->(((ord_less_nat A_82) B_63)->False)))
% FOF formula (forall (A_81:(nat->Prop)) (B_62:(nat->Prop)), (((ord_less_nat_o A_81) B_62)->(((ord_less_nat_o B_62) A_81)->False))) of role axiom named fact_124_order__less__asym_H
% A new axiom: (forall (A_81:(nat->Prop)) (B_62:(nat->Prop)), (((ord_less_nat_o A_81) B_62)->(((ord_less_nat_o B_62) A_81)->False)))
% FOF formula (forall (A_81:(product_unit->Prop)) (B_62:(product_unit->Prop)), (((ord_le232288914unit_o A_81) B_62)->(((ord_le232288914unit_o B_62) A_81)->False))) of role axiom named fact_125_order__less__asym_H
% A new axiom: (forall (A_81:(product_unit->Prop)) (B_62:(product_unit->Prop)), (((ord_le232288914unit_o A_81) B_62)->(((ord_le232288914unit_o B_62) A_81)->False)))
% FOF formula (forall (A_81:(arrow_1429601828e_indi->Prop)) (B_62:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_81) B_62)->(((ord_le777687553indi_o B_62) A_81)->False))) of role axiom named fact_126_order__less__asym_H
% A new axiom: (forall (A_81:(arrow_1429601828e_indi->Prop)) (B_62:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_81) B_62)->(((ord_le777687553indi_o B_62) A_81)->False)))
% FOF formula (forall (A_81:nat) (B_62:nat), (((ord_less_nat A_81) B_62)->(((ord_less_nat B_62) A_81)->False))) of role axiom named fact_127_order__less__asym_H
% A new axiom: (forall (A_81:nat) (B_62:nat), (((ord_less_nat A_81) B_62)->(((ord_less_nat B_62) A_81)->False)))
% FOF formula (forall (P_4:Prop) (X_62:(nat->Prop)) (Y_46:(nat->Prop)), (((ord_less_nat_o X_62) Y_46)->(((ord_less_nat_o Y_46) X_62)->P_4))) of role axiom named fact_128_order__less__imp__triv
% A new axiom: (forall (P_4:Prop) (X_62:(nat->Prop)) (Y_46:(nat->Prop)), (((ord_less_nat_o X_62) Y_46)->(((ord_less_nat_o Y_46) X_62)->P_4)))
% FOF formula (forall (P_4:Prop) (X_62:(product_unit->Prop)) (Y_46:(product_unit->Prop)), (((ord_le232288914unit_o X_62) Y_46)->(((ord_le232288914unit_o Y_46) X_62)->P_4))) of role axiom named fact_129_order__less__imp__triv
% A new axiom: (forall (P_4:Prop) (X_62:(product_unit->Prop)) (Y_46:(product_unit->Prop)), (((ord_le232288914unit_o X_62) Y_46)->(((ord_le232288914unit_o Y_46) X_62)->P_4)))
% FOF formula (forall (P_4:Prop) (X_62:(arrow_1429601828e_indi->Prop)) (Y_46:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_62) Y_46)->(((ord_le777687553indi_o Y_46) X_62)->P_4))) of role axiom named fact_130_order__less__imp__triv
% A new axiom: (forall (P_4:Prop) (X_62:(arrow_1429601828e_indi->Prop)) (Y_46:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_62) Y_46)->(((ord_le777687553indi_o Y_46) X_62)->P_4)))
% FOF formula (forall (P_4:Prop) (X_62:nat) (Y_46:nat), (((ord_less_nat X_62) Y_46)->(((ord_less_nat Y_46) X_62)->P_4))) of role axiom named fact_131_order__less__imp__triv
% A new axiom: (forall (P_4:Prop) (X_62:nat) (Y_46:nat), (((ord_less_nat X_62) Y_46)->(((ord_less_nat Y_46) X_62)->P_4)))
% FOF formula (forall (X_61:(nat->Prop)) (Y_45:(nat->Prop)), (((ord_less_nat_o X_61) Y_45)->(not (((eq (nat->Prop)) Y_45) X_61)))) of role axiom named fact_132_order__less__imp__not__eq2
% A new axiom: (forall (X_61:(nat->Prop)) (Y_45:(nat->Prop)), (((ord_less_nat_o X_61) Y_45)->(not (((eq (nat->Prop)) Y_45) X_61))))
% FOF formula (forall (X_61:(product_unit->Prop)) (Y_45:(product_unit->Prop)), (((ord_le232288914unit_o X_61) Y_45)->(not (((eq (product_unit->Prop)) Y_45) X_61)))) of role axiom named fact_133_order__less__imp__not__eq2
% A new axiom: (forall (X_61:(product_unit->Prop)) (Y_45:(product_unit->Prop)), (((ord_le232288914unit_o X_61) Y_45)->(not (((eq (product_unit->Prop)) Y_45) X_61))))
% FOF formula (forall (X_61:(arrow_1429601828e_indi->Prop)) (Y_45:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_61) Y_45)->(not (((eq (arrow_1429601828e_indi->Prop)) Y_45) X_61)))) of role axiom named fact_134_order__less__imp__not__eq2
% A new axiom: (forall (X_61:(arrow_1429601828e_indi->Prop)) (Y_45:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_61) Y_45)->(not (((eq (arrow_1429601828e_indi->Prop)) Y_45) X_61))))
% FOF formula (forall (X_61:nat) (Y_45:nat), (((ord_less_nat X_61) Y_45)->(not (((eq nat) Y_45) X_61)))) of role axiom named fact_135_order__less__imp__not__eq2
% A new axiom: (forall (X_61:nat) (Y_45:nat), (((ord_less_nat X_61) Y_45)->(not (((eq nat) Y_45) X_61))))
% FOF formula (forall (X_60:(nat->Prop)) (Y_44:(nat->Prop)), (((ord_less_nat_o X_60) Y_44)->(not (((eq (nat->Prop)) X_60) Y_44)))) of role axiom named fact_136_order__less__imp__not__eq
% A new axiom: (forall (X_60:(nat->Prop)) (Y_44:(nat->Prop)), (((ord_less_nat_o X_60) Y_44)->(not (((eq (nat->Prop)) X_60) Y_44))))
% FOF formula (forall (X_60:(product_unit->Prop)) (Y_44:(product_unit->Prop)), (((ord_le232288914unit_o X_60) Y_44)->(not (((eq (product_unit->Prop)) X_60) Y_44)))) of role axiom named fact_137_order__less__imp__not__eq
% A new axiom: (forall (X_60:(product_unit->Prop)) (Y_44:(product_unit->Prop)), (((ord_le232288914unit_o X_60) Y_44)->(not (((eq (product_unit->Prop)) X_60) Y_44))))
% FOF formula (forall (X_60:(arrow_1429601828e_indi->Prop)) (Y_44:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_60) Y_44)->(not (((eq (arrow_1429601828e_indi->Prop)) X_60) Y_44)))) of role axiom named fact_138_order__less__imp__not__eq
% A new axiom: (forall (X_60:(arrow_1429601828e_indi->Prop)) (Y_44:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_60) Y_44)->(not (((eq (arrow_1429601828e_indi->Prop)) X_60) Y_44))))
% FOF formula (forall (X_60:nat) (Y_44:nat), (((ord_less_nat X_60) Y_44)->(not (((eq nat) X_60) Y_44)))) of role axiom named fact_139_order__less__imp__not__eq
% A new axiom: (forall (X_60:nat) (Y_44:nat), (((ord_less_nat X_60) Y_44)->(not (((eq nat) X_60) Y_44))))
% FOF formula (forall (X_59:(nat->Prop)) (Y_43:(nat->Prop)), (((ord_less_nat_o X_59) Y_43)->(((ord_less_nat_o Y_43) X_59)->False))) of role axiom named fact_140_order__less__imp__not__less
% A new axiom: (forall (X_59:(nat->Prop)) (Y_43:(nat->Prop)), (((ord_less_nat_o X_59) Y_43)->(((ord_less_nat_o Y_43) X_59)->False)))
% FOF formula (forall (X_59:(product_unit->Prop)) (Y_43:(product_unit->Prop)), (((ord_le232288914unit_o X_59) Y_43)->(((ord_le232288914unit_o Y_43) X_59)->False))) of role axiom named fact_141_order__less__imp__not__less
% A new axiom: (forall (X_59:(product_unit->Prop)) (Y_43:(product_unit->Prop)), (((ord_le232288914unit_o X_59) Y_43)->(((ord_le232288914unit_o Y_43) X_59)->False)))
% FOF formula (forall (X_59:(arrow_1429601828e_indi->Prop)) (Y_43:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_59) Y_43)->(((ord_le777687553indi_o Y_43) X_59)->False))) of role axiom named fact_142_order__less__imp__not__less
% A new axiom: (forall (X_59:(arrow_1429601828e_indi->Prop)) (Y_43:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_59) Y_43)->(((ord_le777687553indi_o Y_43) X_59)->False)))
% FOF formula (forall (X_59:nat) (Y_43:nat), (((ord_less_nat X_59) Y_43)->(((ord_less_nat Y_43) X_59)->False))) of role axiom named fact_143_order__less__imp__not__less
% A new axiom: (forall (X_59:nat) (Y_43:nat), (((ord_less_nat X_59) Y_43)->(((ord_less_nat Y_43) X_59)->False)))
% FOF formula (forall (X_58:(nat->Prop)) (Y_42:(nat->Prop)), (((ord_less_nat_o X_58) Y_42)->(((ord_less_nat_o Y_42) X_58)->False))) of role axiom named fact_144_order__less__not__sym
% A new axiom: (forall (X_58:(nat->Prop)) (Y_42:(nat->Prop)), (((ord_less_nat_o X_58) Y_42)->(((ord_less_nat_o Y_42) X_58)->False)))
% FOF formula (forall (X_58:(product_unit->Prop)) (Y_42:(product_unit->Prop)), (((ord_le232288914unit_o X_58) Y_42)->(((ord_le232288914unit_o Y_42) X_58)->False))) of role axiom named fact_145_order__less__not__sym
% A new axiom: (forall (X_58:(product_unit->Prop)) (Y_42:(product_unit->Prop)), (((ord_le232288914unit_o X_58) Y_42)->(((ord_le232288914unit_o Y_42) X_58)->False)))
% FOF formula (forall (X_58:(arrow_1429601828e_indi->Prop)) (Y_42:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_58) Y_42)->(((ord_le777687553indi_o Y_42) X_58)->False))) of role axiom named fact_146_order__less__not__sym
% A new axiom: (forall (X_58:(arrow_1429601828e_indi->Prop)) (Y_42:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_58) Y_42)->(((ord_le777687553indi_o Y_42) X_58)->False)))
% FOF formula (forall (X_58:nat) (Y_42:nat), (((ord_less_nat X_58) Y_42)->(((ord_less_nat Y_42) X_58)->False))) of role axiom named fact_147_order__less__not__sym
% A new axiom: (forall (X_58:nat) (Y_42:nat), (((ord_less_nat X_58) Y_42)->(((ord_less_nat Y_42) X_58)->False)))
% FOF formula (forall (X_57:(nat->Prop)) (Y_41:(nat->Prop)), (((ord_less_nat_o X_57) Y_41)->(not (((eq (nat->Prop)) X_57) Y_41)))) of role axiom named fact_148_less__imp__neq
% A new axiom: (forall (X_57:(nat->Prop)) (Y_41:(nat->Prop)), (((ord_less_nat_o X_57) Y_41)->(not (((eq (nat->Prop)) X_57) Y_41))))
% FOF formula (forall (X_57:(product_unit->Prop)) (Y_41:(product_unit->Prop)), (((ord_le232288914unit_o X_57) Y_41)->(not (((eq (product_unit->Prop)) X_57) Y_41)))) of role axiom named fact_149_less__imp__neq
% A new axiom: (forall (X_57:(product_unit->Prop)) (Y_41:(product_unit->Prop)), (((ord_le232288914unit_o X_57) Y_41)->(not (((eq (product_unit->Prop)) X_57) Y_41))))
% FOF formula (forall (X_57:(arrow_1429601828e_indi->Prop)) (Y_41:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_57) Y_41)->(not (((eq (arrow_1429601828e_indi->Prop)) X_57) Y_41)))) of role axiom named fact_150_less__imp__neq
% A new axiom: (forall (X_57:(arrow_1429601828e_indi->Prop)) (Y_41:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_57) Y_41)->(not (((eq (arrow_1429601828e_indi->Prop)) X_57) Y_41))))
% FOF formula (forall (X_57:nat) (Y_41:nat), (((ord_less_nat X_57) Y_41)->(not (((eq nat) X_57) Y_41)))) of role axiom named fact_151_less__imp__neq
% A new axiom: (forall (X_57:nat) (Y_41:nat), (((ord_less_nat X_57) Y_41)->(not (((eq nat) X_57) Y_41))))
% FOF formula (forall (X_56:nat) (Y_40:nat), ((not (((eq nat) X_56) Y_40))->((((ord_less_nat X_56) Y_40)->False)->((ord_less_nat Y_40) X_56)))) of role axiom named fact_152_linorder__neqE
% A new axiom: (forall (X_56:nat) (Y_40:nat), ((not (((eq nat) X_56) Y_40))->((((ord_less_nat X_56) Y_40)->False)->((ord_less_nat Y_40) X_56))))
% FOF formula (forall (Y_39:nat) (X_55:nat), ((((ord_less_nat Y_39) X_55)->False)->((iff (((ord_less_nat X_55) Y_39)->False)) (((eq nat) X_55) Y_39)))) of role axiom named fact_153_linorder__antisym__conv3
% A new axiom: (forall (Y_39:nat) (X_55:nat), ((((ord_less_nat Y_39) X_55)->False)->((iff (((ord_less_nat X_55) Y_39)->False)) (((eq nat) X_55) Y_39))))
% FOF formula (forall (X_54:nat) (Y_38:nat), ((or ((or ((ord_less_nat X_54) Y_38)) (((eq nat) X_54) Y_38))) ((ord_less_nat Y_38) X_54))) of role axiom named fact_154_linorder__less__linear
% A new axiom: (forall (X_54:nat) (Y_38:nat), ((or ((or ((ord_less_nat X_54) Y_38)) (((eq nat) X_54) Y_38))) ((ord_less_nat Y_38) X_54)))
% FOF formula (forall (X_53:nat) (Y_37:nat), ((iff (((ord_less_nat X_53) Y_37)->False)) ((or ((ord_less_nat Y_37) X_53)) (((eq nat) X_53) Y_37)))) of role axiom named fact_155_not__less__iff__gr__or__eq
% A new axiom: (forall (X_53:nat) (Y_37:nat), ((iff (((ord_less_nat X_53) Y_37)->False)) ((or ((ord_less_nat Y_37) X_53)) (((eq nat) X_53) Y_37))))
% FOF formula (forall (X_52:nat) (Y_36:nat), ((iff (not (((eq nat) X_52) Y_36))) ((or ((ord_less_nat X_52) Y_36)) ((ord_less_nat Y_36) X_52)))) of role axiom named fact_156_linorder__neq__iff
% A new axiom: (forall (X_52:nat) (Y_36:nat), ((iff (not (((eq nat) X_52) Y_36))) ((or ((ord_less_nat X_52) Y_36)) ((ord_less_nat Y_36) X_52))))
% FOF formula (forall (X_51:(nat->Prop)), (((ord_less_nat_o X_51) X_51)->False)) of role axiom named fact_157_order__less__irrefl
% A new axiom: (forall (X_51:(nat->Prop)), (((ord_less_nat_o X_51) X_51)->False))
% FOF formula (forall (X_51:(product_unit->Prop)), (((ord_le232288914unit_o X_51) X_51)->False)) of role axiom named fact_158_order__less__irrefl
% A new axiom: (forall (X_51:(product_unit->Prop)), (((ord_le232288914unit_o X_51) X_51)->False))
% FOF formula (forall (X_51:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_51) X_51)->False)) of role axiom named fact_159_order__less__irrefl
% A new axiom: (forall (X_51:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_51) X_51)->False))
% FOF formula (forall (X_51:nat), (((ord_less_nat X_51) X_51)->False)) of role axiom named fact_160_order__less__irrefl
% A new axiom: (forall (X_51:nat), (((ord_less_nat X_51) X_51)->False))
% FOF formula (((eq ((produc1501160679le_alt->Prop)->Prop)) top_to1842727771lt_o_o) (collec94295101_alt_o (fun (X_1:(produc1501160679le_alt->Prop))=> True))) of role axiom named fact_161_UNIV__def
% A new axiom: (((eq ((produc1501160679le_alt->Prop)->Prop)) top_to1842727771lt_o_o) (collec94295101_alt_o (fun (X_1:(produc1501160679le_alt->Prop))=> True)))
% FOF formula (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) top_to2122763103lt_o_o) (collec682858041_alt_o (fun (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> True))) of role axiom named fact_162_UNIV__def
% A new axiom: (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) top_to2122763103lt_o_o) (collec682858041_alt_o (fun (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> True)))
% FOF formula (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) top_to1969627639lt_o_o) (collec2009291517_alt_o (fun (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> True))) of role axiom named fact_163_UNIV__def
% A new axiom: (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) top_to1969627639lt_o_o) (collec2009291517_alt_o (fun (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> True)))
% FOF formula (((eq (produc1501160679le_alt->Prop)) top_to1841428258_alt_o) (collec869865362le_alt (fun (X_1:produc1501160679le_alt)=> True))) of role axiom named fact_164_UNIV__def
% A new axiom: (((eq (produc1501160679le_alt->Prop)) top_to1841428258_alt_o) (collec869865362le_alt (fun (X_1:produc1501160679le_alt)=> True)))
% FOF formula (((eq (arrow_1429601828e_indi->Prop)) top_to988227749indi_o) (collec22405327e_indi (fun (X_1:arrow_1429601828e_indi)=> True))) of role axiom named fact_165_UNIV__def
% A new axiom: (((eq (arrow_1429601828e_indi->Prop)) top_to988227749indi_o) (collec22405327e_indi (fun (X_1:arrow_1429601828e_indi)=> True)))
% FOF formula (((eq (product_unit->Prop)) top_to1984820022unit_o) (collect_Product_unit (fun (X_1:product_unit)=> True))) of role axiom named fact_166_UNIV__def
% A new axiom: (((eq (product_unit->Prop)) top_to1984820022unit_o) (collect_Product_unit (fun (X_1:product_unit)=> True)))
% FOF formula (((eq (nat->Prop)) top_top_nat_o) (collect_nat (fun (X_1:nat)=> True))) of role axiom named fact_167_UNIV__def
% A new axiom: (((eq (nat->Prop)) top_top_nat_o) (collect_nat (fun (X_1:nat)=> True)))
% FOF formula (forall (X_50:arrow_1429601828e_indi) (A_80:(arrow_1429601828e_indi->Prop)), ((iff ((member2052026769e_indi X_50) A_80)) (A_80 X_50))) of role axiom named fact_168_mem__def
% A new axiom: (forall (X_50:arrow_1429601828e_indi) (A_80:(arrow_1429601828e_indi->Prop)), ((iff ((member2052026769e_indi X_50) A_80)) (A_80 X_50)))
% FOF formula (forall (X_50:Prop) (A_80:(Prop->Prop)), ((iff ((member_o X_50) A_80)) (A_80 X_50))) of role axiom named fact_169_mem__def
% A new axiom: (forall (X_50:Prop) (A_80:(Prop->Prop)), ((iff ((member_o X_50) A_80)) (A_80 X_50)))
% FOF formula (forall (X_50:product_unit) (A_80:(product_unit->Prop)), ((iff ((member_Product_unit X_50) A_80)) (A_80 X_50))) of role axiom named fact_170_mem__def
% A new axiom: (forall (X_50:product_unit) (A_80:(product_unit->Prop)), ((iff ((member_Product_unit X_50) A_80)) (A_80 X_50)))
% FOF formula (forall (X_50:produc1501160679le_alt) (A_80:(produc1501160679le_alt->Prop)), ((iff ((member214075476le_alt X_50) A_80)) (A_80 X_50))) of role axiom named fact_171_mem__def
% A new axiom: (forall (X_50:produc1501160679le_alt) (A_80:(produc1501160679le_alt->Prop)), ((iff ((member214075476le_alt X_50) A_80)) (A_80 X_50)))
% FOF formula (forall (X_50:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_80:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member526088951_alt_o X_50) A_80)) (A_80 X_50))) of role axiom named fact_172_mem__def
% A new axiom: (forall (X_50:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_80:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member526088951_alt_o X_50) A_80)) (A_80 X_50)))
% FOF formula (forall (X_50:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_80:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member616898751_alt_o X_50) A_80)) (A_80 X_50))) of role axiom named fact_173_mem__def
% A new axiom: (forall (X_50:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_80:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member616898751_alt_o X_50) A_80)) (A_80 X_50)))
% FOF formula (forall (X_50:(produc1501160679le_alt->Prop)) (A_80:((produc1501160679le_alt->Prop)->Prop)), ((iff ((member377231867_alt_o X_50) A_80)) (A_80 X_50))) of role axiom named fact_174_mem__def
% A new axiom: (forall (X_50:(produc1501160679le_alt->Prop)) (A_80:((produc1501160679le_alt->Prop)->Prop)), ((iff ((member377231867_alt_o X_50) A_80)) (A_80 X_50)))
% FOF formula (forall (X_50:nat) (A_80:(nat->Prop)), ((iff ((member_nat X_50) A_80)) (A_80 X_50))) of role axiom named fact_175_mem__def
% A new axiom: (forall (X_50:nat) (A_80:(nat->Prop)), ((iff ((member_nat X_50) A_80)) (A_80 X_50)))
% FOF formula (forall (P_3:(product_unit->Prop)), (((eq (product_unit->Prop)) (collect_Product_unit P_3)) P_3)) of role axiom named fact_176_Collect__def
% A new axiom: (forall (P_3:(product_unit->Prop)), (((eq (product_unit->Prop)) (collect_Product_unit P_3)) P_3))
% FOF formula (forall (P_3:(arrow_1429601828e_indi->Prop)), (((eq (arrow_1429601828e_indi->Prop)) (collec22405327e_indi P_3)) P_3)) of role axiom named fact_177_Collect__def
% A new axiom: (forall (P_3:(arrow_1429601828e_indi->Prop)), (((eq (arrow_1429601828e_indi->Prop)) (collec22405327e_indi P_3)) P_3))
% FOF formula (forall (P_3:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_3)) P_3)) of role axiom named fact_178_Collect__def
% A new axiom: (forall (P_3:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_3)) P_3))
% FOF formula (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_9) B_5))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_789600939_above L_2) A_9) B_5))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) X) B_5)->((member214075476le_alt ((produc1347929815le_alt A_9) Y)) L_2)))) ((not (((eq arrow_475358991le_alt) X) B_5))->((and ((((eq arrow_475358991le_alt) Y) B_5)->((or (((eq arrow_475358991le_alt) X) A_9)) ((member214075476le_alt ((produc1347929815le_alt X) A_9)) L_2)))) ((not (((eq arrow_475358991le_alt) Y) B_5))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2))))))))) of role axiom named fact_179_in__above
% A new axiom: (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_9) B_5))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_789600939_above L_2) A_9) B_5))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) X) B_5)->((member214075476le_alt ((produc1347929815le_alt A_9) Y)) L_2)))) ((not (((eq arrow_475358991le_alt) X) B_5))->((and ((((eq arrow_475358991le_alt) Y) B_5)->((or (((eq arrow_475358991le_alt) X) A_9)) ((member214075476le_alt ((produc1347929815le_alt X) A_9)) L_2)))) ((not (((eq arrow_475358991le_alt) Y) B_5))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2)))))))))
% FOF formula (forall (S_3:(produc1501160679le_alt->Prop)) (R_3:(produc1501160679le_alt->Prop)), ((iff (forall (X_1:arrow_475358991le_alt) (Xa:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X_1) Xa)) R_3)) ((member214075476le_alt ((produc1347929815le_alt X_1) Xa)) S_3)))) (((eq (produc1501160679le_alt->Prop)) R_3) S_3))) of role axiom named fact_180_pred__equals__eq2
% A new axiom: (forall (S_3:(produc1501160679le_alt->Prop)) (R_3:(produc1501160679le_alt->Prop)), ((iff (forall (X_1:arrow_475358991le_alt) (Xa:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X_1) Xa)) R_3)) ((member214075476le_alt ((produc1347929815le_alt X_1) Xa)) S_3)))) (((eq (produc1501160679le_alt->Prop)) R_3) S_3)))
% FOF formula ((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba)))) of role axiom named fact_181_n_I3_J
% A new axiom: ((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba))))
% FOF formula ((iff ((member214075476le_alt ((produc1347929815le_alt c) e)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba))))) of role axiom named fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am
% A new axiom: ((iff ((member214075476le_alt ((produc1347929815le_alt c) e)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba)))))
% FOF formula (forall (I_1:arrow_1429601828e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) e)) ((arrow_55669061_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) e)) (((arrow_789600939_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member214075476le_alt ((produc1347929815le_alt c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->((member214075476le_alt ((produc1347929815le_alt a) b)) lab))) ((((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->False)->((member214075476le_alt ((produc1347929815le_alt a) b)) lba))))) of role axiom named fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am
% A new axiom: (forall (I_1:arrow_1429601828e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) e)) ((arrow_55669061_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) e)) (((arrow_789600939_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member214075476le_alt ((produc1347929815le_alt c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->((member214075476le_alt ((produc1347929815le_alt a) b)) lab))) ((((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->False)->((member214075476le_alt ((produc1347929815le_alt a) b)) lba)))))
% FOF formula (forall (X_49:arrow_1429601828e_indi) (Y_35:nat) (F_30:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_30) top_to988227749indi_o)->((((eq nat) (F_30 X_49)) Y_35)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat top_to988227749indi_o) F_30) Y_35)) X_49)))) of role axiom named fact_184_inv__f__eq
% A new axiom: (forall (X_49:arrow_1429601828e_indi) (Y_35:nat) (F_30:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_30) top_to988227749indi_o)->((((eq nat) (F_30 X_49)) Y_35)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat top_to988227749indi_o) F_30) Y_35)) X_49))))
% FOF formula (forall (X_49:nat) (Y_35:nat) (F_30:(nat->nat)), (((inj_on_nat_nat F_30) top_top_nat_o)->((((eq nat) (F_30 X_49)) Y_35)->(((eq nat) (((hilber195283148at_nat top_top_nat_o) F_30) Y_35)) X_49)))) of role axiom named fact_185_inv__f__eq
% A new axiom: (forall (X_49:nat) (Y_35:nat) (F_30:(nat->nat)), (((inj_on_nat_nat F_30) top_top_nat_o)->((((eq nat) (F_30 X_49)) Y_35)->(((eq nat) (((hilber195283148at_nat top_top_nat_o) F_30) Y_35)) X_49))))
% FOF formula (forall (X_48:arrow_1429601828e_indi) (F_29:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_29) top_to988227749indi_o)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat top_to988227749indi_o) F_29) (F_29 X_48))) X_48))) of role axiom named fact_186_inv__f__f
% A new axiom: (forall (X_48:arrow_1429601828e_indi) (F_29:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_29) top_to988227749indi_o)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat top_to988227749indi_o) F_29) (F_29 X_48))) X_48)))
% FOF formula (forall (X_48:nat) (F_29:(nat->nat)), (((inj_on_nat_nat F_29) top_top_nat_o)->(((eq nat) (((hilber195283148at_nat top_top_nat_o) F_29) (F_29 X_48))) X_48))) of role axiom named fact_187_inv__f__f
% A new axiom: (forall (X_48:nat) (F_29:(nat->nat)), (((inj_on_nat_nat F_29) top_top_nat_o)->(((eq nat) (((hilber195283148at_nat top_top_nat_o) F_29) (F_29 X_48))) X_48)))
% FOF formula (forall (_TPTP_I:arrow_1429601828e_indi) (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o F_18) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin)))->((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_3) B_61))->(((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (X_1 _TPTP_I))->((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 X_1)))))))->((arrow_1212662430ctator F_18) _TPTP_I)))) of role axiom named fact_188_dictatorI
% A new axiom: (forall (_TPTP_I:arrow_1429601828e_indi) (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o F_18) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin)))->((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_3) B_61))->(((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (X_1 _TPTP_I))->((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 X_1)))))))->((arrow_1212662430ctator F_18) _TPTP_I))))
% FOF formula (forall (X_47:produc1501160679le_alt) (F_28:(produc1501160679le_alt->Prop)) (A_79:(produc1501160679le_alt->Prop)) (B_60:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_28) ((pi_Pro1701359055_alt_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member214075476le_alt X_47) A_79)->False)))) of role axiom named fact_189_PiE
% A new axiom: (forall (X_47:produc1501160679le_alt) (F_28:(produc1501160679le_alt->Prop)) (A_79:(produc1501160679le_alt->Prop)) (B_60:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_28) ((pi_Pro1701359055_alt_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member214075476le_alt X_47) A_79)->False))))
% FOF formula (forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member351225838le_alt F_28) ((pi_Arr329216900le_alt A_79) B_60))->((((member214075476le_alt (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False)))) of role axiom named fact_190_PiE
% A new axiom: (forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member351225838le_alt F_28) ((pi_Arr329216900le_alt A_79) B_60))->((((member214075476le_alt (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False))))
% FOF formula (forall (X_47:Prop) (F_28:(Prop->produc1501160679le_alt)) (A_79:(Prop->Prop)) (B_60:(Prop->(produc1501160679le_alt->Prop))), (((member492167345le_alt F_28) ((pi_o_P657324555le_alt A_79) B_60))->((((member214075476le_alt (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False)))) of role axiom named fact_191_PiE
% A new axiom: (forall (X_47:Prop) (F_28:(Prop->produc1501160679le_alt)) (A_79:(Prop->Prop)) (B_60:(Prop->(produc1501160679le_alt->Prop))), (((member492167345le_alt F_28) ((pi_o_P657324555le_alt A_79) B_60))->((((member214075476le_alt (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False))))
% FOF formula (forall (X_47:product_unit) (F_28:(product_unit->produc1501160679le_alt)) (A_79:(product_unit->Prop)) (B_60:(product_unit->(produc1501160679le_alt->Prop))), (((member495332125le_alt F_28) ((pi_Pro701847987le_alt A_79) B_60))->((((member214075476le_alt (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False)))) of role axiom named fact_192_PiE
% A new axiom: (forall (X_47:product_unit) (F_28:(product_unit->produc1501160679le_alt)) (A_79:(product_unit->Prop)) (B_60:(product_unit->(produc1501160679le_alt->Prop))), (((member495332125le_alt F_28) ((pi_Pro701847987le_alt A_79) B_60))->((((member214075476le_alt (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False))))
% FOF formula (forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1234151027_alt_o F_28) ((pi_Arr1060328391_alt_o A_79) B_60))->((((member526088951_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False)))) of role axiom named fact_193_PiE
% A new axiom: (forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1234151027_alt_o F_28) ((pi_Arr1060328391_alt_o A_79) B_60))->((((member526088951_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False))))
% FOF formula (forall (X_47:Prop) (F_28:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_79:(Prop->Prop)) (B_60:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1394214384_alt_o F_28) ((pi_o_A1182933120_alt_o A_79) B_60))->((((member526088951_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False)))) of role axiom named fact_194_PiE
% A new axiom: (forall (X_47:Prop) (F_28:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_79:(Prop->Prop)) (B_60:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1394214384_alt_o F_28) ((pi_o_A1182933120_alt_o A_79) B_60))->((((member526088951_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False))))
% FOF formula (forall (X_47:product_unit) (F_28:(product_unit->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_79:(product_unit->Prop)) (B_60:(product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member283501700_alt_o F_28) ((pi_Pro1662176984_alt_o A_79) B_60))->((((member526088951_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False)))) of role axiom named fact_195_PiE
% A new axiom: (forall (X_47:product_unit) (F_28:(product_unit->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_79:(product_unit->Prop)) (B_60:(product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member283501700_alt_o F_28) ((pi_Pro1662176984_alt_o A_79) B_60))->((((member526088951_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False))))
% FOF formula (forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member811956313_alt_o F_28) ((pi_Arr1564509167_alt_o A_79) B_60))->((((member616898751_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False)))) of role axiom named fact_196_PiE
% A new axiom: (forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member811956313_alt_o F_28) ((pi_Arr1564509167_alt_o A_79) B_60))->((((member616898751_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False))))
% FOF formula (forall (X_47:Prop) (F_28:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_79:(Prop->Prop)) (B_60:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1957863580_alt_o F_28) ((pi_o_A1186128886_alt_o A_79) B_60))->((((member616898751_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False)))) of role axiom named fact_197_PiE
% A new axiom: (forall (X_47:Prop) (F_28:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_79:(Prop->Prop)) (B_60:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1957863580_alt_o F_28) ((pi_o_A1186128886_alt_o A_79) B_60))->((((member616898751_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False))))
% FOF formula (forall (X_47:product_unit) (F_28:(product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_79:(product_unit->Prop)) (B_60:(product_unit->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1536989448_alt_o F_28) ((pi_Pro1782982558_alt_o A_79) B_60))->((((member616898751_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False)))) of role axiom named fact_198_PiE
% A new axiom: (forall (X_47:product_unit) (F_28:(product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_79:(product_unit->Prop)) (B_60:(product_unit->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1536989448_alt_o F_28) ((pi_Pro1782982558_alt_o A_79) B_60))->((((member616898751_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False))))
% FOF formula (forall (X_47:Prop) (F_28:(Prop->(produc1501160679le_alt->Prop))) (A_79:(Prop->Prop)) (B_60:(Prop->((produc1501160679le_alt->Prop)->Prop))), (((member1862122484_alt_o F_28) ((pi_o_P553196292_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False)))) of role axiom named fact_199_PiE
% A new axiom: (forall (X_47:Prop) (F_28:(Prop->(produc1501160679le_alt->Prop))) (A_79:(Prop->Prop)) (B_60:(Prop->((produc1501160679le_alt->Prop)->Prop))), (((member1862122484_alt_o F_28) ((pi_o_P553196292_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False))))
% FOF formula (forall (X_47:product_unit) (F_28:(product_unit->(produc1501160679le_alt->Prop))) (A_79:(product_unit->Prop)) (B_60:(product_unit->((produc1501160679le_alt->Prop)->Prop))), (((member1661784200_alt_o F_28) ((pi_Pro1312660828_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False)))) of role axiom named fact_200_PiE
% A new axiom: (forall (X_47:product_unit) (F_28:(product_unit->(produc1501160679le_alt->Prop))) (A_79:(product_unit->Prop)) (B_60:(product_unit->((produc1501160679le_alt->Prop)->Prop))), (((member1661784200_alt_o F_28) ((pi_Pro1312660828_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False))))
% FOF formula (forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->nat)) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->(nat->Prop))), (((member1315464153di_nat F_28) ((pi_Arr251692973di_nat A_79) B_60))->((((member_nat (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False)))) of role axiom named fact_201_PiE
% A new axiom: (forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->nat)) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->(nat->Prop))), (((member1315464153di_nat F_28) ((pi_Arr251692973di_nat A_79) B_60))->((((member_nat (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False))))
% FOF formula (forall (X_47:Prop) (F_28:(Prop->nat)) (A_79:(Prop->Prop)) (B_60:(Prop->(nat->Prop))), (((member_o_nat F_28) ((pi_o_nat A_79) B_60))->((((member_nat (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False)))) of role axiom named fact_202_PiE
% A new axiom: (forall (X_47:Prop) (F_28:(Prop->nat)) (A_79:(Prop->Prop)) (B_60:(Prop->(nat->Prop))), (((member_o_nat F_28) ((pi_o_nat A_79) B_60))->((((member_nat (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False))))
% FOF formula (forall (X_47:product_unit) (F_28:(product_unit->nat)) (A_79:(product_unit->Prop)) (B_60:(product_unit->(nat->Prop))), (((member1827227242it_nat F_28) ((pi_Product_unit_nat A_79) B_60))->((((member_nat (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False)))) of role axiom named fact_203_PiE
% A new axiom: (forall (X_47:product_unit) (F_28:(product_unit->nat)) (A_79:(product_unit->Prop)) (B_60:(product_unit->(nat->Prop))), (((member1827227242it_nat F_28) ((pi_Product_unit_nat A_79) B_60))->((((member_nat (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False))))
% FOF formula (forall (X_47:produc1501160679le_alt) (F_28:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_79:(produc1501160679le_alt->Prop)) (B_60:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))), (((member1640632174e_indi F_28) ((pi_Pro1767455108e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member214075476le_alt X_47) A_79)->False)))) of role axiom named fact_204_PiE
% A new axiom: (forall (X_47:produc1501160679le_alt) (F_28:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_79:(produc1501160679le_alt->Prop)) (B_60:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))), (((member1640632174e_indi F_28) ((pi_Pro1767455108e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member214075476le_alt X_47) A_79)->False))))
% FOF formula (forall (X_47:produc1501160679le_alt) (F_28:(produc1501160679le_alt->product_unit)) (A_79:(produc1501160679le_alt->Prop)) (B_60:(produc1501160679le_alt->(product_unit->Prop))), (((member593902749t_unit F_28) ((pi_Pro1475896499t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member214075476le_alt X_47) A_79)->False)))) of role axiom named fact_205_PiE
% A new axiom: (forall (X_47:produc1501160679le_alt) (F_28:(produc1501160679le_alt->product_unit)) (A_79:(produc1501160679le_alt->Prop)) (B_60:(produc1501160679le_alt->(product_unit->Prop))), (((member593902749t_unit F_28) ((pi_Pro1475896499t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member214075476le_alt X_47) A_79)->False))))
% FOF formula (forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member44294883e_indi F_28) ((pi_Arr1232280765e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False)))) of role axiom named fact_206_PiE
% A new axiom: (forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member44294883e_indi F_28) ((pi_Arr1232280765e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False))))
% FOF formula (forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member939334982lt_o_o F_28) ((pi_Arr952516694lt_o_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False)))) of role axiom named fact_207_PiE
% A new axiom: (forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member939334982lt_o_o F_28) ((pi_Arr952516694lt_o_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False))))
% FOF formula (forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->product_unit)) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(product_unit->Prop))), (((member843528338t_unit F_28) ((pi_Arr1963174508t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False)))) of role axiom named fact_208_PiE
% A new axiom: (forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->product_unit)) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(product_unit->Prop))), (((member843528338t_unit F_28) ((pi_Arr1963174508t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False))))
% FOF formula (forall (X_47:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_79:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_60:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member1452482393e_indi F_28) ((pi_Arr338314351e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member616898751_alt_o X_47) A_79)->False)))) of role axiom named fact_209_PiE
% A new axiom: (forall (X_47:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_79:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_60:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member1452482393e_indi F_28) ((pi_Arr338314351e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member616898751_alt_o X_47) A_79)->False))))
% FOF formula (forall (X_47:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_79:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_60:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member1823529808lt_o_o F_28) ((pi_Arr195212324lt_o_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member616898751_alt_o X_47) A_79)->False)))) of role axiom named fact_210_PiE
% A new axiom: (forall (X_47:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_79:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_60:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member1823529808lt_o_o F_28) ((pi_Arr195212324lt_o_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member616898751_alt_o X_47) A_79)->False))))
% FOF formula (forall (X_47:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->product_unit)) (A_79:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_60:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(product_unit->Prop))), (((member1924666376t_unit F_28) ((pi_Arr830584606t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member616898751_alt_o X_47) A_79)->False)))) of role axiom named fact_211_PiE
% A new axiom: (forall (X_47:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->product_unit)) (A_79:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_60:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(product_unit->Prop))), (((member1924666376t_unit F_28) ((pi_Arr830584606t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member616898751_alt_o X_47) A_79)->False))))
% FOF formula (forall (X_47:(produc1501160679le_alt->Prop)) (F_28:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_79:((produc1501160679le_alt->Prop)->Prop)) (B_60:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))), (((member304866663e_indi F_28) ((pi_Pro468373057e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member377231867_alt_o X_47) A_79)->False)))) of role axiom named fact_212_PiE
% A new axiom: (forall (X_47:(produc1501160679le_alt->Prop)) (F_28:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_79:((produc1501160679le_alt->Prop)->Prop)) (B_60:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))), (((member304866663e_indi F_28) ((pi_Pro468373057e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member377231867_alt_o X_47) A_79)->False))))
% FOF formula (forall (X_47:(produc1501160679le_alt->Prop)) (F_28:((produc1501160679le_alt->Prop)->Prop)) (A_79:((produc1501160679le_alt->Prop)->Prop)) (B_60:((produc1501160679le_alt->Prop)->(Prop->Prop))), (((member1961363906lt_o_o F_28) ((pi_Pro422690258lt_o_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member377231867_alt_o X_47) A_79)->False)))) of role axiom named fact_213_PiE
% A new axiom: (forall (X_47:(produc1501160679le_alt->Prop)) (F_28:((produc1501160679le_alt->Prop)->Prop)) (A_79:((produc1501160679le_alt->Prop)->Prop)) (B_60:((produc1501160679le_alt->Prop)->(Prop->Prop))), (((member1961363906lt_o_o F_28) ((pi_Pro422690258lt_o_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member377231867_alt_o X_47) A_79)->False))))
% FOF formula (forall (X_47:(produc1501160679le_alt->Prop)) (F_28:((produc1501160679le_alt->Prop)->product_unit)) (A_79:((produc1501160679le_alt->Prop)->Prop)) (B_60:((produc1501160679le_alt->Prop)->(product_unit->Prop))), (((member221730070t_unit F_28) ((pi_Pro1306850800t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member377231867_alt_o X_47) A_79)->False)))) of role axiom named fact_214_PiE
% A new axiom: (forall (X_47:(produc1501160679le_alt->Prop)) (F_28:((produc1501160679le_alt->Prop)->product_unit)) (A_79:((produc1501160679le_alt->Prop)->Prop)) (B_60:((produc1501160679le_alt->Prop)->(product_unit->Prop))), (((member221730070t_unit F_28) ((pi_Pro1306850800t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member377231867_alt_o X_47) A_79)->False))))
% FOF formula (forall (X_47:nat) (F_28:(nat->arrow_1429601828e_indi)) (A_79:(nat->Prop)) (B_60:(nat->(arrow_1429601828e_indi->Prop))), (((member1391860553e_indi F_28) ((pi_nat1219304995e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member_nat X_47) A_79)->False)))) of role axiom named fact_215_PiE
% A new axiom: (forall (X_47:nat) (F_28:(nat->arrow_1429601828e_indi)) (A_79:(nat->Prop)) (B_60:(nat->(arrow_1429601828e_indi->Prop))), (((member1391860553e_indi F_28) ((pi_nat1219304995e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member_nat X_47) A_79)->False))))
% FOF formula (forall (X_47:nat) (F_28:(nat->Prop)) (A_79:(nat->Prop)) (B_60:(nat->(Prop->Prop))), (((member_nat_o F_28) ((pi_nat_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member_nat X_47) A_79)->False)))) of role axiom named fact_216_PiE
% A new axiom: (forall (X_47:nat) (F_28:(nat->Prop)) (A_79:(nat->Prop)) (B_60:(nat->(Prop->Prop))), (((member_nat_o F_28) ((pi_nat_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member_nat X_47) A_79)->False))))
% FOF formula (forall (X_47:nat) (F_28:(nat->product_unit)) (A_79:(nat->Prop)) (B_60:(nat->(product_unit->Prop))), (((member616671224t_unit F_28) ((pi_nat_Product_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member_nat X_47) A_79)->False)))) of role axiom named fact_217_PiE
% A new axiom: (forall (X_47:nat) (F_28:(nat->product_unit)) (A_79:(nat->Prop)) (B_60:(nat->(product_unit->Prop))), (((member616671224t_unit F_28) ((pi_nat_Product_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member_nat X_47) A_79)->False))))
% FOF formula (forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_28) ((pi_Arr1304755663_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False)))) of role axiom named fact_218_PiE
% A new axiom: (forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_28) ((pi_Arr1304755663_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False))))
% FOF formula (forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_28) ((pi_Arr1929480907_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False)))) of role axiom named fact_219_PiE
% A new axiom: (forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_28) ((pi_Arr1929480907_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False))))
% FOF formula (forall (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_9) B_5))->((ex (produc1501160679le_alt->Prop)) (fun (X_1:(produc1501160679le_alt->Prop))=> ((and ((member377231867_alt_o X_1) arrow_823908191le_Lin)) ((member214075476le_alt ((produc1347929815le_alt A_9) B_5)) X_1)))))) of role axiom named fact_220_complete__Lin
% A new axiom: (forall (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_9) B_5))->((ex (produc1501160679le_alt->Prop)) (fun (X_1:(produc1501160679le_alt->Prop))=> ((and ((member377231867_alt_o X_1) arrow_823908191le_Lin)) ((member214075476le_alt ((produc1347929815le_alt A_9) B_5)) X_1))))))
% FOF formula (forall (A_78:(produc1501160679le_alt->Prop)), (((eq ((produc1501160679le_alt->Prop)->Prop)) ((pi_Pro1701359055_alt_o A_78) (fun (Uu:produc1501160679le_alt)=> top_top_o_o))) top_to1842727771lt_o_o)) of role axiom named fact_221_Pi__UNIV
% A new axiom: (forall (A_78:(produc1501160679le_alt->Prop)), (((eq ((produc1501160679le_alt->Prop)->Prop)) ((pi_Pro1701359055_alt_o A_78) (fun (Uu:produc1501160679le_alt)=> top_top_o_o))) top_to1842727771lt_o_o))
% FOF formula (forall (A_78:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1304755663_alt_o A_78) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> top_to1842727771lt_o_o))) top_to1969627639lt_o_o)) of role axiom named fact_222_Pi__UNIV
% A new axiom: (forall (A_78:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1304755663_alt_o A_78) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> top_to1842727771lt_o_o))) top_to1969627639lt_o_o))
% FOF formula (forall (A_78:(arrow_1429601828e_indi->Prop)), (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1929480907_alt_o A_78) (fun (Uu:arrow_1429601828e_indi)=> top_to1842727771lt_o_o))) top_to2122763103lt_o_o)) of role axiom named fact_223_Pi__UNIV
% A new axiom: (forall (A_78:(arrow_1429601828e_indi->Prop)), (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1929480907_alt_o A_78) (fun (Uu:arrow_1429601828e_indi)=> top_to1842727771lt_o_o))) top_to2122763103lt_o_o))
% FOF formula (forall (X_46:Prop), ((ord_less_eq_o X_46) X_46)) of role axiom named fact_224_order__refl
% A new axiom: (forall (X_46:Prop), ((ord_less_eq_o X_46) X_46))
% FOF formula (forall (X_46:nat), ((ord_less_eq_nat X_46) X_46)) of role axiom named fact_225_order__refl
% A new axiom: (forall (X_46:nat), ((ord_less_eq_nat X_46) X_46))
% FOF formula (forall (X_46:(nat->Prop)), ((ord_less_eq_nat_o X_46) X_46)) of role axiom named fact_226_order__refl
% A new axiom: (forall (X_46:(nat->Prop)), ((ord_less_eq_nat_o X_46) X_46))
% FOF formula ((ex nat) (fun (N_1:nat)=> ((and ((and ((ord_less_nat N_1) (finite97476818e_indi top_to988227749indi_o))) (forall (M:nat), (((ord_less_eq_nat M) N_1)->((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) M)) lab) lba)))))))) ((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N_1) one_one_nat))) lab) lba))))))) of role axiom named fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I
% A new axiom: ((ex nat) (fun (N_1:nat)=> ((and ((and ((ord_less_nat N_1) (finite97476818e_indi top_to988227749indi_o))) (forall (M:nat), (((ord_less_eq_nat M) N_1)->((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) M)) lab) lba)))))))) ((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N_1) one_one_nat))) lab) lba)))))))
% FOF formula ((forall (N_1:nat), (((ord_less_nat N_1) (finite97476818e_indi top_to988227749indi_o))->((forall (M:nat), (((ord_less_eq_nat M) N_1)->((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) M)) lab) lba))))))->(((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N_1) one_one_nat))) lab) lba))))->False))))->False) of role axiom named fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_
% A new axiom: ((forall (N_1:nat), (((ord_less_nat N_1) (finite97476818e_indi top_to988227749indi_o))->((forall (M:nat), (((ord_less_eq_nat M) N_1)->((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) M)) lab) lba))))))->(((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N_1) one_one_nat))) lab) lba))))->False))))->False)
% FOF formula (forall (X_45:nat) (Y_34:nat), ((((ord_less_eq_nat X_45) Y_34)->False)->((ord_less_eq_nat Y_34) X_45))) of role axiom named fact_229_linorder__le__cases
% A new axiom: (forall (X_45:nat) (Y_34:nat), ((((ord_less_eq_nat X_45) Y_34)->False)->((ord_less_eq_nat Y_34) X_45)))
% FOF formula (forall (X_44:nat) (F_27:(nat->Prop)) (G_8:(nat->Prop)), (((ord_less_eq_nat_o F_27) G_8)->((ord_less_eq_o (F_27 X_44)) (G_8 X_44)))) of role axiom named fact_230_le__funE
% A new axiom: (forall (X_44:nat) (F_27:(nat->Prop)) (G_8:(nat->Prop)), (((ord_less_eq_nat_o F_27) G_8)->((ord_less_eq_o (F_27 X_44)) (G_8 X_44))))
% FOF formula (forall (Z_6:Prop) (Y_33:Prop) (X_43:Prop), (((ord_less_eq_o Y_33) X_43)->(((ord_less_eq_o Z_6) Y_33)->((ord_less_eq_o Z_6) X_43)))) of role axiom named fact_231_xt1_I6_J
% A new axiom: (forall (Z_6:Prop) (Y_33:Prop) (X_43:Prop), (((ord_less_eq_o Y_33) X_43)->(((ord_less_eq_o Z_6) Y_33)->((ord_less_eq_o Z_6) X_43))))
% FOF formula (forall (Z_6:nat) (Y_33:nat) (X_43:nat), (((ord_less_eq_nat Y_33) X_43)->(((ord_less_eq_nat Z_6) Y_33)->((ord_less_eq_nat Z_6) X_43)))) of role axiom named fact_232_xt1_I6_J
% A new axiom: (forall (Z_6:nat) (Y_33:nat) (X_43:nat), (((ord_less_eq_nat Y_33) X_43)->(((ord_less_eq_nat Z_6) Y_33)->((ord_less_eq_nat Z_6) X_43))))
% FOF formula (forall (Z_6:(nat->Prop)) (Y_33:(nat->Prop)) (X_43:(nat->Prop)), (((ord_less_eq_nat_o Y_33) X_43)->(((ord_less_eq_nat_o Z_6) Y_33)->((ord_less_eq_nat_o Z_6) X_43)))) of role axiom named fact_233_xt1_I6_J
% A new axiom: (forall (Z_6:(nat->Prop)) (Y_33:(nat->Prop)) (X_43:(nat->Prop)), (((ord_less_eq_nat_o Y_33) X_43)->(((ord_less_eq_nat_o Z_6) Y_33)->((ord_less_eq_nat_o Z_6) X_43))))
% FOF formula (forall (Y_32:Prop) (X_42:Prop), (((ord_less_eq_o Y_32) X_42)->(((ord_less_eq_o X_42) Y_32)->((iff X_42) Y_32)))) of role axiom named fact_234_xt1_I5_J
% A new axiom: (forall (Y_32:Prop) (X_42:Prop), (((ord_less_eq_o Y_32) X_42)->(((ord_less_eq_o X_42) Y_32)->((iff X_42) Y_32))))
% FOF formula (forall (Y_32:nat) (X_42:nat), (((ord_less_eq_nat Y_32) X_42)->(((ord_less_eq_nat X_42) Y_32)->(((eq nat) X_42) Y_32)))) of role axiom named fact_235_xt1_I5_J
% A new axiom: (forall (Y_32:nat) (X_42:nat), (((ord_less_eq_nat Y_32) X_42)->(((ord_less_eq_nat X_42) Y_32)->(((eq nat) X_42) Y_32))))
% FOF formula (forall (Y_32:(nat->Prop)) (X_42:(nat->Prop)), (((ord_less_eq_nat_o Y_32) X_42)->(((ord_less_eq_nat_o X_42) Y_32)->(((eq (nat->Prop)) X_42) Y_32)))) of role axiom named fact_236_xt1_I5_J
% A new axiom: (forall (Y_32:(nat->Prop)) (X_42:(nat->Prop)), (((ord_less_eq_nat_o Y_32) X_42)->(((ord_less_eq_nat_o X_42) Y_32)->(((eq (nat->Prop)) X_42) Y_32))))
% FOF formula (forall (Z_5:Prop) (X_41:Prop) (Y_31:Prop), (((ord_less_eq_o X_41) Y_31)->(((ord_less_eq_o Y_31) Z_5)->((ord_less_eq_o X_41) Z_5)))) of role axiom named fact_237_order__trans
% A new axiom: (forall (Z_5:Prop) (X_41:Prop) (Y_31:Prop), (((ord_less_eq_o X_41) Y_31)->(((ord_less_eq_o Y_31) Z_5)->((ord_less_eq_o X_41) Z_5))))
% FOF formula (forall (Z_5:nat) (X_41:nat) (Y_31:nat), (((ord_less_eq_nat X_41) Y_31)->(((ord_less_eq_nat Y_31) Z_5)->((ord_less_eq_nat X_41) Z_5)))) of role axiom named fact_238_order__trans
% A new axiom: (forall (Z_5:nat) (X_41:nat) (Y_31:nat), (((ord_less_eq_nat X_41) Y_31)->(((ord_less_eq_nat Y_31) Z_5)->((ord_less_eq_nat X_41) Z_5))))
% FOF formula (forall (Z_5:(nat->Prop)) (X_41:(nat->Prop)) (Y_31:(nat->Prop)), (((ord_less_eq_nat_o X_41) Y_31)->(((ord_less_eq_nat_o Y_31) Z_5)->((ord_less_eq_nat_o X_41) Z_5)))) of role axiom named fact_239_order__trans
% A new axiom: (forall (Z_5:(nat->Prop)) (X_41:(nat->Prop)) (Y_31:(nat->Prop)), (((ord_less_eq_nat_o X_41) Y_31)->(((ord_less_eq_nat_o Y_31) Z_5)->((ord_less_eq_nat_o X_41) Z_5))))
% FOF formula (forall (X_40:Prop) (Y_30:Prop), (((ord_less_eq_o X_40) Y_30)->(((ord_less_eq_o Y_30) X_40)->((iff X_40) Y_30)))) of role axiom named fact_240_order__antisym
% A new axiom: (forall (X_40:Prop) (Y_30:Prop), (((ord_less_eq_o X_40) Y_30)->(((ord_less_eq_o Y_30) X_40)->((iff X_40) Y_30))))
% FOF formula (forall (X_40:nat) (Y_30:nat), (((ord_less_eq_nat X_40) Y_30)->(((ord_less_eq_nat Y_30) X_40)->(((eq nat) X_40) Y_30)))) of role axiom named fact_241_order__antisym
% A new axiom: (forall (X_40:nat) (Y_30:nat), (((ord_less_eq_nat X_40) Y_30)->(((ord_less_eq_nat Y_30) X_40)->(((eq nat) X_40) Y_30))))
% FOF formula (forall (X_40:(nat->Prop)) (Y_30:(nat->Prop)), (((ord_less_eq_nat_o X_40) Y_30)->(((ord_less_eq_nat_o Y_30) X_40)->(((eq (nat->Prop)) X_40) Y_30)))) of role axiom named fact_242_order__antisym
% A new axiom: (forall (X_40:(nat->Prop)) (Y_30:(nat->Prop)), (((ord_less_eq_nat_o X_40) Y_30)->(((ord_less_eq_nat_o Y_30) X_40)->(((eq (nat->Prop)) X_40) Y_30))))
% FOF formula (forall (C_32:Prop) (B_59:Prop) (A_77:Prop), (((ord_less_eq_o B_59) A_77)->(((iff B_59) C_32)->((ord_less_eq_o C_32) A_77)))) of role axiom named fact_243_xt1_I4_J
% A new axiom: (forall (C_32:Prop) (B_59:Prop) (A_77:Prop), (((ord_less_eq_o B_59) A_77)->(((iff B_59) C_32)->((ord_less_eq_o C_32) A_77))))
% FOF formula (forall (C_32:nat) (B_59:nat) (A_77:nat), (((ord_less_eq_nat B_59) A_77)->((((eq nat) B_59) C_32)->((ord_less_eq_nat C_32) A_77)))) of role axiom named fact_244_xt1_I4_J
% A new axiom: (forall (C_32:nat) (B_59:nat) (A_77:nat), (((ord_less_eq_nat B_59) A_77)->((((eq nat) B_59) C_32)->((ord_less_eq_nat C_32) A_77))))
% FOF formula (forall (C_32:(nat->Prop)) (B_59:(nat->Prop)) (A_77:(nat->Prop)), (((ord_less_eq_nat_o B_59) A_77)->((((eq (nat->Prop)) B_59) C_32)->((ord_less_eq_nat_o C_32) A_77)))) of role axiom named fact_245_xt1_I4_J
% A new axiom: (forall (C_32:(nat->Prop)) (B_59:(nat->Prop)) (A_77:(nat->Prop)), (((ord_less_eq_nat_o B_59) A_77)->((((eq (nat->Prop)) B_59) C_32)->((ord_less_eq_nat_o C_32) A_77))))
% FOF formula (forall (C_31:Prop) (A_76:Prop) (B_58:Prop), (((ord_less_eq_o A_76) B_58)->(((iff B_58) C_31)->((ord_less_eq_o A_76) C_31)))) of role axiom named fact_246_ord__le__eq__trans
% A new axiom: (forall (C_31:Prop) (A_76:Prop) (B_58:Prop), (((ord_less_eq_o A_76) B_58)->(((iff B_58) C_31)->((ord_less_eq_o A_76) C_31))))
% FOF formula (forall (C_31:nat) (A_76:nat) (B_58:nat), (((ord_less_eq_nat A_76) B_58)->((((eq nat) B_58) C_31)->((ord_less_eq_nat A_76) C_31)))) of role axiom named fact_247_ord__le__eq__trans
% A new axiom: (forall (C_31:nat) (A_76:nat) (B_58:nat), (((ord_less_eq_nat A_76) B_58)->((((eq nat) B_58) C_31)->((ord_less_eq_nat A_76) C_31))))
% FOF formula (forall (C_31:(nat->Prop)) (A_76:(nat->Prop)) (B_58:(nat->Prop)), (((ord_less_eq_nat_o A_76) B_58)->((((eq (nat->Prop)) B_58) C_31)->((ord_less_eq_nat_o A_76) C_31)))) of role axiom named fact_248_ord__le__eq__trans
% A new axiom: (forall (C_31:(nat->Prop)) (A_76:(nat->Prop)) (B_58:(nat->Prop)), (((ord_less_eq_nat_o A_76) B_58)->((((eq (nat->Prop)) B_58) C_31)->((ord_less_eq_nat_o A_76) C_31))))
% FOF formula (forall (C_30:Prop) (B_57:Prop) (A_75:Prop), (((iff A_75) B_57)->(((ord_less_eq_o C_30) B_57)->((ord_less_eq_o C_30) A_75)))) of role axiom named fact_249_xt1_I3_J
% A new axiom: (forall (C_30:Prop) (B_57:Prop) (A_75:Prop), (((iff A_75) B_57)->(((ord_less_eq_o C_30) B_57)->((ord_less_eq_o C_30) A_75))))
% FOF formula (forall (C_30:nat) (A_75:nat) (B_57:nat), ((((eq nat) A_75) B_57)->(((ord_less_eq_nat C_30) B_57)->((ord_less_eq_nat C_30) A_75)))) of role axiom named fact_250_xt1_I3_J
% A new axiom: (forall (C_30:nat) (A_75:nat) (B_57:nat), ((((eq nat) A_75) B_57)->(((ord_less_eq_nat C_30) B_57)->((ord_less_eq_nat C_30) A_75))))
% FOF formula (forall (C_30:(nat->Prop)) (A_75:(nat->Prop)) (B_57:(nat->Prop)), ((((eq (nat->Prop)) A_75) B_57)->(((ord_less_eq_nat_o C_30) B_57)->((ord_less_eq_nat_o C_30) A_75)))) of role axiom named fact_251_xt1_I3_J
% A new axiom: (forall (C_30:(nat->Prop)) (A_75:(nat->Prop)) (B_57:(nat->Prop)), ((((eq (nat->Prop)) A_75) B_57)->(((ord_less_eq_nat_o C_30) B_57)->((ord_less_eq_nat_o C_30) A_75))))
% FOF formula (forall (C_29:Prop) (B_56:Prop) (A_74:Prop), (((iff A_74) B_56)->(((ord_less_eq_o B_56) C_29)->((ord_less_eq_o A_74) C_29)))) of role axiom named fact_252_ord__eq__le__trans
% A new axiom: (forall (C_29:Prop) (B_56:Prop) (A_74:Prop), (((iff A_74) B_56)->(((ord_less_eq_o B_56) C_29)->((ord_less_eq_o A_74) C_29))))
% FOF formula (forall (C_29:nat) (A_74:nat) (B_56:nat), ((((eq nat) A_74) B_56)->(((ord_less_eq_nat B_56) C_29)->((ord_less_eq_nat A_74) C_29)))) of role axiom named fact_253_ord__eq__le__trans
% A new axiom: (forall (C_29:nat) (A_74:nat) (B_56:nat), ((((eq nat) A_74) B_56)->(((ord_less_eq_nat B_56) C_29)->((ord_less_eq_nat A_74) C_29))))
% FOF formula (forall (C_29:(nat->Prop)) (A_74:(nat->Prop)) (B_56:(nat->Prop)), ((((eq (nat->Prop)) A_74) B_56)->(((ord_less_eq_nat_o B_56) C_29)->((ord_less_eq_nat_o A_74) C_29)))) of role axiom named fact_254_ord__eq__le__trans
% A new axiom: (forall (C_29:(nat->Prop)) (A_74:(nat->Prop)) (B_56:(nat->Prop)), ((((eq (nat->Prop)) A_74) B_56)->(((ord_less_eq_nat_o B_56) C_29)->((ord_less_eq_nat_o A_74) C_29))))
% FOF formula (forall (Y_29:Prop) (X_39:Prop), (((ord_less_eq_o Y_29) X_39)->((iff ((ord_less_eq_o X_39) Y_29)) ((iff X_39) Y_29)))) of role axiom named fact_255_order__antisym__conv
% A new axiom: (forall (Y_29:Prop) (X_39:Prop), (((ord_less_eq_o Y_29) X_39)->((iff ((ord_less_eq_o X_39) Y_29)) ((iff X_39) Y_29))))
% FOF formula (forall (Y_29:nat) (X_39:nat), (((ord_less_eq_nat Y_29) X_39)->((iff ((ord_less_eq_nat X_39) Y_29)) (((eq nat) X_39) Y_29)))) of role axiom named fact_256_order__antisym__conv
% A new axiom: (forall (Y_29:nat) (X_39:nat), (((ord_less_eq_nat Y_29) X_39)->((iff ((ord_less_eq_nat X_39) Y_29)) (((eq nat) X_39) Y_29))))
% FOF formula (forall (Y_29:(nat->Prop)) (X_39:(nat->Prop)), (((ord_less_eq_nat_o Y_29) X_39)->((iff ((ord_less_eq_nat_o X_39) Y_29)) (((eq (nat->Prop)) X_39) Y_29)))) of role axiom named fact_257_order__antisym__conv
% A new axiom: (forall (Y_29:(nat->Prop)) (X_39:(nat->Prop)), (((ord_less_eq_nat_o Y_29) X_39)->((iff ((ord_less_eq_nat_o X_39) Y_29)) (((eq (nat->Prop)) X_39) Y_29))))
% FOF formula (forall (X_38:nat) (F_26:(nat->Prop)) (G_7:(nat->Prop)), (((ord_less_eq_nat_o F_26) G_7)->((ord_less_eq_o (F_26 X_38)) (G_7 X_38)))) of role axiom named fact_258_le__funD
% A new axiom: (forall (X_38:nat) (F_26:(nat->Prop)) (G_7:(nat->Prop)), (((ord_less_eq_nat_o F_26) G_7)->((ord_less_eq_o (F_26 X_38)) (G_7 X_38))))
% FOF formula (forall (Y_28:Prop) (X_37:Prop), (((iff X_37) Y_28)->((ord_less_eq_o X_37) Y_28))) of role axiom named fact_259_order__eq__refl
% A new axiom: (forall (Y_28:Prop) (X_37:Prop), (((iff X_37) Y_28)->((ord_less_eq_o X_37) Y_28)))
% FOF formula (forall (X_37:nat) (Y_28:nat), ((((eq nat) X_37) Y_28)->((ord_less_eq_nat X_37) Y_28))) of role axiom named fact_260_order__eq__refl
% A new axiom: (forall (X_37:nat) (Y_28:nat), ((((eq nat) X_37) Y_28)->((ord_less_eq_nat X_37) Y_28)))
% FOF formula (forall (X_37:(nat->Prop)) (Y_28:(nat->Prop)), ((((eq (nat->Prop)) X_37) Y_28)->((ord_less_eq_nat_o X_37) Y_28))) of role axiom named fact_261_order__eq__refl
% A new axiom: (forall (X_37:(nat->Prop)) (Y_28:(nat->Prop)), ((((eq (nat->Prop)) X_37) Y_28)->((ord_less_eq_nat_o X_37) Y_28)))
% FOF formula (forall (Y_27:Prop) (X_36:Prop), ((iff ((iff X_36) Y_27)) ((and ((ord_less_eq_o X_36) Y_27)) ((ord_less_eq_o Y_27) X_36)))) of role axiom named fact_262_order__eq__iff
% A new axiom: (forall (Y_27:Prop) (X_36:Prop), ((iff ((iff X_36) Y_27)) ((and ((ord_less_eq_o X_36) Y_27)) ((ord_less_eq_o Y_27) X_36))))
% FOF formula (forall (X_36:nat) (Y_27:nat), ((iff (((eq nat) X_36) Y_27)) ((and ((ord_less_eq_nat X_36) Y_27)) ((ord_less_eq_nat Y_27) X_36)))) of role axiom named fact_263_order__eq__iff
% A new axiom: (forall (X_36:nat) (Y_27:nat), ((iff (((eq nat) X_36) Y_27)) ((and ((ord_less_eq_nat X_36) Y_27)) ((ord_less_eq_nat Y_27) X_36))))
% FOF formula (forall (X_36:(nat->Prop)) (Y_27:(nat->Prop)), ((iff (((eq (nat->Prop)) X_36) Y_27)) ((and ((ord_less_eq_nat_o X_36) Y_27)) ((ord_less_eq_nat_o Y_27) X_36)))) of role axiom named fact_264_order__eq__iff
% A new axiom: (forall (X_36:(nat->Prop)) (Y_27:(nat->Prop)), ((iff (((eq (nat->Prop)) X_36) Y_27)) ((and ((ord_less_eq_nat_o X_36) Y_27)) ((ord_less_eq_nat_o Y_27) X_36))))
% FOF formula (forall (X_35:nat) (Y_26:nat), ((or ((ord_less_eq_nat X_35) Y_26)) ((ord_less_eq_nat Y_26) X_35))) of role axiom named fact_265_linorder__linear
% A new axiom: (forall (X_35:nat) (Y_26:nat), ((or ((ord_less_eq_nat X_35) Y_26)) ((ord_less_eq_nat Y_26) X_35)))
% FOF formula (forall (F_25:(nat->Prop)) (G_6:(nat->Prop)), ((iff ((ord_less_eq_nat_o F_25) G_6)) (forall (X_1:nat), ((ord_less_eq_o (F_25 X_1)) (G_6 X_1))))) of role axiom named fact_266_le__fun__def
% A new axiom: (forall (F_25:(nat->Prop)) (G_6:(nat->Prop)), ((iff ((ord_less_eq_nat_o F_25) G_6)) (forall (X_1:nat), ((ord_less_eq_o (F_25 X_1)) (G_6 X_1)))))
% FOF formula (forall (X_34:nat) (Y_25:nat), ((iff (((ord_less_nat X_34) Y_25)->False)) ((ord_less_eq_nat Y_25) X_34))) of role axiom named fact_267_linorder__not__less
% A new axiom: (forall (X_34:nat) (Y_25:nat), ((iff (((ord_less_nat X_34) Y_25)->False)) ((ord_less_eq_nat Y_25) X_34)))
% FOF formula (forall (X_33:nat) (Y_24:nat), ((iff (((ord_less_eq_nat X_33) Y_24)->False)) ((ord_less_nat Y_24) X_33))) of role axiom named fact_268_linorder__not__le
% A new axiom: (forall (X_33:nat) (Y_24:nat), ((iff (((ord_less_eq_nat X_33) Y_24)->False)) ((ord_less_nat Y_24) X_33)))
% FOF formula (forall (X_32:nat) (Y_23:nat), ((or ((ord_less_eq_nat X_32) Y_23)) ((ord_less_nat Y_23) X_32))) of role axiom named fact_269_linorder__le__less__linear
% A new axiom: (forall (X_32:nat) (Y_23:nat), ((or ((ord_less_eq_nat X_32) Y_23)) ((ord_less_nat Y_23) X_32)))
% FOF formula (forall (X_31:(product_unit->Prop)) (Y_22:(product_unit->Prop)), ((iff ((ord_le232288914unit_o X_31) Y_22)) ((and ((ord_le1511552390unit_o X_31) Y_22)) (not (((eq (product_unit->Prop)) X_31) Y_22))))) of role axiom named fact_270_order__less__le
% A new axiom: (forall (X_31:(product_unit->Prop)) (Y_22:(product_unit->Prop)), ((iff ((ord_le232288914unit_o X_31) Y_22)) ((and ((ord_le1511552390unit_o X_31) Y_22)) (not (((eq (product_unit->Prop)) X_31) Y_22)))))
% FOF formula (forall (X_31:(arrow_1429601828e_indi->Prop)) (Y_22:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o X_31) Y_22)) ((and ((ord_le1799070453indi_o X_31) Y_22)) (not (((eq (arrow_1429601828e_indi->Prop)) X_31) Y_22))))) of role axiom named fact_271_order__less__le
% A new axiom: (forall (X_31:(arrow_1429601828e_indi->Prop)) (Y_22:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o X_31) Y_22)) ((and ((ord_le1799070453indi_o X_31) Y_22)) (not (((eq (arrow_1429601828e_indi->Prop)) X_31) Y_22)))))
% FOF formula (forall (X_31:Prop) (Y_22:Prop), ((iff ((ord_less_o X_31) Y_22)) ((and ((ord_less_eq_o X_31) Y_22)) (((iff X_31) Y_22)->False)))) of role axiom named fact_272_order__less__le
% A new axiom: (forall (X_31:Prop) (Y_22:Prop), ((iff ((ord_less_o X_31) Y_22)) ((and ((ord_less_eq_o X_31) Y_22)) (((iff X_31) Y_22)->False))))
% FOF formula (forall (X_31:(nat->Prop)) (Y_22:(nat->Prop)), ((iff ((ord_less_nat_o X_31) Y_22)) ((and ((ord_less_eq_nat_o X_31) Y_22)) (not (((eq (nat->Prop)) X_31) Y_22))))) of role axiom named fact_273_order__less__le
% A new axiom: (forall (X_31:(nat->Prop)) (Y_22:(nat->Prop)), ((iff ((ord_less_nat_o X_31) Y_22)) ((and ((ord_less_eq_nat_o X_31) Y_22)) (not (((eq (nat->Prop)) X_31) Y_22)))))
% FOF formula (forall (X_31:nat) (Y_22:nat), ((iff ((ord_less_nat X_31) Y_22)) ((and ((ord_less_eq_nat X_31) Y_22)) (not (((eq nat) X_31) Y_22))))) of role axiom named fact_274_order__less__le
% A new axiom: (forall (X_31:nat) (Y_22:nat), ((iff ((ord_less_nat X_31) Y_22)) ((and ((ord_less_eq_nat X_31) Y_22)) (not (((eq nat) X_31) Y_22)))))
% FOF formula (forall (X_30:(product_unit->Prop)) (Y_21:(product_unit->Prop)), ((iff ((ord_le232288914unit_o X_30) Y_21)) ((and ((ord_le1511552390unit_o X_30) Y_21)) (((ord_le1511552390unit_o Y_21) X_30)->False)))) of role axiom named fact_275_less__le__not__le
% A new axiom: (forall (X_30:(product_unit->Prop)) (Y_21:(product_unit->Prop)), ((iff ((ord_le232288914unit_o X_30) Y_21)) ((and ((ord_le1511552390unit_o X_30) Y_21)) (((ord_le1511552390unit_o Y_21) X_30)->False))))
% FOF formula (forall (X_30:(arrow_1429601828e_indi->Prop)) (Y_21:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o X_30) Y_21)) ((and ((ord_le1799070453indi_o X_30) Y_21)) (((ord_le1799070453indi_o Y_21) X_30)->False)))) of role axiom named fact_276_less__le__not__le
% A new axiom: (forall (X_30:(arrow_1429601828e_indi->Prop)) (Y_21:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o X_30) Y_21)) ((and ((ord_le1799070453indi_o X_30) Y_21)) (((ord_le1799070453indi_o Y_21) X_30)->False))))
% FOF formula (forall (X_30:Prop) (Y_21:Prop), ((iff ((ord_less_o X_30) Y_21)) ((and ((ord_less_eq_o X_30) Y_21)) (((ord_less_eq_o Y_21) X_30)->False)))) of role axiom named fact_277_less__le__not__le
% A new axiom: (forall (X_30:Prop) (Y_21:Prop), ((iff ((ord_less_o X_30) Y_21)) ((and ((ord_less_eq_o X_30) Y_21)) (((ord_less_eq_o Y_21) X_30)->False))))
% FOF formula (forall (X_30:(nat->Prop)) (Y_21:(nat->Prop)), ((iff ((ord_less_nat_o X_30) Y_21)) ((and ((ord_less_eq_nat_o X_30) Y_21)) (((ord_less_eq_nat_o Y_21) X_30)->False)))) of role axiom named fact_278_less__le__not__le
% A new axiom: (forall (X_30:(nat->Prop)) (Y_21:(nat->Prop)), ((iff ((ord_less_nat_o X_30) Y_21)) ((and ((ord_less_eq_nat_o X_30) Y_21)) (((ord_less_eq_nat_o Y_21) X_30)->False))))
% FOF formula (forall (X_30:nat) (Y_21:nat), ((iff ((ord_less_nat X_30) Y_21)) ((and ((ord_less_eq_nat X_30) Y_21)) (((ord_less_eq_nat Y_21) X_30)->False)))) of role axiom named fact_279_less__le__not__le
% A new axiom: (forall (X_30:nat) (Y_21:nat), ((iff ((ord_less_nat X_30) Y_21)) ((and ((ord_less_eq_nat X_30) Y_21)) (((ord_less_eq_nat Y_21) X_30)->False))))
% FOF formula (forall (X_29:(product_unit->Prop)) (Y_20:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o X_29) Y_20)) ((or ((ord_le232288914unit_o X_29) Y_20)) (((eq (product_unit->Prop)) X_29) Y_20)))) of role axiom named fact_280_order__le__less
% A new axiom: (forall (X_29:(product_unit->Prop)) (Y_20:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o X_29) Y_20)) ((or ((ord_le232288914unit_o X_29) Y_20)) (((eq (product_unit->Prop)) X_29) Y_20))))
% FOF formula (forall (X_29:(arrow_1429601828e_indi->Prop)) (Y_20:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o X_29) Y_20)) ((or ((ord_le777687553indi_o X_29) Y_20)) (((eq (arrow_1429601828e_indi->Prop)) X_29) Y_20)))) of role axiom named fact_281_order__le__less
% A new axiom: (forall (X_29:(arrow_1429601828e_indi->Prop)) (Y_20:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o X_29) Y_20)) ((or ((ord_le777687553indi_o X_29) Y_20)) (((eq (arrow_1429601828e_indi->Prop)) X_29) Y_20))))
% FOF formula (forall (X_29:Prop) (Y_20:Prop), ((iff ((ord_less_eq_o X_29) Y_20)) ((or ((ord_less_o X_29) Y_20)) ((iff X_29) Y_20)))) of role axiom named fact_282_order__le__less
% A new axiom: (forall (X_29:Prop) (Y_20:Prop), ((iff ((ord_less_eq_o X_29) Y_20)) ((or ((ord_less_o X_29) Y_20)) ((iff X_29) Y_20))))
% FOF formula (forall (X_29:(nat->Prop)) (Y_20:(nat->Prop)), ((iff ((ord_less_eq_nat_o X_29) Y_20)) ((or ((ord_less_nat_o X_29) Y_20)) (((eq (nat->Prop)) X_29) Y_20)))) of role axiom named fact_283_order__le__less
% A new axiom: (forall (X_29:(nat->Prop)) (Y_20:(nat->Prop)), ((iff ((ord_less_eq_nat_o X_29) Y_20)) ((or ((ord_less_nat_o X_29) Y_20)) (((eq (nat->Prop)) X_29) Y_20))))
% FOF formula (forall (X_29:nat) (Y_20:nat), ((iff ((ord_less_eq_nat X_29) Y_20)) ((or ((ord_less_nat X_29) Y_20)) (((eq nat) X_29) Y_20)))) of role axiom named fact_284_order__le__less
% A new axiom: (forall (X_29:nat) (Y_20:nat), ((iff ((ord_less_eq_nat X_29) Y_20)) ((or ((ord_less_nat X_29) Y_20)) (((eq nat) X_29) Y_20))))
% FOF formula (forall (X_28:nat) (Y_19:nat), ((((ord_less_nat X_28) Y_19)->False)->((ord_less_eq_nat Y_19) X_28))) of role axiom named fact_285_leI
% A new axiom: (forall (X_28:nat) (Y_19:nat), ((((ord_less_nat X_28) Y_19)->False)->((ord_less_eq_nat Y_19) X_28)))
% FOF formula (forall (Y_18:nat) (X_27:nat), ((((ord_less_eq_nat Y_18) X_27)->False)->((ord_less_nat X_27) Y_18))) of role axiom named fact_286_not__leE
% A new axiom: (forall (Y_18:nat) (X_27:nat), ((((ord_less_eq_nat Y_18) X_27)->False)->((ord_less_nat X_27) Y_18)))
% FOF formula (forall (X_26:nat) (Y_17:nat), ((((ord_less_nat X_26) Y_17)->False)->((iff ((ord_less_eq_nat X_26) Y_17)) (((eq nat) X_26) Y_17)))) of role axiom named fact_287_linorder__antisym__conv1
% A new axiom: (forall (X_26:nat) (Y_17:nat), ((((ord_less_nat X_26) Y_17)->False)->((iff ((ord_less_eq_nat X_26) Y_17)) (((eq nat) X_26) Y_17))))
% FOF formula (forall (A_73:(product_unit->Prop)) (B_55:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_73) B_55))->(((ord_le1511552390unit_o A_73) B_55)->((ord_le232288914unit_o A_73) B_55)))) of role axiom named fact_288_order__neq__le__trans
% A new axiom: (forall (A_73:(product_unit->Prop)) (B_55:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_73) B_55))->(((ord_le1511552390unit_o A_73) B_55)->((ord_le232288914unit_o A_73) B_55))))
% FOF formula (forall (A_73:(arrow_1429601828e_indi->Prop)) (B_55:(arrow_1429601828e_indi->Prop)), ((not (((eq (arrow_1429601828e_indi->Prop)) A_73) B_55))->(((ord_le1799070453indi_o A_73) B_55)->((ord_le777687553indi_o A_73) B_55)))) of role axiom named fact_289_order__neq__le__trans
% A new axiom: (forall (A_73:(arrow_1429601828e_indi->Prop)) (B_55:(arrow_1429601828e_indi->Prop)), ((not (((eq (arrow_1429601828e_indi->Prop)) A_73) B_55))->(((ord_le1799070453indi_o A_73) B_55)->((ord_le777687553indi_o A_73) B_55))))
% FOF formula (forall (B_55:Prop) (A_73:Prop), ((((iff A_73) B_55)->False)->(((ord_less_eq_o A_73) B_55)->((ord_less_o A_73) B_55)))) of role axiom named fact_290_order__neq__le__trans
% A new axiom: (forall (B_55:Prop) (A_73:Prop), ((((iff A_73) B_55)->False)->(((ord_less_eq_o A_73) B_55)->((ord_less_o A_73) B_55))))
% FOF formula (forall (A_73:(nat->Prop)) (B_55:(nat->Prop)), ((not (((eq (nat->Prop)) A_73) B_55))->(((ord_less_eq_nat_o A_73) B_55)->((ord_less_nat_o A_73) B_55)))) of role axiom named fact_291_order__neq__le__trans
% A new axiom: (forall (A_73:(nat->Prop)) (B_55:(nat->Prop)), ((not (((eq (nat->Prop)) A_73) B_55))->(((ord_less_eq_nat_o A_73) B_55)->((ord_less_nat_o A_73) B_55))))
% FOF formula (forall (A_73:nat) (B_55:nat), ((not (((eq nat) A_73) B_55))->(((ord_less_eq_nat A_73) B_55)->((ord_less_nat A_73) B_55)))) of role axiom named fact_292_order__neq__le__trans
% A new axiom: (forall (A_73:nat) (B_55:nat), ((not (((eq nat) A_73) B_55))->(((ord_less_eq_nat A_73) B_55)->((ord_less_nat A_73) B_55))))
% FOF formula (forall (A_72:(product_unit->Prop)) (B_54:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_72) B_54))->(((ord_le1511552390unit_o B_54) A_72)->((ord_le232288914unit_o B_54) A_72)))) of role axiom named fact_293_xt1_I12_J
% A new axiom: (forall (A_72:(product_unit->Prop)) (B_54:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_72) B_54))->(((ord_le1511552390unit_o B_54) A_72)->((ord_le232288914unit_o B_54) A_72))))
% FOF formula (forall (A_72:(arrow_1429601828e_indi->Prop)) (B_54:(arrow_1429601828e_indi->Prop)), ((not (((eq (arrow_1429601828e_indi->Prop)) A_72) B_54))->(((ord_le1799070453indi_o B_54) A_72)->((ord_le777687553indi_o B_54) A_72)))) of role axiom named fact_294_xt1_I12_J
% A new axiom: (forall (A_72:(arrow_1429601828e_indi->Prop)) (B_54:(arrow_1429601828e_indi->Prop)), ((not (((eq (arrow_1429601828e_indi->Prop)) A_72) B_54))->(((ord_le1799070453indi_o B_54) A_72)->((ord_le777687553indi_o B_54) A_72))))
% FOF formula (forall (B_54:Prop) (A_72:Prop), ((((iff A_72) B_54)->False)->(((ord_less_eq_o B_54) A_72)->((ord_less_o B_54) A_72)))) of role axiom named fact_295_xt1_I12_J
% A new axiom: (forall (B_54:Prop) (A_72:Prop), ((((iff A_72) B_54)->False)->(((ord_less_eq_o B_54) A_72)->((ord_less_o B_54) A_72))))
% FOF formula (forall (A_72:(nat->Prop)) (B_54:(nat->Prop)), ((not (((eq (nat->Prop)) A_72) B_54))->(((ord_less_eq_nat_o B_54) A_72)->((ord_less_nat_o B_54) A_72)))) of role axiom named fact_296_xt1_I12_J
% A new axiom: (forall (A_72:(nat->Prop)) (B_54:(nat->Prop)), ((not (((eq (nat->Prop)) A_72) B_54))->(((ord_less_eq_nat_o B_54) A_72)->((ord_less_nat_o B_54) A_72))))
% FOF formula (forall (A_72:nat) (B_54:nat), ((not (((eq nat) A_72) B_54))->(((ord_less_eq_nat B_54) A_72)->((ord_less_nat B_54) A_72)))) of role axiom named fact_297_xt1_I12_J
% A new axiom: (forall (A_72:nat) (B_54:nat), ((not (((eq nat) A_72) B_54))->(((ord_less_eq_nat B_54) A_72)->((ord_less_nat B_54) A_72))))
% FOF formula (forall (Y_16:nat) (X_25:nat), (((ord_less_eq_nat Y_16) X_25)->(((ord_less_nat X_25) Y_16)->False))) of role axiom named fact_298_leD
% A new axiom: (forall (Y_16:nat) (X_25:nat), (((ord_less_eq_nat Y_16) X_25)->(((ord_less_nat X_25) Y_16)->False)))
% FOF formula (forall (X_24:(product_unit->Prop)) (Y_15:(product_unit->Prop)), (((ord_le232288914unit_o X_24) Y_15)->((ord_le1511552390unit_o X_24) Y_15))) of role axiom named fact_299_order__less__imp__le
% A new axiom: (forall (X_24:(product_unit->Prop)) (Y_15:(product_unit->Prop)), (((ord_le232288914unit_o X_24) Y_15)->((ord_le1511552390unit_o X_24) Y_15)))
% FOF formula (forall (X_24:(arrow_1429601828e_indi->Prop)) (Y_15:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_24) Y_15)->((ord_le1799070453indi_o X_24) Y_15))) of role axiom named fact_300_order__less__imp__le
% A new axiom: (forall (X_24:(arrow_1429601828e_indi->Prop)) (Y_15:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_24) Y_15)->((ord_le1799070453indi_o X_24) Y_15)))
% FOF formula (forall (X_24:Prop) (Y_15:Prop), (((ord_less_o X_24) Y_15)->((ord_less_eq_o X_24) Y_15))) of role axiom named fact_301_order__less__imp__le
% A new axiom: (forall (X_24:Prop) (Y_15:Prop), (((ord_less_o X_24) Y_15)->((ord_less_eq_o X_24) Y_15)))
% FOF formula (forall (X_24:(nat->Prop)) (Y_15:(nat->Prop)), (((ord_less_nat_o X_24) Y_15)->((ord_less_eq_nat_o X_24) Y_15))) of role axiom named fact_302_order__less__imp__le
% A new axiom: (forall (X_24:(nat->Prop)) (Y_15:(nat->Prop)), (((ord_less_nat_o X_24) Y_15)->((ord_less_eq_nat_o X_24) Y_15)))
% FOF formula (forall (X_24:nat) (Y_15:nat), (((ord_less_nat X_24) Y_15)->((ord_less_eq_nat X_24) Y_15))) of role axiom named fact_303_order__less__imp__le
% A new axiom: (forall (X_24:nat) (Y_15:nat), (((ord_less_nat X_24) Y_15)->((ord_less_eq_nat X_24) Y_15)))
% FOF formula (forall (X_23:nat) (Y_14:nat), (((ord_less_eq_nat X_23) Y_14)->((iff (((ord_less_nat X_23) Y_14)->False)) (((eq nat) X_23) Y_14)))) of role axiom named fact_304_linorder__antisym__conv2
% A new axiom: (forall (X_23:nat) (Y_14:nat), (((ord_less_eq_nat X_23) Y_14)->((iff (((ord_less_nat X_23) Y_14)->False)) (((eq nat) X_23) Y_14))))
% FOF formula (forall (X_22:(product_unit->Prop)) (Y_13:(product_unit->Prop)), (((ord_le1511552390unit_o X_22) Y_13)->((or ((ord_le232288914unit_o X_22) Y_13)) (((eq (product_unit->Prop)) X_22) Y_13)))) of role axiom named fact_305_order__le__imp__less__or__eq
% A new axiom: (forall (X_22:(product_unit->Prop)) (Y_13:(product_unit->Prop)), (((ord_le1511552390unit_o X_22) Y_13)->((or ((ord_le232288914unit_o X_22) Y_13)) (((eq (product_unit->Prop)) X_22) Y_13))))
% FOF formula (forall (X_22:(arrow_1429601828e_indi->Prop)) (Y_13:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o X_22) Y_13)->((or ((ord_le777687553indi_o X_22) Y_13)) (((eq (arrow_1429601828e_indi->Prop)) X_22) Y_13)))) of role axiom named fact_306_order__le__imp__less__or__eq
% A new axiom: (forall (X_22:(arrow_1429601828e_indi->Prop)) (Y_13:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o X_22) Y_13)->((or ((ord_le777687553indi_o X_22) Y_13)) (((eq (arrow_1429601828e_indi->Prop)) X_22) Y_13))))
% FOF formula (forall (X_22:Prop) (Y_13:Prop), (((ord_less_eq_o X_22) Y_13)->((or ((ord_less_o X_22) Y_13)) ((iff X_22) Y_13)))) of role axiom named fact_307_order__le__imp__less__or__eq
% A new axiom: (forall (X_22:Prop) (Y_13:Prop), (((ord_less_eq_o X_22) Y_13)->((or ((ord_less_o X_22) Y_13)) ((iff X_22) Y_13))))
% FOF formula (forall (X_22:(nat->Prop)) (Y_13:(nat->Prop)), (((ord_less_eq_nat_o X_22) Y_13)->((or ((ord_less_nat_o X_22) Y_13)) (((eq (nat->Prop)) X_22) Y_13)))) of role axiom named fact_308_order__le__imp__less__or__eq
% A new axiom: (forall (X_22:(nat->Prop)) (Y_13:(nat->Prop)), (((ord_less_eq_nat_o X_22) Y_13)->((or ((ord_less_nat_o X_22) Y_13)) (((eq (nat->Prop)) X_22) Y_13))))
% FOF formula (forall (X_22:nat) (Y_13:nat), (((ord_less_eq_nat X_22) Y_13)->((or ((ord_less_nat X_22) Y_13)) (((eq nat) X_22) Y_13)))) of role axiom named fact_309_order__le__imp__less__or__eq
% A new axiom: (forall (X_22:nat) (Y_13:nat), (((ord_less_eq_nat X_22) Y_13)->((or ((ord_less_nat X_22) Y_13)) (((eq nat) X_22) Y_13))))
% FOF formula (forall (A_71:(product_unit->Prop)) (B_53:(product_unit->Prop)), (((ord_le1511552390unit_o A_71) B_53)->((not (((eq (product_unit->Prop)) A_71) B_53))->((ord_le232288914unit_o A_71) B_53)))) of role axiom named fact_310_order__le__neq__trans
% A new axiom: (forall (A_71:(product_unit->Prop)) (B_53:(product_unit->Prop)), (((ord_le1511552390unit_o A_71) B_53)->((not (((eq (product_unit->Prop)) A_71) B_53))->((ord_le232288914unit_o A_71) B_53))))
% FOF formula (forall (A_71:(arrow_1429601828e_indi->Prop)) (B_53:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_71) B_53)->((not (((eq (arrow_1429601828e_indi->Prop)) A_71) B_53))->((ord_le777687553indi_o A_71) B_53)))) of role axiom named fact_311_order__le__neq__trans
% A new axiom: (forall (A_71:(arrow_1429601828e_indi->Prop)) (B_53:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_71) B_53)->((not (((eq (arrow_1429601828e_indi->Prop)) A_71) B_53))->((ord_le777687553indi_o A_71) B_53))))
% FOF formula (forall (A_71:Prop) (B_53:Prop), (((ord_less_eq_o A_71) B_53)->((((iff A_71) B_53)->False)->((ord_less_o A_71) B_53)))) of role axiom named fact_312_order__le__neq__trans
% A new axiom: (forall (A_71:Prop) (B_53:Prop), (((ord_less_eq_o A_71) B_53)->((((iff A_71) B_53)->False)->((ord_less_o A_71) B_53))))
% FOF formula (forall (A_71:(nat->Prop)) (B_53:(nat->Prop)), (((ord_less_eq_nat_o A_71) B_53)->((not (((eq (nat->Prop)) A_71) B_53))->((ord_less_nat_o A_71) B_53)))) of role axiom named fact_313_order__le__neq__trans
% A new axiom: (forall (A_71:(nat->Prop)) (B_53:(nat->Prop)), (((ord_less_eq_nat_o A_71) B_53)->((not (((eq (nat->Prop)) A_71) B_53))->((ord_less_nat_o A_71) B_53))))
% FOF formula (forall (A_71:nat) (B_53:nat), (((ord_less_eq_nat A_71) B_53)->((not (((eq nat) A_71) B_53))->((ord_less_nat A_71) B_53)))) of role axiom named fact_314_order__le__neq__trans
% A new axiom: (forall (A_71:nat) (B_53:nat), (((ord_less_eq_nat A_71) B_53)->((not (((eq nat) A_71) B_53))->((ord_less_nat A_71) B_53))))
% FOF formula (forall (B_52:(nat->Prop)) (A_70:(nat->Prop)), (((ord_less_eq_nat_o B_52) A_70)->((not (((eq (nat->Prop)) A_70) B_52))->((ord_less_nat_o B_52) A_70)))) of role axiom named fact_315_xt1_I11_J
% A new axiom: (forall (B_52:(nat->Prop)) (A_70:(nat->Prop)), (((ord_less_eq_nat_o B_52) A_70)->((not (((eq (nat->Prop)) A_70) B_52))->((ord_less_nat_o B_52) A_70))))
% FOF formula (forall (B_52:(product_unit->Prop)) (A_70:(product_unit->Prop)), (((ord_le1511552390unit_o B_52) A_70)->((not (((eq (product_unit->Prop)) A_70) B_52))->((ord_le232288914unit_o B_52) A_70)))) of role axiom named fact_316_xt1_I11_J
% A new axiom: (forall (B_52:(product_unit->Prop)) (A_70:(product_unit->Prop)), (((ord_le1511552390unit_o B_52) A_70)->((not (((eq (product_unit->Prop)) A_70) B_52))->((ord_le232288914unit_o B_52) A_70))))
% FOF formula (forall (B_52:(arrow_1429601828e_indi->Prop)) (A_70:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o B_52) A_70)->((not (((eq (arrow_1429601828e_indi->Prop)) A_70) B_52))->((ord_le777687553indi_o B_52) A_70)))) of role axiom named fact_317_xt1_I11_J
% A new axiom: (forall (B_52:(arrow_1429601828e_indi->Prop)) (A_70:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o B_52) A_70)->((not (((eq (arrow_1429601828e_indi->Prop)) A_70) B_52))->((ord_le777687553indi_o B_52) A_70))))
% FOF formula (forall (B_52:nat) (A_70:nat), (((ord_less_eq_nat B_52) A_70)->((not (((eq nat) A_70) B_52))->((ord_less_nat B_52) A_70)))) of role axiom named fact_318_xt1_I11_J
% A new axiom: (forall (B_52:nat) (A_70:nat), (((ord_less_eq_nat B_52) A_70)->((not (((eq nat) A_70) B_52))->((ord_less_nat B_52) A_70))))
% FOF formula (forall (B_52:Prop) (A_70:Prop), (((ord_less_eq_o B_52) A_70)->((((iff A_70) B_52)->False)->((ord_less_o B_52) A_70)))) of role axiom named fact_319_xt1_I11_J
% A new axiom: (forall (B_52:Prop) (A_70:Prop), (((ord_less_eq_o B_52) A_70)->((((iff A_70) B_52)->False)->((ord_less_o B_52) A_70))))
% FOF formula (forall (Z_4:(nat->Prop)) (X_21:(nat->Prop)) (Y_12:(nat->Prop)), (((ord_less_nat_o X_21) Y_12)->(((ord_less_eq_nat_o Y_12) Z_4)->((ord_less_nat_o X_21) Z_4)))) of role axiom named fact_320_order__less__le__trans
% A new axiom: (forall (Z_4:(nat->Prop)) (X_21:(nat->Prop)) (Y_12:(nat->Prop)), (((ord_less_nat_o X_21) Y_12)->(((ord_less_eq_nat_o Y_12) Z_4)->((ord_less_nat_o X_21) Z_4))))
% FOF formula (forall (Z_4:(product_unit->Prop)) (X_21:(product_unit->Prop)) (Y_12:(product_unit->Prop)), (((ord_le232288914unit_o X_21) Y_12)->(((ord_le1511552390unit_o Y_12) Z_4)->((ord_le232288914unit_o X_21) Z_4)))) of role axiom named fact_321_order__less__le__trans
% A new axiom: (forall (Z_4:(product_unit->Prop)) (X_21:(product_unit->Prop)) (Y_12:(product_unit->Prop)), (((ord_le232288914unit_o X_21) Y_12)->(((ord_le1511552390unit_o Y_12) Z_4)->((ord_le232288914unit_o X_21) Z_4))))
% FOF formula (forall (Z_4:(arrow_1429601828e_indi->Prop)) (X_21:(arrow_1429601828e_indi->Prop)) (Y_12:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_21) Y_12)->(((ord_le1799070453indi_o Y_12) Z_4)->((ord_le777687553indi_o X_21) Z_4)))) of role axiom named fact_322_order__less__le__trans
% A new axiom: (forall (Z_4:(arrow_1429601828e_indi->Prop)) (X_21:(arrow_1429601828e_indi->Prop)) (Y_12:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_21) Y_12)->(((ord_le1799070453indi_o Y_12) Z_4)->((ord_le777687553indi_o X_21) Z_4))))
% FOF formula (forall (Z_4:nat) (X_21:nat) (Y_12:nat), (((ord_less_nat X_21) Y_12)->(((ord_less_eq_nat Y_12) Z_4)->((ord_less_nat X_21) Z_4)))) of role axiom named fact_323_order__less__le__trans
% A new axiom: (forall (Z_4:nat) (X_21:nat) (Y_12:nat), (((ord_less_nat X_21) Y_12)->(((ord_less_eq_nat Y_12) Z_4)->((ord_less_nat X_21) Z_4))))
% FOF formula (forall (Z_4:Prop) (X_21:Prop) (Y_12:Prop), (((ord_less_o X_21) Y_12)->(((ord_less_eq_o Y_12) Z_4)->((ord_less_o X_21) Z_4)))) of role axiom named fact_324_order__less__le__trans
% A new axiom: (forall (Z_4:Prop) (X_21:Prop) (Y_12:Prop), (((ord_less_o X_21) Y_12)->(((ord_less_eq_o Y_12) Z_4)->((ord_less_o X_21) Z_4))))
% FOF formula (forall (Z_3:(nat->Prop)) (Y_11:(nat->Prop)) (X_20:(nat->Prop)), (((ord_less_nat_o Y_11) X_20)->(((ord_less_eq_nat_o Z_3) Y_11)->((ord_less_nat_o Z_3) X_20)))) of role axiom named fact_325_xt1_I7_J
% A new axiom: (forall (Z_3:(nat->Prop)) (Y_11:(nat->Prop)) (X_20:(nat->Prop)), (((ord_less_nat_o Y_11) X_20)->(((ord_less_eq_nat_o Z_3) Y_11)->((ord_less_nat_o Z_3) X_20))))
% FOF formula (forall (Z_3:(product_unit->Prop)) (Y_11:(product_unit->Prop)) (X_20:(product_unit->Prop)), (((ord_le232288914unit_o Y_11) X_20)->(((ord_le1511552390unit_o Z_3) Y_11)->((ord_le232288914unit_o Z_3) X_20)))) of role axiom named fact_326_xt1_I7_J
% A new axiom: (forall (Z_3:(product_unit->Prop)) (Y_11:(product_unit->Prop)) (X_20:(product_unit->Prop)), (((ord_le232288914unit_o Y_11) X_20)->(((ord_le1511552390unit_o Z_3) Y_11)->((ord_le232288914unit_o Z_3) X_20))))
% FOF formula (forall (Z_3:(arrow_1429601828e_indi->Prop)) (Y_11:(arrow_1429601828e_indi->Prop)) (X_20:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o Y_11) X_20)->(((ord_le1799070453indi_o Z_3) Y_11)->((ord_le777687553indi_o Z_3) X_20)))) of role axiom named fact_327_xt1_I7_J
% A new axiom: (forall (Z_3:(arrow_1429601828e_indi->Prop)) (Y_11:(arrow_1429601828e_indi->Prop)) (X_20:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o Y_11) X_20)->(((ord_le1799070453indi_o Z_3) Y_11)->((ord_le777687553indi_o Z_3) X_20))))
% FOF formula (forall (Z_3:nat) (Y_11:nat) (X_20:nat), (((ord_less_nat Y_11) X_20)->(((ord_less_eq_nat Z_3) Y_11)->((ord_less_nat Z_3) X_20)))) of role axiom named fact_328_xt1_I7_J
% A new axiom: (forall (Z_3:nat) (Y_11:nat) (X_20:nat), (((ord_less_nat Y_11) X_20)->(((ord_less_eq_nat Z_3) Y_11)->((ord_less_nat Z_3) X_20))))
% FOF formula (forall (Z_3:Prop) (Y_11:Prop) (X_20:Prop), (((ord_less_o Y_11) X_20)->(((ord_less_eq_o Z_3) Y_11)->((ord_less_o Z_3) X_20)))) of role axiom named fact_329_xt1_I7_J
% A new axiom: (forall (Z_3:Prop) (Y_11:Prop) (X_20:Prop), (((ord_less_o Y_11) X_20)->(((ord_less_eq_o Z_3) Y_11)->((ord_less_o Z_3) X_20))))
% FOF formula (forall (Z_2:(nat->Prop)) (X_19:(nat->Prop)) (Y_10:(nat->Prop)), (((ord_less_eq_nat_o X_19) Y_10)->(((ord_less_nat_o Y_10) Z_2)->((ord_less_nat_o X_19) Z_2)))) of role axiom named fact_330_order__le__less__trans
% A new axiom: (forall (Z_2:(nat->Prop)) (X_19:(nat->Prop)) (Y_10:(nat->Prop)), (((ord_less_eq_nat_o X_19) Y_10)->(((ord_less_nat_o Y_10) Z_2)->((ord_less_nat_o X_19) Z_2))))
% FOF formula (forall (Z_2:(product_unit->Prop)) (X_19:(product_unit->Prop)) (Y_10:(product_unit->Prop)), (((ord_le1511552390unit_o X_19) Y_10)->(((ord_le232288914unit_o Y_10) Z_2)->((ord_le232288914unit_o X_19) Z_2)))) of role axiom named fact_331_order__le__less__trans
% A new axiom: (forall (Z_2:(product_unit->Prop)) (X_19:(product_unit->Prop)) (Y_10:(product_unit->Prop)), (((ord_le1511552390unit_o X_19) Y_10)->(((ord_le232288914unit_o Y_10) Z_2)->((ord_le232288914unit_o X_19) Z_2))))
% FOF formula (forall (Z_2:(arrow_1429601828e_indi->Prop)) (X_19:(arrow_1429601828e_indi->Prop)) (Y_10:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o X_19) Y_10)->(((ord_le777687553indi_o Y_10) Z_2)->((ord_le777687553indi_o X_19) Z_2)))) of role axiom named fact_332_order__le__less__trans
% A new axiom: (forall (Z_2:(arrow_1429601828e_indi->Prop)) (X_19:(arrow_1429601828e_indi->Prop)) (Y_10:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o X_19) Y_10)->(((ord_le777687553indi_o Y_10) Z_2)->((ord_le777687553indi_o X_19) Z_2))))
% FOF formula (forall (Z_2:nat) (X_19:nat) (Y_10:nat), (((ord_less_eq_nat X_19) Y_10)->(((ord_less_nat Y_10) Z_2)->((ord_less_nat X_19) Z_2)))) of role axiom named fact_333_order__le__less__trans
% A new axiom: (forall (Z_2:nat) (X_19:nat) (Y_10:nat), (((ord_less_eq_nat X_19) Y_10)->(((ord_less_nat Y_10) Z_2)->((ord_less_nat X_19) Z_2))))
% FOF formula (forall (Z_2:Prop) (X_19:Prop) (Y_10:Prop), (((ord_less_eq_o X_19) Y_10)->(((ord_less_o Y_10) Z_2)->((ord_less_o X_19) Z_2)))) of role axiom named fact_334_order__le__less__trans
% A new axiom: (forall (Z_2:Prop) (X_19:Prop) (Y_10:Prop), (((ord_less_eq_o X_19) Y_10)->(((ord_less_o Y_10) Z_2)->((ord_less_o X_19) Z_2))))
% FOF formula (forall (Z_1:(nat->Prop)) (Y_9:(nat->Prop)) (X_18:(nat->Prop)), (((ord_less_eq_nat_o Y_9) X_18)->(((ord_less_nat_o Z_1) Y_9)->((ord_less_nat_o Z_1) X_18)))) of role axiom named fact_335_xt1_I8_J
% A new axiom: (forall (Z_1:(nat->Prop)) (Y_9:(nat->Prop)) (X_18:(nat->Prop)), (((ord_less_eq_nat_o Y_9) X_18)->(((ord_less_nat_o Z_1) Y_9)->((ord_less_nat_o Z_1) X_18))))
% FOF formula (forall (Z_1:(product_unit->Prop)) (Y_9:(product_unit->Prop)) (X_18:(product_unit->Prop)), (((ord_le1511552390unit_o Y_9) X_18)->(((ord_le232288914unit_o Z_1) Y_9)->((ord_le232288914unit_o Z_1) X_18)))) of role axiom named fact_336_xt1_I8_J
% A new axiom: (forall (Z_1:(product_unit->Prop)) (Y_9:(product_unit->Prop)) (X_18:(product_unit->Prop)), (((ord_le1511552390unit_o Y_9) X_18)->(((ord_le232288914unit_o Z_1) Y_9)->((ord_le232288914unit_o Z_1) X_18))))
% FOF formula (forall (Z_1:(arrow_1429601828e_indi->Prop)) (Y_9:(arrow_1429601828e_indi->Prop)) (X_18:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o Y_9) X_18)->(((ord_le777687553indi_o Z_1) Y_9)->((ord_le777687553indi_o Z_1) X_18)))) of role axiom named fact_337_xt1_I8_J
% A new axiom: (forall (Z_1:(arrow_1429601828e_indi->Prop)) (Y_9:(arrow_1429601828e_indi->Prop)) (X_18:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o Y_9) X_18)->(((ord_le777687553indi_o Z_1) Y_9)->((ord_le777687553indi_o Z_1) X_18))))
% FOF formula (forall (Z_1:nat) (Y_9:nat) (X_18:nat), (((ord_less_eq_nat Y_9) X_18)->(((ord_less_nat Z_1) Y_9)->((ord_less_nat Z_1) X_18)))) of role axiom named fact_338_xt1_I8_J
% A new axiom: (forall (Z_1:nat) (Y_9:nat) (X_18:nat), (((ord_less_eq_nat Y_9) X_18)->(((ord_less_nat Z_1) Y_9)->((ord_less_nat Z_1) X_18))))
% FOF formula (forall (Z_1:Prop) (Y_9:Prop) (X_18:Prop), (((ord_less_eq_o Y_9) X_18)->(((ord_less_o Z_1) Y_9)->((ord_less_o Z_1) X_18)))) of role axiom named fact_339_xt1_I8_J
% A new axiom: (forall (Z_1:Prop) (Y_9:Prop) (X_18:Prop), (((ord_less_eq_o Y_9) X_18)->(((ord_less_o Z_1) Y_9)->((ord_less_o Z_1) X_18))))
% FOF formula (forall (A_69:Prop), ((ord_less_eq_o A_69) top_top_o)) of role axiom named fact_340_top__greatest
% A new axiom: (forall (A_69:Prop), ((ord_less_eq_o A_69) top_top_o))
% FOF formula (forall (A_69:((produc1501160679le_alt->Prop)->Prop)), ((ord_le1063113995lt_o_o A_69) top_to1842727771lt_o_o)) of role axiom named fact_341_top__greatest
% A new axiom: (forall (A_69:((produc1501160679le_alt->Prop)->Prop)), ((ord_le1063113995lt_o_o A_69) top_to1842727771lt_o_o))
% FOF formula (forall (A_69:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((ord_le134800455lt_o_o A_69) top_to1969627639lt_o_o)) of role axiom named fact_342_top__greatest
% A new axiom: (forall (A_69:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((ord_le134800455lt_o_o A_69) top_to1969627639lt_o_o))
% FOF formula (forall (A_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((ord_le1992928527lt_o_o A_69) top_to2122763103lt_o_o)) of role axiom named fact_343_top__greatest
% A new axiom: (forall (A_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((ord_le1992928527lt_o_o A_69) top_to2122763103lt_o_o))
% FOF formula (forall (A_69:(produc1501160679le_alt->Prop)), ((ord_le97612146_alt_o A_69) top_to1841428258_alt_o)) of role axiom named fact_344_top__greatest
% A new axiom: (forall (A_69:(produc1501160679le_alt->Prop)), ((ord_le97612146_alt_o A_69) top_to1841428258_alt_o))
% FOF formula (forall (A_69:(nat->Prop)), ((ord_less_eq_nat_o A_69) top_top_nat_o)) of role axiom named fact_345_top__greatest
% A new axiom: (forall (A_69:(nat->Prop)), ((ord_less_eq_nat_o A_69) top_top_nat_o))
% FOF formula (forall (A_69:(product_unit->Prop)), ((ord_le1511552390unit_o A_69) top_to1984820022unit_o)) of role axiom named fact_346_top__greatest
% A new axiom: (forall (A_69:(product_unit->Prop)), ((ord_le1511552390unit_o A_69) top_to1984820022unit_o))
% FOF formula (forall (A_69:(arrow_1429601828e_indi->Prop)), ((ord_le1799070453indi_o A_69) top_to988227749indi_o)) of role axiom named fact_347_top__greatest
% A new axiom: (forall (A_69:(arrow_1429601828e_indi->Prop)), ((ord_le1799070453indi_o A_69) top_to988227749indi_o))
% FOF formula (forall (A_68:Prop), ((iff ((ord_less_eq_o top_top_o) A_68)) ((iff A_68) top_top_o))) of role axiom named fact_348_top__unique
% A new axiom: (forall (A_68:Prop), ((iff ((ord_less_eq_o top_top_o) A_68)) ((iff A_68) top_top_o)))
% FOF formula (forall (A_68:((produc1501160679le_alt->Prop)->Prop)), ((iff ((ord_le1063113995lt_o_o top_to1842727771lt_o_o) A_68)) (((eq ((produc1501160679le_alt->Prop)->Prop)) A_68) top_to1842727771lt_o_o))) of role axiom named fact_349_top__unique
% A new axiom: (forall (A_68:((produc1501160679le_alt->Prop)->Prop)), ((iff ((ord_le1063113995lt_o_o top_to1842727771lt_o_o) A_68)) (((eq ((produc1501160679le_alt->Prop)->Prop)) A_68) top_to1842727771lt_o_o)))
% FOF formula (forall (A_68:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le134800455lt_o_o top_to1969627639lt_o_o) A_68)) (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) A_68) top_to1969627639lt_o_o))) of role axiom named fact_350_top__unique
% A new axiom: (forall (A_68:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le134800455lt_o_o top_to1969627639lt_o_o) A_68)) (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) A_68) top_to1969627639lt_o_o)))
% FOF formula (forall (A_68:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le1992928527lt_o_o top_to2122763103lt_o_o) A_68)) (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) A_68) top_to2122763103lt_o_o))) of role axiom named fact_351_top__unique
% A new axiom: (forall (A_68:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le1992928527lt_o_o top_to2122763103lt_o_o) A_68)) (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) A_68) top_to2122763103lt_o_o)))
% FOF formula (forall (A_68:(produc1501160679le_alt->Prop)), ((iff ((ord_le97612146_alt_o top_to1841428258_alt_o) A_68)) (((eq (produc1501160679le_alt->Prop)) A_68) top_to1841428258_alt_o))) of role axiom named fact_352_top__unique
% A new axiom: (forall (A_68:(produc1501160679le_alt->Prop)), ((iff ((ord_le97612146_alt_o top_to1841428258_alt_o) A_68)) (((eq (produc1501160679le_alt->Prop)) A_68) top_to1841428258_alt_o)))
% FOF formula (forall (A_68:(nat->Prop)), ((iff ((ord_less_eq_nat_o top_top_nat_o) A_68)) (((eq (nat->Prop)) A_68) top_top_nat_o))) of role axiom named fact_353_top__unique
% A new axiom: (forall (A_68:(nat->Prop)), ((iff ((ord_less_eq_nat_o top_top_nat_o) A_68)) (((eq (nat->Prop)) A_68) top_top_nat_o)))
% FOF formula (forall (A_68:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o top_to1984820022unit_o) A_68)) (((eq (product_unit->Prop)) A_68) top_to1984820022unit_o))) of role axiom named fact_354_top__unique
% A new axiom: (forall (A_68:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o top_to1984820022unit_o) A_68)) (((eq (product_unit->Prop)) A_68) top_to1984820022unit_o)))
% FOF formula (forall (A_68:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o top_to988227749indi_o) A_68)) (((eq (arrow_1429601828e_indi->Prop)) A_68) top_to988227749indi_o))) of role axiom named fact_355_top__unique
% A new axiom: (forall (A_68:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o top_to988227749indi_o) A_68)) (((eq (arrow_1429601828e_indi->Prop)) A_68) top_to988227749indi_o)))
% FOF formula (forall (A_67:Prop), (((ord_less_eq_o top_top_o) A_67)->((iff A_67) top_top_o))) of role axiom named fact_356_top__le
% A new axiom: (forall (A_67:Prop), (((ord_less_eq_o top_top_o) A_67)->((iff A_67) top_top_o)))
% FOF formula (forall (A_67:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o top_to1842727771lt_o_o) A_67)->(((eq ((produc1501160679le_alt->Prop)->Prop)) A_67) top_to1842727771lt_o_o))) of role axiom named fact_357_top__le
% A new axiom: (forall (A_67:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o top_to1842727771lt_o_o) A_67)->(((eq ((produc1501160679le_alt->Prop)->Prop)) A_67) top_to1842727771lt_o_o)))
% FOF formula (forall (A_67:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o top_to1969627639lt_o_o) A_67)->(((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) A_67) top_to1969627639lt_o_o))) of role axiom named fact_358_top__le
% A new axiom: (forall (A_67:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o top_to1969627639lt_o_o) A_67)->(((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) A_67) top_to1969627639lt_o_o)))
% FOF formula (forall (A_67:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o top_to2122763103lt_o_o) A_67)->(((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) A_67) top_to2122763103lt_o_o))) of role axiom named fact_359_top__le
% A new axiom: (forall (A_67:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o top_to2122763103lt_o_o) A_67)->(((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) A_67) top_to2122763103lt_o_o)))
% FOF formula (forall (A_67:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o top_to1841428258_alt_o) A_67)->(((eq (produc1501160679le_alt->Prop)) A_67) top_to1841428258_alt_o))) of role axiom named fact_360_top__le
% A new axiom: (forall (A_67:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o top_to1841428258_alt_o) A_67)->(((eq (produc1501160679le_alt->Prop)) A_67) top_to1841428258_alt_o)))
% FOF formula (forall (A_67:(nat->Prop)), (((ord_less_eq_nat_o top_top_nat_o) A_67)->(((eq (nat->Prop)) A_67) top_top_nat_o))) of role axiom named fact_361_top__le
% A new axiom: (forall (A_67:(nat->Prop)), (((ord_less_eq_nat_o top_top_nat_o) A_67)->(((eq (nat->Prop)) A_67) top_top_nat_o)))
% FOF formula (forall (A_67:(product_unit->Prop)), (((ord_le1511552390unit_o top_to1984820022unit_o) A_67)->(((eq (product_unit->Prop)) A_67) top_to1984820022unit_o))) of role axiom named fact_362_top__le
% A new axiom: (forall (A_67:(product_unit->Prop)), (((ord_le1511552390unit_o top_to1984820022unit_o) A_67)->(((eq (product_unit->Prop)) A_67) top_to1984820022unit_o)))
% FOF formula (forall (A_67:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o top_to988227749indi_o) A_67)->(((eq (arrow_1429601828e_indi->Prop)) A_67) top_to988227749indi_o))) of role axiom named fact_363_top__le
% A new axiom: (forall (A_67:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o top_to988227749indi_o) A_67)->(((eq (arrow_1429601828e_indi->Prop)) A_67) top_to988227749indi_o)))
% FOF formula (forall (F_24:(nat->nat)) (A_66:(nat->Prop)), ((iff ((inj_on_nat_nat F_24) A_66)) (forall (X_1:nat), (((member_nat X_1) A_66)->(forall (Xa:nat), (((member_nat Xa) A_66)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq nat) X_1) Xa)))))))) of role axiom named fact_364_inj__on__def
% A new axiom: (forall (F_24:(nat->nat)) (A_66:(nat->Prop)), ((iff ((inj_on_nat_nat F_24) A_66)) (forall (X_1:nat), (((member_nat X_1) A_66)->(forall (Xa:nat), (((member_nat Xa) A_66)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq nat) X_1) Xa))))))))
% FOF formula (forall (F_24:(arrow_1429601828e_indi->nat)) (A_66:(arrow_1429601828e_indi->Prop)), ((iff ((inj_on978774663di_nat F_24) A_66)) (forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_66)->(forall (Xa:arrow_1429601828e_indi), (((member2052026769e_indi Xa) A_66)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq arrow_1429601828e_indi) X_1) Xa)))))))) of role axiom named fact_365_inj__on__def
% A new axiom: (forall (F_24:(arrow_1429601828e_indi->nat)) (A_66:(arrow_1429601828e_indi->Prop)), ((iff ((inj_on978774663di_nat F_24) A_66)) (forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_66)->(forall (Xa:arrow_1429601828e_indi), (((member2052026769e_indi Xa) A_66)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq arrow_1429601828e_indi) X_1) Xa))))))))
% FOF formula (forall (X_17:nat) (Y_8:nat) (F_23:(nat->nat)) (A_65:(nat->Prop)), (((inj_on_nat_nat F_23) A_65)->((not (((eq nat) X_17) Y_8))->(((member_nat X_17) A_65)->(((member_nat Y_8) A_65)->(not (((eq nat) (F_23 X_17)) (F_23 Y_8)))))))) of role axiom named fact_366_inj__on__contraD
% A new axiom: (forall (X_17:nat) (Y_8:nat) (F_23:(nat->nat)) (A_65:(nat->Prop)), (((inj_on_nat_nat F_23) A_65)->((not (((eq nat) X_17) Y_8))->(((member_nat X_17) A_65)->(((member_nat Y_8) A_65)->(not (((eq nat) (F_23 X_17)) (F_23 Y_8))))))))
% FOF formula (forall (X_17:arrow_1429601828e_indi) (Y_8:arrow_1429601828e_indi) (F_23:(arrow_1429601828e_indi->nat)) (A_65:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_23) A_65)->((not (((eq arrow_1429601828e_indi) X_17) Y_8))->(((member2052026769e_indi X_17) A_65)->(((member2052026769e_indi Y_8) A_65)->(not (((eq nat) (F_23 X_17)) (F_23 Y_8)))))))) of role axiom named fact_367_inj__on__contraD
% A new axiom: (forall (X_17:arrow_1429601828e_indi) (Y_8:arrow_1429601828e_indi) (F_23:(arrow_1429601828e_indi->nat)) (A_65:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_23) A_65)->((not (((eq arrow_1429601828e_indi) X_17) Y_8))->(((member2052026769e_indi X_17) A_65)->(((member2052026769e_indi Y_8) A_65)->(not (((eq nat) (F_23 X_17)) (F_23 Y_8))))))))
% FOF formula (forall (Y_7:nat) (X_16:nat) (F_22:(nat->nat)) (A_64:(nat->Prop)), (((inj_on_nat_nat F_22) A_64)->(((member_nat X_16) A_64)->(((member_nat Y_7) A_64)->((iff (((eq nat) (F_22 X_16)) (F_22 Y_7))) (((eq nat) X_16) Y_7)))))) of role axiom named fact_368_inj__on__iff
% A new axiom: (forall (Y_7:nat) (X_16:nat) (F_22:(nat->nat)) (A_64:(nat->Prop)), (((inj_on_nat_nat F_22) A_64)->(((member_nat X_16) A_64)->(((member_nat Y_7) A_64)->((iff (((eq nat) (F_22 X_16)) (F_22 Y_7))) (((eq nat) X_16) Y_7))))))
% FOF formula (forall (Y_7:arrow_1429601828e_indi) (X_16:arrow_1429601828e_indi) (F_22:(arrow_1429601828e_indi->nat)) (A_64:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_22) A_64)->(((member2052026769e_indi X_16) A_64)->(((member2052026769e_indi Y_7) A_64)->((iff (((eq nat) (F_22 X_16)) (F_22 Y_7))) (((eq arrow_1429601828e_indi) X_16) Y_7)))))) of role axiom named fact_369_inj__on__iff
% A new axiom: (forall (Y_7:arrow_1429601828e_indi) (X_16:arrow_1429601828e_indi) (F_22:(arrow_1429601828e_indi->nat)) (A_64:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_22) A_64)->(((member2052026769e_indi X_16) A_64)->(((member2052026769e_indi Y_7) A_64)->((iff (((eq nat) (F_22 X_16)) (F_22 Y_7))) (((eq arrow_1429601828e_indi) X_16) Y_7))))))
% FOF formula (forall (X_15:nat) (Y_6:nat) (F_21:(nat->nat)) (A_63:(nat->Prop)), (((inj_on_nat_nat F_21) A_63)->((((eq nat) (F_21 X_15)) (F_21 Y_6))->(((member_nat X_15) A_63)->(((member_nat Y_6) A_63)->(((eq nat) X_15) Y_6)))))) of role axiom named fact_370_inj__onD
% A new axiom: (forall (X_15:nat) (Y_6:nat) (F_21:(nat->nat)) (A_63:(nat->Prop)), (((inj_on_nat_nat F_21) A_63)->((((eq nat) (F_21 X_15)) (F_21 Y_6))->(((member_nat X_15) A_63)->(((member_nat Y_6) A_63)->(((eq nat) X_15) Y_6))))))
% FOF formula (forall (X_15:arrow_1429601828e_indi) (Y_6:arrow_1429601828e_indi) (F_21:(arrow_1429601828e_indi->nat)) (A_63:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_21) A_63)->((((eq nat) (F_21 X_15)) (F_21 Y_6))->(((member2052026769e_indi X_15) A_63)->(((member2052026769e_indi Y_6) A_63)->(((eq arrow_1429601828e_indi) X_15) Y_6)))))) of role axiom named fact_371_inj__onD
% A new axiom: (forall (X_15:arrow_1429601828e_indi) (Y_6:arrow_1429601828e_indi) (F_21:(arrow_1429601828e_indi->nat)) (A_63:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_21) A_63)->((((eq nat) (F_21 X_15)) (F_21 Y_6))->(((member2052026769e_indi X_15) A_63)->(((member2052026769e_indi Y_6) A_63)->(((eq arrow_1429601828e_indi) X_15) Y_6))))))
% FOF formula (forall (X_14:produc1501160679le_alt) (F_20:(produc1501160679le_alt->Prop)) (A_62:(produc1501160679le_alt->Prop)) (B_51:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_20) ((pi_Pro1701359055_alt_o A_62) B_51))->(((member214075476le_alt X_14) A_62)->((member_o (F_20 X_14)) (B_51 X_14))))) of role axiom named fact_372_Pi__mem
% A new axiom: (forall (X_14:produc1501160679le_alt) (F_20:(produc1501160679le_alt->Prop)) (A_62:(produc1501160679le_alt->Prop)) (B_51:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_20) ((pi_Pro1701359055_alt_o A_62) B_51))->(((member214075476le_alt X_14) A_62)->((member_o (F_20 X_14)) (B_51 X_14)))))
% FOF formula (forall (X_14:arrow_1429601828e_indi) (F_20:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_62:(arrow_1429601828e_indi->Prop)) (B_51:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_20) ((pi_Arr1929480907_alt_o A_62) B_51))->(((member2052026769e_indi X_14) A_62)->((member377231867_alt_o (F_20 X_14)) (B_51 X_14))))) of role axiom named fact_373_Pi__mem
% A new axiom: (forall (X_14:arrow_1429601828e_indi) (F_20:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_62:(arrow_1429601828e_indi->Prop)) (B_51:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_20) ((pi_Arr1929480907_alt_o A_62) B_51))->(((member2052026769e_indi X_14) A_62)->((member377231867_alt_o (F_20 X_14)) (B_51 X_14)))))
% FOF formula (forall (X_14:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_20:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_62:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_51:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_20) ((pi_Arr1304755663_alt_o A_62) B_51))->(((member526088951_alt_o X_14) A_62)->((member377231867_alt_o (F_20 X_14)) (B_51 X_14))))) of role axiom named fact_374_Pi__mem
% A new axiom: (forall (X_14:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_20:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_62:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_51:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_20) ((pi_Arr1304755663_alt_o A_62) B_51))->(((member526088951_alt_o X_14) A_62)->((member377231867_alt_o (F_20 X_14)) (B_51 X_14)))))
% FOF formula (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) arrow_734252939e_Prof) ((pi_Arr1929480907_alt_o top_to988227749indi_o) (fun (Uu:arrow_1429601828e_indi)=> arrow_823908191le_Lin))) of role axiom named fact_375_Prof__def
% A new axiom: (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) arrow_734252939e_Prof) ((pi_Arr1929480907_alt_o top_to988227749indi_o) (fun (Uu:arrow_1429601828e_indi)=> arrow_823908191le_Lin)))
% FOF formula (forall (A_61:(nat->Prop)), ((inj_on_nat_nat (fun (X_1:nat)=> X_1)) A_61)) of role axiom named fact_376_inj__on__id2
% A new axiom: (forall (A_61:(nat->Prop)), ((inj_on_nat_nat (fun (X_1:nat)=> X_1)) A_61))
% FOF formula (forall (X_13:produc1501160679le_alt) (F_19:(produc1501160679le_alt->Prop)) (A_60:(produc1501160679le_alt->Prop)) (B_50:(Prop->Prop)), (((member377231867_alt_o F_19) ((pi_Pro1701359055_alt_o A_60) (fun (Uu:produc1501160679le_alt)=> B_50)))->(((member214075476le_alt X_13) A_60)->((member_o (F_19 X_13)) B_50)))) of role axiom named fact_377_funcset__mem
% A new axiom: (forall (X_13:produc1501160679le_alt) (F_19:(produc1501160679le_alt->Prop)) (A_60:(produc1501160679le_alt->Prop)) (B_50:(Prop->Prop)), (((member377231867_alt_o F_19) ((pi_Pro1701359055_alt_o A_60) (fun (Uu:produc1501160679le_alt)=> B_50)))->(((member214075476le_alt X_13) A_60)->((member_o (F_19 X_13)) B_50))))
% FOF formula (forall (X_13:arrow_1429601828e_indi) (F_19:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_60:(arrow_1429601828e_indi->Prop)) (B_50:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_19) ((pi_Arr1929480907_alt_o A_60) (fun (Uu:arrow_1429601828e_indi)=> B_50)))->(((member2052026769e_indi X_13) A_60)->((member377231867_alt_o (F_19 X_13)) B_50)))) of role axiom named fact_378_funcset__mem
% A new axiom: (forall (X_13:arrow_1429601828e_indi) (F_19:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_60:(arrow_1429601828e_indi->Prop)) (B_50:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_19) ((pi_Arr1929480907_alt_o A_60) (fun (Uu:arrow_1429601828e_indi)=> B_50)))->(((member2052026769e_indi X_13) A_60)->((member377231867_alt_o (F_19 X_13)) B_50))))
% FOF formula (forall (X_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_50:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_19) ((pi_Arr1304755663_alt_o A_60) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_50)))->(((member526088951_alt_o X_13) A_60)->((member377231867_alt_o (F_19 X_13)) B_50)))) of role axiom named fact_379_funcset__mem
% A new axiom: (forall (X_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_50:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_19) ((pi_Arr1304755663_alt_o A_60) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_50)))->(((member526088951_alt_o X_13) A_60)->((member377231867_alt_o (F_19 X_13)) B_50))))
% FOF formula (forall (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (_TPTP_I:arrow_1429601828e_indi), ((iff ((arrow_1212662430ctator F_18) _TPTP_I)) (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(((eq (produc1501160679le_alt->Prop)) (F_18 X_1)) (X_1 _TPTP_I)))))) of role axiom named fact_380_dictator__def
% A new axiom: (forall (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (_TPTP_I:arrow_1429601828e_indi), ((iff ((arrow_1212662430ctator F_18) _TPTP_I)) (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(((eq (produc1501160679le_alt->Prop)) (F_18 X_1)) (X_1 _TPTP_I))))))
% FOF formula (forall (X_12:nat) (Y_5:nat) (F_17:(nat->nat)), (((inj_on_nat_nat F_17) top_top_nat_o)->((iff (((eq nat) (F_17 X_12)) (F_17 Y_5))) (((eq nat) X_12) Y_5)))) of role axiom named fact_381_inj__eq
% A new axiom: (forall (X_12:nat) (Y_5:nat) (F_17:(nat->nat)), (((inj_on_nat_nat F_17) top_top_nat_o)->((iff (((eq nat) (F_17 X_12)) (F_17 Y_5))) (((eq nat) X_12) Y_5))))
% FOF formula (forall (X_12:arrow_1429601828e_indi) (Y_5:arrow_1429601828e_indi) (F_17:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_17) top_to988227749indi_o)->((iff (((eq nat) (F_17 X_12)) (F_17 Y_5))) (((eq arrow_1429601828e_indi) X_12) Y_5)))) of role axiom named fact_382_inj__eq
% A new axiom: (forall (X_12:arrow_1429601828e_indi) (Y_5:arrow_1429601828e_indi) (F_17:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_17) top_to988227749indi_o)->((iff (((eq nat) (F_17 X_12)) (F_17 Y_5))) (((eq arrow_1429601828e_indi) X_12) Y_5))))
% FOF formula (forall (X_11:nat) (Y_4:nat) (F_16:(nat->nat)), (((inj_on_nat_nat F_16) top_top_nat_o)->((((eq nat) (F_16 X_11)) (F_16 Y_4))->(((eq nat) X_11) Y_4)))) of role axiom named fact_383_injD
% A new axiom: (forall (X_11:nat) (Y_4:nat) (F_16:(nat->nat)), (((inj_on_nat_nat F_16) top_top_nat_o)->((((eq nat) (F_16 X_11)) (F_16 Y_4))->(((eq nat) X_11) Y_4))))
% FOF formula (forall (X_11:arrow_1429601828e_indi) (Y_4:arrow_1429601828e_indi) (F_16:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_16) top_to988227749indi_o)->((((eq nat) (F_16 X_11)) (F_16 Y_4))->(((eq arrow_1429601828e_indi) X_11) Y_4)))) of role axiom named fact_384_injD
% A new axiom: (forall (X_11:arrow_1429601828e_indi) (Y_4:arrow_1429601828e_indi) (F_16:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_16) top_to988227749indi_o)->((((eq nat) (F_16 X_11)) (F_16 Y_4))->(((eq arrow_1429601828e_indi) X_11) Y_4))))
% FOF formula (forall (X_10:nat) (F_15:(nat->nat)) (A_59:(nat->Prop)), (((inj_on_nat_nat F_15) A_59)->(((member_nat X_10) A_59)->(((eq nat) (((hilber195283148at_nat A_59) F_15) (F_15 X_10))) X_10)))) of role axiom named fact_385_inv__into__f__f
% A new axiom: (forall (X_10:nat) (F_15:(nat->nat)) (A_59:(nat->Prop)), (((inj_on_nat_nat F_15) A_59)->(((member_nat X_10) A_59)->(((eq nat) (((hilber195283148at_nat A_59) F_15) (F_15 X_10))) X_10))))
% FOF formula (forall (X_10:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->nat)) (A_59:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_15) A_59)->(((member2052026769e_indi X_10) A_59)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat A_59) F_15) (F_15 X_10))) X_10)))) of role axiom named fact_386_inv__into__f__f
% A new axiom: (forall (X_10:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->nat)) (A_59:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_15) A_59)->(((member2052026769e_indi X_10) A_59)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat A_59) F_15) (F_15 X_10))) X_10))))
% FOF formula (forall (Y_3:nat) (X_9:nat) (F_14:(nat->nat)) (A_58:(nat->Prop)), (((inj_on_nat_nat F_14) A_58)->(((member_nat X_9) A_58)->((((eq nat) (F_14 X_9)) Y_3)->(((eq nat) (((hilber195283148at_nat A_58) F_14) Y_3)) X_9))))) of role axiom named fact_387_inv__into__f__eq
% A new axiom: (forall (Y_3:nat) (X_9:nat) (F_14:(nat->nat)) (A_58:(nat->Prop)), (((inj_on_nat_nat F_14) A_58)->(((member_nat X_9) A_58)->((((eq nat) (F_14 X_9)) Y_3)->(((eq nat) (((hilber195283148at_nat A_58) F_14) Y_3)) X_9)))))
% FOF formula (forall (Y_3:nat) (X_9:arrow_1429601828e_indi) (F_14:(arrow_1429601828e_indi->nat)) (A_58:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_14) A_58)->(((member2052026769e_indi X_9) A_58)->((((eq nat) (F_14 X_9)) Y_3)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat A_58) F_14) Y_3)) X_9))))) of role axiom named fact_388_inv__into__f__eq
% A new axiom: (forall (Y_3:nat) (X_9:arrow_1429601828e_indi) (F_14:(arrow_1429601828e_indi->nat)) (A_58:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_14) A_58)->(((member2052026769e_indi X_9) A_58)->((((eq nat) (F_14 X_9)) Y_3)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat A_58) F_14) Y_3)) X_9)))))
% FOF formula (forall (F_13:(produc1501160679le_alt->Prop)) (B_49:(produc1501160679le_alt->(Prop->Prop))) (A_57:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_57)->((member_o (F_13 X_1)) (B_49 X_1))))->((member377231867_alt_o F_13) ((pi_Pro1701359055_alt_o A_57) B_49)))) of role axiom named fact_389_Pi__I
% A new axiom: (forall (F_13:(produc1501160679le_alt->Prop)) (B_49:(produc1501160679le_alt->(Prop->Prop))) (A_57:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_57)->((member_o (F_13 X_1)) (B_49 X_1))))->((member377231867_alt_o F_13) ((pi_Pro1701359055_alt_o A_57) B_49))))
% FOF formula (forall (F_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_49:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_57:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_57)->((member377231867_alt_o (F_13 X_1)) (B_49 X_1))))->((member526088951_alt_o F_13) ((pi_Arr1929480907_alt_o A_57) B_49)))) of role axiom named fact_390_Pi__I
% A new axiom: (forall (F_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_49:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_57:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_57)->((member377231867_alt_o (F_13 X_1)) (B_49 X_1))))->((member526088951_alt_o F_13) ((pi_Arr1929480907_alt_o A_57) B_49))))
% FOF formula (forall (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_49:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_57:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_57)->((member377231867_alt_o (F_13 X_1)) (B_49 X_1))))->((member616898751_alt_o F_13) ((pi_Arr1304755663_alt_o A_57) B_49)))) of role axiom named fact_391_Pi__I
% A new axiom: (forall (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_49:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_57:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_57)->((member377231867_alt_o (F_13 X_1)) (B_49 X_1))))->((member616898751_alt_o F_13) ((pi_Arr1304755663_alt_o A_57) B_49))))
% FOF formula (forall (G_5:(nat->nat)) (F_12:(nat->nat)), (((inj_on_nat_nat F_12) top_top_nat_o)->((forall (X_1:nat), (((eq nat) (F_12 (G_5 X_1))) X_1))->(((eq (nat->nat)) ((hilber195283148at_nat top_top_nat_o) F_12)) G_5)))) of role axiom named fact_392_inj__imp__inv__eq
% A new axiom: (forall (G_5:(nat->nat)) (F_12:(nat->nat)), (((inj_on_nat_nat F_12) top_top_nat_o)->((forall (X_1:nat), (((eq nat) (F_12 (G_5 X_1))) X_1))->(((eq (nat->nat)) ((hilber195283148at_nat top_top_nat_o) F_12)) G_5))))
% FOF formula (forall (G_5:(nat->arrow_1429601828e_indi)) (F_12:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_12) top_to988227749indi_o)->((forall (X_1:nat), (((eq nat) (F_12 (G_5 X_1))) X_1))->(((eq (nat->arrow_1429601828e_indi)) ((hilber598459244di_nat top_to988227749indi_o) F_12)) G_5)))) of role axiom named fact_393_inj__imp__inv__eq
% A new axiom: (forall (G_5:(nat->arrow_1429601828e_indi)) (F_12:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_12) top_to988227749indi_o)->((forall (X_1:nat), (((eq nat) (F_12 (G_5 X_1))) X_1))->(((eq (nat->arrow_1429601828e_indi)) ((hilber598459244di_nat top_to988227749indi_o) F_12)) G_5))))
% FOF formula (forall (A_56:nat), ((ord_less_nat A_56) ((plus_plus_nat A_56) one_one_nat))) of role axiom named fact_394_less__add__one
% A new axiom: (forall (A_56:nat), ((ord_less_nat A_56) ((plus_plus_nat A_56) one_one_nat)))
% FOF formula (forall (C_28:nat) (D_3:nat) (A_55:nat) (B_48:nat), (((ord_less_nat A_55) B_48)->(((ord_less_eq_nat C_28) D_3)->((ord_less_nat ((plus_plus_nat A_55) C_28)) ((plus_plus_nat B_48) D_3))))) of role axiom named fact_395_add__less__le__mono
% A new axiom: (forall (C_28:nat) (D_3:nat) (A_55:nat) (B_48:nat), (((ord_less_nat A_55) B_48)->(((ord_less_eq_nat C_28) D_3)->((ord_less_nat ((plus_plus_nat A_55) C_28)) ((plus_plus_nat B_48) D_3)))))
% FOF formula (forall (C_27:nat) (D_2:nat) (A_54:nat) (B_47:nat), (((ord_less_eq_nat A_54) B_47)->(((ord_less_nat C_27) D_2)->((ord_less_nat ((plus_plus_nat A_54) C_27)) ((plus_plus_nat B_47) D_2))))) of role axiom named fact_396_add__le__less__mono
% A new axiom: (forall (C_27:nat) (D_2:nat) (A_54:nat) (B_47:nat), (((ord_less_eq_nat A_54) B_47)->(((ord_less_nat C_27) D_2)->((ord_less_nat ((plus_plus_nat A_54) C_27)) ((plus_plus_nat B_47) D_2)))))
% FOF formula (forall (F_11:(nat->nat)), ((forall (X_1:nat) (Y_1:nat), ((((eq nat) (F_11 X_1)) (F_11 Y_1))->(((eq nat) X_1) Y_1)))->((inj_on_nat_nat F_11) top_top_nat_o))) of role axiom named fact_397_injI
% A new axiom: (forall (F_11:(nat->nat)), ((forall (X_1:nat) (Y_1:nat), ((((eq nat) (F_11 X_1)) (F_11 Y_1))->(((eq nat) X_1) Y_1)))->((inj_on_nat_nat F_11) top_top_nat_o)))
% FOF formula (forall (F_11:(arrow_1429601828e_indi->nat)), ((forall (X_1:arrow_1429601828e_indi) (Y_1:arrow_1429601828e_indi), ((((eq nat) (F_11 X_1)) (F_11 Y_1))->(((eq arrow_1429601828e_indi) X_1) Y_1)))->((inj_on978774663di_nat F_11) top_to988227749indi_o))) of role axiom named fact_398_injI
% A new axiom: (forall (F_11:(arrow_1429601828e_indi->nat)), ((forall (X_1:arrow_1429601828e_indi) (Y_1:arrow_1429601828e_indi), ((((eq nat) (F_11 X_1)) (F_11 Y_1))->(((eq arrow_1429601828e_indi) X_1) Y_1)))->((inj_on978774663di_nat F_11) top_to988227749indi_o)))
% FOF formula (forall (F_10:(nat->Prop)) (G_4:(nat->Prop)), ((iff ((ord_less_nat_o F_10) G_4)) ((and ((ord_less_eq_nat_o F_10) G_4)) (((ord_less_eq_nat_o G_4) F_10)->False)))) of role axiom named fact_399_less__fun__def
% A new axiom: (forall (F_10:(nat->Prop)) (G_4:(nat->Prop)), ((iff ((ord_less_nat_o F_10) G_4)) ((and ((ord_less_eq_nat_o F_10) G_4)) (((ord_less_eq_nat_o G_4) F_10)->False))))
% FOF formula (forall (F_10:(product_unit->Prop)) (G_4:(product_unit->Prop)), ((iff ((ord_le232288914unit_o F_10) G_4)) ((and ((ord_le1511552390unit_o F_10) G_4)) (((ord_le1511552390unit_o G_4) F_10)->False)))) of role axiom named fact_400_less__fun__def
% A new axiom: (forall (F_10:(product_unit->Prop)) (G_4:(product_unit->Prop)), ((iff ((ord_le232288914unit_o F_10) G_4)) ((and ((ord_le1511552390unit_o F_10) G_4)) (((ord_le1511552390unit_o G_4) F_10)->False))))
% FOF formula (forall (F_10:(arrow_1429601828e_indi->Prop)) (G_4:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o F_10) G_4)) ((and ((ord_le1799070453indi_o F_10) G_4)) (((ord_le1799070453indi_o G_4) F_10)->False)))) of role axiom named fact_401_less__fun__def
% A new axiom: (forall (F_10:(arrow_1429601828e_indi->Prop)) (G_4:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o F_10) G_4)) ((and ((ord_le1799070453indi_o F_10) G_4)) (((ord_le1799070453indi_o G_4) F_10)->False))))
% FOF formula (forall (B_46:(produc1501160679le_alt->(Prop->Prop))) (A_53:(produc1501160679le_alt->Prop)) (A_52:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_53) A_52)->((ord_le1063113995lt_o_o ((pi_Pro1701359055_alt_o A_52) B_46)) ((pi_Pro1701359055_alt_o A_53) B_46)))) of role axiom named fact_402_Pi__anti__mono
% A new axiom: (forall (B_46:(produc1501160679le_alt->(Prop->Prop))) (A_53:(produc1501160679le_alt->Prop)) (A_52:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_53) A_52)->((ord_le1063113995lt_o_o ((pi_Pro1701359055_alt_o A_52) B_46)) ((pi_Pro1701359055_alt_o A_53) B_46))))
% FOF formula (forall (B_46:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_53:(arrow_1429601828e_indi->Prop)) (A_52:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_53) A_52)->((ord_le1992928527lt_o_o ((pi_Arr1929480907_alt_o A_52) B_46)) ((pi_Arr1929480907_alt_o A_53) B_46)))) of role axiom named fact_403_Pi__anti__mono
% A new axiom: (forall (B_46:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_53:(arrow_1429601828e_indi->Prop)) (A_52:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_53) A_52)->((ord_le1992928527lt_o_o ((pi_Arr1929480907_alt_o A_52) B_46)) ((pi_Arr1929480907_alt_o A_53) B_46))))
% FOF formula (forall (B_46:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_53:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_52:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_53) A_52)->((ord_le134800455lt_o_o ((pi_Arr1304755663_alt_o A_52) B_46)) ((pi_Arr1304755663_alt_o A_53) B_46)))) of role axiom named fact_404_Pi__anti__mono
% A new axiom: (forall (B_46:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_53:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_52:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_53) A_52)->((ord_le134800455lt_o_o ((pi_Arr1304755663_alt_o A_52) B_46)) ((pi_Arr1304755663_alt_o A_53) B_46))))
% FOF formula (forall (R_2:(produc1501160679le_alt->Prop)) (S_2:(produc1501160679le_alt->Prop)), ((iff ((ord_le2080035663_alt_o (fun (X_1:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt)=> ((member214075476le_alt ((produc1347929815le_alt X_1) Y_1)) R_2))) (fun (X_1:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt)=> ((member214075476le_alt ((produc1347929815le_alt X_1) Y_1)) S_2)))) ((ord_le97612146_alt_o R_2) S_2))) of role axiom named fact_405_pred__subset__eq2
% A new axiom: (forall (R_2:(produc1501160679le_alt->Prop)) (S_2:(produc1501160679le_alt->Prop)), ((iff ((ord_le2080035663_alt_o (fun (X_1:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt)=> ((member214075476le_alt ((produc1347929815le_alt X_1) Y_1)) R_2))) (fun (X_1:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt)=> ((member214075476le_alt ((produc1347929815le_alt X_1) Y_1)) S_2)))) ((ord_le97612146_alt_o R_2) S_2)))
% FOF formula (forall (A_51:((produc1501160679le_alt->Prop)->Prop)), ((ord_le1063113995lt_o_o A_51) top_to1842727771lt_o_o)) of role axiom named fact_406_subset__UNIV
% A new axiom: (forall (A_51:((produc1501160679le_alt->Prop)->Prop)), ((ord_le1063113995lt_o_o A_51) top_to1842727771lt_o_o))
% FOF formula (forall (A_51:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((ord_le134800455lt_o_o A_51) top_to1969627639lt_o_o)) of role axiom named fact_407_subset__UNIV
% A new axiom: (forall (A_51:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((ord_le134800455lt_o_o A_51) top_to1969627639lt_o_o))
% FOF formula (forall (A_51:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((ord_le1992928527lt_o_o A_51) top_to2122763103lt_o_o)) of role axiom named fact_408_subset__UNIV
% A new axiom: (forall (A_51:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((ord_le1992928527lt_o_o A_51) top_to2122763103lt_o_o))
% FOF formula (forall (A_51:(produc1501160679le_alt->Prop)), ((ord_le97612146_alt_o A_51) top_to1841428258_alt_o)) of role axiom named fact_409_subset__UNIV
% A new axiom: (forall (A_51:(produc1501160679le_alt->Prop)), ((ord_le97612146_alt_o A_51) top_to1841428258_alt_o))
% FOF formula (forall (A_51:(nat->Prop)), ((ord_less_eq_nat_o A_51) top_top_nat_o)) of role axiom named fact_410_subset__UNIV
% A new axiom: (forall (A_51:(nat->Prop)), ((ord_less_eq_nat_o A_51) top_top_nat_o))
% FOF formula (forall (A_51:(product_unit->Prop)), ((ord_le1511552390unit_o A_51) top_to1984820022unit_o)) of role axiom named fact_411_subset__UNIV
% A new axiom: (forall (A_51:(product_unit->Prop)), ((ord_le1511552390unit_o A_51) top_to1984820022unit_o))
% FOF formula (forall (A_51:(arrow_1429601828e_indi->Prop)), ((ord_le1799070453indi_o A_51) top_to988227749indi_o)) of role axiom named fact_412_subset__UNIV
% A new axiom: (forall (A_51:(arrow_1429601828e_indi->Prop)), ((ord_le1799070453indi_o A_51) top_to988227749indi_o))
% FOF formula (forall (A_50:(nat->Prop)) (F_9:(nat->nat)) (B_45:(nat->Prop)), (((inj_on_nat_nat F_9) B_45)->(((ord_less_eq_nat_o A_50) B_45)->((inj_on_nat_nat F_9) A_50)))) of role axiom named fact_413_subset__inj__on
% A new axiom: (forall (A_50:(nat->Prop)) (F_9:(nat->nat)) (B_45:(nat->Prop)), (((inj_on_nat_nat F_9) B_45)->(((ord_less_eq_nat_o A_50) B_45)->((inj_on_nat_nat F_9) A_50))))
% FOF formula (forall (A_50:(arrow_1429601828e_indi->Prop)) (F_9:(arrow_1429601828e_indi->nat)) (B_45:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_9) B_45)->(((ord_le1799070453indi_o A_50) B_45)->((inj_on978774663di_nat F_9) A_50)))) of role axiom named fact_414_subset__inj__on
% A new axiom: (forall (A_50:(arrow_1429601828e_indi->Prop)) (F_9:(arrow_1429601828e_indi->nat)) (B_45:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_9) B_45)->(((ord_le1799070453indi_o A_50) B_45)->((inj_on978774663di_nat F_9) A_50))))
% FOF formula (forall (B_44:nat) (A_49:nat) (C_26:nat), ((((eq nat) ((plus_plus_nat B_44) A_49)) ((plus_plus_nat C_26) A_49))->(((eq nat) B_44) C_26))) of role axiom named fact_415_add__right__imp__eq
% A new axiom: (forall (B_44:nat) (A_49:nat) (C_26:nat), ((((eq nat) ((plus_plus_nat B_44) A_49)) ((plus_plus_nat C_26) A_49))->(((eq nat) B_44) C_26)))
% FOF formula (forall (A_48:nat) (B_43:nat) (C_25:nat), ((((eq nat) ((plus_plus_nat A_48) B_43)) ((plus_plus_nat A_48) C_25))->(((eq nat) B_43) C_25))) of role axiom named fact_416_add__imp__eq
% A new axiom: (forall (A_48:nat) (B_43:nat) (C_25:nat), ((((eq nat) ((plus_plus_nat A_48) B_43)) ((plus_plus_nat A_48) C_25))->(((eq nat) B_43) C_25)))
% FOF formula (forall (A_47:nat) (B_42:nat) (C_24:nat), ((((eq nat) ((plus_plus_nat A_47) B_42)) ((plus_plus_nat A_47) C_24))->(((eq nat) B_42) C_24))) of role axiom named fact_417_add__left__imp__eq
% A new axiom: (forall (A_47:nat) (B_42:nat) (C_24:nat), ((((eq nat) ((plus_plus_nat A_47) B_42)) ((plus_plus_nat A_47) C_24))->(((eq nat) B_42) C_24)))
% FOF formula (forall (B_41:nat) (A_46:nat) (C_23:nat), ((iff (((eq nat) ((plus_plus_nat B_41) A_46)) ((plus_plus_nat C_23) A_46))) (((eq nat) B_41) C_23))) of role axiom named fact_418_add__right__cancel
% A new axiom: (forall (B_41:nat) (A_46:nat) (C_23:nat), ((iff (((eq nat) ((plus_plus_nat B_41) A_46)) ((plus_plus_nat C_23) A_46))) (((eq nat) B_41) C_23)))
% FOF formula (forall (A_45:nat) (B_40:nat) (C_22:nat), ((iff (((eq nat) ((plus_plus_nat A_45) B_40)) ((plus_plus_nat A_45) C_22))) (((eq nat) B_40) C_22))) of role axiom named fact_419_add__left__cancel
% A new axiom: (forall (A_45:nat) (B_40:nat) (C_22:nat), ((iff (((eq nat) ((plus_plus_nat A_45) B_40)) ((plus_plus_nat A_45) C_22))) (((eq nat) B_40) C_22)))
% FOF formula (forall (A_44:nat) (B_39:nat) (C_21:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_44) B_39)) C_21)) ((plus_plus_nat A_44) ((plus_plus_nat B_39) C_21)))) of role axiom named fact_420_ab__semigroup__add__class_Oadd__ac_I1_J
% A new axiom: (forall (A_44:nat) (B_39:nat) (C_21:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_44) B_39)) C_21)) ((plus_plus_nat A_44) ((plus_plus_nat B_39) C_21))))
% FOF formula (forall (X_8:nat), ((iff (((eq nat) one_one_nat) X_8)) (((eq nat) X_8) one_one_nat))) of role axiom named fact_421_one__reorient
% A new axiom: (forall (X_8:nat), ((iff (((eq nat) one_one_nat) X_8)) (((eq nat) X_8) one_one_nat)))
% FOF formula (forall (C_20:nat) (A_43:nat) (B_38:nat), (((ord_less_eq_nat ((plus_plus_nat C_20) A_43)) ((plus_plus_nat C_20) B_38))->((ord_less_eq_nat A_43) B_38))) of role axiom named fact_422_add__le__imp__le__left
% A new axiom: (forall (C_20:nat) (A_43:nat) (B_38:nat), (((ord_less_eq_nat ((plus_plus_nat C_20) A_43)) ((plus_plus_nat C_20) B_38))->((ord_less_eq_nat A_43) B_38)))
% FOF formula (forall (A_42:nat) (C_19:nat) (B_37:nat), (((ord_less_eq_nat ((plus_plus_nat A_42) C_19)) ((plus_plus_nat B_37) C_19))->((ord_less_eq_nat A_42) B_37))) of role axiom named fact_423_add__le__imp__le__right
% A new axiom: (forall (A_42:nat) (C_19:nat) (B_37:nat), (((ord_less_eq_nat ((plus_plus_nat A_42) C_19)) ((plus_plus_nat B_37) C_19))->((ord_less_eq_nat A_42) B_37)))
% FOF formula (forall (C_18:nat) (D_1:nat) (A_41:nat) (B_36:nat), (((ord_less_eq_nat A_41) B_36)->(((ord_less_eq_nat C_18) D_1)->((ord_less_eq_nat ((plus_plus_nat A_41) C_18)) ((plus_plus_nat B_36) D_1))))) of role axiom named fact_424_add__mono
% A new axiom: (forall (C_18:nat) (D_1:nat) (A_41:nat) (B_36:nat), (((ord_less_eq_nat A_41) B_36)->(((ord_less_eq_nat C_18) D_1)->((ord_less_eq_nat ((plus_plus_nat A_41) C_18)) ((plus_plus_nat B_36) D_1)))))
% FOF formula (forall (C_17:nat) (A_40:nat) (B_35:nat), (((ord_less_eq_nat A_40) B_35)->((ord_less_eq_nat ((plus_plus_nat C_17) A_40)) ((plus_plus_nat C_17) B_35)))) of role axiom named fact_425_add__left__mono
% A new axiom: (forall (C_17:nat) (A_40:nat) (B_35:nat), (((ord_less_eq_nat A_40) B_35)->((ord_less_eq_nat ((plus_plus_nat C_17) A_40)) ((plus_plus_nat C_17) B_35))))
% FOF formula (forall (C_16:nat) (A_39:nat) (B_34:nat), (((ord_less_eq_nat A_39) B_34)->((ord_less_eq_nat ((plus_plus_nat A_39) C_16)) ((plus_plus_nat B_34) C_16)))) of role axiom named fact_426_add__right__mono
% A new axiom: (forall (C_16:nat) (A_39:nat) (B_34:nat), (((ord_less_eq_nat A_39) B_34)->((ord_less_eq_nat ((plus_plus_nat A_39) C_16)) ((plus_plus_nat B_34) C_16))))
% FOF formula (forall (C_15:nat) (A_38:nat) (B_33:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_15) A_38)) ((plus_plus_nat C_15) B_33))) ((ord_less_eq_nat A_38) B_33))) of role axiom named fact_427_add__le__cancel__left
% A new axiom: (forall (C_15:nat) (A_38:nat) (B_33:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_15) A_38)) ((plus_plus_nat C_15) B_33))) ((ord_less_eq_nat A_38) B_33)))
% FOF formula (forall (A_37:nat) (C_14:nat) (B_32:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_37) C_14)) ((plus_plus_nat B_32) C_14))) ((ord_less_eq_nat A_37) B_32))) of role axiom named fact_428_add__le__cancel__right
% A new axiom: (forall (A_37:nat) (C_14:nat) (B_32:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_37) C_14)) ((plus_plus_nat B_32) C_14))) ((ord_less_eq_nat A_37) B_32)))
% FOF formula (forall (C_13:nat) (A_36:nat) (B_31:nat), (((ord_less_nat ((plus_plus_nat C_13) A_36)) ((plus_plus_nat C_13) B_31))->((ord_less_nat A_36) B_31))) of role axiom named fact_429_add__less__imp__less__left
% A new axiom: (forall (C_13:nat) (A_36:nat) (B_31:nat), (((ord_less_nat ((plus_plus_nat C_13) A_36)) ((plus_plus_nat C_13) B_31))->((ord_less_nat A_36) B_31)))
% FOF formula (forall (A_35:nat) (C_12:nat) (B_30:nat), (((ord_less_nat ((plus_plus_nat A_35) C_12)) ((plus_plus_nat B_30) C_12))->((ord_less_nat A_35) B_30))) of role axiom named fact_430_add__less__imp__less__right
% A new axiom: (forall (A_35:nat) (C_12:nat) (B_30:nat), (((ord_less_nat ((plus_plus_nat A_35) C_12)) ((plus_plus_nat B_30) C_12))->((ord_less_nat A_35) B_30)))
% FOF formula (forall (C_11:nat) (D:nat) (A_34:nat) (B_29:nat), (((ord_less_nat A_34) B_29)->(((ord_less_nat C_11) D)->((ord_less_nat ((plus_plus_nat A_34) C_11)) ((plus_plus_nat B_29) D))))) of role axiom named fact_431_add__strict__mono
% A new axiom: (forall (C_11:nat) (D:nat) (A_34:nat) (B_29:nat), (((ord_less_nat A_34) B_29)->(((ord_less_nat C_11) D)->((ord_less_nat ((plus_plus_nat A_34) C_11)) ((plus_plus_nat B_29) D)))))
% FOF formula (forall (C_10:nat) (A_33:nat) (B_28:nat), (((ord_less_nat A_33) B_28)->((ord_less_nat ((plus_plus_nat C_10) A_33)) ((plus_plus_nat C_10) B_28)))) of role axiom named fact_432_add__strict__left__mono
% A new axiom: (forall (C_10:nat) (A_33:nat) (B_28:nat), (((ord_less_nat A_33) B_28)->((ord_less_nat ((plus_plus_nat C_10) A_33)) ((plus_plus_nat C_10) B_28))))
% FOF formula (forall (C_9:nat) (A_32:nat) (B_27:nat), (((ord_less_nat A_32) B_27)->((ord_less_nat ((plus_plus_nat A_32) C_9)) ((plus_plus_nat B_27) C_9)))) of role axiom named fact_433_add__strict__right__mono
% A new axiom: (forall (C_9:nat) (A_32:nat) (B_27:nat), (((ord_less_nat A_32) B_27)->((ord_less_nat ((plus_plus_nat A_32) C_9)) ((plus_plus_nat B_27) C_9))))
% FOF formula (forall (C_8:nat) (A_31:nat) (B_26:nat), ((iff ((ord_less_nat ((plus_plus_nat C_8) A_31)) ((plus_plus_nat C_8) B_26))) ((ord_less_nat A_31) B_26))) of role axiom named fact_434_add__less__cancel__left
% A new axiom: (forall (C_8:nat) (A_31:nat) (B_26:nat), ((iff ((ord_less_nat ((plus_plus_nat C_8) A_31)) ((plus_plus_nat C_8) B_26))) ((ord_less_nat A_31) B_26)))
% FOF formula (forall (A_30:nat) (C_7:nat) (B_25:nat), ((iff ((ord_less_nat ((plus_plus_nat A_30) C_7)) ((plus_plus_nat B_25) C_7))) ((ord_less_nat A_30) B_25))) of role axiom named fact_435_add__less__cancel__right
% A new axiom: (forall (A_30:nat) (C_7:nat) (B_25:nat), ((iff ((ord_less_nat ((plus_plus_nat A_30) C_7)) ((plus_plus_nat B_25) C_7))) ((ord_less_nat A_30) B_25)))
% FOF formula (forall (F_8:(nat->Prop)) (G_3:(nat->Prop)), ((forall (X_1:nat), ((ord_less_eq_o (F_8 X_1)) (G_3 X_1)))->((ord_less_eq_nat_o F_8) G_3))) of role axiom named fact_436_le__funI
% A new axiom: (forall (F_8:(nat->Prop)) (G_3:(nat->Prop)), ((forall (X_1:nat), ((ord_less_eq_o (F_8 X_1)) (G_3 X_1)))->((ord_less_eq_nat_o F_8) G_3)))
% FOF formula (forall (A_29:(nat->Prop)) (B_24:(nat->Prop)), (((ord_less_eq_nat_o A_29) B_24)->(((ord_less_eq_nat_o B_24) A_29)->(((eq (nat->Prop)) A_29) B_24)))) of role axiom named fact_437_equalityI
% A new axiom: (forall (A_29:(nat->Prop)) (B_24:(nat->Prop)), (((ord_less_eq_nat_o A_29) B_24)->(((ord_less_eq_nat_o B_24) A_29)->(((eq (nat->Prop)) A_29) B_24))))
% FOF formula (forall (C_6:Prop) (A_28:(Prop->Prop)) (B_23:(Prop->Prop)), (((ord_less_eq_o_o A_28) B_23)->(((member_o C_6) A_28)->((member_o C_6) B_23)))) of role axiom named fact_438_subsetD
% A new axiom: (forall (C_6:Prop) (A_28:(Prop->Prop)) (B_23:(Prop->Prop)), (((ord_less_eq_o_o A_28) B_23)->(((member_o C_6) A_28)->((member_o C_6) B_23))))
% FOF formula (forall (C_6:product_unit) (A_28:(product_unit->Prop)) (B_23:(product_unit->Prop)), (((ord_le1511552390unit_o A_28) B_23)->(((member_Product_unit C_6) A_28)->((member_Product_unit C_6) B_23)))) of role axiom named fact_439_subsetD
% A new axiom: (forall (C_6:product_unit) (A_28:(product_unit->Prop)) (B_23:(product_unit->Prop)), (((ord_le1511552390unit_o A_28) B_23)->(((member_Product_unit C_6) A_28)->((member_Product_unit C_6) B_23))))
% FOF formula (forall (C_6:arrow_1429601828e_indi) (A_28:(arrow_1429601828e_indi->Prop)) (B_23:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_28) B_23)->(((member2052026769e_indi C_6) A_28)->((member2052026769e_indi C_6) B_23)))) of role axiom named fact_440_subsetD
% A new axiom: (forall (C_6:arrow_1429601828e_indi) (A_28:(arrow_1429601828e_indi->Prop)) (B_23:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_28) B_23)->(((member2052026769e_indi C_6) A_28)->((member2052026769e_indi C_6) B_23))))
% FOF formula (forall (C_6:nat) (A_28:(nat->Prop)) (B_23:(nat->Prop)), (((ord_less_eq_nat_o A_28) B_23)->(((member_nat C_6) A_28)->((member_nat C_6) B_23)))) of role axiom named fact_441_subsetD
% A new axiom: (forall (C_6:nat) (A_28:(nat->Prop)) (B_23:(nat->Prop)), (((ord_less_eq_nat_o A_28) B_23)->(((member_nat C_6) A_28)->((member_nat C_6) B_23))))
% FOF formula (forall (C_6:(produc1501160679le_alt->Prop)) (A_28:((produc1501160679le_alt->Prop)->Prop)) (B_23:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o A_28) B_23)->(((member377231867_alt_o C_6) A_28)->((member377231867_alt_o C_6) B_23)))) of role axiom named fact_442_subsetD
% A new axiom: (forall (C_6:(produc1501160679le_alt->Prop)) (A_28:((produc1501160679le_alt->Prop)->Prop)) (B_23:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o A_28) B_23)->(((member377231867_alt_o C_6) A_28)->((member377231867_alt_o C_6) B_23))))
% FOF formula (forall (C_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_23:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o A_28) B_23)->(((member616898751_alt_o C_6) A_28)->((member616898751_alt_o C_6) B_23)))) of role axiom named fact_443_subsetD
% A new axiom: (forall (C_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_23:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o A_28) B_23)->(((member616898751_alt_o C_6) A_28)->((member616898751_alt_o C_6) B_23))))
% FOF formula (forall (C_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_23:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_28) B_23)->(((member526088951_alt_o C_6) A_28)->((member526088951_alt_o C_6) B_23)))) of role axiom named fact_444_subsetD
% A new axiom: (forall (C_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_23:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_28) B_23)->(((member526088951_alt_o C_6) A_28)->((member526088951_alt_o C_6) B_23))))
% FOF formula (forall (C_6:produc1501160679le_alt) (A_28:(produc1501160679le_alt->Prop)) (B_23:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_28) B_23)->(((member214075476le_alt C_6) A_28)->((member214075476le_alt C_6) B_23)))) of role axiom named fact_445_subsetD
% A new axiom: (forall (C_6:produc1501160679le_alt) (A_28:(produc1501160679le_alt->Prop)) (B_23:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_28) B_23)->(((member214075476le_alt C_6) A_28)->((member214075476le_alt C_6) B_23))))
% FOF formula (forall (A_27:(nat->Prop)) (B_22:(nat->Prop)), ((iff ((ord_less_nat_o A_27) B_22)) ((and ((ord_less_eq_nat_o A_27) B_22)) (not (((eq (nat->Prop)) A_27) B_22))))) of role axiom named fact_446_psubset__eq
% A new axiom: (forall (A_27:(nat->Prop)) (B_22:(nat->Prop)), ((iff ((ord_less_nat_o A_27) B_22)) ((and ((ord_less_eq_nat_o A_27) B_22)) (not (((eq (nat->Prop)) A_27) B_22)))))
% FOF formula (forall (A_27:(product_unit->Prop)) (B_22:(product_unit->Prop)), ((iff ((ord_le232288914unit_o A_27) B_22)) ((and ((ord_le1511552390unit_o A_27) B_22)) (not (((eq (product_unit->Prop)) A_27) B_22))))) of role axiom named fact_447_psubset__eq
% A new axiom: (forall (A_27:(product_unit->Prop)) (B_22:(product_unit->Prop)), ((iff ((ord_le232288914unit_o A_27) B_22)) ((and ((ord_le1511552390unit_o A_27) B_22)) (not (((eq (product_unit->Prop)) A_27) B_22)))))
% FOF formula (forall (A_27:(arrow_1429601828e_indi->Prop)) (B_22:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o A_27) B_22)) ((and ((ord_le1799070453indi_o A_27) B_22)) (not (((eq (arrow_1429601828e_indi->Prop)) A_27) B_22))))) of role axiom named fact_448_psubset__eq
% A new axiom: (forall (A_27:(arrow_1429601828e_indi->Prop)) (B_22:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o A_27) B_22)) ((and ((ord_le1799070453indi_o A_27) B_22)) (not (((eq (arrow_1429601828e_indi->Prop)) A_27) B_22)))))
% FOF formula (forall (A_26:(nat->Prop)) (B_21:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_26) B_21)) ((or ((ord_less_nat_o A_26) B_21)) (((eq (nat->Prop)) A_26) B_21)))) of role axiom named fact_449_subset__iff__psubset__eq
% A new axiom: (forall (A_26:(nat->Prop)) (B_21:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_26) B_21)) ((or ((ord_less_nat_o A_26) B_21)) (((eq (nat->Prop)) A_26) B_21))))
% FOF formula (forall (A_26:(product_unit->Prop)) (B_21:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o A_26) B_21)) ((or ((ord_le232288914unit_o A_26) B_21)) (((eq (product_unit->Prop)) A_26) B_21)))) of role axiom named fact_450_subset__iff__psubset__eq
% A new axiom: (forall (A_26:(product_unit->Prop)) (B_21:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o A_26) B_21)) ((or ((ord_le232288914unit_o A_26) B_21)) (((eq (product_unit->Prop)) A_26) B_21))))
% FOF formula (forall (A_26:(arrow_1429601828e_indi->Prop)) (B_21:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o A_26) B_21)) ((or ((ord_le777687553indi_o A_26) B_21)) (((eq (arrow_1429601828e_indi->Prop)) A_26) B_21)))) of role axiom named fact_451_subset__iff__psubset__eq
% A new axiom: (forall (A_26:(arrow_1429601828e_indi->Prop)) (B_21:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o A_26) B_21)) ((or ((ord_le777687553indi_o A_26) B_21)) (((eq (arrow_1429601828e_indi->Prop)) A_26) B_21))))
% FOF formula (forall (A_25:(nat->Prop)) (B_20:(nat->Prop)), (((ord_less_nat_o A_25) B_20)->((ord_less_eq_nat_o A_25) B_20))) of role axiom named fact_452_psubset__imp__subset
% A new axiom: (forall (A_25:(nat->Prop)) (B_20:(nat->Prop)), (((ord_less_nat_o A_25) B_20)->((ord_less_eq_nat_o A_25) B_20)))
% FOF formula (forall (A_25:(product_unit->Prop)) (B_20:(product_unit->Prop)), (((ord_le232288914unit_o A_25) B_20)->((ord_le1511552390unit_o A_25) B_20))) of role axiom named fact_453_psubset__imp__subset
% A new axiom: (forall (A_25:(product_unit->Prop)) (B_20:(product_unit->Prop)), (((ord_le232288914unit_o A_25) B_20)->((ord_le1511552390unit_o A_25) B_20)))
% FOF formula (forall (A_25:(arrow_1429601828e_indi->Prop)) (B_20:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_25) B_20)->((ord_le1799070453indi_o A_25) B_20))) of role axiom named fact_454_psubset__imp__subset
% A new axiom: (forall (A_25:(arrow_1429601828e_indi->Prop)) (B_20:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_25) B_20)->((ord_le1799070453indi_o A_25) B_20)))
% FOF formula (forall (C_5:(nat->Prop)) (A_24:(nat->Prop)) (B_19:(nat->Prop)), (((ord_less_nat_o A_24) B_19)->(((ord_less_eq_nat_o B_19) C_5)->((ord_less_nat_o A_24) C_5)))) of role axiom named fact_455_psubset__subset__trans
% A new axiom: (forall (C_5:(nat->Prop)) (A_24:(nat->Prop)) (B_19:(nat->Prop)), (((ord_less_nat_o A_24) B_19)->(((ord_less_eq_nat_o B_19) C_5)->((ord_less_nat_o A_24) C_5))))
% FOF formula (forall (C_5:(product_unit->Prop)) (A_24:(product_unit->Prop)) (B_19:(product_unit->Prop)), (((ord_le232288914unit_o A_24) B_19)->(((ord_le1511552390unit_o B_19) C_5)->((ord_le232288914unit_o A_24) C_5)))) of role axiom named fact_456_psubset__subset__trans
% A new axiom: (forall (C_5:(product_unit->Prop)) (A_24:(product_unit->Prop)) (B_19:(product_unit->Prop)), (((ord_le232288914unit_o A_24) B_19)->(((ord_le1511552390unit_o B_19) C_5)->((ord_le232288914unit_o A_24) C_5))))
% FOF formula (forall (C_5:(arrow_1429601828e_indi->Prop)) (A_24:(arrow_1429601828e_indi->Prop)) (B_19:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_24) B_19)->(((ord_le1799070453indi_o B_19) C_5)->((ord_le777687553indi_o A_24) C_5)))) of role axiom named fact_457_psubset__subset__trans
% A new axiom: (forall (C_5:(arrow_1429601828e_indi->Prop)) (A_24:(arrow_1429601828e_indi->Prop)) (B_19:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_24) B_19)->(((ord_le1799070453indi_o B_19) C_5)->((ord_le777687553indi_o A_24) C_5))))
% FOF formula (forall (C_4:(nat->Prop)) (A_23:(nat->Prop)) (B_18:(nat->Prop)), (((ord_less_eq_nat_o A_23) B_18)->(((ord_less_nat_o B_18) C_4)->((ord_less_nat_o A_23) C_4)))) of role axiom named fact_458_subset__psubset__trans
% A new axiom: (forall (C_4:(nat->Prop)) (A_23:(nat->Prop)) (B_18:(nat->Prop)), (((ord_less_eq_nat_o A_23) B_18)->(((ord_less_nat_o B_18) C_4)->((ord_less_nat_o A_23) C_4))))
% FOF formula (forall (C_4:(product_unit->Prop)) (A_23:(product_unit->Prop)) (B_18:(product_unit->Prop)), (((ord_le1511552390unit_o A_23) B_18)->(((ord_le232288914unit_o B_18) C_4)->((ord_le232288914unit_o A_23) C_4)))) of role axiom named fact_459_subset__psubset__trans
% A new axiom: (forall (C_4:(product_unit->Prop)) (A_23:(product_unit->Prop)) (B_18:(product_unit->Prop)), (((ord_le1511552390unit_o A_23) B_18)->(((ord_le232288914unit_o B_18) C_4)->((ord_le232288914unit_o A_23) C_4))))
% FOF formula (forall (C_4:(arrow_1429601828e_indi->Prop)) (A_23:(arrow_1429601828e_indi->Prop)) (B_18:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_23) B_18)->(((ord_le777687553indi_o B_18) C_4)->((ord_le777687553indi_o A_23) C_4)))) of role axiom named fact_460_subset__psubset__trans
% A new axiom: (forall (C_4:(arrow_1429601828e_indi->Prop)) (A_23:(arrow_1429601828e_indi->Prop)) (B_18:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_23) B_18)->(((ord_le777687553indi_o B_18) C_4)->((ord_le777687553indi_o A_23) C_4))))
% FOF formula (forall (A_22:(nat->Prop)) (B_17:(nat->Prop)), ((((eq (nat->Prop)) A_22) B_17)->((((ord_less_eq_nat_o A_22) B_17)->(((ord_less_eq_nat_o B_17) A_22)->False))->False))) of role axiom named fact_461_equalityE
% A new axiom: (forall (A_22:(nat->Prop)) (B_17:(nat->Prop)), ((((eq (nat->Prop)) A_22) B_17)->((((ord_less_eq_nat_o A_22) B_17)->(((ord_less_eq_nat_o B_17) A_22)->False))->False)))
% FOF formula (forall (C_3:(nat->Prop)) (A_21:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_21) B_16)->(((ord_less_eq_nat_o B_16) C_3)->((ord_less_eq_nat_o A_21) C_3)))) of role axiom named fact_462_subset__trans
% A new axiom: (forall (C_3:(nat->Prop)) (A_21:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_21) B_16)->(((ord_less_eq_nat_o B_16) C_3)->((ord_less_eq_nat_o A_21) C_3))))
% FOF formula (forall (X_7:Prop) (A_20:(Prop->Prop)) (B_15:(Prop->Prop)), (((ord_less_eq_o_o A_20) B_15)->(((member_o X_7) A_20)->((member_o X_7) B_15)))) of role axiom named fact_463_set__mp
% A new axiom: (forall (X_7:Prop) (A_20:(Prop->Prop)) (B_15:(Prop->Prop)), (((ord_less_eq_o_o A_20) B_15)->(((member_o X_7) A_20)->((member_o X_7) B_15))))
% FOF formula (forall (X_7:product_unit) (A_20:(product_unit->Prop)) (B_15:(product_unit->Prop)), (((ord_le1511552390unit_o A_20) B_15)->(((member_Product_unit X_7) A_20)->((member_Product_unit X_7) B_15)))) of role axiom named fact_464_set__mp
% A new axiom: (forall (X_7:product_unit) (A_20:(product_unit->Prop)) (B_15:(product_unit->Prop)), (((ord_le1511552390unit_o A_20) B_15)->(((member_Product_unit X_7) A_20)->((member_Product_unit X_7) B_15))))
% FOF formula (forall (X_7:arrow_1429601828e_indi) (A_20:(arrow_1429601828e_indi->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_20) B_15)->(((member2052026769e_indi X_7) A_20)->((member2052026769e_indi X_7) B_15)))) of role axiom named fact_465_set__mp
% A new axiom: (forall (X_7:arrow_1429601828e_indi) (A_20:(arrow_1429601828e_indi->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_20) B_15)->(((member2052026769e_indi X_7) A_20)->((member2052026769e_indi X_7) B_15))))
% FOF formula (forall (X_7:nat) (A_20:(nat->Prop)) (B_15:(nat->Prop)), (((ord_less_eq_nat_o A_20) B_15)->(((member_nat X_7) A_20)->((member_nat X_7) B_15)))) of role axiom named fact_466_set__mp
% A new axiom: (forall (X_7:nat) (A_20:(nat->Prop)) (B_15:(nat->Prop)), (((ord_less_eq_nat_o A_20) B_15)->(((member_nat X_7) A_20)->((member_nat X_7) B_15))))
% FOF formula (forall (X_7:(produc1501160679le_alt->Prop)) (A_20:((produc1501160679le_alt->Prop)->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o A_20) B_15)->(((member377231867_alt_o X_7) A_20)->((member377231867_alt_o X_7) B_15)))) of role axiom named fact_467_set__mp
% A new axiom: (forall (X_7:(produc1501160679le_alt->Prop)) (A_20:((produc1501160679le_alt->Prop)->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o A_20) B_15)->(((member377231867_alt_o X_7) A_20)->((member377231867_alt_o X_7) B_15))))
% FOF formula (forall (X_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_20:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o A_20) B_15)->(((member616898751_alt_o X_7) A_20)->((member616898751_alt_o X_7) B_15)))) of role axiom named fact_468_set__mp
% A new axiom: (forall (X_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_20:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o A_20) B_15)->(((member616898751_alt_o X_7) A_20)->((member616898751_alt_o X_7) B_15))))
% FOF formula (forall (X_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_20:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_20) B_15)->(((member526088951_alt_o X_7) A_20)->((member526088951_alt_o X_7) B_15)))) of role axiom named fact_469_set__mp
% A new axiom: (forall (X_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_20:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_20) B_15)->(((member526088951_alt_o X_7) A_20)->((member526088951_alt_o X_7) B_15))))
% FOF formula (forall (X_7:produc1501160679le_alt) (A_20:(produc1501160679le_alt->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_20) B_15)->(((member214075476le_alt X_7) A_20)->((member214075476le_alt X_7) B_15)))) of role axiom named fact_470_set__mp
% A new axiom: (forall (X_7:produc1501160679le_alt) (A_20:(produc1501160679le_alt->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_20) B_15)->(((member214075476le_alt X_7) A_20)->((member214075476le_alt X_7) B_15))))
% FOF formula (forall (B_14:(Prop->Prop)) (X_6:Prop) (A_19:(Prop->Prop)), (((member_o X_6) A_19)->(((ord_less_eq_o_o A_19) B_14)->((member_o X_6) B_14)))) of role axiom named fact_471_set__rev__mp
% A new axiom: (forall (B_14:(Prop->Prop)) (X_6:Prop) (A_19:(Prop->Prop)), (((member_o X_6) A_19)->(((ord_less_eq_o_o A_19) B_14)->((member_o X_6) B_14))))
% FOF formula (forall (B_14:(product_unit->Prop)) (X_6:product_unit) (A_19:(product_unit->Prop)), (((member_Product_unit X_6) A_19)->(((ord_le1511552390unit_o A_19) B_14)->((member_Product_unit X_6) B_14)))) of role axiom named fact_472_set__rev__mp
% A new axiom: (forall (B_14:(product_unit->Prop)) (X_6:product_unit) (A_19:(product_unit->Prop)), (((member_Product_unit X_6) A_19)->(((ord_le1511552390unit_o A_19) B_14)->((member_Product_unit X_6) B_14))))
% FOF formula (forall (B_14:(arrow_1429601828e_indi->Prop)) (X_6:arrow_1429601828e_indi) (A_19:(arrow_1429601828e_indi->Prop)), (((member2052026769e_indi X_6) A_19)->(((ord_le1799070453indi_o A_19) B_14)->((member2052026769e_indi X_6) B_14)))) of role axiom named fact_473_set__rev__mp
% A new axiom: (forall (B_14:(arrow_1429601828e_indi->Prop)) (X_6:arrow_1429601828e_indi) (A_19:(arrow_1429601828e_indi->Prop)), (((member2052026769e_indi X_6) A_19)->(((ord_le1799070453indi_o A_19) B_14)->((member2052026769e_indi X_6) B_14))))
% FOF formula (forall (B_14:(nat->Prop)) (X_6:nat) (A_19:(nat->Prop)), (((member_nat X_6) A_19)->(((ord_less_eq_nat_o A_19) B_14)->((member_nat X_6) B_14)))) of role axiom named fact_474_set__rev__mp
% A new axiom: (forall (B_14:(nat->Prop)) (X_6:nat) (A_19:(nat->Prop)), (((member_nat X_6) A_19)->(((ord_less_eq_nat_o A_19) B_14)->((member_nat X_6) B_14))))
% FOF formula (forall (B_14:((produc1501160679le_alt->Prop)->Prop)) (X_6:(produc1501160679le_alt->Prop)) (A_19:((produc1501160679le_alt->Prop)->Prop)), (((member377231867_alt_o X_6) A_19)->(((ord_le1063113995lt_o_o A_19) B_14)->((member377231867_alt_o X_6) B_14)))) of role axiom named fact_475_set__rev__mp
% A new axiom: (forall (B_14:((produc1501160679le_alt->Prop)->Prop)) (X_6:(produc1501160679le_alt->Prop)) (A_19:((produc1501160679le_alt->Prop)->Prop)), (((member377231867_alt_o X_6) A_19)->(((ord_le1063113995lt_o_o A_19) B_14)->((member377231867_alt_o X_6) B_14))))
% FOF formula (forall (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (X_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member616898751_alt_o X_6) A_19)->(((ord_le134800455lt_o_o A_19) B_14)->((member616898751_alt_o X_6) B_14)))) of role axiom named fact_476_set__rev__mp
% A new axiom: (forall (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (X_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member616898751_alt_o X_6) A_19)->(((ord_le134800455lt_o_o A_19) B_14)->((member616898751_alt_o X_6) B_14))))
% FOF formula (forall (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (X_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member526088951_alt_o X_6) A_19)->(((ord_le1992928527lt_o_o A_19) B_14)->((member526088951_alt_o X_6) B_14)))) of role axiom named fact_477_set__rev__mp
% A new axiom: (forall (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (X_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member526088951_alt_o X_6) A_19)->(((ord_le1992928527lt_o_o A_19) B_14)->((member526088951_alt_o X_6) B_14))))
% FOF formula (forall (B_14:(produc1501160679le_alt->Prop)) (X_6:produc1501160679le_alt) (A_19:(produc1501160679le_alt->Prop)), (((member214075476le_alt X_6) A_19)->(((ord_le97612146_alt_o A_19) B_14)->((member214075476le_alt X_6) B_14)))) of role axiom named fact_478_set__rev__mp
% A new axiom: (forall (B_14:(produc1501160679le_alt->Prop)) (X_6:produc1501160679le_alt) (A_19:(produc1501160679le_alt->Prop)), (((member214075476le_alt X_6) A_19)->(((ord_le97612146_alt_o A_19) B_14)->((member214075476le_alt X_6) B_14))))
% FOF formula (forall (X_5:nat) (P_2:(nat->Prop)) (Q_1:(nat->Prop)), (((ord_less_eq_nat_o P_2) Q_1)->((P_2 X_5)->(Q_1 X_5)))) of role axiom named fact_479_predicate1D
% A new axiom: (forall (X_5:nat) (P_2:(nat->Prop)) (Q_1:(nat->Prop)), (((ord_less_eq_nat_o P_2) Q_1)->((P_2 X_5)->(Q_1 X_5))))
% FOF formula (forall (X_4:Prop) (A_18:(Prop->Prop)) (B_13:(Prop->Prop)), (((ord_less_eq_o_o A_18) B_13)->(((member_o X_4) A_18)->((member_o X_4) B_13)))) of role axiom named fact_480_in__mono
% A new axiom: (forall (X_4:Prop) (A_18:(Prop->Prop)) (B_13:(Prop->Prop)), (((ord_less_eq_o_o A_18) B_13)->(((member_o X_4) A_18)->((member_o X_4) B_13))))
% FOF formula (forall (X_4:product_unit) (A_18:(product_unit->Prop)) (B_13:(product_unit->Prop)), (((ord_le1511552390unit_o A_18) B_13)->(((member_Product_unit X_4) A_18)->((member_Product_unit X_4) B_13)))) of role axiom named fact_481_in__mono
% A new axiom: (forall (X_4:product_unit) (A_18:(product_unit->Prop)) (B_13:(product_unit->Prop)), (((ord_le1511552390unit_o A_18) B_13)->(((member_Product_unit X_4) A_18)->((member_Product_unit X_4) B_13))))
% FOF formula (forall (X_4:arrow_1429601828e_indi) (A_18:(arrow_1429601828e_indi->Prop)) (B_13:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_18) B_13)->(((member2052026769e_indi X_4) A_18)->((member2052026769e_indi X_4) B_13)))) of role axiom named fact_482_in__mono
% A new axiom: (forall (X_4:arrow_1429601828e_indi) (A_18:(arrow_1429601828e_indi->Prop)) (B_13:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_18) B_13)->(((member2052026769e_indi X_4) A_18)->((member2052026769e_indi X_4) B_13))))
% FOF formula (forall (X_4:nat) (A_18:(nat->Prop)) (B_13:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_13)->(((member_nat X_4) A_18)->((member_nat X_4) B_13)))) of role axiom named fact_483_in__mono
% A new axiom: (forall (X_4:nat) (A_18:(nat->Prop)) (B_13:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_13)->(((member_nat X_4) A_18)->((member_nat X_4) B_13))))
% FOF formula (forall (X_4:(produc1501160679le_alt->Prop)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_13:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o A_18) B_13)->(((member377231867_alt_o X_4) A_18)->((member377231867_alt_o X_4) B_13)))) of role axiom named fact_484_in__mono
% A new axiom: (forall (X_4:(produc1501160679le_alt->Prop)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_13:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o A_18) B_13)->(((member377231867_alt_o X_4) A_18)->((member377231867_alt_o X_4) B_13))))
% FOF formula (forall (X_4:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o A_18) B_13)->(((member616898751_alt_o X_4) A_18)->((member616898751_alt_o X_4) B_13)))) of role axiom named fact_485_in__mono
% A new axiom: (forall (X_4:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o A_18) B_13)->(((member616898751_alt_o X_4) A_18)->((member616898751_alt_o X_4) B_13))))
% FOF formula (forall (X_4:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_18) B_13)->(((member526088951_alt_o X_4) A_18)->((member526088951_alt_o X_4) B_13)))) of role axiom named fact_486_in__mono
% A new axiom: (forall (X_4:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_18) B_13)->(((member526088951_alt_o X_4) A_18)->((member526088951_alt_o X_4) B_13))))
% FOF formula (forall (X_4:produc1501160679le_alt) (A_18:(produc1501160679le_alt->Prop)) (B_13:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_18) B_13)->(((member214075476le_alt X_4) A_18)->((member214075476le_alt X_4) B_13)))) of role axiom named fact_487_in__mono
% A new axiom: (forall (X_4:produc1501160679le_alt) (A_18:(produc1501160679le_alt->Prop)) (B_13:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_18) B_13)->(((member214075476le_alt X_4) A_18)->((member214075476le_alt X_4) B_13))))
% FOF formula (forall (A_17:(nat->Prop)) (B_12:(nat->Prop)), ((((eq (nat->Prop)) A_17) B_12)->((ord_less_eq_nat_o B_12) A_17))) of role axiom named fact_488_equalityD2
% A new axiom: (forall (A_17:(nat->Prop)) (B_12:(nat->Prop)), ((((eq (nat->Prop)) A_17) B_12)->((ord_less_eq_nat_o B_12) A_17)))
% FOF formula (forall (A_16:(nat->Prop)) (B_11:(nat->Prop)), ((((eq (nat->Prop)) A_16) B_11)->((ord_less_eq_nat_o A_16) B_11))) of role axiom named fact_489_equalityD1
% A new axiom: (forall (A_16:(nat->Prop)) (B_11:(nat->Prop)), ((((eq (nat->Prop)) A_16) B_11)->((ord_less_eq_nat_o A_16) B_11)))
% FOF formula (forall (Q:(nat->Prop)) (P_1:(nat->Prop)) (X_3:nat), ((P_1 X_3)->(((ord_less_eq_nat_o P_1) Q)->(Q X_3)))) of role axiom named fact_490_rev__predicate1D
% A new axiom: (forall (Q:(nat->Prop)) (P_1:(nat->Prop)) (X_3:nat), ((P_1 X_3)->(((ord_less_eq_nat_o P_1) Q)->(Q X_3))))
% FOF formula (forall (A_15:(nat->Prop)) (B_10:(nat->Prop)), ((iff (((eq (nat->Prop)) A_15) B_10)) ((and ((ord_less_eq_nat_o A_15) B_10)) ((ord_less_eq_nat_o B_10) A_15)))) of role axiom named fact_491_set__eq__subset
% A new axiom: (forall (A_15:(nat->Prop)) (B_10:(nat->Prop)), ((iff (((eq (nat->Prop)) A_15) B_10)) ((and ((ord_less_eq_nat_o A_15) B_10)) ((ord_less_eq_nat_o B_10) A_15))))
% FOF formula (forall (A_14:(nat->Prop)), ((ord_less_eq_nat_o A_14) A_14)) of role axiom named fact_492_subset__refl
% A new axiom: (forall (A_14:(nat->Prop)), ((ord_less_eq_nat_o A_14) A_14))
% FOF formula (forall (R_1:(Prop->Prop)) (S_1:(Prop->Prop)), ((iff ((ord_less_eq_o_o (fun (X_1:Prop)=> ((member_o X_1) R_1))) (fun (X_1:Prop)=> ((member_o X_1) S_1)))) ((ord_less_eq_o_o R_1) S_1))) of role axiom named fact_493_pred__subset__eq
% A new axiom: (forall (R_1:(Prop->Prop)) (S_1:(Prop->Prop)), ((iff ((ord_less_eq_o_o (fun (X_1:Prop)=> ((member_o X_1) R_1))) (fun (X_1:Prop)=> ((member_o X_1) S_1)))) ((ord_less_eq_o_o R_1) S_1)))
% FOF formula (forall (R_1:(product_unit->Prop)) (S_1:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o (fun (X_1:product_unit)=> ((member_Product_unit X_1) R_1))) (fun (X_1:product_unit)=> ((member_Product_unit X_1) S_1)))) ((ord_le1511552390unit_o R_1) S_1))) of role axiom named fact_494_pred__subset__eq
% A new axiom: (forall (R_1:(product_unit->Prop)) (S_1:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o (fun (X_1:product_unit)=> ((member_Product_unit X_1) R_1))) (fun (X_1:product_unit)=> ((member_Product_unit X_1) S_1)))) ((ord_le1511552390unit_o R_1) S_1)))
% FOF formula (forall (R_1:(arrow_1429601828e_indi->Prop)) (S_1:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o (fun (X_1:arrow_1429601828e_indi)=> ((member2052026769e_indi X_1) R_1))) (fun (X_1:arrow_1429601828e_indi)=> ((member2052026769e_indi X_1) S_1)))) ((ord_le1799070453indi_o R_1) S_1))) of role axiom named fact_495_pred__subset__eq
% A new axiom: (forall (R_1:(arrow_1429601828e_indi->Prop)) (S_1:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o (fun (X_1:arrow_1429601828e_indi)=> ((member2052026769e_indi X_1) R_1))) (fun (X_1:arrow_1429601828e_indi)=> ((member2052026769e_indi X_1) S_1)))) ((ord_le1799070453indi_o R_1) S_1)))
% FOF formula (forall (R_1:(nat->Prop)) (S_1:(nat->Prop)), ((iff ((ord_less_eq_nat_o (fun (X_1:nat)=> ((member_nat X_1) R_1))) (fun (X_1:nat)=> ((member_nat X_1) S_1)))) ((ord_less_eq_nat_o R_1) S_1))) of role axiom named fact_496_pred__subset__eq
% A new axiom: (forall (R_1:(nat->Prop)) (S_1:(nat->Prop)), ((iff ((ord_less_eq_nat_o (fun (X_1:nat)=> ((member_nat X_1) R_1))) (fun (X_1:nat)=> ((member_nat X_1) S_1)))) ((ord_less_eq_nat_o R_1) S_1)))
% FOF formula (forall (R_1:((produc1501160679le_alt->Prop)->Prop)) (S_1:((produc1501160679le_alt->Prop)->Prop)), ((iff ((ord_le1063113995lt_o_o (fun (X_1:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o X_1) R_1))) (fun (X_1:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o X_1) S_1)))) ((ord_le1063113995lt_o_o R_1) S_1))) of role axiom named fact_497_pred__subset__eq
% A new axiom: (forall (R_1:((produc1501160679le_alt->Prop)->Prop)) (S_1:((produc1501160679le_alt->Prop)->Prop)), ((iff ((ord_le1063113995lt_o_o (fun (X_1:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o X_1) R_1))) (fun (X_1:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o X_1) S_1)))) ((ord_le1063113995lt_o_o R_1) S_1)))
% FOF formula (forall (R_1:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (S_1:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le134800455lt_o_o (fun (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> ((member616898751_alt_o X_1) R_1))) (fun (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> ((member616898751_alt_o X_1) S_1)))) ((ord_le134800455lt_o_o R_1) S_1))) of role axiom named fact_498_pred__subset__eq
% A new axiom: (forall (R_1:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (S_1:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le134800455lt_o_o (fun (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> ((member616898751_alt_o X_1) R_1))) (fun (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> ((member616898751_alt_o X_1) S_1)))) ((ord_le134800455lt_o_o R_1) S_1)))
% FOF formula (forall (R_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (S_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le1992928527lt_o_o (fun (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> ((member526088951_alt_o X_1) R_1))) (fun (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> ((member526088951_alt_o X_1) S_1)))) ((ord_le1992928527lt_o_o R_1) S_1))) of role axiom named fact_499_pred__subset__eq
% A new axiom: (forall (R_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (S_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le1992928527lt_o_o (fun (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> ((member526088951_alt_o X_1) R_1))) (fun (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> ((member526088951_alt_o X_1) S_1)))) ((ord_le1992928527lt_o_o R_1) S_1)))
% FOF formula (forall (R_1:(produc1501160679le_alt->Prop)) (S_1:(produc1501160679le_alt->Prop)), ((iff ((ord_le97612146_alt_o (fun (X_1:produc1501160679le_alt)=> ((member214075476le_alt X_1) R_1))) (fun (X_1:produc1501160679le_alt)=> ((member214075476le_alt X_1) S_1)))) ((ord_le97612146_alt_o R_1) S_1))) of role axiom named fact_500_pred__subset__eq
% A new axiom: (forall (R_1:(produc1501160679le_alt->Prop)) (S_1:(produc1501160679le_alt->Prop)), ((iff ((ord_le97612146_alt_o (fun (X_1:produc1501160679le_alt)=> ((member214075476le_alt X_1) R_1))) (fun (X_1:produc1501160679le_alt)=> ((member214075476le_alt X_1) S_1)))) ((ord_le97612146_alt_o R_1) S_1)))
% FOF formula (forall (B_9:(produc1501160679le_alt->(Prop->Prop))) (C_2:(produc1501160679le_alt->(Prop->Prop))) (A_13:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_13)->((ord_less_eq_o_o (B_9 X_1)) (C_2 X_1))))->((ord_le1063113995lt_o_o ((pi_Pro1701359055_alt_o A_13) B_9)) ((pi_Pro1701359055_alt_o A_13) C_2)))) of role axiom named fact_501_Pi__mono
% A new axiom: (forall (B_9:(produc1501160679le_alt->(Prop->Prop))) (C_2:(produc1501160679le_alt->(Prop->Prop))) (A_13:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_13)->((ord_less_eq_o_o (B_9 X_1)) (C_2 X_1))))->((ord_le1063113995lt_o_o ((pi_Pro1701359055_alt_o A_13) B_9)) ((pi_Pro1701359055_alt_o A_13) C_2))))
% FOF formula (forall (B_9:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (C_2:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_13:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_13)->((ord_le1063113995lt_o_o (B_9 X_1)) (C_2 X_1))))->((ord_le1992928527lt_o_o ((pi_Arr1929480907_alt_o A_13) B_9)) ((pi_Arr1929480907_alt_o A_13) C_2)))) of role axiom named fact_502_Pi__mono
% A new axiom: (forall (B_9:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (C_2:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_13:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_13)->((ord_le1063113995lt_o_o (B_9 X_1)) (C_2 X_1))))->((ord_le1992928527lt_o_o ((pi_Arr1929480907_alt_o A_13) B_9)) ((pi_Arr1929480907_alt_o A_13) C_2))))
% FOF formula (forall (B_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (C_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_13)->((ord_le1063113995lt_o_o (B_9 X_1)) (C_2 X_1))))->((ord_le134800455lt_o_o ((pi_Arr1304755663_alt_o A_13) B_9)) ((pi_Arr1304755663_alt_o A_13) C_2)))) of role axiom named fact_503_Pi__mono
% A new axiom: (forall (B_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (C_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_13)->((ord_le1063113995lt_o_o (B_9 X_1)) (C_2 X_1))))->((ord_le134800455lt_o_o ((pi_Arr1304755663_alt_o A_13) B_9)) ((pi_Arr1304755663_alt_o A_13) C_2))))
% FOF formula (forall (B_8:(Prop->Prop)) (A_12:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_12)->((member_o X_1) B_8)))->((ord_less_eq_o_o A_12) B_8))) of role axiom named fact_504_subsetI
% A new axiom: (forall (B_8:(Prop->Prop)) (A_12:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_12)->((member_o X_1) B_8)))->((ord_less_eq_o_o A_12) B_8)))
% FOF formula (forall (B_8:(product_unit->Prop)) (A_12:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_12)->((member_Product_unit X_1) B_8)))->((ord_le1511552390unit_o A_12) B_8))) of role axiom named fact_505_subsetI
% A new axiom: (forall (B_8:(product_unit->Prop)) (A_12:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_12)->((member_Product_unit X_1) B_8)))->((ord_le1511552390unit_o A_12) B_8)))
% FOF formula (forall (B_8:(arrow_1429601828e_indi->Prop)) (A_12:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_12)->((member2052026769e_indi X_1) B_8)))->((ord_le1799070453indi_o A_12) B_8))) of role axiom named fact_506_subsetI
% A new axiom: (forall (B_8:(arrow_1429601828e_indi->Prop)) (A_12:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_12)->((member2052026769e_indi X_1) B_8)))->((ord_le1799070453indi_o A_12) B_8)))
% FOF formula (forall (B_8:(nat->Prop)) (A_12:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_12)->((member_nat X_1) B_8)))->((ord_less_eq_nat_o A_12) B_8))) of role axiom named fact_507_subsetI
% A new axiom: (forall (B_8:(nat->Prop)) (A_12:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_12)->((member_nat X_1) B_8)))->((ord_less_eq_nat_o A_12) B_8)))
% FOF formula (forall (B_8:((produc1501160679le_alt->Prop)->Prop)) (A_12:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_1) A_12)->((member377231867_alt_o X_1) B_8)))->((ord_le1063113995lt_o_o A_12) B_8))) of role axiom named fact_508_subsetI
% A new axiom: (forall (B_8:((produc1501160679le_alt->Prop)->Prop)) (A_12:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_1) A_12)->((member377231867_alt_o X_1) B_8)))->((ord_le1063113995lt_o_o A_12) B_8)))
% FOF formula (forall (B_8:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_1) A_12)->((member616898751_alt_o X_1) B_8)))->((ord_le134800455lt_o_o A_12) B_8))) of role axiom named fact_509_subsetI
% A new axiom: (forall (B_8:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_1) A_12)->((member616898751_alt_o X_1) B_8)))->((ord_le134800455lt_o_o A_12) B_8)))
% FOF formula (forall (B_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_12)->((member526088951_alt_o X_1) B_8)))->((ord_le1992928527lt_o_o A_12) B_8))) of role axiom named fact_510_subsetI
% A new axiom: (forall (B_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_12)->((member526088951_alt_o X_1) B_8)))->((ord_le1992928527lt_o_o A_12) B_8)))
% FOF formula (forall (B_8:(produc1501160679le_alt->Prop)) (A_12:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_12)->((member214075476le_alt X_1) B_8)))->((ord_le97612146_alt_o A_12) B_8))) of role axiom named fact_511_subsetI
% A new axiom: (forall (B_8:(produc1501160679le_alt->Prop)) (A_12:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_12)->((member214075476le_alt X_1) B_8)))->((ord_le97612146_alt_o A_12) B_8)))
% FOF formula (forall (C_1:Prop) (A_11:(Prop->Prop)) (B_7:(Prop->Prop)), (((ord_less_o_o A_11) B_7)->(((member_o C_1) A_11)->((member_o C_1) B_7)))) of role axiom named fact_512_psubsetD
% A new axiom: (forall (C_1:Prop) (A_11:(Prop->Prop)) (B_7:(Prop->Prop)), (((ord_less_o_o A_11) B_7)->(((member_o C_1) A_11)->((member_o C_1) B_7))))
% FOF formula (forall (C_1:product_unit) (A_11:(product_unit->Prop)) (B_7:(product_unit->Prop)), (((ord_le232288914unit_o A_11) B_7)->(((member_Product_unit C_1) A_11)->((member_Product_unit C_1) B_7)))) of role axiom named fact_513_psubsetD
% A new axiom: (forall (C_1:product_unit) (A_11:(product_unit->Prop)) (B_7:(product_unit->Prop)), (((ord_le232288914unit_o A_11) B_7)->(((member_Product_unit C_1) A_11)->((member_Product_unit C_1) B_7))))
% FOF formula (forall (C_1:arrow_1429601828e_indi) (A_11:(arrow_1429601828e_indi->Prop)) (B_7:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_11) B_7)->(((member2052026769e_indi C_1) A_11)->((member2052026769e_indi C_1) B_7)))) of role axiom named fact_514_psubsetD
% A new axiom: (forall (C_1:arrow_1429601828e_indi) (A_11:(arrow_1429601828e_indi->Prop)) (B_7:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_11) B_7)->(((member2052026769e_indi C_1) A_11)->((member2052026769e_indi C_1) B_7))))
% FOF formula (forall (C_1:nat) (A_11:(nat->Prop)) (B_7:(nat->Prop)), (((ord_less_nat_o A_11) B_7)->(((member_nat C_1) A_11)->((member_nat C_1) B_7)))) of role axiom named fact_515_psubsetD
% A new axiom: (forall (C_1:nat) (A_11:(nat->Prop)) (B_7:(nat->Prop)), (((ord_less_nat_o A_11) B_7)->(((member_nat C_1) A_11)->((member_nat C_1) B_7))))
% FOF formula (forall (C_1:(produc1501160679le_alt->Prop)) (A_11:((produc1501160679le_alt->Prop)->Prop)) (B_7:((produc1501160679le_alt->Prop)->Prop)), (((ord_le910298367lt_o_o A_11) B_7)->(((member377231867_alt_o C_1) A_11)->((member377231867_alt_o C_1) B_7)))) of role axiom named fact_516_psubsetD
% A new axiom: (forall (C_1:(produc1501160679le_alt->Prop)) (A_11:((produc1501160679le_alt->Prop)->Prop)) (B_7:((produc1501160679le_alt->Prop)->Prop)), (((ord_le910298367lt_o_o A_11) B_7)->(((member377231867_alt_o C_1) A_11)->((member377231867_alt_o C_1) B_7))))
% FOF formula (forall (C_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_7:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1859604819lt_o_o A_11) B_7)->(((member616898751_alt_o C_1) A_11)->((member616898751_alt_o C_1) B_7)))) of role axiom named fact_517_psubsetD
% A new axiom: (forall (C_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_7:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1859604819lt_o_o A_11) B_7)->(((member616898751_alt_o C_1) A_11)->((member616898751_alt_o C_1) B_7))))
% FOF formula (forall (C_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le157835011lt_o_o A_11) B_7)->(((member526088951_alt_o C_1) A_11)->((member526088951_alt_o C_1) B_7)))) of role axiom named fact_518_psubsetD
% A new axiom: (forall (C_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le157835011lt_o_o A_11) B_7)->(((member526088951_alt_o C_1) A_11)->((member526088951_alt_o C_1) B_7))))
% FOF formula (forall (C_1:produc1501160679le_alt) (A_11:(produc1501160679le_alt->Prop)) (B_7:(produc1501160679le_alt->Prop)), (((ord_le988258430_alt_o A_11) B_7)->(((member214075476le_alt C_1) A_11)->((member214075476le_alt C_1) B_7)))) of role axiom named fact_519_psubsetD
% A new axiom: (forall (C_1:produc1501160679le_alt) (A_11:(produc1501160679le_alt->Prop)) (B_7:(produc1501160679le_alt->Prop)), (((ord_le988258430_alt_o A_11) B_7)->(((member214075476le_alt C_1) A_11)->((member214075476le_alt C_1) B_7))))
% FOF formula (forall (C:(nat->Prop)) (A_10:(nat->Prop)) (B_6:(nat->Prop)), (((ord_less_nat_o A_10) B_6)->(((ord_less_nat_o B_6) C)->((ord_less_nat_o A_10) C)))) of role axiom named fact_520_psubset__trans
% A new axiom: (forall (C:(nat->Prop)) (A_10:(nat->Prop)) (B_6:(nat->Prop)), (((ord_less_nat_o A_10) B_6)->(((ord_less_nat_o B_6) C)->((ord_less_nat_o A_10) C))))
% FOF formula (forall (C:(product_unit->Prop)) (A_10:(product_unit->Prop)) (B_6:(product_unit->Prop)), (((ord_le232288914unit_o A_10) B_6)->(((ord_le232288914unit_o B_6) C)->((ord_le232288914unit_o A_10) C)))) of role axiom named fact_521_psubset__trans
% A new axiom: (forall (C:(product_unit->Prop)) (A_10:(product_unit->Prop)) (B_6:(product_unit->Prop)), (((ord_le232288914unit_o A_10) B_6)->(((ord_le232288914unit_o B_6) C)->((ord_le232288914unit_o A_10) C))))
% FOF formula (forall (C:(arrow_1429601828e_indi->Prop)) (A_10:(arrow_1429601828e_indi->Prop)) (B_6:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_10) B_6)->(((ord_le777687553indi_o B_6) C)->((ord_le777687553indi_o A_10) C)))) of role axiom named fact_522_psubset__trans
% A new axiom: (forall (C:(arrow_1429601828e_indi->Prop)) (A_10:(arrow_1429601828e_indi->Prop)) (B_6:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_10) B_6)->(((ord_le777687553indi_o B_6) C)->((ord_le777687553indi_o A_10) C))))
% FOF formula (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_9) B_5))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_2098199487_below L_2) A_9) B_5))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) Y) A_9)->((member214075476le_alt ((produc1347929815le_alt X) B_5)) L_2)))) ((not (((eq arrow_475358991le_alt) Y) A_9))->((and ((((eq arrow_475358991le_alt) X) A_9)->((or (((eq arrow_475358991le_alt) Y) B_5)) ((member214075476le_alt ((produc1347929815le_alt B_5) Y)) L_2)))) ((not (((eq arrow_475358991le_alt) X) A_9))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2))))))))) of role axiom named fact_523_in__below
% A new axiom: (forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_9) B_5))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_2098199487_below L_2) A_9) B_5))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) Y) A_9)->((member214075476le_alt ((produc1347929815le_alt X) B_5)) L_2)))) ((not (((eq arrow_475358991le_alt) Y) A_9))->((and ((((eq arrow_475358991le_alt) X) A_9)->((or (((eq arrow_475358991le_alt) Y) B_5)) ((member214075476le_alt ((produc1347929815le_alt B_5) Y)) L_2)))) ((not (((eq arrow_475358991le_alt) X) A_9))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2)))))))))
% FOF formula (forall (M_2:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M_2) K)) N)->((((ord_less_eq_nat M_2) N)->(((ord_less_eq_nat K) N)->False))->False))) of role axiom named fact_524_add__leE
% A new axiom: (forall (M_2:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M_2) K)) N)->((((ord_less_eq_nat M_2) N)->(((ord_less_eq_nat K) N)->False))->False)))
% FOF formula (forall (M_2:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M_2) K)) N)->((ord_less_eq_nat M_2) N))) of role axiom named fact_525_add__leD1
% A new axiom: (forall (M_2:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M_2) K)) N)->((ord_less_eq_nat M_2) N)))
% FOF formula (forall (M_2:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M_2) K)) N)->((ord_less_eq_nat K) N))) of role axiom named fact_526_add__leD2
% A new axiom: (forall (M_2:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M_2) K)) N)->((ord_less_eq_nat K) N)))
% FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_527_less__not__refl
% A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% FOF formula (forall (M_2:nat) (N:nat), ((iff (not (((eq nat) M_2) N))) ((or ((ord_less_nat M_2) N)) ((ord_less_nat N) M_2)))) of role axiom named fact_528_nat__neq__iff
% A new axiom: (forall (M_2:nat) (N:nat), ((iff (not (((eq nat) M_2) N))) ((or ((ord_less_nat M_2) N)) ((ord_less_nat N) M_2))))
% FOF formula (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))) of role axiom named fact_529_linorder__neqE__nat
% A new axiom: (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X))))
% FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_530_less__irrefl__nat
% A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% FOF formula (forall (N:nat) (M_2:nat), (((ord_less_nat N) M_2)->(not (((eq nat) M_2) N)))) of role axiom named fact_531_less__not__refl2
% A new axiom: (forall (N:nat) (M_2:nat), (((ord_less_nat N) M_2)->(not (((eq nat) M_2) N))))
% FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_532_less__not__refl3
% A new axiom: (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T))))
% FOF formula (forall (P:(nat->(nat->Prop))) (M_2:nat) (N:nat), ((((ord_less_nat M_2) N)->((P N) M_2))->(((((eq nat) M_2) N)->((P N) M_2))->((((ord_less_nat N) M_2)->((P N) M_2))->((P N) M_2))))) of role axiom named fact_533_nat__less__cases
% A new axiom: (forall (P:(nat->(nat->Prop))) (M_2:nat) (N:nat), ((((ord_less_nat M_2) N)->((P N) M_2))->(((((eq nat) M_2) N)->((P N) M_2))->((((ord_less_nat N) M_2)->((P N) M_2))->((P N) M_2)))))
% FOF formula (forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat M_2) N)) ((plus_plus_nat N) M_2))) of role axiom named fact_534_nat__add__commute
% A new axiom: (forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat M_2) N)) ((plus_plus_nat N) M_2)))
% FOF formula (forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z)))) of role axiom named fact_535_nat__add__left__commute
% A new axiom: (forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z))))
% FOF formula (forall (M_2:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M_2) N)) K)) ((plus_plus_nat M_2) ((plus_plus_nat N) K)))) of role axiom named fact_536_nat__add__assoc
% A new axiom: (forall (M_2:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M_2) N)) K)) ((plus_plus_nat M_2) ((plus_plus_nat N) K))))
% FOF formula (forall (K:nat) (M_2:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M_2)) ((plus_plus_nat K) N))) (((eq nat) M_2) N))) of role axiom named fact_537_nat__add__left__cancel
% A new axiom: (forall (K:nat) (M_2:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M_2)) ((plus_plus_nat K) N))) (((eq nat) M_2) N)))
% FOF formula (forall (M_2:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M_2) K)) ((plus_plus_nat N) K))) (((eq nat) M_2) N))) of role axiom named fact_538_nat__add__right__cancel
% A new axiom: (forall (M_2:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M_2) K)) ((plus_plus_nat N) K))) (((eq nat) M_2) N)))
% FOF formula (forall (N:nat), ((ord_less_eq_nat N) N)) of role axiom named fact_539_le__refl
% A new axiom: (forall (N:nat), ((ord_less_eq_nat N) N))
% FOF formula (forall (M_2:nat) (N:nat), ((or ((ord_less_eq_nat M_2) N)) ((ord_less_eq_nat N) M_2))) of role axiom named fact_540_nat__le__linear
% A new axiom: (forall (M_2:nat) (N:nat), ((or ((ord_less_eq_nat M_2) N)) ((ord_less_eq_nat N) M_2)))
% FOF formula (forall (M_2:nat) (N:nat), ((((eq nat) M_2) N)->((ord_less_eq_nat M_2) N))) of role axiom named fact_541_eq__imp__le
% A new axiom: (forall (M_2:nat) (N:nat), ((((eq nat) M_2) N)->((ord_less_eq_nat M_2) N)))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->(((ord_less_eq_nat J_1) K)->((ord_less_eq_nat _TPTP_I) K)))) of role axiom named fact_542_le__trans
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->(((ord_less_eq_nat J_1) K)->((ord_less_eq_nat _TPTP_I) K))))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->(((ord_less_eq_nat N) M_2)->(((eq nat) M_2) N)))) of role axiom named fact_543_le__antisym
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->(((ord_less_eq_nat N) M_2)->(((eq nat) M_2) N))))
% FOF formula (forall (L_2:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_2098199487_below L_2) X) Y)) arrow_823908191le_Lin)))) of role axiom named fact_544_below__Lin
% A new axiom: (forall (L_2:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_2098199487_below L_2) X) Y)) arrow_823908191le_Lin))))
% FOF formula (forall (K:nat) (N_2:(nat->Prop)), ((inj_on_nat_nat (fun (N_1:nat)=> ((plus_plus_nat N_1) K))) N_2)) of role axiom named fact_545_inj__on__add__nat
% A new axiom: (forall (K:nat) (N_2:(nat->Prop)), ((inj_on_nat_nat (fun (N_1:nat)=> ((plus_plus_nat N_1) K))) N_2))
% FOF formula (forall (_TPTP_I:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J_1)) _TPTP_I)->False)) of role axiom named fact_546_not__add__less1
% A new axiom: (forall (_TPTP_I:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J_1)) _TPTP_I)->False))
% FOF formula (forall (J_1:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J_1) _TPTP_I)) _TPTP_I)->False)) of role axiom named fact_547_not__add__less2
% A new axiom: (forall (J_1:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J_1) _TPTP_I)) _TPTP_I)->False))
% FOF formula (forall (K:nat) (M_2:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M_2)) ((plus_plus_nat K) N))) ((ord_less_nat M_2) N))) of role axiom named fact_548_nat__add__left__cancel__less
% A new axiom: (forall (K:nat) (M_2:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M_2)) ((plus_plus_nat K) N))) ((ord_less_nat M_2) N)))
% FOF formula (forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat _TPTP_I) ((plus_plus_nat J_1) M_2)))) of role axiom named fact_549_trans__less__add1
% A new axiom: (forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat _TPTP_I) ((plus_plus_nat J_1) M_2))))
% FOF formula (forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat _TPTP_I) ((plus_plus_nat M_2) J_1)))) of role axiom named fact_550_trans__less__add2
% A new axiom: (forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat _TPTP_I) ((plus_plus_nat M_2) J_1))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) K)))) of role axiom named fact_551_add__less__mono1
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) K))))
% FOF formula (forall (K:nat) (L:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) L))))) of role axiom named fact_552_add__less__mono
% A new axiom: (forall (K:nat) (L:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) L)))))
% FOF formula (forall (M_2:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M_2) L)) ((plus_plus_nat K) N))->((ord_less_nat M_2) N)))) of role axiom named fact_553_less__add__eq__less
% A new axiom: (forall (M_2:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M_2) L)) ((plus_plus_nat K) N))->((ord_less_nat M_2) N))))
% FOF formula (forall (_TPTP_I:nat) (J_1:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J_1)) K)->((ord_less_nat _TPTP_I) K))) of role axiom named fact_554_add__lessD1
% A new axiom: (forall (_TPTP_I:nat) (J_1:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J_1)) K)->((ord_less_nat _TPTP_I) K)))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) N)) ((and ((ord_less_eq_nat M_2) N)) (not (((eq nat) M_2) N))))) of role axiom named fact_555_nat__less__le
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) N)) ((and ((ord_less_eq_nat M_2) N)) (not (((eq nat) M_2) N)))))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat M_2) N)) ((or ((ord_less_nat M_2) N)) (((eq nat) M_2) N)))) of role axiom named fact_556_le__eq__less__or__eq
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat M_2) N)) ((or ((ord_less_nat M_2) N)) (((eq nat) M_2) N))))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_eq_nat M_2) N))) of role axiom named fact_557_less__imp__le__nat
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_eq_nat M_2) N)))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((not (((eq nat) M_2) N))->((ord_less_nat M_2) N)))) of role axiom named fact_558_le__neq__implies__less
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((not (((eq nat) M_2) N))->((ord_less_nat M_2) N))))
% FOF formula (forall (M_2:nat) (N:nat), (((or ((ord_less_nat M_2) N)) (((eq nat) M_2) N))->((ord_less_eq_nat M_2) N))) of role axiom named fact_559_less__or__eq__imp__le
% A new axiom: (forall (M_2:nat) (N:nat), (((or ((ord_less_nat M_2) N)) (((eq nat) M_2) N))->((ord_less_eq_nat M_2) N)))
% FOF formula (forall (N:nat) (M_2:nat), ((ord_less_eq_nat N) ((plus_plus_nat M_2) N))) of role axiom named fact_560_le__add2
% A new axiom: (forall (N:nat) (M_2:nat), ((ord_less_eq_nat N) ((plus_plus_nat M_2) N)))
% FOF formula (forall (N:nat) (M_2:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M_2))) of role axiom named fact_561_le__add1
% A new axiom: (forall (N:nat) (M_2:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M_2)))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat M_2) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M_2) K_1)))))) of role axiom named fact_562_le__iff__add
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat M_2) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M_2) K_1))))))
% FOF formula (forall (K:nat) (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M_2)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M_2) N))) of role axiom named fact_563_nat__add__left__cancel__le
% A new axiom: (forall (K:nat) (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M_2)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M_2) N)))
% FOF formula (forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J_1) M_2)))) of role axiom named fact_564_trans__le__add1
% A new axiom: (forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J_1) M_2))))
% FOF formula (forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M_2) J_1)))) of role axiom named fact_565_trans__le__add2
% A new axiom: (forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M_2) J_1))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) K)))) of role axiom named fact_566_add__le__mono1
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) K))))
% FOF formula (forall (K:nat) (L:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) L))))) of role axiom named fact_567_add__le__mono
% A new axiom: (forall (K:nat) (L:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) L)))))
% FOF formula (forall (M_2:nat) (K:nat) (F:(nat->nat)), ((forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_nat (F M)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M_2)) K)) (F ((plus_plus_nat M_2) K))))) of role axiom named fact_568_mono__nat__linear__lb
% A new axiom: (forall (M_2:nat) (K:nat) (F:(nat->nat)), ((forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_nat (F M)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M_2)) K)) (F ((plus_plus_nat M_2) K)))))
% FOF formula (forall (_TPTP_I:nat) (J_1:nat) (F:(nat->nat)), ((forall (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat (F I_1)) (F J))))->(((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat (F _TPTP_I)) (F J_1))))) of role axiom named fact_569_less__mono__imp__le__mono
% A new axiom: (forall (_TPTP_I:nat) (J_1:nat) (F:(nat->nat)), ((forall (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat (F I_1)) (F J))))->(((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat (F _TPTP_I)) (F J_1)))))
% FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z)))) of role axiom named fact_570_termination__basic__simps_I3_J
% A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z))))
% FOF formula (forall (Y:nat) (X:nat) (Z:nat), (((ord_less_eq_nat X) Z)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z)))) of role axiom named fact_571_termination__basic__simps_I4_J
% A new axiom: (forall (Y:nat) (X:nat) (Z:nat), (((ord_less_eq_nat X) Z)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z))))
% FOF formula (forall (Y:nat) (X:nat) (Z:nat), (((ord_less_nat X) Z)->((ord_less_nat X) ((plus_plus_nat Y) Z)))) of role axiom named fact_572_termination__basic__simps_I2_J
% A new axiom: (forall (Y:nat) (X:nat) (Z:nat), (((ord_less_nat X) Z)->((ord_less_nat X) ((plus_plus_nat Y) Z))))
% FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_nat X) ((plus_plus_nat Y) Z)))) of role axiom named fact_573_termination__basic__simps_I1_J
% A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_nat X) ((plus_plus_nat Y) Z))))
% FOF formula (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y))) of role axiom named fact_574_termination__basic__simps_I5_J
% A new axiom: (forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y)))
% FOF formula (forall (R:(produc1501160679le_alt->Prop)) (X_2:arrow_475358991le_alt) (Y_2:arrow_475358991le_alt), ((iff (((in_rel1252994498le_alt R) X_2) Y_2)) ((member214075476le_alt ((produc1347929815le_alt X_2) Y_2)) R))) of role axiom named fact_575_in__rel__def
% A new axiom: (forall (R:(produc1501160679le_alt->Prop)) (X_2:arrow_475358991le_alt) (Y_2:arrow_475358991le_alt), ((iff (((in_rel1252994498le_alt R) X_2) Y_2)) ((member214075476le_alt ((produc1347929815le_alt X_2) Y_2)) R)))
% FOF formula (forall (F_7:(produc1501160679le_alt->Prop)) (B_4:(Prop->Prop)) (A_8:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_8)->((member_o (F_7 X_1)) B_4)))->((member377231867_alt_o F_7) ((pi_Pro1701359055_alt_o A_8) (fun (Uu:produc1501160679le_alt)=> B_4))))) of role axiom named fact_576_funcsetI
% A new axiom: (forall (F_7:(produc1501160679le_alt->Prop)) (B_4:(Prop->Prop)) (A_8:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_8)->((member_o (F_7 X_1)) B_4)))->((member377231867_alt_o F_7) ((pi_Pro1701359055_alt_o A_8) (fun (Uu:produc1501160679le_alt)=> B_4)))))
% FOF formula (forall (F_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_4:((produc1501160679le_alt->Prop)->Prop)) (A_8:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_8)->((member377231867_alt_o (F_7 X_1)) B_4)))->((member526088951_alt_o F_7) ((pi_Arr1929480907_alt_o A_8) (fun (Uu:arrow_1429601828e_indi)=> B_4))))) of role axiom named fact_577_funcsetI
% A new axiom: (forall (F_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_4:((produc1501160679le_alt->Prop)->Prop)) (A_8:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_8)->((member377231867_alt_o (F_7 X_1)) B_4)))->((member526088951_alt_o F_7) ((pi_Arr1929480907_alt_o A_8) (fun (Uu:arrow_1429601828e_indi)=> B_4)))))
% FOF formula (forall (F_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_4:((produc1501160679le_alt->Prop)->Prop)) (A_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_8)->((member377231867_alt_o (F_7 X_1)) B_4)))->((member616898751_alt_o F_7) ((pi_Arr1304755663_alt_o A_8) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_4))))) of role axiom named fact_578_funcsetI
% A new axiom: (forall (F_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_4:((produc1501160679le_alt->Prop)->Prop)) (A_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_8)->((member377231867_alt_o (F_7 X_1)) B_4)))->((member616898751_alt_o F_7) ((pi_Arr1304755663_alt_o A_8) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_4)))))
% FOF formula ((ex (produc1501160679le_alt->Prop)) (fun (L_1:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o L_1) arrow_823908191le_Lin))) of role axiom named fact_579_linear__alt
% A new axiom: ((ex (produc1501160679le_alt->Prop)) (fun (L_1:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o L_1) arrow_823908191le_Lin)))
% FOF formula (forall (B_3:(produc1501160679le_alt->(Prop->Prop))) (G_2:(produc1501160679le_alt->Prop)) (F_6:(produc1501160679le_alt->Prop)) (A_7:(produc1501160679le_alt->Prop)), ((forall (W:produc1501160679le_alt), (((member214075476le_alt W) A_7)->((iff (F_6 W)) (G_2 W))))->((iff ((member377231867_alt_o F_6) ((pi_Pro1701359055_alt_o A_7) B_3))) ((member377231867_alt_o G_2) ((pi_Pro1701359055_alt_o A_7) B_3))))) of role axiom named fact_580_Pi__cong
% A new axiom: (forall (B_3:(produc1501160679le_alt->(Prop->Prop))) (G_2:(produc1501160679le_alt->Prop)) (F_6:(produc1501160679le_alt->Prop)) (A_7:(produc1501160679le_alt->Prop)), ((forall (W:produc1501160679le_alt), (((member214075476le_alt W) A_7)->((iff (F_6 W)) (G_2 W))))->((iff ((member377231867_alt_o F_6) ((pi_Pro1701359055_alt_o A_7) B_3))) ((member377231867_alt_o G_2) ((pi_Pro1701359055_alt_o A_7) B_3)))))
% FOF formula (forall (B_3:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (F_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (G_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_7:(arrow_1429601828e_indi->Prop)), ((forall (W:arrow_1429601828e_indi), (((member2052026769e_indi W) A_7)->(((eq (produc1501160679le_alt->Prop)) (F_6 W)) (G_2 W))))->((iff ((member526088951_alt_o F_6) ((pi_Arr1929480907_alt_o A_7) B_3))) ((member526088951_alt_o G_2) ((pi_Arr1929480907_alt_o A_7) B_3))))) of role axiom named fact_581_Pi__cong
% A new axiom: (forall (B_3:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (F_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (G_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_7:(arrow_1429601828e_indi->Prop)), ((forall (W:arrow_1429601828e_indi), (((member2052026769e_indi W) A_7)->(((eq (produc1501160679le_alt->Prop)) (F_6 W)) (G_2 W))))->((iff ((member526088951_alt_o F_6) ((pi_Arr1929480907_alt_o A_7) B_3))) ((member526088951_alt_o G_2) ((pi_Arr1929480907_alt_o A_7) B_3)))))
% FOF formula (forall (B_3:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (F_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (G_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (W:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o W) A_7)->(((eq (produc1501160679le_alt->Prop)) (F_6 W)) (G_2 W))))->((iff ((member616898751_alt_o F_6) ((pi_Arr1304755663_alt_o A_7) B_3))) ((member616898751_alt_o G_2) ((pi_Arr1304755663_alt_o A_7) B_3))))) of role axiom named fact_582_Pi__cong
% A new axiom: (forall (B_3:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (F_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (G_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (W:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o W) A_7)->(((eq (produc1501160679le_alt->Prop)) (F_6 W)) (G_2 W))))->((iff ((member616898751_alt_o F_6) ((pi_Arr1304755663_alt_o A_7) B_3))) ((member616898751_alt_o G_2) ((pi_Arr1304755663_alt_o A_7) B_3)))))
% FOF formula (forall (F_5:(produc1501160679le_alt->Prop)) (B_2:(produc1501160679le_alt->(Prop->Prop))) (A_6:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_6)->((member_o (F_5 X_1)) (B_2 X_1))))->((member377231867_alt_o F_5) ((pi_Pro1701359055_alt_o A_6) B_2)))) of role axiom named fact_583_Pi__I_H
% A new axiom: (forall (F_5:(produc1501160679le_alt->Prop)) (B_2:(produc1501160679le_alt->(Prop->Prop))) (A_6:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_6)->((member_o (F_5 X_1)) (B_2 X_1))))->((member377231867_alt_o F_5) ((pi_Pro1701359055_alt_o A_6) B_2))))
% FOF formula (forall (F_5:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_2:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_6:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_6)->((member377231867_alt_o (F_5 X_1)) (B_2 X_1))))->((member526088951_alt_o F_5) ((pi_Arr1929480907_alt_o A_6) B_2)))) of role axiom named fact_584_Pi__I_H
% A new axiom: (forall (F_5:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_2:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_6:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_6)->((member377231867_alt_o (F_5 X_1)) (B_2 X_1))))->((member526088951_alt_o F_5) ((pi_Arr1929480907_alt_o A_6) B_2))))
% FOF formula (forall (F_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_6)->((member377231867_alt_o (F_5 X_1)) (B_2 X_1))))->((member616898751_alt_o F_5) ((pi_Arr1304755663_alt_o A_6) B_2)))) of role axiom named fact_585_Pi__I_H
% A new axiom: (forall (F_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_6)->((member377231867_alt_o (F_5 X_1)) (B_2 X_1))))->((member616898751_alt_o F_5) ((pi_Arr1304755663_alt_o A_6) B_2))))
% FOF formula (forall (F_4:(nat->nat)) (A_5:(nat->Prop)) (B_1:(nat->Prop)), (((member_nat_nat F_4) ((pi_nat_nat A_5) (fun (Uu:nat)=> B_1)))->(((inj_on_nat_nat F_4) A_5)->((finite_finite_nat B_1)->((ord_less_eq_nat (finite_card_nat A_5)) (finite_card_nat B_1)))))) of role axiom named fact_586_card__inj
% A new axiom: (forall (F_4:(nat->nat)) (A_5:(nat->Prop)) (B_1:(nat->Prop)), (((member_nat_nat F_4) ((pi_nat_nat A_5) (fun (Uu:nat)=> B_1)))->(((inj_on_nat_nat F_4) A_5)->((finite_finite_nat B_1)->((ord_less_eq_nat (finite_card_nat A_5)) (finite_card_nat B_1))))))
% FOF formula (forall (F_4:(arrow_1429601828e_indi->nat)) (A_5:(arrow_1429601828e_indi->Prop)) (B_1:(nat->Prop)), (((member1315464153di_nat F_4) ((pi_Arr251692973di_nat A_5) (fun (Uu:arrow_1429601828e_indi)=> B_1)))->(((inj_on978774663di_nat F_4) A_5)->((finite_finite_nat B_1)->((ord_less_eq_nat (finite97476818e_indi A_5)) (finite_card_nat B_1)))))) of role axiom named fact_587_card__inj
% A new axiom: (forall (F_4:(arrow_1429601828e_indi->nat)) (A_5:(arrow_1429601828e_indi->Prop)) (B_1:(nat->Prop)), (((member1315464153di_nat F_4) ((pi_Arr251692973di_nat A_5) (fun (Uu:arrow_1429601828e_indi)=> B_1)))->(((inj_on978774663di_nat F_4) A_5)->((finite_finite_nat B_1)->((ord_less_eq_nat (finite97476818e_indi A_5)) (finite_card_nat B_1))))))
% FOF formula (forall (F_4:(produc1501160679le_alt->Prop)) (A_5:(produc1501160679le_alt->Prop)) (B_1:(Prop->Prop)), (((member377231867_alt_o F_4) ((pi_Pro1701359055_alt_o A_5) (fun (Uu:produc1501160679le_alt)=> B_1)))->(((inj_on1911943593_alt_o F_4) A_5)->((finite_finite_o B_1)->((ord_less_eq_nat (finite537683861le_alt A_5)) (finite_card_o B_1)))))) of role axiom named fact_588_card__inj
% A new axiom: (forall (F_4:(produc1501160679le_alt->Prop)) (A_5:(produc1501160679le_alt->Prop)) (B_1:(Prop->Prop)), (((member377231867_alt_o F_4) ((pi_Pro1701359055_alt_o A_5) (fun (Uu:produc1501160679le_alt)=> B_1)))->(((inj_on1911943593_alt_o F_4) A_5)->((finite_finite_o B_1)->((ord_less_eq_nat (finite537683861le_alt A_5)) (finite_card_o B_1))))))
% FOF formula (forall (F_4:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_5:(arrow_1429601828e_indi->Prop)) (B_1:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_4) ((pi_Arr1929480907_alt_o A_5) (fun (Uu:arrow_1429601828e_indi)=> B_1)))->(((inj_on1190919077_alt_o F_4) A_5)->((finite2112685307_alt_o B_1)->((ord_less_eq_nat (finite97476818e_indi A_5)) (finite28306938_alt_o B_1)))))) of role axiom named fact_589_card__inj
% A new axiom: (forall (F_4:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_5:(arrow_1429601828e_indi->Prop)) (B_1:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_4) ((pi_Arr1929480907_alt_o A_5) (fun (Uu:arrow_1429601828e_indi)=> B_1)))->(((inj_on1190919077_alt_o F_4) A_5)->((finite2112685307_alt_o B_1)->((ord_less_eq_nat (finite97476818e_indi A_5)) (finite28306938_alt_o B_1))))))
% FOF formula (forall (F_4:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_1:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_4) ((pi_Arr1304755663_alt_o A_5) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_1)))->(((inj_on1284293749_alt_o F_4) A_5)->((finite2112685307_alt_o B_1)->((ord_less_eq_nat (finite120663670_alt_o A_5)) (finite28306938_alt_o B_1)))))) of role axiom named fact_590_card__inj
% A new axiom: (forall (F_4:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_1:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_4) ((pi_Arr1304755663_alt_o A_5) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_1)))->(((inj_on1284293749_alt_o F_4) A_5)->((finite2112685307_alt_o B_1)->((ord_less_eq_nat (finite120663670_alt_o A_5)) (finite28306938_alt_o B_1))))))
% FOF formula (forall (F_3:(nat->nat)) (A_4:(nat->Prop)), ((forall (X_1:nat) (Y_1:nat), (((member_nat X_1) A_4)->(((member_nat Y_1) A_4)->((((eq nat) (F_3 X_1)) (F_3 Y_1))->(((eq nat) X_1) Y_1)))))->((inj_on_nat_nat F_3) A_4))) of role axiom named fact_591_inj__onI
% A new axiom: (forall (F_3:(nat->nat)) (A_4:(nat->Prop)), ((forall (X_1:nat) (Y_1:nat), (((member_nat X_1) A_4)->(((member_nat Y_1) A_4)->((((eq nat) (F_3 X_1)) (F_3 Y_1))->(((eq nat) X_1) Y_1)))))->((inj_on_nat_nat F_3) A_4)))
% FOF formula (forall (F_3:(arrow_1429601828e_indi->nat)) (A_4:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi) (Y_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_4)->(((member2052026769e_indi Y_1) A_4)->((((eq nat) (F_3 X_1)) (F_3 Y_1))->(((eq arrow_1429601828e_indi) X_1) Y_1)))))->((inj_on978774663di_nat F_3) A_4))) of role axiom named fact_592_inj__onI
% A new axiom: (forall (F_3:(arrow_1429601828e_indi->nat)) (A_4:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi) (Y_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_4)->(((member2052026769e_indi Y_1) A_4)->((((eq nat) (F_3 X_1)) (F_3 Y_1))->(((eq arrow_1429601828e_indi) X_1) Y_1)))))->((inj_on978774663di_nat F_3) A_4)))
% FOF formula (forall (F_2:(nat->nat)) (G_1:(nat->nat)) (A_2:(nat->Prop)), ((forall (A_3:nat), (((member_nat A_3) A_2)->(((eq nat) (F_2 A_3)) (G_1 A_3))))->((iff ((inj_on_nat_nat F_2) A_2)) ((inj_on_nat_nat G_1) A_2)))) of role axiom named fact_593_inj__on__cong
% A new axiom: (forall (F_2:(nat->nat)) (G_1:(nat->nat)) (A_2:(nat->Prop)), ((forall (A_3:nat), (((member_nat A_3) A_2)->(((eq nat) (F_2 A_3)) (G_1 A_3))))->((iff ((inj_on_nat_nat F_2) A_2)) ((inj_on_nat_nat G_1) A_2))))
% FOF formula (forall (F_2:(arrow_1429601828e_indi->nat)) (G_1:(arrow_1429601828e_indi->nat)) (A_2:(arrow_1429601828e_indi->Prop)), ((forall (A_3:arrow_1429601828e_indi), (((member2052026769e_indi A_3) A_2)->(((eq nat) (F_2 A_3)) (G_1 A_3))))->((iff ((inj_on978774663di_nat F_2) A_2)) ((inj_on978774663di_nat G_1) A_2)))) of role axiom named fact_594_inj__on__cong
% A new axiom: (forall (F_2:(arrow_1429601828e_indi->nat)) (G_1:(arrow_1429601828e_indi->nat)) (A_2:(arrow_1429601828e_indi->Prop)), ((forall (A_3:arrow_1429601828e_indi), (((member2052026769e_indi A_3) A_2)->(((eq nat) (F_2 A_3)) (G_1 A_3))))->((iff ((inj_on978774663di_nat F_2) A_2)) ((inj_on978774663di_nat G_1) A_2))))
% FOF formula (finite664979089e_indi top_to988227749indi_o) of role axiom named fact_595_finite__indi
% A new axiom: (finite664979089e_indi top_to988227749indi_o)
% FOF formula (forall (G:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_1:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_1:((produc1501160679le_alt->Prop)->Prop)) (B:(arrow_1429601828e_indi->Prop)), (((member304866663e_indi F_1) ((pi_Pro468373057e_indi A_1) (fun (Uu:(produc1501160679le_alt->Prop))=> B)))->(((inj_on1877294875e_indi F_1) A_1)->(((member526088951_alt_o G) ((pi_Arr1929480907_alt_o B) (fun (Uu:arrow_1429601828e_indi)=> A_1)))->(((inj_on1190919077_alt_o G) B)->((finite2112685307_alt_o A_1)->((finite664979089e_indi B)->(((eq nat) (finite28306938_alt_o A_1)) (finite97476818e_indi B))))))))) of role axiom named fact_596_card__bij
% A new axiom: (forall (G:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_1:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_1:((produc1501160679le_alt->Prop)->Prop)) (B:(arrow_1429601828e_indi->Prop)), (((member304866663e_indi F_1) ((pi_Pro468373057e_indi A_1) (fun (Uu:(produc1501160679le_alt->Prop))=> B)))->(((inj_on1877294875e_indi F_1) A_1)->(((member526088951_alt_o G) ((pi_Arr1929480907_alt_o B) (fun (Uu:arrow_1429601828e_indi)=> A_1)))->(((inj_on1190919077_alt_o G) B)->((finite2112685307_alt_o A_1)->((finite664979089e_indi B)->(((eq nat) (finite28306938_alt_o A_1)) (finite97476818e_indi B)))))))))
% FOF formula (forall (G:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_1:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_1:((produc1501160679le_alt->Prop)->Prop)) (B:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member530241719_alt_o F_1) ((pi_Pro763888199_alt_o A_1) (fun (Uu:(produc1501160679le_alt->Prop))=> B)))->(((inj_on743426285_alt_o F_1) A_1)->(((member616898751_alt_o G) ((pi_Arr1304755663_alt_o B) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> A_1)))->(((inj_on1284293749_alt_o G) B)->((finite2112685307_alt_o A_1)->((finite1956767223_alt_o B)->(((eq nat) (finite28306938_alt_o A_1)) (finite120663670_alt_o B))))))))) of role axiom named fact_597_card__bij
% A new axiom: (forall (G:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_1:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_1:((produc1501160679le_alt->Prop)->Prop)) (B:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member530241719_alt_o F_1) ((pi_Pro763888199_alt_o A_1) (fun (Uu:(produc1501160679le_alt->Prop))=> B)))->(((inj_on743426285_alt_o F_1) A_1)->(((member616898751_alt_o G) ((pi_Arr1304755663_alt_o B) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> A_1)))->(((inj_on1284293749_alt_o G) B)->((finite2112685307_alt_o A_1)->((finite1956767223_alt_o B)->(((eq nat) (finite28306938_alt_o A_1)) (finite120663670_alt_o B)))))))))
% FOF formula (forall (G:(Prop->produc1501160679le_alt)) (F_1:(produc1501160679le_alt->Prop)) (A_1:(produc1501160679le_alt->Prop)) (B:(Prop->Prop)), (((member377231867_alt_o F_1) ((pi_Pro1701359055_alt_o A_1) (fun (Uu:produc1501160679le_alt)=> B)))->(((inj_on1911943593_alt_o F_1) A_1)->(((member492167345le_alt G) ((pi_o_P657324555le_alt B) (fun (Uu:Prop)=> A_1)))->(((inj_on867909093le_alt G) B)->((finite449174868le_alt A_1)->((finite_finite_o B)->(((eq nat) (finite537683861le_alt A_1)) (finite_card_o B))))))))) of role axiom named fact_598_card__bij
% A new axiom: (forall (G:(Prop->produc1501160679le_alt)) (F_1:(produc1501160679le_alt->Prop)) (A_1:(produc1501160679le_alt->Prop)) (B:(Prop->Prop)), (((member377231867_alt_o F_1) ((pi_Pro1701359055_alt_o A_1) (fun (Uu:produc1501160679le_alt)=> B)))->(((inj_on1911943593_alt_o F_1) A_1)->(((member492167345le_alt G) ((pi_o_P657324555le_alt B) (fun (Uu:Prop)=> A_1)))->(((inj_on867909093le_alt G) B)->((finite449174868le_alt A_1)->((finite_finite_o B)->(((eq nat) (finite537683861le_alt A_1)) (finite_card_o B)))))))))
% FOF formula (forall (G:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (F_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_1:(arrow_1429601828e_indi->Prop)) (B:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_1) ((pi_Arr1929480907_alt_o A_1) (fun (Uu:arrow_1429601828e_indi)=> B)))->(((inj_on1190919077_alt_o F_1) A_1)->(((member304866663e_indi G) ((pi_Pro468373057e_indi B) (fun (Uu:(produc1501160679le_alt->Prop))=> A_1)))->(((inj_on1877294875e_indi G) B)->((finite664979089e_indi A_1)->((finite2112685307_alt_o B)->(((eq nat) (finite97476818e_indi A_1)) (finite28306938_alt_o B))))))))) of role axiom named fact_599_card__bij
% A new axiom: (forall (G:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (F_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_1:(arrow_1429601828e_indi->Prop)) (B:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_1) ((pi_Arr1929480907_alt_o A_1) (fun (Uu:arrow_1429601828e_indi)=> B)))->(((inj_on1190919077_alt_o F_1) A_1)->(((member304866663e_indi G) ((pi_Pro468373057e_indi B) (fun (Uu:(produc1501160679le_alt->Prop))=> A_1)))->(((inj_on1877294875e_indi G) B)->((finite664979089e_indi A_1)->((finite2112685307_alt_o B)->(((eq nat) (finite97476818e_indi A_1)) (finite28306938_alt_o B)))))))))
% FOF formula (forall (G:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (F_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_1) ((pi_Arr1304755663_alt_o A_1) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B)))->(((inj_on1284293749_alt_o F_1) A_1)->(((member530241719_alt_o G) ((pi_Pro763888199_alt_o B) (fun (Uu:(produc1501160679le_alt->Prop))=> A_1)))->(((inj_on743426285_alt_o G) B)->((finite1956767223_alt_o A_1)->((finite2112685307_alt_o B)->(((eq nat) (finite120663670_alt_o A_1)) (finite28306938_alt_o B))))))))) of role axiom named fact_600_card__bij
% A new axiom: (forall (G:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (F_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_1) ((pi_Arr1304755663_alt_o A_1) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B)))->(((inj_on1284293749_alt_o F_1) A_1)->(((member530241719_alt_o G) ((pi_Pro763888199_alt_o B) (fun (Uu:(produc1501160679le_alt->Prop))=> A_1)))->(((inj_on743426285_alt_o G) B)->((finite1956767223_alt_o A_1)->((finite2112685307_alt_o B)->(((eq nat) (finite120663670_alt_o A_1)) (finite28306938_alt_o B)))))))))
% FOF formula (forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_nat N_1) K))))) of role axiom named fact_601_finite__Collect__less__nat
% A new axiom: (forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_nat N_1) K)))))
% FOF formula (forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat N_1) K))))) of role axiom named fact_602_finite__Collect__le__nat
% A new axiom: (forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat N_1) K)))))
% FOF formula (((eq nat) (finite1949902593t_unit top_to1984820022unit_o)) one_one_nat) of role axiom named fact_603_card__UNIV__unit
% A new axiom: (((eq nat) (finite1949902593t_unit top_to1984820022unit_o)) one_one_nat)
% FOF formula (forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_nat I_1) N))))) N)) of role axiom named fact_604_card__Collect__less__nat
% A new axiom: (forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_nat I_1) N))))) N))
% FOF formula ((finite_finite_nat top_top_nat_o)->False) of role axiom named fact_605_infinite__UNIV__nat
% A new axiom: ((finite_finite_nat top_top_nat_o)->False)
% FOF formula (forall (P:(nat->Prop)) (_TPTP_I:nat), (finite_finite_nat (collect_nat (fun (K_1:nat)=> ((and (P K_1)) ((ord_less_nat K_1) _TPTP_I)))))) of role axiom named fact_606_finite__M__bounded__by__nat
% A new axiom: (forall (P:(nat->Prop)) (_TPTP_I:nat), (finite_finite_nat (collect_nat (fun (K_1:nat)=> ((and (P K_1)) ((ord_less_nat K_1) _TPTP_I))))))
% FOF formula (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_eq_nat X_1) M))))))) of role axiom named fact_607_finite__nat__set__iff__bounded__le
% A new axiom: (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_eq_nat X_1) M)))))))
% FOF formula (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) M))))))) of role axiom named fact_608_finite__nat__set__iff__bounded
% A new axiom: (forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) M)))))))
% FOF formula (forall (U:nat) (F:(nat->nat)), ((forall (N_1:nat), ((ord_less_eq_nat N_1) (F N_1)))->(finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat (F N_1)) U)))))) of role axiom named fact_609_finite__less__ub
% A new axiom: (forall (U:nat) (F:(nat->nat)), ((forall (N_1:nat), ((ord_less_eq_nat N_1) (F N_1)))->(finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat (F N_1)) U))))))
% FOF formula (forall (N:nat) (N_2:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) N)))->(finite_finite_nat N_2))) of role axiom named fact_610_bounded__nat__set__is__finite
% A new axiom: (forall (N:nat) (N_2:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) N)))->(finite_finite_nat N_2)))
% FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_611_less__zeroE
% A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_612_le0
% A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% FOF formula (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))) of role axiom named fact_613_gr0I
% A new axiom: (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N)))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->(not (((eq nat) N) zero_zero_nat)))) of role axiom named fact_614_gr__implies__not0
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->(not (((eq nat) N) zero_zero_nat))))
% FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_615_less__nat__zero__code
% A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% FOF formula (forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))) of role axiom named fact_616_neq0__conv
% A new axiom: (forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N)))
% FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_617_not__less0
% A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% FOF formula (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)) of role axiom named fact_618_plus__nat_Oadd__0
% A new axiom: (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N))
% FOF formula (forall (M_2:nat), (((eq nat) ((plus_plus_nat M_2) zero_zero_nat)) M_2)) of role axiom named fact_619_Nat_Oadd__0__right
% A new axiom: (forall (M_2:nat), (((eq nat) ((plus_plus_nat M_2) zero_zero_nat)) M_2))
% FOF formula (forall (M_2:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M_2) N)) zero_zero_nat)) ((and (((eq nat) M_2) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_620_add__is__0
% A new axiom: (forall (M_2:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M_2) N)) zero_zero_nat)) ((and (((eq nat) M_2) zero_zero_nat)) (((eq nat) N) zero_zero_nat))))
% FOF formula (forall (M_2:nat) (N:nat), ((((eq nat) ((plus_plus_nat M_2) N)) M_2)->(((eq nat) N) zero_zero_nat))) of role axiom named fact_621_add__eq__self__zero
% A new axiom: (forall (M_2:nat) (N:nat), ((((eq nat) ((plus_plus_nat M_2) N)) M_2)->(((eq nat) N) zero_zero_nat)))
% FOF formula (forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_622_le__0__eq
% A new axiom: (forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))
% FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_623_less__eq__nat_Osimps_I1_J
% A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M_2) N))) ((or ((ord_less_nat zero_zero_nat) M_2)) ((ord_less_nat zero_zero_nat) N)))) of role axiom named fact_624_add__gr__0
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M_2) N))) ((or ((ord_less_nat zero_zero_nat) M_2)) ((ord_less_nat zero_zero_nat) N))))
% FOF formula (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (I_1:nat), (((ord_less_eq_nat I_1) K_1)->((P I_1)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))) of role axiom named fact_625_ex__least__nat__less
% A new axiom: (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (I_1:nat), (((ord_less_eq_nat I_1) K_1)->((P I_1)->False))))) (P ((plus_plus_nat K_1) one_one_nat))))))))
% FOF formula (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (I_1:nat), (((ord_less_nat I_1) K_1)->((P I_1)->False))))) (P K_1))))))) of role axiom named fact_626_ex__least__nat__le
% A new axiom: (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (I_1:nat), (((ord_less_nat I_1) K_1)->((P I_1)->False))))) (P K_1)))))))
% FOF formula (forall (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat _TPTP_I) K_1)) J_1)))))) of role axiom named fact_627_less__imp__add__positive
% A new axiom: (forall (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat _TPTP_I) K_1)) J_1))))))
% FOF formula (forall (N:nat), ((ord_less_nat N) (suc N))) of role axiom named fact_628_lessI
% A new axiom: (forall (N:nat), ((ord_less_nat N) (suc N)))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_nat (suc M_2)) (suc N)))) of role axiom named fact_629_Suc__mono
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_nat (suc M_2)) (suc N))))
% FOF formula (forall (N:nat), ((ord_less_nat zero_zero_nat) (suc N))) of role axiom named fact_630_zero__less__Suc
% A new axiom: (forall (N:nat), ((ord_less_nat zero_zero_nat) (suc N)))
% FOF formula (forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False)) of role axiom named fact_631_Suc__n__not__le__n
% A new axiom: (forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False))
% FOF formula (forall (M_2:nat) (N:nat), ((iff (((ord_less_eq_nat M_2) N)->False)) ((ord_less_eq_nat (suc N)) M_2))) of role axiom named fact_632_not__less__eq__eq
% A new axiom: (forall (M_2:nat) (N:nat), ((iff (((ord_less_eq_nat M_2) N)->False)) ((ord_less_eq_nat (suc N)) M_2)))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat M_2) (suc N))) ((or ((ord_less_eq_nat M_2) N)) (((eq nat) M_2) (suc N))))) of role axiom named fact_633_le__Suc__eq
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat M_2) (suc N))) ((or ((ord_less_eq_nat M_2) N)) (((eq nat) M_2) (suc N)))))
% FOF formula (forall (N:nat) (M_2:nat), ((iff ((ord_less_eq_nat (suc N)) (suc M_2))) ((ord_less_eq_nat N) M_2))) of role axiom named fact_634_Suc__le__mono
% A new axiom: (forall (N:nat) (M_2:nat), ((iff ((ord_less_eq_nat (suc N)) (suc M_2))) ((ord_less_eq_nat N) M_2)))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((ord_less_eq_nat M_2) (suc N)))) of role axiom named fact_635_le__SucI
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((ord_less_eq_nat M_2) (suc N))))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) (suc N))->((((ord_less_eq_nat M_2) N)->False)->(((eq nat) M_2) (suc N))))) of role axiom named fact_636_le__SucE
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) (suc N))->((((ord_less_eq_nat M_2) N)->False)->(((eq nat) M_2) (suc N)))))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_eq_nat (suc M_2)) N)->((ord_less_eq_nat M_2) N))) of role axiom named fact_637_Suc__leD
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_eq_nat (suc M_2)) N)->((ord_less_eq_nat M_2) N)))
% FOF formula (forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y))) of role axiom named fact_638_Suc__inject
% A new axiom: (forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y)))
% FOF formula (forall (Nat_3:nat) (Nat_1:nat), ((iff (((eq nat) (suc Nat_3)) (suc Nat_1))) (((eq nat) Nat_3) Nat_1))) of role axiom named fact_639_nat_Oinject
% A new axiom: (forall (Nat_3:nat) (Nat_1:nat), ((iff (((eq nat) (suc Nat_3)) (suc Nat_1))) (((eq nat) Nat_3) Nat_1)))
% FOF formula (forall (N:nat), (not (((eq nat) (suc N)) N))) of role axiom named fact_640_Suc__n__not__n
% A new axiom: (forall (N:nat), (not (((eq nat) (suc N)) N)))
% FOF formula (forall (N:nat), (not (((eq nat) N) (suc N)))) of role axiom named fact_641_n__not__Suc__n
% A new axiom: (forall (N:nat), (not (((eq nat) N) (suc N))))
% FOF formula (forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M_2)) N)) ((plus_plus_nat M_2) (suc N)))) of role axiom named fact_642_add__Suc__shift
% A new axiom: (forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M_2)) N)) ((plus_plus_nat M_2) (suc N))))
% FOF formula (forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M_2)) N)) (suc ((plus_plus_nat M_2) N)))) of role axiom named fact_643_add__Suc
% A new axiom: (forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M_2)) N)) (suc ((plus_plus_nat M_2) N))))
% FOF formula (forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat M_2) (suc N))) (suc ((plus_plus_nat M_2) N)))) of role axiom named fact_644_add__Suc__right
% A new axiom: (forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat M_2) (suc N))) (suc ((plus_plus_nat M_2) N))))
% FOF formula (forall (M_2:nat) (N:nat), ((iff (((ord_less_nat M_2) N)->False)) ((ord_less_nat N) (suc M_2)))) of role axiom named fact_645_not__less__eq
% A new axiom: (forall (M_2:nat) (N:nat), ((iff (((ord_less_nat M_2) N)->False)) ((ord_less_nat N) (suc M_2))))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) (suc N))) ((or ((ord_less_nat M_2) N)) (((eq nat) M_2) N)))) of role axiom named fact_646_less__Suc__eq
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) (suc N))) ((or ((ord_less_nat M_2) N)) (((eq nat) M_2) N))))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat (suc M_2)) (suc N))) ((ord_less_nat M_2) N))) of role axiom named fact_647_Suc__less__eq
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat (suc M_2)) (suc N))) ((ord_less_nat M_2) N)))
% FOF formula (forall (N:nat) (M_2:nat), ((((ord_less_nat N) M_2)->False)->((iff ((ord_less_nat N) (suc M_2))) (((eq nat) N) M_2)))) of role axiom named fact_648_not__less__less__Suc__eq
% A new axiom: (forall (N:nat) (M_2:nat), ((((ord_less_nat N) M_2)->False)->((iff ((ord_less_nat N) (suc M_2))) (((eq nat) N) M_2))))
% FOF formula (forall (N:nat) (M_2:nat), ((((ord_less_nat N) M_2)->False)->(((ord_less_nat N) (suc M_2))->(((eq nat) M_2) N)))) of role axiom named fact_649_less__antisym
% A new axiom: (forall (N:nat) (M_2:nat), ((((ord_less_nat N) M_2)->False)->(((ord_less_nat N) (suc M_2))->(((eq nat) M_2) N))))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_nat M_2) (suc N)))) of role axiom named fact_650_less__SucI
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_nat M_2) (suc N))))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((not (((eq nat) (suc M_2)) N))->((ord_less_nat (suc M_2)) N)))) of role axiom named fact_651_Suc__lessI
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((not (((eq nat) (suc M_2)) N))->((ord_less_nat (suc M_2)) N))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->(((ord_less_nat J_1) K)->((ord_less_nat (suc _TPTP_I)) K)))) of role axiom named fact_652_less__trans__Suc
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->(((ord_less_nat J_1) K)->((ord_less_nat (suc _TPTP_I)) K))))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) (suc N))->((((ord_less_nat M_2) N)->False)->(((eq nat) M_2) N)))) of role axiom named fact_653_less__SucE
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) (suc N))->((((ord_less_nat M_2) N)->False)->(((eq nat) M_2) N))))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_nat (suc M_2)) N)->((ord_less_nat M_2) N))) of role axiom named fact_654_Suc__lessD
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_nat (suc M_2)) N)->((ord_less_nat M_2) N)))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_nat (suc M_2)) (suc N))->((ord_less_nat M_2) N))) of role axiom named fact_655_Suc__less__SucD
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_nat (suc M_2)) (suc N))->((ord_less_nat M_2) N)))
% FOF formula (((eq nat) one_one_nat) (suc zero_zero_nat)) of role axiom named fact_656_One__nat__def
% A new axiom: (((eq nat) one_one_nat) (suc zero_zero_nat))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_eq_nat (suc M_2)) N)->((ord_less_nat M_2) N))) of role axiom named fact_657_Suc__le__lessD
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_eq_nat (suc M_2)) N)->((ord_less_nat M_2) N)))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((iff ((ord_less_nat N) (suc M_2))) (((eq nat) N) M_2)))) of role axiom named fact_658_le__less__Suc__eq
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((iff ((ord_less_nat N) (suc M_2))) (((eq nat) N) M_2))))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_eq_nat (suc M_2)) N))) of role axiom named fact_659_Suc__leI
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_eq_nat (suc M_2)) N)))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((ord_less_nat M_2) (suc N)))) of role axiom named fact_660_le__imp__less__Suc
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((ord_less_nat M_2) (suc N))))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M_2)) N)) ((ord_less_nat M_2) N))) of role axiom named fact_661_Suc__le__eq
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M_2)) N)) ((ord_less_nat M_2) N)))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) (suc N))) ((ord_less_eq_nat M_2) N))) of role axiom named fact_662_less__Suc__eq__le
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) (suc N))) ((ord_less_eq_nat M_2) N)))
% FOF formula (forall (N:nat) (M_2:nat), ((iff ((ord_less_nat N) M_2)) ((ord_less_eq_nat (suc N)) M_2))) of role axiom named fact_663_less__eq__Suc__le
% A new axiom: (forall (N:nat) (M_2:nat), ((iff ((ord_less_nat N) M_2)) ((ord_less_eq_nat (suc N)) M_2)))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M_2) K_1))))))) of role axiom named fact_664_less__iff__Suc__add
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M_2) K_1)))))))
% FOF formula (forall (_TPTP_I:nat) (M_2:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat M_2) _TPTP_I)))) of role axiom named fact_665_less__add__Suc2
% A new axiom: (forall (_TPTP_I:nat) (M_2:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat M_2) _TPTP_I))))
% FOF formula (forall (_TPTP_I:nat) (M_2:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat _TPTP_I) M_2)))) of role axiom named fact_666_less__add__Suc1
% A new axiom: (forall (_TPTP_I:nat) (M_2:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat _TPTP_I) M_2))))
% FOF formula (forall (M_2:nat) (N:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M_2) N))) ((or ((and (((eq nat) M_2) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M_2) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat)))))) of role axiom named fact_667_one__is__add
% A new axiom: (forall (M_2:nat) (N:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M_2) N))) ((or ((and (((eq nat) M_2) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M_2) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat))))))
% FOF formula (forall (M_2:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M_2) N)) (suc zero_zero_nat))) ((or ((and (((eq nat) M_2) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M_2) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat)))))) of role axiom named fact_668_add__is__1
% A new axiom: (forall (M_2:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M_2) N)) (suc zero_zero_nat))) ((or ((and (((eq nat) M_2) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M_2) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat))))))
% FOF formula (forall (N:nat), ((iff ((ord_less_nat zero_zero_nat) N)) ((ex nat) (fun (M:nat)=> (((eq nat) N) (suc M)))))) of role axiom named fact_669_gr0__conv__Suc
% A new axiom: (forall (N:nat), ((iff ((ord_less_nat zero_zero_nat) N)) ((ex nat) (fun (M:nat)=> (((eq nat) N) (suc M))))))
% FOF formula (forall (N:nat), ((iff ((ord_less_nat N) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) of role axiom named fact_670_less__Suc0
% A new axiom: (forall (N:nat), ((iff ((ord_less_nat N) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat)))
% FOF formula (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) (suc N))) ((or (((eq nat) M_2) zero_zero_nat)) ((ex nat) (fun (J:nat)=> ((and (((eq nat) M_2) (suc J))) ((ord_less_nat J) N))))))) of role axiom named fact_671_less__Suc__eq__0__disj
% A new axiom: (forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) (suc N))) ((or (((eq nat) M_2) zero_zero_nat)) ((ex nat) (fun (J:nat)=> ((and (((eq nat) M_2) (suc J))) ((ord_less_nat J) N)))))))
% FOF formula (forall (N_2:(nat->Prop)), ((inj_on_nat_nat suc) N_2)) of role axiom named fact_672_inj__Suc
% A new axiom: (forall (N_2:(nat->Prop)), ((inj_on_nat_nat suc) N_2))
% FOF formula (forall (M_2:nat), (not (((eq nat) (suc M_2)) zero_zero_nat))) of role axiom named fact_673_Suc__neq__Zero
% A new axiom: (forall (M_2:nat), (not (((eq nat) (suc M_2)) zero_zero_nat)))
% FOF formula (forall (M_2:nat), (not (((eq nat) zero_zero_nat) (suc M_2)))) of role axiom named fact_674_Zero__neq__Suc
% A new axiom: (forall (M_2:nat), (not (((eq nat) zero_zero_nat) (suc M_2))))
% FOF formula (forall (Nat_2:nat), (not (((eq nat) (suc Nat_2)) zero_zero_nat))) of role axiom named fact_675_nat_Osimps_I3_J
% A new axiom: (forall (Nat_2:nat), (not (((eq nat) (suc Nat_2)) zero_zero_nat)))
% FOF formula (forall (M_2:nat), (not (((eq nat) (suc M_2)) zero_zero_nat))) of role axiom named fact_676_Suc__not__Zero
% A new axiom: (forall (M_2:nat), (not (((eq nat) (suc M_2)) zero_zero_nat)))
% FOF formula (forall (Nat_1:nat), (not (((eq nat) zero_zero_nat) (suc Nat_1)))) of role axiom named fact_677_nat_Osimps_I2_J
% A new axiom: (forall (Nat_1:nat), (not (((eq nat) zero_zero_nat) (suc Nat_1))))
% FOF formula (forall (M_2:nat), (not (((eq nat) zero_zero_nat) (suc M_2)))) of role axiom named fact_678_Zero__not__Suc
% A new axiom: (forall (M_2:nat), (not (((eq nat) zero_zero_nat) (suc M_2))))
% FOF formula (forall (X_1:nat), (((eq (nat->Prop)) (ord_less_nat X_1)) (ord_less_eq_nat (suc X_1)))) of role axiom named fact_679_less__eq__Suc__le__raw
% A new axiom: (forall (X_1:nat), (((eq (nat->Prop)) (ord_less_nat X_1)) (ord_less_eq_nat (suc X_1))))
% FOF formula (forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_eq_nat I_1) N))))) (suc N))) of role axiom named fact_680_card__Collect__le__nat
% A new axiom: (forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_eq_nat I_1) N))))) (suc N)))
% FOF formula (forall (_TPTP_I:nat) (M_3:(nat->Prop)), (((member_nat zero_zero_nat) M_3)->(((eq nat) (suc (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_3)) ((ord_less_nat K_1) _TPTP_I))))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_3)) ((ord_less_nat K_1) (suc _TPTP_I))))))))) of role axiom named fact_681_card__less__Suc
% A new axiom: (forall (_TPTP_I:nat) (M_3:(nat->Prop)), (((member_nat zero_zero_nat) M_3)->(((eq nat) (suc (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_3)) ((ord_less_nat K_1) _TPTP_I))))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_3)) ((ord_less_nat K_1) (suc _TPTP_I)))))))))
% FOF formula (forall (_TPTP_I:nat) (M_3:(nat->Prop)), (((member_nat zero_zero_nat) M_3)->(not (((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_3)) ((ord_less_nat K_1) (suc _TPTP_I))))))) zero_zero_nat)))) of role axiom named fact_682_card__less
% A new axiom: (forall (_TPTP_I:nat) (M_3:(nat->Prop)), (((member_nat zero_zero_nat) M_3)->(not (((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_3)) ((ord_less_nat K_1) (suc _TPTP_I))))))) zero_zero_nat))))
% FOF formula (forall (_TPTP_I:nat) (M_3:(nat->Prop)), ((((member_nat zero_zero_nat) M_3)->False)->(((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_3)) ((ord_less_nat K_1) _TPTP_I)))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_3)) ((ord_less_nat K_1) (suc _TPTP_I))))))))) of role axiom named fact_683_card__less__Suc2
% A new axiom: (forall (_TPTP_I:nat) (M_3:(nat->Prop)), ((((member_nat zero_zero_nat) M_3)->False)->(((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_3)) ((ord_less_nat K_1) _TPTP_I)))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_3)) ((ord_less_nat K_1) (suc _TPTP_I)))))))))
% FOF formula (forall (P:(nat->Prop)) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((P J_1)->((forall (I_1:nat), (((ord_less_nat I_1) J_1)->((P (suc I_1))->(P I_1))))->(P _TPTP_I))))) of role axiom named fact_684_inc__induct
% A new axiom: (forall (P:(nat->Prop)) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((P J_1)->((forall (I_1:nat), (((ord_less_nat I_1) J_1)->((P (suc I_1))->(P I_1))))->(P _TPTP_I)))))
% FOF formula (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M_2) K_1))))))) of role axiom named fact_685_less__imp__Suc__add
% A new axiom: (forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M_2) K_1)))))))
% FOF formula (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->((ex nat) (fun (M:nat)=> (((eq nat) N) (suc M)))))) of role axiom named fact_686_gr0__implies__Suc
% A new axiom: (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->((ex nat) (fun (M:nat)=> (((eq nat) N) (suc M))))))
% FOF formula (forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat one_one_nat) N))) of role axiom named fact_687_Suc__eq__plus1__left
% A new axiom: (forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat one_one_nat) N)))
% FOF formula (forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat N) one_one_nat))) of role axiom named fact_688_Suc__eq__plus1
% A new axiom: (forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat N) one_one_nat)))
% FOF formula (forall (N:nat) (M_1:nat), (((ord_less_eq_nat (suc N)) M_1)->((ex nat) (fun (M:nat)=> (((eq nat) M_1) (suc M)))))) of role axiom named fact_689_Suc__le__D
% A new axiom: (forall (N:nat) (M_1:nat), (((ord_less_eq_nat (suc N)) M_1)->((ex nat) (fun (M:nat)=> (((eq nat) M_1) (suc M))))))
% FOF formula (forall (_TPTP_I:nat) (K:nat), (((ord_less_nat _TPTP_I) K)->((not (((eq nat) K) (suc _TPTP_I)))->((forall (J:nat), (((ord_less_nat _TPTP_I) J)->(not (((eq nat) K) (suc J)))))->False)))) of role axiom named fact_690_lessE
% A new axiom: (forall (_TPTP_I:nat) (K:nat), (((ord_less_nat _TPTP_I) K)->((not (((eq nat) K) (suc _TPTP_I)))->((forall (J:nat), (((ord_less_nat _TPTP_I) J)->(not (((eq nat) K) (suc J)))))->False))))
% FOF formula (forall (_TPTP_I:nat) (K:nat), (((ord_less_nat (suc _TPTP_I)) K)->((forall (J:nat), (((ord_less_nat _TPTP_I) J)->(not (((eq nat) K) (suc J)))))->False))) of role axiom named fact_691_Suc__lessE
% A new axiom: (forall (_TPTP_I:nat) (K:nat), (((ord_less_nat (suc _TPTP_I)) K)->((forall (J:nat), (((ord_less_nat _TPTP_I) J)->(not (((eq nat) K) (suc J)))))->False)))
% FOF formula (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ex nat) (fun (M:nat)=> (((eq nat) N) (suc M)))))) of role axiom named fact_692_not0__implies__Suc
% A new axiom: (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ex nat) (fun (M:nat)=> (((eq nat) N) (suc M))))))
% FOF formula (forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat:nat), (not (((eq nat) Y) (suc Nat))))->False))) of role axiom named fact_693_nat_Oexhaust
% A new axiom: (forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat:nat), (not (((eq nat) Y) (suc Nat))))->False)))
% FOF formula (forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_1:nat), ((P (suc N_1))->(P N_1)))->(P zero_zero_nat)))) of role axiom named fact_694_zero__induct
% A new axiom: (forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_1:nat), ((P (suc N_1))->(P N_1)))->(P zero_zero_nat))))
% FOF formula (forall (N:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N_1:nat), ((P N_1)->(P (suc N_1))))->(P N)))) of role axiom named fact_695_nat__induct
% A new axiom: (forall (N:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N_1:nat), ((P N_1)->(P (suc N_1))))->(P N))))
% FOF formula (((eq (nat->Prop)) ((image_484224243di_nat h) top_to988227749indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite97476818e_indi top_to988227749indi_o))) of role axiom named fact_696_surjh
% A new axiom: (((eq (nat->Prop)) ((image_484224243di_nat h) top_to988227749indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite97476818e_indi top_to988227749indi_o)))
% FOF formula (forall (L:nat) (U:nat), (finite_finite_nat ((ord_at4362885an_nat L) U))) of role axiom named fact_697_finite__atLeastLessThan
% A new axiom: (forall (L:nat) (U:nat), (finite_finite_nat ((ord_at4362885an_nat L) U)))
% FOF formula ((forall (H:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat H) top_to988227749indi_o)->(not (((eq (nat->Prop)) ((image_484224243di_nat H) top_to988227749indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite97476818e_indi top_to988227749indi_o))))))->False) of role axiom named fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123
% A new axiom: ((forall (H:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat H) top_to988227749indi_o)->(not (((eq (nat->Prop)) ((image_484224243di_nat H) top_to988227749indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite97476818e_indi top_to988227749indi_o))))))->False)
% FOF formula (forall (A:(nat->Prop)) (K:nat), (((ord_less_eq_nat_o A) ((ord_at4362885an_nat K) ((plus_plus_nat K) (finite_card_nat A))))->(((eq (nat->Prop)) A) ((ord_at4362885an_nat K) ((plus_plus_nat K) (finite_card_nat A)))))) of role axiom named fact_699_subset__card__intvl__is__intvl
% A new axiom: (forall (A:(nat->Prop)) (K:nat), (((ord_less_eq_nat_o A) ((ord_at4362885an_nat K) ((plus_plus_nat K) (finite_card_nat A))))->(((eq (nat->Prop)) A) ((ord_at4362885an_nat K) ((plus_plus_nat K) (finite_card_nat A))))))
% FOF formula (forall (X:(produc1501160679le_alt->Prop)) (Y:(produc1501160679le_alt->Prop)), (((eq (produc1501160679le_alt->Prop)) (((if_Pro1561232536_alt_o True) X) Y)) X)) of role axiom named help_If_1_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% A new axiom: (forall (X:(produc1501160679le_alt->Prop)) (Y:(produc1501160679le_alt->Prop)), (((eq (produc1501160679le_alt->Prop)) (((if_Pro1561232536_alt_o True) X) Y)) X))
% FOF formula (forall (X:(produc1501160679le_alt->Prop)) (Y:(produc1501160679le_alt->Prop)), (((eq (produc1501160679le_alt->Prop)) (((if_Pro1561232536_alt_o False) X) Y)) Y)) of role axiom named help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% A new axiom: (forall (X:(produc1501160679le_alt->Prop)) (Y:(produc1501160679le_alt->Prop)), (((eq (produc1501160679le_alt->Prop)) (((if_Pro1561232536_alt_o False) X) Y)) Y))
% FOF formula (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) of role axiom named help_If_3_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_
% A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% FOF formula ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)) of role conjecture named conj_0
% Conjecture to prove = ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)):Prop
% Parameter arrow_1429601828e_indi_DUMMY:arrow_1429601828e_indi.
% Parameter product_unit_DUMMY:product_unit.
% Parameter produc1501160679le_alt_DUMMY:produc1501160679le_alt.
% We need to prove ['((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))']
% Parameter arrow_475358991le_alt:Type.
% Parameter arrow_1429601828e_indi:Type.
% Parameter nat:Type.
% Parameter product_unit:Type.
% Parameter produc1501160679le_alt:Type.
% Parameter all:((produc1501160679le_alt->Prop)->Prop).
% Parameter arrow_797024463le_IIA:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop).
% Parameter arrow_823908191le_Lin:((produc1501160679le_alt->Prop)->Prop).
% Parameter arrow_734252939e_Prof:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop).
% Parameter arrow_789600939_above:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->(produc1501160679le_alt->Prop)))).
% Parameter arrow_2098199487_below:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->(produc1501160679le_alt->Prop)))).
% Parameter arrow_1212662430ctator:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop)).
% Parameter arrow_2054445623_mkbot:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(produc1501160679le_alt->Prop))).
% Parameter arrow_55669061_mktop:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(produc1501160679le_alt->Prop))).
% Parameter arrow_1706409458nimity:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop).
% Parameter finite120663670_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->nat).
% Parameter finite28306938_alt_o:(((produc1501160679le_alt->Prop)->Prop)->nat).
% Parameter finite_card_o:((Prop->Prop)->nat).
% Parameter finite97476818e_indi:((arrow_1429601828e_indi->Prop)->nat).
% Parameter finite_card_nat:((nat->Prop)->nat).
% Parameter finite1949902593t_unit:((product_unit->Prop)->nat).
% Parameter finite537683861le_alt:((produc1501160679le_alt->Prop)->nat).
% Parameter finite1956767223_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop).
% Parameter finite2112685307_alt_o:(((produc1501160679le_alt->Prop)->Prop)->Prop).
% Parameter finite_finite_o:((Prop->Prop)->Prop).
% Parameter finite664979089e_indi:((arrow_1429601828e_indi->Prop)->Prop).
% Parameter finite_finite_nat:((nat->Prop)->Prop).
% Parameter finite449174868le_alt:((produc1501160679le_alt->Prop)->Prop).
% Parameter in_rel1252994498le_alt:((produc1501160679le_alt->Prop)->(arrow_475358991le_alt->(arrow_475358991le_alt->Prop))).
% Parameter inj_on1284293749_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter inj_on743426285_alt_o:(((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((produc1501160679le_alt->Prop)->Prop)->Prop)).
% Parameter inj_on1877294875e_indi:(((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->(((produc1501160679le_alt->Prop)->Prop)->Prop)).
% Parameter inj_on867909093le_alt:((Prop->produc1501160679le_alt)->((Prop->Prop)->Prop)).
% Parameter inj_on1190919077_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((arrow_1429601828e_indi->Prop)->Prop)).
% Parameter inj_on978774663di_nat:((arrow_1429601828e_indi->nat)->((arrow_1429601828e_indi->Prop)->Prop)).
% Parameter inj_on_nat_nat:((nat->nat)->((nat->Prop)->Prop)).
% Parameter inj_on1911943593_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->Prop)->Prop)).
% Parameter pi_Arr195212324lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop))).
% Parameter pi_Arr338314351e_indi:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop))).
% Parameter pi_Arr830584606t_unit:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(product_unit->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->product_unit)->Prop))).
% Parameter pi_Arr1304755663_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))).
% Parameter pi_Arr952516694lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop))).
% Parameter pi_Arr1232280765e_indi:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop))).
% Parameter pi_Arr1963174508t_unit:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(product_unit->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->product_unit)->Prop))).
% Parameter pi_Pro763888199_alt_o:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->(((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Pro422690258lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(Prop->Prop))->(((produc1501160679le_alt->Prop)->Prop)->Prop))).
% Parameter pi_Pro468373057e_indi:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))->(((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->Prop))).
% Parameter pi_Pro1306850800t_unit:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->(product_unit->Prop))->(((produc1501160679le_alt->Prop)->product_unit)->Prop))).
% Parameter pi_o_A1186128886_alt_o:((Prop->Prop)->((Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_o_A1182933120_alt_o:((Prop->Prop)->((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_o_P553196292_alt_o:((Prop->Prop)->((Prop->((produc1501160679le_alt->Prop)->Prop))->((Prop->(produc1501160679le_alt->Prop))->Prop))).
% Parameter pi_o_nat:((Prop->Prop)->((Prop->(nat->Prop))->((Prop->nat)->Prop))).
% Parameter pi_o_P657324555le_alt:((Prop->Prop)->((Prop->(produc1501160679le_alt->Prop))->((Prop->produc1501160679le_alt)->Prop))).
% Parameter pi_Arr1564509167_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Arr1060328391_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Arr1929480907_alt_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))).
% Parameter pi_Arr251692973di_nat:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->(nat->Prop))->((arrow_1429601828e_indi->nat)->Prop))).
% Parameter pi_Arr329216900le_alt:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((arrow_1429601828e_indi->produc1501160679le_alt)->Prop))).
% Parameter pi_nat_o:((nat->Prop)->((nat->(Prop->Prop))->((nat->Prop)->Prop))).
% Parameter pi_nat1219304995e_indi:((nat->Prop)->((nat->(arrow_1429601828e_indi->Prop))->((nat->arrow_1429601828e_indi)->Prop))).
% Parameter pi_nat_nat:((nat->Prop)->((nat->(nat->Prop))->((nat->nat)->Prop))).
% Parameter pi_nat_Product_unit:((nat->Prop)->((nat->(product_unit->Prop))->((nat->product_unit)->Prop))).
% Parameter pi_Pro1782982558_alt_o:((product_unit->Prop)->((product_unit->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))->((product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Pro1662176984_alt_o:((product_unit->Prop)->((product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))->((product_unit->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop))).
% Parameter pi_Pro1312660828_alt_o:((product_unit->Prop)->((product_unit->((produc1501160679le_alt->Prop)->Prop))->((product_unit->(produc1501160679le_alt->Prop))->Prop))).
% Parameter pi_Product_unit_nat:((product_unit->Prop)->((product_unit->(nat->Prop))->((product_unit->nat)->Prop))).
% Parameter pi_Pro701847987le_alt:((product_unit->Prop)->((product_unit->(produc1501160679le_alt->Prop))->((product_unit->produc1501160679le_alt)->Prop))).
% Parameter pi_Pro1701359055_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(Prop->Prop))->((produc1501160679le_alt->Prop)->Prop))).
% Parameter pi_Pro1767455108e_indi:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(arrow_1429601828e_indi->Prop))->((produc1501160679le_alt->arrow_1429601828e_indi)->Prop))).
% Parameter pi_Pro1475896499t_unit:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->(product_unit->Prop))->((produc1501160679le_alt->product_unit)->Prop))).
% Parameter one_one_nat:nat.
% Parameter plus_plus_nat:(nat->(nat->nat)).
% Parameter zero_zero_nat:nat.
% Parameter hilber598459244di_nat:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->nat)->(nat->arrow_1429601828e_indi))).
% Parameter hilber195283148at_nat:((nat->Prop)->((nat->nat)->(nat->nat))).
% Parameter if_Pro1561232536_alt_o:(Prop->((produc1501160679le_alt->Prop)->((produc1501160679le_alt->Prop)->(produc1501160679le_alt->Prop)))).
% Parameter suc:(nat->nat).
% Parameter ord_le1859604819lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter ord_le157835011lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter ord_le910298367lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->Prop)->Prop)).
% Parameter ord_less_o_o:((Prop->Prop)->((Prop->Prop)->Prop)).
% Parameter ord_le777687553indi_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->Prop)->Prop)).
% Parameter ord_less_nat_o:((nat->Prop)->((nat->Prop)->Prop)).
% Parameter ord_le232288914unit_o:((product_unit->Prop)->((product_unit->Prop)->Prop)).
% Parameter ord_le988258430_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->Prop)->Prop)).
% Parameter ord_less_o:(Prop->(Prop->Prop)).
% Parameter ord_less_nat:(nat->(nat->Prop)).
% Parameter ord_le134800455lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter ord_le1992928527lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter ord_le1063113995lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->(((produc1501160679le_alt->Prop)->Prop)->Prop)).
% Parameter ord_less_eq_o_o:((Prop->Prop)->((Prop->Prop)->Prop)).
% Parameter ord_le2080035663_alt_o:((arrow_475358991le_alt->(arrow_475358991le_alt->Prop))->((arrow_475358991le_alt->(arrow_475358991le_alt->Prop))->Prop)).
% Parameter ord_le1799070453indi_o:((arrow_1429601828e_indi->Prop)->((arrow_1429601828e_indi->Prop)->Prop)).
% Parameter ord_less_eq_nat_o:((nat->Prop)->((nat->Prop)->Prop)).
% Parameter ord_le1511552390unit_o:((product_unit->Prop)->((product_unit->Prop)->Prop)).
% Parameter ord_le97612146_alt_o:((produc1501160679le_alt->Prop)->((produc1501160679le_alt->Prop)->Prop)).
% Parameter ord_less_eq_o:(Prop->(Prop->Prop)).
% Parameter ord_less_eq_nat:(nat->(nat->Prop)).
% Parameter top_to1969627639lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop).
% Parameter top_to2122763103lt_o_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop).
% Parameter top_to1842727771lt_o_o:((produc1501160679le_alt->Prop)->Prop).
% Parameter top_top_o_o:(Prop->Prop).
% Parameter top_to988227749indi_o:(arrow_1429601828e_indi->Prop).
% Parameter top_top_nat_o:(nat->Prop).
% Parameter top_to1984820022unit_o:(product_unit->Prop).
% Parameter top_to1841428258_alt_o:(produc1501160679le_alt->Prop).
% Parameter top_top_o:Prop.
% Parameter produc1347929815le_alt:(arrow_475358991le_alt->(arrow_475358991le_alt->produc1501160679le_alt)).
% Parameter ord_at4362885an_nat:(nat->(nat->(nat->Prop))).
% Parameter collec2009291517_alt_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)).
% Parameter collec682858041_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)).
% Parameter collec94295101_alt_o:(((produc1501160679le_alt->Prop)->Prop)->((produc1501160679le_alt->Prop)->Prop)).
% Parameter collec22405327e_indi:((arrow_1429601828e_indi->Prop)->(arrow_1429601828e_indi->Prop)).
% Parameter collect_nat:((nat->Prop)->(nat->Prop)).
% Parameter collect_Product_unit:((product_unit->Prop)->(product_unit->Prop)).
% Parameter collec869865362le_alt:((produc1501160679le_alt->Prop)->(produc1501160679le_alt->Prop)).
% Parameter image_484224243di_nat:((arrow_1429601828e_indi->nat)->((arrow_1429601828e_indi->Prop)->(nat->Prop))).
% Parameter member1823529808lt_o_o:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop)->Prop)).
% Parameter member1452482393e_indi:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)->Prop)).
% Parameter member1924666376t_unit:((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->product_unit)->(((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->product_unit)->Prop)->Prop)).
% Parameter member616898751_alt_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter member939334982lt_o_o:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)->Prop)).
% Parameter member44294883e_indi:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)->Prop)->Prop)).
% Parameter member843528338t_unit:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->product_unit)->((((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->product_unit)->Prop)->Prop)).
% Parameter member530241719_alt_o:(((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->((((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member1961363906lt_o_o:(((produc1501160679le_alt->Prop)->Prop)->((((produc1501160679le_alt->Prop)->Prop)->Prop)->Prop)).
% Parameter member304866663e_indi:(((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->((((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)->Prop)->Prop)).
% Parameter member221730070t_unit:(((produc1501160679le_alt->Prop)->product_unit)->((((produc1501160679le_alt->Prop)->product_unit)->Prop)->Prop)).
% Parameter member1957863580_alt_o:((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member1394214384_alt_o:((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member1862122484_alt_o:((Prop->(produc1501160679le_alt->Prop))->(((Prop->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter member_o_nat:((Prop->nat)->(((Prop->nat)->Prop)->Prop)).
% Parameter member492167345le_alt:((Prop->produc1501160679le_alt)->(((Prop->produc1501160679le_alt)->Prop)->Prop)).
% Parameter member811956313_alt_o:((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member1234151027_alt_o:((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member526088951_alt_o:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter member1315464153di_nat:((arrow_1429601828e_indi->nat)->(((arrow_1429601828e_indi->nat)->Prop)->Prop)).
% Parameter member351225838le_alt:((arrow_1429601828e_indi->produc1501160679le_alt)->(((arrow_1429601828e_indi->produc1501160679le_alt)->Prop)->Prop)).
% Parameter member_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->Prop)).
% Parameter member1391860553e_indi:((nat->arrow_1429601828e_indi)->(((nat->arrow_1429601828e_indi)->Prop)->Prop)).
% Parameter member_nat_nat:((nat->nat)->(((nat->nat)->Prop)->Prop)).
% Parameter member616671224t_unit:((nat->product_unit)->(((nat->product_unit)->Prop)->Prop)).
% Parameter member1536989448_alt_o:((product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->(((product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member283501700_alt_o:((product_unit->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->(((product_unit->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))->Prop)->Prop)).
% Parameter member1661784200_alt_o:((product_unit->(produc1501160679le_alt->Prop))->(((product_unit->(produc1501160679le_alt->Prop))->Prop)->Prop)).
% Parameter member1827227242it_nat:((product_unit->nat)->(((product_unit->nat)->Prop)->Prop)).
% Parameter member495332125le_alt:((product_unit->produc1501160679le_alt)->(((product_unit->produc1501160679le_alt)->Prop)->Prop)).
% Parameter member377231867_alt_o:((produc1501160679le_alt->Prop)->(((produc1501160679le_alt->Prop)->Prop)->Prop)).
% Parameter member1640632174e_indi:((produc1501160679le_alt->arrow_1429601828e_indi)->(((produc1501160679le_alt->arrow_1429601828e_indi)->Prop)->Prop)).
% Parameter member593902749t_unit:((produc1501160679le_alt->product_unit)->(((produc1501160679le_alt->product_unit)->Prop)->Prop)).
% Parameter member_o:(Prop->((Prop->Prop)->Prop)).
% Parameter member2052026769e_indi:(arrow_1429601828e_indi->((arrow_1429601828e_indi->Prop)->Prop)).
% Parameter member_nat:(nat->((nat->Prop)->Prop)).
% Parameter member_Product_unit:(product_unit->((product_unit->Prop)->Prop)).
% Parameter member214075476le_alt:(produc1501160679le_alt->((produc1501160679le_alt->Prop)->Prop)).
% Parameter f:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)).
% Parameter lab:(produc1501160679le_alt->Prop).
% Parameter lba:(produc1501160679le_alt->Prop).
% Parameter p:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)).
% Parameter a:arrow_475358991le_alt.
% Parameter b:arrow_475358991le_alt.
% Parameter c:arrow_475358991le_alt.
% Parameter d:arrow_475358991le_alt.
% Parameter e:arrow_475358991le_alt.
% Parameter h:(arrow_1429601828e_indi->nat).
% Parameter n:nat.
% Axiom fact_0_assms_I3_J:(arrow_797024463le_IIA f).
% Axiom fact_1_u:(arrow_1706409458nimity f).
% Axiom fact_2__096c_A_126_061_Ad_096:(not (((eq arrow_475358991le_alt) c) d)).
% Axiom fact_3__096P_A_058_AProf_096:((member526088951_alt_o p) arrow_734252939e_Prof).
% Axiom fact_4_in__mkbot:(forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (Z:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_2054445623_mkbot L_2) Z))) ((and ((and (not (((eq arrow_475358991le_alt) Y) Z))) ((((eq arrow_475358991le_alt) X) Z)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) X) Z))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2))))).
% Axiom fact_5_in__mktop:(forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (Z:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) ((arrow_55669061_mktop L_2) Z))) ((and ((and (not (((eq arrow_475358991le_alt) X) Z))) ((((eq arrow_475358991le_alt) Y) Z)->(not (((eq arrow_475358991le_alt) X) Y))))) ((not (((eq arrow_475358991le_alt) Y) Z))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2))))).
% Axiom fact_6__C2_C:(forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_94:arrow_475358991le_alt) (B_73:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) A_94) B_73))->((not (((eq arrow_475358991le_alt) A_93) B_73))->((not (((eq arrow_475358991le_alt) B_72) A_94))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (f P_8))))))))))).
% Axiom fact_7__C1_C:(forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_94:arrow_475358991le_alt) (B_73:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) A_94) B_73))->((not (((eq arrow_475358991le_alt) A_93) B_73))->((not (((eq arrow_475358991le_alt) B_72) A_94))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (P_8 I_1))))->(((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))->((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (f P_8))))))))))).
% Axiom fact_8__C4_C:(forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (C_37:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) B_72) C_37))->((not (((eq arrow_475358991le_alt) A_93) C_37))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt B_72) C_37)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt B_72) C_37)) (f P_8)))))))))).
% Axiom fact_9_pairwise__neutrality:(forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_94:arrow_475358991le_alt) (B_73:arrow_475358991le_alt) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->((not (((eq arrow_475358991le_alt) A_94) B_73))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt A_94) B_73)) (f P_8))))))))).
% Axiom fact_10__C3_C:(forall (P_8:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (P_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_93:arrow_475358991le_alt) (B_72:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_93) B_72))->(((member526088951_alt_o P_7) arrow_734252939e_Prof)->(((member526088951_alt_o P_8) arrow_734252939e_Prof)->((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (P_7 I_1))) ((member214075476le_alt ((produc1347929815le_alt B_72) A_93)) (P_8 I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_93) B_72)) (f P_7))) ((member214075476le_alt ((produc1347929815le_alt B_72) A_93)) (f P_8)))))))).
% Axiom fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J:(forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt c) d)) (p I_1))) ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) d)) ((arrow_55669061_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) d)) (((arrow_789600939_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member214075476le_alt ((produc1347929815le_alt c) d)) ((arrow_2054445623_mkbot (p I_1)) e)))))))).
% Axiom fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0:((member214075476le_alt ((produc1347929815le_alt c) d)) (p (((hilber598459244di_nat top_to988227749indi_o) h) n))).
% Axiom fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto:((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))).
% Axiom fact_14_PW:((iff ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))) ((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))).
% Axiom fact_15_split__paired__All:(forall (P_6:(produc1501160679le_alt->Prop)), ((iff (all P_6)) (forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), (P_6 ((produc1347929815le_alt A_3) B_61))))).
% Axiom fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai:((member526088951_alt_o (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))) arrow_734252939e_Prof).
% Axiom fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto:((member214075476le_alt ((produc1347929815le_alt c) e)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))).
% Axiom fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto:((member214075476le_alt ((produc1347929815le_alt e) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))).
% Axiom fact_19_n_I1_J:((ord_less_nat n) (finite97476818e_indi top_to988227749indi_o)).
% Axiom fact_20_injh:((inj_on978774663di_nat h) top_to988227749indi_o).
% Axiom fact_21_Pair__inject:(forall (A_92:arrow_475358991le_alt) (B_71:arrow_475358991le_alt) (A_91:arrow_475358991le_alt) (B_70:arrow_475358991le_alt), ((((eq produc1501160679le_alt) ((produc1347929815le_alt A_92) B_71)) ((produc1347929815le_alt A_91) B_70))->(((((eq arrow_475358991le_alt) A_92) A_91)->(not (((eq arrow_475358991le_alt) B_71) B_70)))->False))).
% Axiom fact_22_Pair__eq:(forall (A_90:arrow_475358991le_alt) (B_69:arrow_475358991le_alt) (A_89:arrow_475358991le_alt) (B_68:arrow_475358991le_alt), ((iff (((eq produc1501160679le_alt) ((produc1347929815le_alt A_90) B_69)) ((produc1347929815le_alt A_89) B_68))) ((and (((eq arrow_475358991le_alt) A_90) A_89)) (((eq arrow_475358991le_alt) B_69) B_68)))).
% Axiom fact_23_IIA__def:(forall (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_797024463le_IIA F_18)) (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(forall (Xa:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o Xa) arrow_734252939e_Prof)->(forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), ((forall (I_1:arrow_1429601828e_indi), ((iff ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (X_1 I_1))) ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (Xa I_1))))->((iff ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 X_1))) ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 Xa))))))))))).
% Axiom fact_24_unanimity__def:(forall (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (arrow_1706409458nimity F_18)) (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), ((forall (I_1:arrow_1429601828e_indi), ((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (X_1 I_1)))->((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 X_1)))))))).
% Axiom fact_25_top1I:(forall (X_70:(produc1501160679le_alt->Prop)), (top_to1842727771lt_o_o X_70)).
% Axiom fact_26_top1I:(forall (X_70:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (top_to2122763103lt_o_o X_70)).
% Axiom fact_27_top1I:(forall (X_70:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (top_to1969627639lt_o_o X_70)).
% Axiom fact_28_top1I:(forall (X_70:produc1501160679le_alt), (top_to1841428258_alt_o X_70)).
% Axiom fact_29_top1I:(forall (X_70:arrow_1429601828e_indi), (top_to988227749indi_o X_70)).
% Axiom fact_30_top1I:(forall (X_70:product_unit), (top_to1984820022unit_o X_70)).
% Axiom fact_31_top1I:(forall (X_70:nat), (top_top_nat_o X_70)).
% Axiom fact_32_UNIV__I:(forall (X_69:Prop), ((member_o X_69) top_top_o_o)).
% Axiom fact_33_UNIV__I:(forall (X_69:arrow_1429601828e_indi), ((member2052026769e_indi X_69) top_to988227749indi_o)).
% Axiom fact_34_UNIV__I:(forall (X_69:product_unit), ((member_Product_unit X_69) top_to1984820022unit_o)).
% Axiom fact_35_UNIV__I:(forall (X_69:produc1501160679le_alt), ((member214075476le_alt X_69) top_to1841428258_alt_o)).
% Axiom fact_36_UNIV__I:(forall (X_69:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_69) top_to2122763103lt_o_o)).
% Axiom fact_37_UNIV__I:(forall (X_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_69) top_to1969627639lt_o_o)).
% Axiom fact_38_UNIV__I:(forall (X_69:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_69) top_to1842727771lt_o_o)).
% Axiom fact_39_UNIV__I:(forall (X_69:nat), ((member_nat X_69) top_top_nat_o)).
% Axiom fact_40_iso__tuple__UNIV__I:(forall (X_68:Prop), ((member_o X_68) top_top_o_o)).
% Axiom fact_41_iso__tuple__UNIV__I:(forall (X_68:arrow_1429601828e_indi), ((member2052026769e_indi X_68) top_to988227749indi_o)).
% Axiom fact_42_iso__tuple__UNIV__I:(forall (X_68:product_unit), ((member_Product_unit X_68) top_to1984820022unit_o)).
% Axiom fact_43_iso__tuple__UNIV__I:(forall (X_68:produc1501160679le_alt), ((member214075476le_alt X_68) top_to1841428258_alt_o)).
% Axiom fact_44_iso__tuple__UNIV__I:(forall (X_68:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((member526088951_alt_o X_68) top_to2122763103lt_o_o)).
% Axiom fact_45_iso__tuple__UNIV__I:(forall (X_68:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((member616898751_alt_o X_68) top_to1969627639lt_o_o)).
% Axiom fact_46_iso__tuple__UNIV__I:(forall (X_68:(produc1501160679le_alt->Prop)), ((member377231867_alt_o X_68) top_to1842727771lt_o_o)).
% Axiom fact_47_iso__tuple__UNIV__I:(forall (X_68:nat), ((member_nat X_68) top_top_nat_o)).
% Axiom fact_48_top__apply:(forall (X_67:(produc1501160679le_alt->Prop)), ((iff (top_to1842727771lt_o_o X_67)) top_top_o)).
% Axiom fact_49_top__apply:(forall (X_67:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), ((iff (top_to2122763103lt_o_o X_67)) top_top_o)).
% Axiom fact_50_top__apply:(forall (X_67:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), ((iff (top_to1969627639lt_o_o X_67)) top_top_o)).
% Axiom fact_51_top__apply:(forall (X_67:produc1501160679le_alt), ((iff (top_to1841428258_alt_o X_67)) top_top_o)).
% Axiom fact_52_top__apply:(forall (X_67:arrow_1429601828e_indi), ((iff (top_to988227749indi_o X_67)) top_top_o)).
% Axiom fact_53_top__apply:(forall (X_67:product_unit), ((iff (top_to1984820022unit_o X_67)) top_top_o)).
% Axiom fact_54_top__apply:(forall (X_67:nat), ((iff (top_top_nat_o X_67)) top_top_o)).
% Axiom fact_55_not__top__less:(forall (A_88:((produc1501160679le_alt->Prop)->Prop)), (((ord_le910298367lt_o_o top_to1842727771lt_o_o) A_88)->False)).
% Axiom fact_56_not__top__less:(forall (A_88:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le157835011lt_o_o top_to2122763103lt_o_o) A_88)->False)).
% Axiom fact_57_not__top__less:(forall (A_88:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1859604819lt_o_o top_to1969627639lt_o_o) A_88)->False)).
% Axiom fact_58_not__top__less:(forall (A_88:Prop), (((ord_less_o top_top_o) A_88)->False)).
% Axiom fact_59_not__top__less:(forall (A_88:(produc1501160679le_alt->Prop)), (((ord_le988258430_alt_o top_to1841428258_alt_o) A_88)->False)).
% Axiom fact_60_not__top__less:(forall (A_88:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o top_to988227749indi_o) A_88)->False)).
% Axiom fact_61_not__top__less:(forall (A_88:(product_unit->Prop)), (((ord_le232288914unit_o top_to1984820022unit_o) A_88)->False)).
% Axiom fact_62_not__top__less:(forall (A_88:(nat->Prop)), (((ord_less_nat_o top_top_nat_o) A_88)->False)).
% Axiom fact_63_less__top:(forall (A_87:((produc1501160679le_alt->Prop)->Prop)), ((iff (not (((eq ((produc1501160679le_alt->Prop)->Prop)) A_87) top_to1842727771lt_o_o))) ((ord_le910298367lt_o_o A_87) top_to1842727771lt_o_o))).
% Axiom fact_64_less__top:(forall (A_87:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff (not (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) A_87) top_to2122763103lt_o_o))) ((ord_le157835011lt_o_o A_87) top_to2122763103lt_o_o))).
% Axiom fact_65_less__top:(forall (A_87:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff (not (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) A_87) top_to1969627639lt_o_o))) ((ord_le1859604819lt_o_o A_87) top_to1969627639lt_o_o))).
% Axiom fact_66_less__top:(forall (A_87:Prop), ((iff (((iff A_87) top_top_o)->False)) ((ord_less_o A_87) top_top_o))).
% Axiom fact_67_less__top:(forall (A_87:(produc1501160679le_alt->Prop)), ((iff (not (((eq (produc1501160679le_alt->Prop)) A_87) top_to1841428258_alt_o))) ((ord_le988258430_alt_o A_87) top_to1841428258_alt_o))).
% Axiom fact_68_less__top:(forall (A_87:(arrow_1429601828e_indi->Prop)), ((iff (not (((eq (arrow_1429601828e_indi->Prop)) A_87) top_to988227749indi_o))) ((ord_le777687553indi_o A_87) top_to988227749indi_o))).
% Axiom fact_69_less__top:(forall (A_87:(product_unit->Prop)), ((iff (not (((eq (product_unit->Prop)) A_87) top_to1984820022unit_o))) ((ord_le232288914unit_o A_87) top_to1984820022unit_o))).
% Axiom fact_70_less__top:(forall (A_87:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_87) top_top_nat_o))) ((ord_less_nat_o A_87) top_top_nat_o))).
% Axiom fact_71_assms_I1_J:((member616898751_alt_o f) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin))).
% Axiom fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk:((iff ((member214075476le_alt ((produc1347929815le_alt e) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) lab) lba))))).
% Axiom fact_73__096Lab_A_058_ALin_096:((member377231867_alt_o lab) arrow_823908191le_Lin).
% Axiom fact_74__096Lba_A_058_ALin_096:((member377231867_alt_o lba) arrow_823908191le_Lin).
% Axiom fact_75__096a_A_126_061_Ab_096:(not (((eq arrow_475358991le_alt) a) b)).
% Axiom fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096:((member214075476le_alt ((produc1347929815le_alt a) b)) lab).
% Axiom fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096:((member214075476le_alt ((produc1347929815le_alt b) a)) lba).
% Axiom fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096:(((member214075476le_alt ((produc1347929815le_alt a) b)) lba)->False).
% Axiom fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096:(((member214075476le_alt ((produc1347929815le_alt b) a)) lab)->False).
% Axiom fact_80_PiProf:(forall (N:nat), ((member526088951_alt_o (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) N)) lab) lba))) arrow_734252939e_Prof)).
% Axiom fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_:((forall (Lab:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt a) b)) Lab)->(((member377231867_alt_o Lab) arrow_823908191le_Lin)->False)))->False).
% Axiom fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_:((forall (Lba:(produc1501160679le_alt->Prop)), (((member214075476le_alt ((produc1347929815le_alt b) a)) Lba)->(((member377231867_alt_o Lba) arrow_823908191le_Lin)->False)))->False).
% Axiom fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk:(forall (I_1:arrow_1429601828e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt e) d)) ((arrow_55669061_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt e) d)) (((arrow_789600939_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member214075476le_alt ((produc1347929815le_alt e) d)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt b) a)) lab))) ((((ord_less_nat (h I_1)) n)->False)->((member214075476le_alt ((produc1347929815le_alt b) a)) lba))))).
% Axiom fact_84_n_I2_J:(forall (M:nat), (((ord_less_eq_nat M) n)->((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) M)) lab) lba)))))).
% Axiom fact_85_notin__Lin__iff:(forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((not (((eq arrow_475358991le_alt) X) Y))->((iff (((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2)->False)) ((member214075476le_alt ((produc1347929815le_alt Y) X)) L_2))))).
% Axiom fact_86_Lin__irrefl:(forall (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->(((member214075476le_alt ((produc1347929815le_alt A_9) B_5)) L_2)->(((member214075476le_alt ((produc1347929815le_alt B_5) A_9)) L_2)->False)))).
% Axiom fact_87_mktop__Lin:(forall (X:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_55669061_mktop L_2) X)) arrow_823908191le_Lin))).
% Axiom fact_88_mkbot__Lin:(forall (X:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o ((arrow_2054445623_mkbot L_2) X)) arrow_823908191le_Lin))).
% Axiom fact_89_above__Lin:(forall (L_2:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_789600939_above L_2) X) Y)) arrow_823908191le_Lin)))).
% Axiom fact_90_const__Lin__Prof:(forall (L_2:(produc1501160679le_alt->Prop)), (((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member526088951_alt_o (fun (P_5:arrow_1429601828e_indi)=> L_2)) arrow_734252939e_Prof))).
% Axiom fact_91_linorder__cases:(forall (X_66:nat) (Y_50:nat), ((((ord_less_nat X_66) Y_50)->False)->((not (((eq nat) X_66) Y_50))->((ord_less_nat Y_50) X_66)))).
% Axiom fact_92_order__less__asym:(forall (X_65:(nat->Prop)) (Y_49:(nat->Prop)), (((ord_less_nat_o X_65) Y_49)->(((ord_less_nat_o Y_49) X_65)->False))).
% Axiom fact_93_order__less__asym:(forall (X_65:(product_unit->Prop)) (Y_49:(product_unit->Prop)), (((ord_le232288914unit_o X_65) Y_49)->(((ord_le232288914unit_o Y_49) X_65)->False))).
% Axiom fact_94_order__less__asym:(forall (X_65:(arrow_1429601828e_indi->Prop)) (Y_49:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_65) Y_49)->(((ord_le777687553indi_o Y_49) X_65)->False))).
% Axiom fact_95_order__less__asym:(forall (X_65:nat) (Y_49:nat), (((ord_less_nat X_65) Y_49)->(((ord_less_nat Y_49) X_65)->False))).
% Axiom fact_96_xt1_I10_J:(forall (Z_8:(nat->Prop)) (Y_48:(nat->Prop)) (X_64:(nat->Prop)), (((ord_less_nat_o Y_48) X_64)->(((ord_less_nat_o Z_8) Y_48)->((ord_less_nat_o Z_8) X_64)))).
% Axiom fact_97_xt1_I10_J:(forall (Z_8:(product_unit->Prop)) (Y_48:(product_unit->Prop)) (X_64:(product_unit->Prop)), (((ord_le232288914unit_o Y_48) X_64)->(((ord_le232288914unit_o Z_8) Y_48)->((ord_le232288914unit_o Z_8) X_64)))).
% Axiom fact_98_xt1_I10_J:(forall (Z_8:(arrow_1429601828e_indi->Prop)) (Y_48:(arrow_1429601828e_indi->Prop)) (X_64:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o Y_48) X_64)->(((ord_le777687553indi_o Z_8) Y_48)->((ord_le777687553indi_o Z_8) X_64)))).
% Axiom fact_99_xt1_I10_J:(forall (Z_8:nat) (Y_48:nat) (X_64:nat), (((ord_less_nat Y_48) X_64)->(((ord_less_nat Z_8) Y_48)->((ord_less_nat Z_8) X_64)))).
% Axiom fact_100_order__less__trans:(forall (Z_7:(nat->Prop)) (X_63:(nat->Prop)) (Y_47:(nat->Prop)), (((ord_less_nat_o X_63) Y_47)->(((ord_less_nat_o Y_47) Z_7)->((ord_less_nat_o X_63) Z_7)))).
% Axiom fact_101_order__less__trans:(forall (Z_7:(product_unit->Prop)) (X_63:(product_unit->Prop)) (Y_47:(product_unit->Prop)), (((ord_le232288914unit_o X_63) Y_47)->(((ord_le232288914unit_o Y_47) Z_7)->((ord_le232288914unit_o X_63) Z_7)))).
% Axiom fact_102_order__less__trans:(forall (Z_7:(arrow_1429601828e_indi->Prop)) (X_63:(arrow_1429601828e_indi->Prop)) (Y_47:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_63) Y_47)->(((ord_le777687553indi_o Y_47) Z_7)->((ord_le777687553indi_o X_63) Z_7)))).
% Axiom fact_103_order__less__trans:(forall (Z_7:nat) (X_63:nat) (Y_47:nat), (((ord_less_nat X_63) Y_47)->(((ord_less_nat Y_47) Z_7)->((ord_less_nat X_63) Z_7)))).
% Axiom fact_104_xt1_I2_J:(forall (C_36:(nat->Prop)) (B_67:(nat->Prop)) (A_86:(nat->Prop)), (((ord_less_nat_o B_67) A_86)->((((eq (nat->Prop)) B_67) C_36)->((ord_less_nat_o C_36) A_86)))).
% Axiom fact_105_xt1_I2_J:(forall (C_36:(product_unit->Prop)) (B_67:(product_unit->Prop)) (A_86:(product_unit->Prop)), (((ord_le232288914unit_o B_67) A_86)->((((eq (product_unit->Prop)) B_67) C_36)->((ord_le232288914unit_o C_36) A_86)))).
% Axiom fact_106_xt1_I2_J:(forall (C_36:(arrow_1429601828e_indi->Prop)) (B_67:(arrow_1429601828e_indi->Prop)) (A_86:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o B_67) A_86)->((((eq (arrow_1429601828e_indi->Prop)) B_67) C_36)->((ord_le777687553indi_o C_36) A_86)))).
% Axiom fact_107_xt1_I2_J:(forall (C_36:nat) (B_67:nat) (A_86:nat), (((ord_less_nat B_67) A_86)->((((eq nat) B_67) C_36)->((ord_less_nat C_36) A_86)))).
% Axiom fact_108_ord__less__eq__trans:(forall (C_35:(nat->Prop)) (A_85:(nat->Prop)) (B_66:(nat->Prop)), (((ord_less_nat_o A_85) B_66)->((((eq (nat->Prop)) B_66) C_35)->((ord_less_nat_o A_85) C_35)))).
% Axiom fact_109_ord__less__eq__trans:(forall (C_35:(product_unit->Prop)) (A_85:(product_unit->Prop)) (B_66:(product_unit->Prop)), (((ord_le232288914unit_o A_85) B_66)->((((eq (product_unit->Prop)) B_66) C_35)->((ord_le232288914unit_o A_85) C_35)))).
% Axiom fact_110_ord__less__eq__trans:(forall (C_35:(arrow_1429601828e_indi->Prop)) (A_85:(arrow_1429601828e_indi->Prop)) (B_66:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_85) B_66)->((((eq (arrow_1429601828e_indi->Prop)) B_66) C_35)->((ord_le777687553indi_o A_85) C_35)))).
% Axiom fact_111_ord__less__eq__trans:(forall (C_35:nat) (A_85:nat) (B_66:nat), (((ord_less_nat A_85) B_66)->((((eq nat) B_66) C_35)->((ord_less_nat A_85) C_35)))).
% Axiom fact_112_xt1_I1_J:(forall (C_34:(nat->Prop)) (A_84:(nat->Prop)) (B_65:(nat->Prop)), ((((eq (nat->Prop)) A_84) B_65)->(((ord_less_nat_o C_34) B_65)->((ord_less_nat_o C_34) A_84)))).
% Axiom fact_113_xt1_I1_J:(forall (C_34:(product_unit->Prop)) (A_84:(product_unit->Prop)) (B_65:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_84) B_65)->(((ord_le232288914unit_o C_34) B_65)->((ord_le232288914unit_o C_34) A_84)))).
% Axiom fact_114_xt1_I1_J:(forall (C_34:(arrow_1429601828e_indi->Prop)) (A_84:(arrow_1429601828e_indi->Prop)) (B_65:(arrow_1429601828e_indi->Prop)), ((((eq (arrow_1429601828e_indi->Prop)) A_84) B_65)->(((ord_le777687553indi_o C_34) B_65)->((ord_le777687553indi_o C_34) A_84)))).
% Axiom fact_115_xt1_I1_J:(forall (C_34:nat) (A_84:nat) (B_65:nat), ((((eq nat) A_84) B_65)->(((ord_less_nat C_34) B_65)->((ord_less_nat C_34) A_84)))).
% Axiom fact_116_ord__eq__less__trans:(forall (C_33:(nat->Prop)) (A_83:(nat->Prop)) (B_64:(nat->Prop)), ((((eq (nat->Prop)) A_83) B_64)->(((ord_less_nat_o B_64) C_33)->((ord_less_nat_o A_83) C_33)))).
% Axiom fact_117_ord__eq__less__trans:(forall (C_33:(product_unit->Prop)) (A_83:(product_unit->Prop)) (B_64:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_83) B_64)->(((ord_le232288914unit_o B_64) C_33)->((ord_le232288914unit_o A_83) C_33)))).
% Axiom fact_118_ord__eq__less__trans:(forall (C_33:(arrow_1429601828e_indi->Prop)) (A_83:(arrow_1429601828e_indi->Prop)) (B_64:(arrow_1429601828e_indi->Prop)), ((((eq (arrow_1429601828e_indi->Prop)) A_83) B_64)->(((ord_le777687553indi_o B_64) C_33)->((ord_le777687553indi_o A_83) C_33)))).
% Axiom fact_119_ord__eq__less__trans:(forall (C_33:nat) (A_83:nat) (B_64:nat), ((((eq nat) A_83) B_64)->(((ord_less_nat B_64) C_33)->((ord_less_nat A_83) C_33)))).
% Axiom fact_120_xt1_I9_J:(forall (B_63:(nat->Prop)) (A_82:(nat->Prop)), (((ord_less_nat_o B_63) A_82)->(((ord_less_nat_o A_82) B_63)->False))).
% Axiom fact_121_xt1_I9_J:(forall (B_63:(product_unit->Prop)) (A_82:(product_unit->Prop)), (((ord_le232288914unit_o B_63) A_82)->(((ord_le232288914unit_o A_82) B_63)->False))).
% Axiom fact_122_xt1_I9_J:(forall (B_63:(arrow_1429601828e_indi->Prop)) (A_82:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o B_63) A_82)->(((ord_le777687553indi_o A_82) B_63)->False))).
% Axiom fact_123_xt1_I9_J:(forall (B_63:nat) (A_82:nat), (((ord_less_nat B_63) A_82)->(((ord_less_nat A_82) B_63)->False))).
% Axiom fact_124_order__less__asym_H:(forall (A_81:(nat->Prop)) (B_62:(nat->Prop)), (((ord_less_nat_o A_81) B_62)->(((ord_less_nat_o B_62) A_81)->False))).
% Axiom fact_125_order__less__asym_H:(forall (A_81:(product_unit->Prop)) (B_62:(product_unit->Prop)), (((ord_le232288914unit_o A_81) B_62)->(((ord_le232288914unit_o B_62) A_81)->False))).
% Axiom fact_126_order__less__asym_H:(forall (A_81:(arrow_1429601828e_indi->Prop)) (B_62:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_81) B_62)->(((ord_le777687553indi_o B_62) A_81)->False))).
% Axiom fact_127_order__less__asym_H:(forall (A_81:nat) (B_62:nat), (((ord_less_nat A_81) B_62)->(((ord_less_nat B_62) A_81)->False))).
% Axiom fact_128_order__less__imp__triv:(forall (P_4:Prop) (X_62:(nat->Prop)) (Y_46:(nat->Prop)), (((ord_less_nat_o X_62) Y_46)->(((ord_less_nat_o Y_46) X_62)->P_4))).
% Axiom fact_129_order__less__imp__triv:(forall (P_4:Prop) (X_62:(product_unit->Prop)) (Y_46:(product_unit->Prop)), (((ord_le232288914unit_o X_62) Y_46)->(((ord_le232288914unit_o Y_46) X_62)->P_4))).
% Axiom fact_130_order__less__imp__triv:(forall (P_4:Prop) (X_62:(arrow_1429601828e_indi->Prop)) (Y_46:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_62) Y_46)->(((ord_le777687553indi_o Y_46) X_62)->P_4))).
% Axiom fact_131_order__less__imp__triv:(forall (P_4:Prop) (X_62:nat) (Y_46:nat), (((ord_less_nat X_62) Y_46)->(((ord_less_nat Y_46) X_62)->P_4))).
% Axiom fact_132_order__less__imp__not__eq2:(forall (X_61:(nat->Prop)) (Y_45:(nat->Prop)), (((ord_less_nat_o X_61) Y_45)->(not (((eq (nat->Prop)) Y_45) X_61)))).
% Axiom fact_133_order__less__imp__not__eq2:(forall (X_61:(product_unit->Prop)) (Y_45:(product_unit->Prop)), (((ord_le232288914unit_o X_61) Y_45)->(not (((eq (product_unit->Prop)) Y_45) X_61)))).
% Axiom fact_134_order__less__imp__not__eq2:(forall (X_61:(arrow_1429601828e_indi->Prop)) (Y_45:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_61) Y_45)->(not (((eq (arrow_1429601828e_indi->Prop)) Y_45) X_61)))).
% Axiom fact_135_order__less__imp__not__eq2:(forall (X_61:nat) (Y_45:nat), (((ord_less_nat X_61) Y_45)->(not (((eq nat) Y_45) X_61)))).
% Axiom fact_136_order__less__imp__not__eq:(forall (X_60:(nat->Prop)) (Y_44:(nat->Prop)), (((ord_less_nat_o X_60) Y_44)->(not (((eq (nat->Prop)) X_60) Y_44)))).
% Axiom fact_137_order__less__imp__not__eq:(forall (X_60:(product_unit->Prop)) (Y_44:(product_unit->Prop)), (((ord_le232288914unit_o X_60) Y_44)->(not (((eq (product_unit->Prop)) X_60) Y_44)))).
% Axiom fact_138_order__less__imp__not__eq:(forall (X_60:(arrow_1429601828e_indi->Prop)) (Y_44:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_60) Y_44)->(not (((eq (arrow_1429601828e_indi->Prop)) X_60) Y_44)))).
% Axiom fact_139_order__less__imp__not__eq:(forall (X_60:nat) (Y_44:nat), (((ord_less_nat X_60) Y_44)->(not (((eq nat) X_60) Y_44)))).
% Axiom fact_140_order__less__imp__not__less:(forall (X_59:(nat->Prop)) (Y_43:(nat->Prop)), (((ord_less_nat_o X_59) Y_43)->(((ord_less_nat_o Y_43) X_59)->False))).
% Axiom fact_141_order__less__imp__not__less:(forall (X_59:(product_unit->Prop)) (Y_43:(product_unit->Prop)), (((ord_le232288914unit_o X_59) Y_43)->(((ord_le232288914unit_o Y_43) X_59)->False))).
% Axiom fact_142_order__less__imp__not__less:(forall (X_59:(arrow_1429601828e_indi->Prop)) (Y_43:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_59) Y_43)->(((ord_le777687553indi_o Y_43) X_59)->False))).
% Axiom fact_143_order__less__imp__not__less:(forall (X_59:nat) (Y_43:nat), (((ord_less_nat X_59) Y_43)->(((ord_less_nat Y_43) X_59)->False))).
% Axiom fact_144_order__less__not__sym:(forall (X_58:(nat->Prop)) (Y_42:(nat->Prop)), (((ord_less_nat_o X_58) Y_42)->(((ord_less_nat_o Y_42) X_58)->False))).
% Axiom fact_145_order__less__not__sym:(forall (X_58:(product_unit->Prop)) (Y_42:(product_unit->Prop)), (((ord_le232288914unit_o X_58) Y_42)->(((ord_le232288914unit_o Y_42) X_58)->False))).
% Axiom fact_146_order__less__not__sym:(forall (X_58:(arrow_1429601828e_indi->Prop)) (Y_42:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_58) Y_42)->(((ord_le777687553indi_o Y_42) X_58)->False))).
% Axiom fact_147_order__less__not__sym:(forall (X_58:nat) (Y_42:nat), (((ord_less_nat X_58) Y_42)->(((ord_less_nat Y_42) X_58)->False))).
% Axiom fact_148_less__imp__neq:(forall (X_57:(nat->Prop)) (Y_41:(nat->Prop)), (((ord_less_nat_o X_57) Y_41)->(not (((eq (nat->Prop)) X_57) Y_41)))).
% Axiom fact_149_less__imp__neq:(forall (X_57:(product_unit->Prop)) (Y_41:(product_unit->Prop)), (((ord_le232288914unit_o X_57) Y_41)->(not (((eq (product_unit->Prop)) X_57) Y_41)))).
% Axiom fact_150_less__imp__neq:(forall (X_57:(arrow_1429601828e_indi->Prop)) (Y_41:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_57) Y_41)->(not (((eq (arrow_1429601828e_indi->Prop)) X_57) Y_41)))).
% Axiom fact_151_less__imp__neq:(forall (X_57:nat) (Y_41:nat), (((ord_less_nat X_57) Y_41)->(not (((eq nat) X_57) Y_41)))).
% Axiom fact_152_linorder__neqE:(forall (X_56:nat) (Y_40:nat), ((not (((eq nat) X_56) Y_40))->((((ord_less_nat X_56) Y_40)->False)->((ord_less_nat Y_40) X_56)))).
% Axiom fact_153_linorder__antisym__conv3:(forall (Y_39:nat) (X_55:nat), ((((ord_less_nat Y_39) X_55)->False)->((iff (((ord_less_nat X_55) Y_39)->False)) (((eq nat) X_55) Y_39)))).
% Axiom fact_154_linorder__less__linear:(forall (X_54:nat) (Y_38:nat), ((or ((or ((ord_less_nat X_54) Y_38)) (((eq nat) X_54) Y_38))) ((ord_less_nat Y_38) X_54))).
% Axiom fact_155_not__less__iff__gr__or__eq:(forall (X_53:nat) (Y_37:nat), ((iff (((ord_less_nat X_53) Y_37)->False)) ((or ((ord_less_nat Y_37) X_53)) (((eq nat) X_53) Y_37)))).
% Axiom fact_156_linorder__neq__iff:(forall (X_52:nat) (Y_36:nat), ((iff (not (((eq nat) X_52) Y_36))) ((or ((ord_less_nat X_52) Y_36)) ((ord_less_nat Y_36) X_52)))).
% Axiom fact_157_order__less__irrefl:(forall (X_51:(nat->Prop)), (((ord_less_nat_o X_51) X_51)->False)).
% Axiom fact_158_order__less__irrefl:(forall (X_51:(product_unit->Prop)), (((ord_le232288914unit_o X_51) X_51)->False)).
% Axiom fact_159_order__less__irrefl:(forall (X_51:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_51) X_51)->False)).
% Axiom fact_160_order__less__irrefl:(forall (X_51:nat), (((ord_less_nat X_51) X_51)->False)).
% Axiom fact_161_UNIV__def:(((eq ((produc1501160679le_alt->Prop)->Prop)) top_to1842727771lt_o_o) (collec94295101_alt_o (fun (X_1:(produc1501160679le_alt->Prop))=> True))).
% Axiom fact_162_UNIV__def:(((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) top_to2122763103lt_o_o) (collec682858041_alt_o (fun (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> True))).
% Axiom fact_163_UNIV__def:(((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) top_to1969627639lt_o_o) (collec2009291517_alt_o (fun (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> True))).
% Axiom fact_164_UNIV__def:(((eq (produc1501160679le_alt->Prop)) top_to1841428258_alt_o) (collec869865362le_alt (fun (X_1:produc1501160679le_alt)=> True))).
% Axiom fact_165_UNIV__def:(((eq (arrow_1429601828e_indi->Prop)) top_to988227749indi_o) (collec22405327e_indi (fun (X_1:arrow_1429601828e_indi)=> True))).
% Axiom fact_166_UNIV__def:(((eq (product_unit->Prop)) top_to1984820022unit_o) (collect_Product_unit (fun (X_1:product_unit)=> True))).
% Axiom fact_167_UNIV__def:(((eq (nat->Prop)) top_top_nat_o) (collect_nat (fun (X_1:nat)=> True))).
% Axiom fact_168_mem__def:(forall (X_50:arrow_1429601828e_indi) (A_80:(arrow_1429601828e_indi->Prop)), ((iff ((member2052026769e_indi X_50) A_80)) (A_80 X_50))).
% Axiom fact_169_mem__def:(forall (X_50:Prop) (A_80:(Prop->Prop)), ((iff ((member_o X_50) A_80)) (A_80 X_50))).
% Axiom fact_170_mem__def:(forall (X_50:product_unit) (A_80:(product_unit->Prop)), ((iff ((member_Product_unit X_50) A_80)) (A_80 X_50))).
% Axiom fact_171_mem__def:(forall (X_50:produc1501160679le_alt) (A_80:(produc1501160679le_alt->Prop)), ((iff ((member214075476le_alt X_50) A_80)) (A_80 X_50))).
% Axiom fact_172_mem__def:(forall (X_50:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_80:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member526088951_alt_o X_50) A_80)) (A_80 X_50))).
% Axiom fact_173_mem__def:(forall (X_50:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_80:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((member616898751_alt_o X_50) A_80)) (A_80 X_50))).
% Axiom fact_174_mem__def:(forall (X_50:(produc1501160679le_alt->Prop)) (A_80:((produc1501160679le_alt->Prop)->Prop)), ((iff ((member377231867_alt_o X_50) A_80)) (A_80 X_50))).
% Axiom fact_175_mem__def:(forall (X_50:nat) (A_80:(nat->Prop)), ((iff ((member_nat X_50) A_80)) (A_80 X_50))).
% Axiom fact_176_Collect__def:(forall (P_3:(product_unit->Prop)), (((eq (product_unit->Prop)) (collect_Product_unit P_3)) P_3)).
% Axiom fact_177_Collect__def:(forall (P_3:(arrow_1429601828e_indi->Prop)), (((eq (arrow_1429601828e_indi->Prop)) (collec22405327e_indi P_3)) P_3)).
% Axiom fact_178_Collect__def:(forall (P_3:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_3)) P_3)).
% Axiom fact_179_in__above:(forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_9) B_5))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_789600939_above L_2) A_9) B_5))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) X) B_5)->((member214075476le_alt ((produc1347929815le_alt A_9) Y)) L_2)))) ((not (((eq arrow_475358991le_alt) X) B_5))->((and ((((eq arrow_475358991le_alt) Y) B_5)->((or (((eq arrow_475358991le_alt) X) A_9)) ((member214075476le_alt ((produc1347929815le_alt X) A_9)) L_2)))) ((not (((eq arrow_475358991le_alt) Y) B_5))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2))))))))).
% Axiom fact_180_pred__equals__eq2:(forall (S_3:(produc1501160679le_alt->Prop)) (R_3:(produc1501160679le_alt->Prop)), ((iff (forall (X_1:arrow_475358991le_alt) (Xa:arrow_475358991le_alt), ((iff ((member214075476le_alt ((produc1347929815le_alt X_1) Xa)) R_3)) ((member214075476le_alt ((produc1347929815le_alt X_1) Xa)) S_3)))) (((eq (produc1501160679le_alt->Prop)) R_3) S_3))).
% Axiom fact_181_n_I3_J:((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba)))).
% Axiom fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am:((iff ((member214075476le_alt ((produc1347929815le_alt c) e)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba))))).
% Axiom fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am:(forall (I_1:arrow_1429601828e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) e)) ((arrow_55669061_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member214075476le_alt ((produc1347929815le_alt c) e)) (((arrow_789600939_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member214075476le_alt ((produc1347929815le_alt c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->((member214075476le_alt ((produc1347929815le_alt a) b)) lab))) ((((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->False)->((member214075476le_alt ((produc1347929815le_alt a) b)) lba))))).
% Axiom fact_184_inv__f__eq:(forall (X_49:arrow_1429601828e_indi) (Y_35:nat) (F_30:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_30) top_to988227749indi_o)->((((eq nat) (F_30 X_49)) Y_35)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat top_to988227749indi_o) F_30) Y_35)) X_49)))).
% Axiom fact_185_inv__f__eq:(forall (X_49:nat) (Y_35:nat) (F_30:(nat->nat)), (((inj_on_nat_nat F_30) top_top_nat_o)->((((eq nat) (F_30 X_49)) Y_35)->(((eq nat) (((hilber195283148at_nat top_top_nat_o) F_30) Y_35)) X_49)))).
% Axiom fact_186_inv__f__f:(forall (X_48:arrow_1429601828e_indi) (F_29:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_29) top_to988227749indi_o)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat top_to988227749indi_o) F_29) (F_29 X_48))) X_48))).
% Axiom fact_187_inv__f__f:(forall (X_48:nat) (F_29:(nat->nat)), (((inj_on_nat_nat F_29) top_top_nat_o)->(((eq nat) (((hilber195283148at_nat top_top_nat_o) F_29) (F_29 X_48))) X_48))).
% Axiom fact_188_dictatorI:(forall (_TPTP_I:arrow_1429601828e_indi) (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o F_18) ((pi_Arr1304755663_alt_o arrow_734252939e_Prof) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> arrow_823908191le_Lin)))->((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(forall (A_3:arrow_475358991le_alt) (B_61:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_3) B_61))->(((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (X_1 _TPTP_I))->((member214075476le_alt ((produc1347929815le_alt A_3) B_61)) (F_18 X_1)))))))->((arrow_1212662430ctator F_18) _TPTP_I)))).
% Axiom fact_189_PiE:(forall (X_47:produc1501160679le_alt) (F_28:(produc1501160679le_alt->Prop)) (A_79:(produc1501160679le_alt->Prop)) (B_60:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_28) ((pi_Pro1701359055_alt_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member214075476le_alt X_47) A_79)->False)))).
% Axiom fact_190_PiE:(forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->produc1501160679le_alt)) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member351225838le_alt F_28) ((pi_Arr329216900le_alt A_79) B_60))->((((member214075476le_alt (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False)))).
% Axiom fact_191_PiE:(forall (X_47:Prop) (F_28:(Prop->produc1501160679le_alt)) (A_79:(Prop->Prop)) (B_60:(Prop->(produc1501160679le_alt->Prop))), (((member492167345le_alt F_28) ((pi_o_P657324555le_alt A_79) B_60))->((((member214075476le_alt (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False)))).
% Axiom fact_192_PiE:(forall (X_47:product_unit) (F_28:(product_unit->produc1501160679le_alt)) (A_79:(product_unit->Prop)) (B_60:(product_unit->(produc1501160679le_alt->Prop))), (((member495332125le_alt F_28) ((pi_Pro701847987le_alt A_79) B_60))->((((member214075476le_alt (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False)))).
% Axiom fact_193_PiE:(forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1234151027_alt_o F_28) ((pi_Arr1060328391_alt_o A_79) B_60))->((((member526088951_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False)))).
% Axiom fact_194_PiE:(forall (X_47:Prop) (F_28:(Prop->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_79:(Prop->Prop)) (B_60:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member1394214384_alt_o F_28) ((pi_o_A1182933120_alt_o A_79) B_60))->((((member526088951_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False)))).
% Axiom fact_195_PiE:(forall (X_47:product_unit) (F_28:(product_unit->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_79:(product_unit->Prop)) (B_60:(product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop))), (((member283501700_alt_o F_28) ((pi_Pro1662176984_alt_o A_79) B_60))->((((member526088951_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False)))).
% Axiom fact_196_PiE:(forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member811956313_alt_o F_28) ((pi_Arr1564509167_alt_o A_79) B_60))->((((member616898751_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False)))).
% Axiom fact_197_PiE:(forall (X_47:Prop) (F_28:(Prop->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_79:(Prop->Prop)) (B_60:(Prop->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1957863580_alt_o F_28) ((pi_o_A1186128886_alt_o A_79) B_60))->((((member616898751_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False)))).
% Axiom fact_198_PiE:(forall (X_47:product_unit) (F_28:(product_unit->((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))) (A_79:(product_unit->Prop)) (B_60:(product_unit->(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop))), (((member1536989448_alt_o F_28) ((pi_Pro1782982558_alt_o A_79) B_60))->((((member616898751_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False)))).
% Axiom fact_199_PiE:(forall (X_47:Prop) (F_28:(Prop->(produc1501160679le_alt->Prop))) (A_79:(Prop->Prop)) (B_60:(Prop->((produc1501160679le_alt->Prop)->Prop))), (((member1862122484_alt_o F_28) ((pi_o_P553196292_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False)))).
% Axiom fact_200_PiE:(forall (X_47:product_unit) (F_28:(product_unit->(produc1501160679le_alt->Prop))) (A_79:(product_unit->Prop)) (B_60:(product_unit->((produc1501160679le_alt->Prop)->Prop))), (((member1661784200_alt_o F_28) ((pi_Pro1312660828_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False)))).
% Axiom fact_201_PiE:(forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->nat)) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->(nat->Prop))), (((member1315464153di_nat F_28) ((pi_Arr251692973di_nat A_79) B_60))->((((member_nat (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False)))).
% Axiom fact_202_PiE:(forall (X_47:Prop) (F_28:(Prop->nat)) (A_79:(Prop->Prop)) (B_60:(Prop->(nat->Prop))), (((member_o_nat F_28) ((pi_o_nat A_79) B_60))->((((member_nat (F_28 X_47)) (B_60 X_47))->False)->(((member_o X_47) A_79)->False)))).
% Axiom fact_203_PiE:(forall (X_47:product_unit) (F_28:(product_unit->nat)) (A_79:(product_unit->Prop)) (B_60:(product_unit->(nat->Prop))), (((member1827227242it_nat F_28) ((pi_Product_unit_nat A_79) B_60))->((((member_nat (F_28 X_47)) (B_60 X_47))->False)->(((member_Product_unit X_47) A_79)->False)))).
% Axiom fact_204_PiE:(forall (X_47:produc1501160679le_alt) (F_28:(produc1501160679le_alt->arrow_1429601828e_indi)) (A_79:(produc1501160679le_alt->Prop)) (B_60:(produc1501160679le_alt->(arrow_1429601828e_indi->Prop))), (((member1640632174e_indi F_28) ((pi_Pro1767455108e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member214075476le_alt X_47) A_79)->False)))).
% Axiom fact_205_PiE:(forall (X_47:produc1501160679le_alt) (F_28:(produc1501160679le_alt->product_unit)) (A_79:(produc1501160679le_alt->Prop)) (B_60:(produc1501160679le_alt->(product_unit->Prop))), (((member593902749t_unit F_28) ((pi_Pro1475896499t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member214075476le_alt X_47) A_79)->False)))).
% Axiom fact_206_PiE:(forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member44294883e_indi F_28) ((pi_Arr1232280765e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False)))).
% Axiom fact_207_PiE:(forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member939334982lt_o_o F_28) ((pi_Arr952516694lt_o_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False)))).
% Axiom fact_208_PiE:(forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->product_unit)) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(product_unit->Prop))), (((member843528338t_unit F_28) ((pi_Arr1963174508t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False)))).
% Axiom fact_209_PiE:(forall (X_47:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->arrow_1429601828e_indi)) (A_79:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_60:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(arrow_1429601828e_indi->Prop))), (((member1452482393e_indi F_28) ((pi_Arr338314351e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member616898751_alt_o X_47) A_79)->False)))).
% Axiom fact_210_PiE:(forall (X_47:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_79:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_60:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(Prop->Prop))), (((member1823529808lt_o_o F_28) ((pi_Arr195212324lt_o_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member616898751_alt_o X_47) A_79)->False)))).
% Axiom fact_211_PiE:(forall (X_47:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->product_unit)) (A_79:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_60:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->(product_unit->Prop))), (((member1924666376t_unit F_28) ((pi_Arr830584606t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member616898751_alt_o X_47) A_79)->False)))).
% Axiom fact_212_PiE:(forall (X_47:(produc1501160679le_alt->Prop)) (F_28:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_79:((produc1501160679le_alt->Prop)->Prop)) (B_60:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->Prop))), (((member304866663e_indi F_28) ((pi_Pro468373057e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member377231867_alt_o X_47) A_79)->False)))).
% Axiom fact_213_PiE:(forall (X_47:(produc1501160679le_alt->Prop)) (F_28:((produc1501160679le_alt->Prop)->Prop)) (A_79:((produc1501160679le_alt->Prop)->Prop)) (B_60:((produc1501160679le_alt->Prop)->(Prop->Prop))), (((member1961363906lt_o_o F_28) ((pi_Pro422690258lt_o_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member377231867_alt_o X_47) A_79)->False)))).
% Axiom fact_214_PiE:(forall (X_47:(produc1501160679le_alt->Prop)) (F_28:((produc1501160679le_alt->Prop)->product_unit)) (A_79:((produc1501160679le_alt->Prop)->Prop)) (B_60:((produc1501160679le_alt->Prop)->(product_unit->Prop))), (((member221730070t_unit F_28) ((pi_Pro1306850800t_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member377231867_alt_o X_47) A_79)->False)))).
% Axiom fact_215_PiE:(forall (X_47:nat) (F_28:(nat->arrow_1429601828e_indi)) (A_79:(nat->Prop)) (B_60:(nat->(arrow_1429601828e_indi->Prop))), (((member1391860553e_indi F_28) ((pi_nat1219304995e_indi A_79) B_60))->((((member2052026769e_indi (F_28 X_47)) (B_60 X_47))->False)->(((member_nat X_47) A_79)->False)))).
% Axiom fact_216_PiE:(forall (X_47:nat) (F_28:(nat->Prop)) (A_79:(nat->Prop)) (B_60:(nat->(Prop->Prop))), (((member_nat_o F_28) ((pi_nat_o A_79) B_60))->((((member_o (F_28 X_47)) (B_60 X_47))->False)->(((member_nat X_47) A_79)->False)))).
% Axiom fact_217_PiE:(forall (X_47:nat) (F_28:(nat->product_unit)) (A_79:(nat->Prop)) (B_60:(nat->(product_unit->Prop))), (((member616671224t_unit F_28) ((pi_nat_Product_unit A_79) B_60))->((((member_Product_unit (F_28 X_47)) (B_60 X_47))->False)->(((member_nat X_47) A_79)->False)))).
% Axiom fact_218_PiE:(forall (X_47:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_79:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_28) ((pi_Arr1304755663_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member526088951_alt_o X_47) A_79)->False)))).
% Axiom fact_219_PiE:(forall (X_47:arrow_1429601828e_indi) (F_28:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_79:(arrow_1429601828e_indi->Prop)) (B_60:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_28) ((pi_Arr1929480907_alt_o A_79) B_60))->((((member377231867_alt_o (F_28 X_47)) (B_60 X_47))->False)->(((member2052026769e_indi X_47) A_79)->False)))).
% Axiom fact_220_complete__Lin:(forall (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_9) B_5))->((ex (produc1501160679le_alt->Prop)) (fun (X_1:(produc1501160679le_alt->Prop))=> ((and ((member377231867_alt_o X_1) arrow_823908191le_Lin)) ((member214075476le_alt ((produc1347929815le_alt A_9) B_5)) X_1)))))).
% Axiom fact_221_Pi__UNIV:(forall (A_78:(produc1501160679le_alt->Prop)), (((eq ((produc1501160679le_alt->Prop)->Prop)) ((pi_Pro1701359055_alt_o A_78) (fun (Uu:produc1501160679le_alt)=> top_top_o_o))) top_to1842727771lt_o_o)).
% Axiom fact_222_Pi__UNIV:(forall (A_78:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1304755663_alt_o A_78) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> top_to1842727771lt_o_o))) top_to1969627639lt_o_o)).
% Axiom fact_223_Pi__UNIV:(forall (A_78:(arrow_1429601828e_indi->Prop)), (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) ((pi_Arr1929480907_alt_o A_78) (fun (Uu:arrow_1429601828e_indi)=> top_to1842727771lt_o_o))) top_to2122763103lt_o_o)).
% Axiom fact_224_order__refl:(forall (X_46:Prop), ((ord_less_eq_o X_46) X_46)).
% Axiom fact_225_order__refl:(forall (X_46:nat), ((ord_less_eq_nat X_46) X_46)).
% Axiom fact_226_order__refl:(forall (X_46:(nat->Prop)), ((ord_less_eq_nat_o X_46) X_46)).
% Axiom fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I:((ex nat) (fun (N_1:nat)=> ((and ((and ((ord_less_nat N_1) (finite97476818e_indi top_to988227749indi_o))) (forall (M:nat), (((ord_less_eq_nat M) N_1)->((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) M)) lab) lba)))))))) ((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N_1) one_one_nat))) lab) lba))))))).
% Axiom fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_:((forall (N_1:nat), (((ord_less_nat N_1) (finite97476818e_indi top_to988227749indi_o))->((forall (M:nat), (((ord_less_eq_nat M) N_1)->((member214075476le_alt ((produc1347929815le_alt b) a)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) M)) lab) lba))))))->(((member214075476le_alt ((produc1347929815le_alt a) b)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N_1) one_one_nat))) lab) lba))))->False))))->False).
% Axiom fact_229_linorder__le__cases:(forall (X_45:nat) (Y_34:nat), ((((ord_less_eq_nat X_45) Y_34)->False)->((ord_less_eq_nat Y_34) X_45))).
% Axiom fact_230_le__funE:(forall (X_44:nat) (F_27:(nat->Prop)) (G_8:(nat->Prop)), (((ord_less_eq_nat_o F_27) G_8)->((ord_less_eq_o (F_27 X_44)) (G_8 X_44)))).
% Axiom fact_231_xt1_I6_J:(forall (Z_6:Prop) (Y_33:Prop) (X_43:Prop), (((ord_less_eq_o Y_33) X_43)->(((ord_less_eq_o Z_6) Y_33)->((ord_less_eq_o Z_6) X_43)))).
% Axiom fact_232_xt1_I6_J:(forall (Z_6:nat) (Y_33:nat) (X_43:nat), (((ord_less_eq_nat Y_33) X_43)->(((ord_less_eq_nat Z_6) Y_33)->((ord_less_eq_nat Z_6) X_43)))).
% Axiom fact_233_xt1_I6_J:(forall (Z_6:(nat->Prop)) (Y_33:(nat->Prop)) (X_43:(nat->Prop)), (((ord_less_eq_nat_o Y_33) X_43)->(((ord_less_eq_nat_o Z_6) Y_33)->((ord_less_eq_nat_o Z_6) X_43)))).
% Axiom fact_234_xt1_I5_J:(forall (Y_32:Prop) (X_42:Prop), (((ord_less_eq_o Y_32) X_42)->(((ord_less_eq_o X_42) Y_32)->((iff X_42) Y_32)))).
% Axiom fact_235_xt1_I5_J:(forall (Y_32:nat) (X_42:nat), (((ord_less_eq_nat Y_32) X_42)->(((ord_less_eq_nat X_42) Y_32)->(((eq nat) X_42) Y_32)))).
% Axiom fact_236_xt1_I5_J:(forall (Y_32:(nat->Prop)) (X_42:(nat->Prop)), (((ord_less_eq_nat_o Y_32) X_42)->(((ord_less_eq_nat_o X_42) Y_32)->(((eq (nat->Prop)) X_42) Y_32)))).
% Axiom fact_237_order__trans:(forall (Z_5:Prop) (X_41:Prop) (Y_31:Prop), (((ord_less_eq_o X_41) Y_31)->(((ord_less_eq_o Y_31) Z_5)->((ord_less_eq_o X_41) Z_5)))).
% Axiom fact_238_order__trans:(forall (Z_5:nat) (X_41:nat) (Y_31:nat), (((ord_less_eq_nat X_41) Y_31)->(((ord_less_eq_nat Y_31) Z_5)->((ord_less_eq_nat X_41) Z_5)))).
% Axiom fact_239_order__trans:(forall (Z_5:(nat->Prop)) (X_41:(nat->Prop)) (Y_31:(nat->Prop)), (((ord_less_eq_nat_o X_41) Y_31)->(((ord_less_eq_nat_o Y_31) Z_5)->((ord_less_eq_nat_o X_41) Z_5)))).
% Axiom fact_240_order__antisym:(forall (X_40:Prop) (Y_30:Prop), (((ord_less_eq_o X_40) Y_30)->(((ord_less_eq_o Y_30) X_40)->((iff X_40) Y_30)))).
% Axiom fact_241_order__antisym:(forall (X_40:nat) (Y_30:nat), (((ord_less_eq_nat X_40) Y_30)->(((ord_less_eq_nat Y_30) X_40)->(((eq nat) X_40) Y_30)))).
% Axiom fact_242_order__antisym:(forall (X_40:(nat->Prop)) (Y_30:(nat->Prop)), (((ord_less_eq_nat_o X_40) Y_30)->(((ord_less_eq_nat_o Y_30) X_40)->(((eq (nat->Prop)) X_40) Y_30)))).
% Axiom fact_243_xt1_I4_J:(forall (C_32:Prop) (B_59:Prop) (A_77:Prop), (((ord_less_eq_o B_59) A_77)->(((iff B_59) C_32)->((ord_less_eq_o C_32) A_77)))).
% Axiom fact_244_xt1_I4_J:(forall (C_32:nat) (B_59:nat) (A_77:nat), (((ord_less_eq_nat B_59) A_77)->((((eq nat) B_59) C_32)->((ord_less_eq_nat C_32) A_77)))).
% Axiom fact_245_xt1_I4_J:(forall (C_32:(nat->Prop)) (B_59:(nat->Prop)) (A_77:(nat->Prop)), (((ord_less_eq_nat_o B_59) A_77)->((((eq (nat->Prop)) B_59) C_32)->((ord_less_eq_nat_o C_32) A_77)))).
% Axiom fact_246_ord__le__eq__trans:(forall (C_31:Prop) (A_76:Prop) (B_58:Prop), (((ord_less_eq_o A_76) B_58)->(((iff B_58) C_31)->((ord_less_eq_o A_76) C_31)))).
% Axiom fact_247_ord__le__eq__trans:(forall (C_31:nat) (A_76:nat) (B_58:nat), (((ord_less_eq_nat A_76) B_58)->((((eq nat) B_58) C_31)->((ord_less_eq_nat A_76) C_31)))).
% Axiom fact_248_ord__le__eq__trans:(forall (C_31:(nat->Prop)) (A_76:(nat->Prop)) (B_58:(nat->Prop)), (((ord_less_eq_nat_o A_76) B_58)->((((eq (nat->Prop)) B_58) C_31)->((ord_less_eq_nat_o A_76) C_31)))).
% Axiom fact_249_xt1_I3_J:(forall (C_30:Prop) (B_57:Prop) (A_75:Prop), (((iff A_75) B_57)->(((ord_less_eq_o C_30) B_57)->((ord_less_eq_o C_30) A_75)))).
% Axiom fact_250_xt1_I3_J:(forall (C_30:nat) (A_75:nat) (B_57:nat), ((((eq nat) A_75) B_57)->(((ord_less_eq_nat C_30) B_57)->((ord_less_eq_nat C_30) A_75)))).
% Axiom fact_251_xt1_I3_J:(forall (C_30:(nat->Prop)) (A_75:(nat->Prop)) (B_57:(nat->Prop)), ((((eq (nat->Prop)) A_75) B_57)->(((ord_less_eq_nat_o C_30) B_57)->((ord_less_eq_nat_o C_30) A_75)))).
% Axiom fact_252_ord__eq__le__trans:(forall (C_29:Prop) (B_56:Prop) (A_74:Prop), (((iff A_74) B_56)->(((ord_less_eq_o B_56) C_29)->((ord_less_eq_o A_74) C_29)))).
% Axiom fact_253_ord__eq__le__trans:(forall (C_29:nat) (A_74:nat) (B_56:nat), ((((eq nat) A_74) B_56)->(((ord_less_eq_nat B_56) C_29)->((ord_less_eq_nat A_74) C_29)))).
% Axiom fact_254_ord__eq__le__trans:(forall (C_29:(nat->Prop)) (A_74:(nat->Prop)) (B_56:(nat->Prop)), ((((eq (nat->Prop)) A_74) B_56)->(((ord_less_eq_nat_o B_56) C_29)->((ord_less_eq_nat_o A_74) C_29)))).
% Axiom fact_255_order__antisym__conv:(forall (Y_29:Prop) (X_39:Prop), (((ord_less_eq_o Y_29) X_39)->((iff ((ord_less_eq_o X_39) Y_29)) ((iff X_39) Y_29)))).
% Axiom fact_256_order__antisym__conv:(forall (Y_29:nat) (X_39:nat), (((ord_less_eq_nat Y_29) X_39)->((iff ((ord_less_eq_nat X_39) Y_29)) (((eq nat) X_39) Y_29)))).
% Axiom fact_257_order__antisym__conv:(forall (Y_29:(nat->Prop)) (X_39:(nat->Prop)), (((ord_less_eq_nat_o Y_29) X_39)->((iff ((ord_less_eq_nat_o X_39) Y_29)) (((eq (nat->Prop)) X_39) Y_29)))).
% Axiom fact_258_le__funD:(forall (X_38:nat) (F_26:(nat->Prop)) (G_7:(nat->Prop)), (((ord_less_eq_nat_o F_26) G_7)->((ord_less_eq_o (F_26 X_38)) (G_7 X_38)))).
% Axiom fact_259_order__eq__refl:(forall (Y_28:Prop) (X_37:Prop), (((iff X_37) Y_28)->((ord_less_eq_o X_37) Y_28))).
% Axiom fact_260_order__eq__refl:(forall (X_37:nat) (Y_28:nat), ((((eq nat) X_37) Y_28)->((ord_less_eq_nat X_37) Y_28))).
% Axiom fact_261_order__eq__refl:(forall (X_37:(nat->Prop)) (Y_28:(nat->Prop)), ((((eq (nat->Prop)) X_37) Y_28)->((ord_less_eq_nat_o X_37) Y_28))).
% Axiom fact_262_order__eq__iff:(forall (Y_27:Prop) (X_36:Prop), ((iff ((iff X_36) Y_27)) ((and ((ord_less_eq_o X_36) Y_27)) ((ord_less_eq_o Y_27) X_36)))).
% Axiom fact_263_order__eq__iff:(forall (X_36:nat) (Y_27:nat), ((iff (((eq nat) X_36) Y_27)) ((and ((ord_less_eq_nat X_36) Y_27)) ((ord_less_eq_nat Y_27) X_36)))).
% Axiom fact_264_order__eq__iff:(forall (X_36:(nat->Prop)) (Y_27:(nat->Prop)), ((iff (((eq (nat->Prop)) X_36) Y_27)) ((and ((ord_less_eq_nat_o X_36) Y_27)) ((ord_less_eq_nat_o Y_27) X_36)))).
% Axiom fact_265_linorder__linear:(forall (X_35:nat) (Y_26:nat), ((or ((ord_less_eq_nat X_35) Y_26)) ((ord_less_eq_nat Y_26) X_35))).
% Axiom fact_266_le__fun__def:(forall (F_25:(nat->Prop)) (G_6:(nat->Prop)), ((iff ((ord_less_eq_nat_o F_25) G_6)) (forall (X_1:nat), ((ord_less_eq_o (F_25 X_1)) (G_6 X_1))))).
% Axiom fact_267_linorder__not__less:(forall (X_34:nat) (Y_25:nat), ((iff (((ord_less_nat X_34) Y_25)->False)) ((ord_less_eq_nat Y_25) X_34))).
% Axiom fact_268_linorder__not__le:(forall (X_33:nat) (Y_24:nat), ((iff (((ord_less_eq_nat X_33) Y_24)->False)) ((ord_less_nat Y_24) X_33))).
% Axiom fact_269_linorder__le__less__linear:(forall (X_32:nat) (Y_23:nat), ((or ((ord_less_eq_nat X_32) Y_23)) ((ord_less_nat Y_23) X_32))).
% Axiom fact_270_order__less__le:(forall (X_31:(product_unit->Prop)) (Y_22:(product_unit->Prop)), ((iff ((ord_le232288914unit_o X_31) Y_22)) ((and ((ord_le1511552390unit_o X_31) Y_22)) (not (((eq (product_unit->Prop)) X_31) Y_22))))).
% Axiom fact_271_order__less__le:(forall (X_31:(arrow_1429601828e_indi->Prop)) (Y_22:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o X_31) Y_22)) ((and ((ord_le1799070453indi_o X_31) Y_22)) (not (((eq (arrow_1429601828e_indi->Prop)) X_31) Y_22))))).
% Axiom fact_272_order__less__le:(forall (X_31:Prop) (Y_22:Prop), ((iff ((ord_less_o X_31) Y_22)) ((and ((ord_less_eq_o X_31) Y_22)) (((iff X_31) Y_22)->False)))).
% Axiom fact_273_order__less__le:(forall (X_31:(nat->Prop)) (Y_22:(nat->Prop)), ((iff ((ord_less_nat_o X_31) Y_22)) ((and ((ord_less_eq_nat_o X_31) Y_22)) (not (((eq (nat->Prop)) X_31) Y_22))))).
% Axiom fact_274_order__less__le:(forall (X_31:nat) (Y_22:nat), ((iff ((ord_less_nat X_31) Y_22)) ((and ((ord_less_eq_nat X_31) Y_22)) (not (((eq nat) X_31) Y_22))))).
% Axiom fact_275_less__le__not__le:(forall (X_30:(product_unit->Prop)) (Y_21:(product_unit->Prop)), ((iff ((ord_le232288914unit_o X_30) Y_21)) ((and ((ord_le1511552390unit_o X_30) Y_21)) (((ord_le1511552390unit_o Y_21) X_30)->False)))).
% Axiom fact_276_less__le__not__le:(forall (X_30:(arrow_1429601828e_indi->Prop)) (Y_21:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o X_30) Y_21)) ((and ((ord_le1799070453indi_o X_30) Y_21)) (((ord_le1799070453indi_o Y_21) X_30)->False)))).
% Axiom fact_277_less__le__not__le:(forall (X_30:Prop) (Y_21:Prop), ((iff ((ord_less_o X_30) Y_21)) ((and ((ord_less_eq_o X_30) Y_21)) (((ord_less_eq_o Y_21) X_30)->False)))).
% Axiom fact_278_less__le__not__le:(forall (X_30:(nat->Prop)) (Y_21:(nat->Prop)), ((iff ((ord_less_nat_o X_30) Y_21)) ((and ((ord_less_eq_nat_o X_30) Y_21)) (((ord_less_eq_nat_o Y_21) X_30)->False)))).
% Axiom fact_279_less__le__not__le:(forall (X_30:nat) (Y_21:nat), ((iff ((ord_less_nat X_30) Y_21)) ((and ((ord_less_eq_nat X_30) Y_21)) (((ord_less_eq_nat Y_21) X_30)->False)))).
% Axiom fact_280_order__le__less:(forall (X_29:(product_unit->Prop)) (Y_20:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o X_29) Y_20)) ((or ((ord_le232288914unit_o X_29) Y_20)) (((eq (product_unit->Prop)) X_29) Y_20)))).
% Axiom fact_281_order__le__less:(forall (X_29:(arrow_1429601828e_indi->Prop)) (Y_20:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o X_29) Y_20)) ((or ((ord_le777687553indi_o X_29) Y_20)) (((eq (arrow_1429601828e_indi->Prop)) X_29) Y_20)))).
% Axiom fact_282_order__le__less:(forall (X_29:Prop) (Y_20:Prop), ((iff ((ord_less_eq_o X_29) Y_20)) ((or ((ord_less_o X_29) Y_20)) ((iff X_29) Y_20)))).
% Axiom fact_283_order__le__less:(forall (X_29:(nat->Prop)) (Y_20:(nat->Prop)), ((iff ((ord_less_eq_nat_o X_29) Y_20)) ((or ((ord_less_nat_o X_29) Y_20)) (((eq (nat->Prop)) X_29) Y_20)))).
% Axiom fact_284_order__le__less:(forall (X_29:nat) (Y_20:nat), ((iff ((ord_less_eq_nat X_29) Y_20)) ((or ((ord_less_nat X_29) Y_20)) (((eq nat) X_29) Y_20)))).
% Axiom fact_285_leI:(forall (X_28:nat) (Y_19:nat), ((((ord_less_nat X_28) Y_19)->False)->((ord_less_eq_nat Y_19) X_28))).
% Axiom fact_286_not__leE:(forall (Y_18:nat) (X_27:nat), ((((ord_less_eq_nat Y_18) X_27)->False)->((ord_less_nat X_27) Y_18))).
% Axiom fact_287_linorder__antisym__conv1:(forall (X_26:nat) (Y_17:nat), ((((ord_less_nat X_26) Y_17)->False)->((iff ((ord_less_eq_nat X_26) Y_17)) (((eq nat) X_26) Y_17)))).
% Axiom fact_288_order__neq__le__trans:(forall (A_73:(product_unit->Prop)) (B_55:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_73) B_55))->(((ord_le1511552390unit_o A_73) B_55)->((ord_le232288914unit_o A_73) B_55)))).
% Axiom fact_289_order__neq__le__trans:(forall (A_73:(arrow_1429601828e_indi->Prop)) (B_55:(arrow_1429601828e_indi->Prop)), ((not (((eq (arrow_1429601828e_indi->Prop)) A_73) B_55))->(((ord_le1799070453indi_o A_73) B_55)->((ord_le777687553indi_o A_73) B_55)))).
% Axiom fact_290_order__neq__le__trans:(forall (B_55:Prop) (A_73:Prop), ((((iff A_73) B_55)->False)->(((ord_less_eq_o A_73) B_55)->((ord_less_o A_73) B_55)))).
% Axiom fact_291_order__neq__le__trans:(forall (A_73:(nat->Prop)) (B_55:(nat->Prop)), ((not (((eq (nat->Prop)) A_73) B_55))->(((ord_less_eq_nat_o A_73) B_55)->((ord_less_nat_o A_73) B_55)))).
% Axiom fact_292_order__neq__le__trans:(forall (A_73:nat) (B_55:nat), ((not (((eq nat) A_73) B_55))->(((ord_less_eq_nat A_73) B_55)->((ord_less_nat A_73) B_55)))).
% Axiom fact_293_xt1_I12_J:(forall (A_72:(product_unit->Prop)) (B_54:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_72) B_54))->(((ord_le1511552390unit_o B_54) A_72)->((ord_le232288914unit_o B_54) A_72)))).
% Axiom fact_294_xt1_I12_J:(forall (A_72:(arrow_1429601828e_indi->Prop)) (B_54:(arrow_1429601828e_indi->Prop)), ((not (((eq (arrow_1429601828e_indi->Prop)) A_72) B_54))->(((ord_le1799070453indi_o B_54) A_72)->((ord_le777687553indi_o B_54) A_72)))).
% Axiom fact_295_xt1_I12_J:(forall (B_54:Prop) (A_72:Prop), ((((iff A_72) B_54)->False)->(((ord_less_eq_o B_54) A_72)->((ord_less_o B_54) A_72)))).
% Axiom fact_296_xt1_I12_J:(forall (A_72:(nat->Prop)) (B_54:(nat->Prop)), ((not (((eq (nat->Prop)) A_72) B_54))->(((ord_less_eq_nat_o B_54) A_72)->((ord_less_nat_o B_54) A_72)))).
% Axiom fact_297_xt1_I12_J:(forall (A_72:nat) (B_54:nat), ((not (((eq nat) A_72) B_54))->(((ord_less_eq_nat B_54) A_72)->((ord_less_nat B_54) A_72)))).
% Axiom fact_298_leD:(forall (Y_16:nat) (X_25:nat), (((ord_less_eq_nat Y_16) X_25)->(((ord_less_nat X_25) Y_16)->False))).
% Axiom fact_299_order__less__imp__le:(forall (X_24:(product_unit->Prop)) (Y_15:(product_unit->Prop)), (((ord_le232288914unit_o X_24) Y_15)->((ord_le1511552390unit_o X_24) Y_15))).
% Axiom fact_300_order__less__imp__le:(forall (X_24:(arrow_1429601828e_indi->Prop)) (Y_15:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_24) Y_15)->((ord_le1799070453indi_o X_24) Y_15))).
% Axiom fact_301_order__less__imp__le:(forall (X_24:Prop) (Y_15:Prop), (((ord_less_o X_24) Y_15)->((ord_less_eq_o X_24) Y_15))).
% Axiom fact_302_order__less__imp__le:(forall (X_24:(nat->Prop)) (Y_15:(nat->Prop)), (((ord_less_nat_o X_24) Y_15)->((ord_less_eq_nat_o X_24) Y_15))).
% Axiom fact_303_order__less__imp__le:(forall (X_24:nat) (Y_15:nat), (((ord_less_nat X_24) Y_15)->((ord_less_eq_nat X_24) Y_15))).
% Axiom fact_304_linorder__antisym__conv2:(forall (X_23:nat) (Y_14:nat), (((ord_less_eq_nat X_23) Y_14)->((iff (((ord_less_nat X_23) Y_14)->False)) (((eq nat) X_23) Y_14)))).
% Axiom fact_305_order__le__imp__less__or__eq:(forall (X_22:(product_unit->Prop)) (Y_13:(product_unit->Prop)), (((ord_le1511552390unit_o X_22) Y_13)->((or ((ord_le232288914unit_o X_22) Y_13)) (((eq (product_unit->Prop)) X_22) Y_13)))).
% Axiom fact_306_order__le__imp__less__or__eq:(forall (X_22:(arrow_1429601828e_indi->Prop)) (Y_13:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o X_22) Y_13)->((or ((ord_le777687553indi_o X_22) Y_13)) (((eq (arrow_1429601828e_indi->Prop)) X_22) Y_13)))).
% Axiom fact_307_order__le__imp__less__or__eq:(forall (X_22:Prop) (Y_13:Prop), (((ord_less_eq_o X_22) Y_13)->((or ((ord_less_o X_22) Y_13)) ((iff X_22) Y_13)))).
% Axiom fact_308_order__le__imp__less__or__eq:(forall (X_22:(nat->Prop)) (Y_13:(nat->Prop)), (((ord_less_eq_nat_o X_22) Y_13)->((or ((ord_less_nat_o X_22) Y_13)) (((eq (nat->Prop)) X_22) Y_13)))).
% Axiom fact_309_order__le__imp__less__or__eq:(forall (X_22:nat) (Y_13:nat), (((ord_less_eq_nat X_22) Y_13)->((or ((ord_less_nat X_22) Y_13)) (((eq nat) X_22) Y_13)))).
% Axiom fact_310_order__le__neq__trans:(forall (A_71:(product_unit->Prop)) (B_53:(product_unit->Prop)), (((ord_le1511552390unit_o A_71) B_53)->((not (((eq (product_unit->Prop)) A_71) B_53))->((ord_le232288914unit_o A_71) B_53)))).
% Axiom fact_311_order__le__neq__trans:(forall (A_71:(arrow_1429601828e_indi->Prop)) (B_53:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_71) B_53)->((not (((eq (arrow_1429601828e_indi->Prop)) A_71) B_53))->((ord_le777687553indi_o A_71) B_53)))).
% Axiom fact_312_order__le__neq__trans:(forall (A_71:Prop) (B_53:Prop), (((ord_less_eq_o A_71) B_53)->((((iff A_71) B_53)->False)->((ord_less_o A_71) B_53)))).
% Axiom fact_313_order__le__neq__trans:(forall (A_71:(nat->Prop)) (B_53:(nat->Prop)), (((ord_less_eq_nat_o A_71) B_53)->((not (((eq (nat->Prop)) A_71) B_53))->((ord_less_nat_o A_71) B_53)))).
% Axiom fact_314_order__le__neq__trans:(forall (A_71:nat) (B_53:nat), (((ord_less_eq_nat A_71) B_53)->((not (((eq nat) A_71) B_53))->((ord_less_nat A_71) B_53)))).
% Axiom fact_315_xt1_I11_J:(forall (B_52:(nat->Prop)) (A_70:(nat->Prop)), (((ord_less_eq_nat_o B_52) A_70)->((not (((eq (nat->Prop)) A_70) B_52))->((ord_less_nat_o B_52) A_70)))).
% Axiom fact_316_xt1_I11_J:(forall (B_52:(product_unit->Prop)) (A_70:(product_unit->Prop)), (((ord_le1511552390unit_o B_52) A_70)->((not (((eq (product_unit->Prop)) A_70) B_52))->((ord_le232288914unit_o B_52) A_70)))).
% Axiom fact_317_xt1_I11_J:(forall (B_52:(arrow_1429601828e_indi->Prop)) (A_70:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o B_52) A_70)->((not (((eq (arrow_1429601828e_indi->Prop)) A_70) B_52))->((ord_le777687553indi_o B_52) A_70)))).
% Axiom fact_318_xt1_I11_J:(forall (B_52:nat) (A_70:nat), (((ord_less_eq_nat B_52) A_70)->((not (((eq nat) A_70) B_52))->((ord_less_nat B_52) A_70)))).
% Axiom fact_319_xt1_I11_J:(forall (B_52:Prop) (A_70:Prop), (((ord_less_eq_o B_52) A_70)->((((iff A_70) B_52)->False)->((ord_less_o B_52) A_70)))).
% Axiom fact_320_order__less__le__trans:(forall (Z_4:(nat->Prop)) (X_21:(nat->Prop)) (Y_12:(nat->Prop)), (((ord_less_nat_o X_21) Y_12)->(((ord_less_eq_nat_o Y_12) Z_4)->((ord_less_nat_o X_21) Z_4)))).
% Axiom fact_321_order__less__le__trans:(forall (Z_4:(product_unit->Prop)) (X_21:(product_unit->Prop)) (Y_12:(product_unit->Prop)), (((ord_le232288914unit_o X_21) Y_12)->(((ord_le1511552390unit_o Y_12) Z_4)->((ord_le232288914unit_o X_21) Z_4)))).
% Axiom fact_322_order__less__le__trans:(forall (Z_4:(arrow_1429601828e_indi->Prop)) (X_21:(arrow_1429601828e_indi->Prop)) (Y_12:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o X_21) Y_12)->(((ord_le1799070453indi_o Y_12) Z_4)->((ord_le777687553indi_o X_21) Z_4)))).
% Axiom fact_323_order__less__le__trans:(forall (Z_4:nat) (X_21:nat) (Y_12:nat), (((ord_less_nat X_21) Y_12)->(((ord_less_eq_nat Y_12) Z_4)->((ord_less_nat X_21) Z_4)))).
% Axiom fact_324_order__less__le__trans:(forall (Z_4:Prop) (X_21:Prop) (Y_12:Prop), (((ord_less_o X_21) Y_12)->(((ord_less_eq_o Y_12) Z_4)->((ord_less_o X_21) Z_4)))).
% Axiom fact_325_xt1_I7_J:(forall (Z_3:(nat->Prop)) (Y_11:(nat->Prop)) (X_20:(nat->Prop)), (((ord_less_nat_o Y_11) X_20)->(((ord_less_eq_nat_o Z_3) Y_11)->((ord_less_nat_o Z_3) X_20)))).
% Axiom fact_326_xt1_I7_J:(forall (Z_3:(product_unit->Prop)) (Y_11:(product_unit->Prop)) (X_20:(product_unit->Prop)), (((ord_le232288914unit_o Y_11) X_20)->(((ord_le1511552390unit_o Z_3) Y_11)->((ord_le232288914unit_o Z_3) X_20)))).
% Axiom fact_327_xt1_I7_J:(forall (Z_3:(arrow_1429601828e_indi->Prop)) (Y_11:(arrow_1429601828e_indi->Prop)) (X_20:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o Y_11) X_20)->(((ord_le1799070453indi_o Z_3) Y_11)->((ord_le777687553indi_o Z_3) X_20)))).
% Axiom fact_328_xt1_I7_J:(forall (Z_3:nat) (Y_11:nat) (X_20:nat), (((ord_less_nat Y_11) X_20)->(((ord_less_eq_nat Z_3) Y_11)->((ord_less_nat Z_3) X_20)))).
% Axiom fact_329_xt1_I7_J:(forall (Z_3:Prop) (Y_11:Prop) (X_20:Prop), (((ord_less_o Y_11) X_20)->(((ord_less_eq_o Z_3) Y_11)->((ord_less_o Z_3) X_20)))).
% Axiom fact_330_order__le__less__trans:(forall (Z_2:(nat->Prop)) (X_19:(nat->Prop)) (Y_10:(nat->Prop)), (((ord_less_eq_nat_o X_19) Y_10)->(((ord_less_nat_o Y_10) Z_2)->((ord_less_nat_o X_19) Z_2)))).
% Axiom fact_331_order__le__less__trans:(forall (Z_2:(product_unit->Prop)) (X_19:(product_unit->Prop)) (Y_10:(product_unit->Prop)), (((ord_le1511552390unit_o X_19) Y_10)->(((ord_le232288914unit_o Y_10) Z_2)->((ord_le232288914unit_o X_19) Z_2)))).
% Axiom fact_332_order__le__less__trans:(forall (Z_2:(arrow_1429601828e_indi->Prop)) (X_19:(arrow_1429601828e_indi->Prop)) (Y_10:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o X_19) Y_10)->(((ord_le777687553indi_o Y_10) Z_2)->((ord_le777687553indi_o X_19) Z_2)))).
% Axiom fact_333_order__le__less__trans:(forall (Z_2:nat) (X_19:nat) (Y_10:nat), (((ord_less_eq_nat X_19) Y_10)->(((ord_less_nat Y_10) Z_2)->((ord_less_nat X_19) Z_2)))).
% Axiom fact_334_order__le__less__trans:(forall (Z_2:Prop) (X_19:Prop) (Y_10:Prop), (((ord_less_eq_o X_19) Y_10)->(((ord_less_o Y_10) Z_2)->((ord_less_o X_19) Z_2)))).
% Axiom fact_335_xt1_I8_J:(forall (Z_1:(nat->Prop)) (Y_9:(nat->Prop)) (X_18:(nat->Prop)), (((ord_less_eq_nat_o Y_9) X_18)->(((ord_less_nat_o Z_1) Y_9)->((ord_less_nat_o Z_1) X_18)))).
% Axiom fact_336_xt1_I8_J:(forall (Z_1:(product_unit->Prop)) (Y_9:(product_unit->Prop)) (X_18:(product_unit->Prop)), (((ord_le1511552390unit_o Y_9) X_18)->(((ord_le232288914unit_o Z_1) Y_9)->((ord_le232288914unit_o Z_1) X_18)))).
% Axiom fact_337_xt1_I8_J:(forall (Z_1:(arrow_1429601828e_indi->Prop)) (Y_9:(arrow_1429601828e_indi->Prop)) (X_18:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o Y_9) X_18)->(((ord_le777687553indi_o Z_1) Y_9)->((ord_le777687553indi_o Z_1) X_18)))).
% Axiom fact_338_xt1_I8_J:(forall (Z_1:nat) (Y_9:nat) (X_18:nat), (((ord_less_eq_nat Y_9) X_18)->(((ord_less_nat Z_1) Y_9)->((ord_less_nat Z_1) X_18)))).
% Axiom fact_339_xt1_I8_J:(forall (Z_1:Prop) (Y_9:Prop) (X_18:Prop), (((ord_less_eq_o Y_9) X_18)->(((ord_less_o Z_1) Y_9)->((ord_less_o Z_1) X_18)))).
% Axiom fact_340_top__greatest:(forall (A_69:Prop), ((ord_less_eq_o A_69) top_top_o)).
% Axiom fact_341_top__greatest:(forall (A_69:((produc1501160679le_alt->Prop)->Prop)), ((ord_le1063113995lt_o_o A_69) top_to1842727771lt_o_o)).
% Axiom fact_342_top__greatest:(forall (A_69:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((ord_le134800455lt_o_o A_69) top_to1969627639lt_o_o)).
% Axiom fact_343_top__greatest:(forall (A_69:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((ord_le1992928527lt_o_o A_69) top_to2122763103lt_o_o)).
% Axiom fact_344_top__greatest:(forall (A_69:(produc1501160679le_alt->Prop)), ((ord_le97612146_alt_o A_69) top_to1841428258_alt_o)).
% Axiom fact_345_top__greatest:(forall (A_69:(nat->Prop)), ((ord_less_eq_nat_o A_69) top_top_nat_o)).
% Axiom fact_346_top__greatest:(forall (A_69:(product_unit->Prop)), ((ord_le1511552390unit_o A_69) top_to1984820022unit_o)).
% Axiom fact_347_top__greatest:(forall (A_69:(arrow_1429601828e_indi->Prop)), ((ord_le1799070453indi_o A_69) top_to988227749indi_o)).
% Axiom fact_348_top__unique:(forall (A_68:Prop), ((iff ((ord_less_eq_o top_top_o) A_68)) ((iff A_68) top_top_o))).
% Axiom fact_349_top__unique:(forall (A_68:((produc1501160679le_alt->Prop)->Prop)), ((iff ((ord_le1063113995lt_o_o top_to1842727771lt_o_o) A_68)) (((eq ((produc1501160679le_alt->Prop)->Prop)) A_68) top_to1842727771lt_o_o))).
% Axiom fact_350_top__unique:(forall (A_68:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le134800455lt_o_o top_to1969627639lt_o_o) A_68)) (((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) A_68) top_to1969627639lt_o_o))).
% Axiom fact_351_top__unique:(forall (A_68:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le1992928527lt_o_o top_to2122763103lt_o_o) A_68)) (((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) A_68) top_to2122763103lt_o_o))).
% Axiom fact_352_top__unique:(forall (A_68:(produc1501160679le_alt->Prop)), ((iff ((ord_le97612146_alt_o top_to1841428258_alt_o) A_68)) (((eq (produc1501160679le_alt->Prop)) A_68) top_to1841428258_alt_o))).
% Axiom fact_353_top__unique:(forall (A_68:(nat->Prop)), ((iff ((ord_less_eq_nat_o top_top_nat_o) A_68)) (((eq (nat->Prop)) A_68) top_top_nat_o))).
% Axiom fact_354_top__unique:(forall (A_68:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o top_to1984820022unit_o) A_68)) (((eq (product_unit->Prop)) A_68) top_to1984820022unit_o))).
% Axiom fact_355_top__unique:(forall (A_68:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o top_to988227749indi_o) A_68)) (((eq (arrow_1429601828e_indi->Prop)) A_68) top_to988227749indi_o))).
% Axiom fact_356_top__le:(forall (A_67:Prop), (((ord_less_eq_o top_top_o) A_67)->((iff A_67) top_top_o))).
% Axiom fact_357_top__le:(forall (A_67:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o top_to1842727771lt_o_o) A_67)->(((eq ((produc1501160679le_alt->Prop)->Prop)) A_67) top_to1842727771lt_o_o))).
% Axiom fact_358_top__le:(forall (A_67:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o top_to1969627639lt_o_o) A_67)->(((eq (((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) A_67) top_to1969627639lt_o_o))).
% Axiom fact_359_top__le:(forall (A_67:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o top_to2122763103lt_o_o) A_67)->(((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) A_67) top_to2122763103lt_o_o))).
% Axiom fact_360_top__le:(forall (A_67:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o top_to1841428258_alt_o) A_67)->(((eq (produc1501160679le_alt->Prop)) A_67) top_to1841428258_alt_o))).
% Axiom fact_361_top__le:(forall (A_67:(nat->Prop)), (((ord_less_eq_nat_o top_top_nat_o) A_67)->(((eq (nat->Prop)) A_67) top_top_nat_o))).
% Axiom fact_362_top__le:(forall (A_67:(product_unit->Prop)), (((ord_le1511552390unit_o top_to1984820022unit_o) A_67)->(((eq (product_unit->Prop)) A_67) top_to1984820022unit_o))).
% Axiom fact_363_top__le:(forall (A_67:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o top_to988227749indi_o) A_67)->(((eq (arrow_1429601828e_indi->Prop)) A_67) top_to988227749indi_o))).
% Axiom fact_364_inj__on__def:(forall (F_24:(nat->nat)) (A_66:(nat->Prop)), ((iff ((inj_on_nat_nat F_24) A_66)) (forall (X_1:nat), (((member_nat X_1) A_66)->(forall (Xa:nat), (((member_nat Xa) A_66)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq nat) X_1) Xa)))))))).
% Axiom fact_365_inj__on__def:(forall (F_24:(arrow_1429601828e_indi->nat)) (A_66:(arrow_1429601828e_indi->Prop)), ((iff ((inj_on978774663di_nat F_24) A_66)) (forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_66)->(forall (Xa:arrow_1429601828e_indi), (((member2052026769e_indi Xa) A_66)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq arrow_1429601828e_indi) X_1) Xa)))))))).
% Axiom fact_366_inj__on__contraD:(forall (X_17:nat) (Y_8:nat) (F_23:(nat->nat)) (A_65:(nat->Prop)), (((inj_on_nat_nat F_23) A_65)->((not (((eq nat) X_17) Y_8))->(((member_nat X_17) A_65)->(((member_nat Y_8) A_65)->(not (((eq nat) (F_23 X_17)) (F_23 Y_8)))))))).
% Axiom fact_367_inj__on__contraD:(forall (X_17:arrow_1429601828e_indi) (Y_8:arrow_1429601828e_indi) (F_23:(arrow_1429601828e_indi->nat)) (A_65:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_23) A_65)->((not (((eq arrow_1429601828e_indi) X_17) Y_8))->(((member2052026769e_indi X_17) A_65)->(((member2052026769e_indi Y_8) A_65)->(not (((eq nat) (F_23 X_17)) (F_23 Y_8)))))))).
% Axiom fact_368_inj__on__iff:(forall (Y_7:nat) (X_16:nat) (F_22:(nat->nat)) (A_64:(nat->Prop)), (((inj_on_nat_nat F_22) A_64)->(((member_nat X_16) A_64)->(((member_nat Y_7) A_64)->((iff (((eq nat) (F_22 X_16)) (F_22 Y_7))) (((eq nat) X_16) Y_7)))))).
% Axiom fact_369_inj__on__iff:(forall (Y_7:arrow_1429601828e_indi) (X_16:arrow_1429601828e_indi) (F_22:(arrow_1429601828e_indi->nat)) (A_64:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_22) A_64)->(((member2052026769e_indi X_16) A_64)->(((member2052026769e_indi Y_7) A_64)->((iff (((eq nat) (F_22 X_16)) (F_22 Y_7))) (((eq arrow_1429601828e_indi) X_16) Y_7)))))).
% Axiom fact_370_inj__onD:(forall (X_15:nat) (Y_6:nat) (F_21:(nat->nat)) (A_63:(nat->Prop)), (((inj_on_nat_nat F_21) A_63)->((((eq nat) (F_21 X_15)) (F_21 Y_6))->(((member_nat X_15) A_63)->(((member_nat Y_6) A_63)->(((eq nat) X_15) Y_6)))))).
% Axiom fact_371_inj__onD:(forall (X_15:arrow_1429601828e_indi) (Y_6:arrow_1429601828e_indi) (F_21:(arrow_1429601828e_indi->nat)) (A_63:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_21) A_63)->((((eq nat) (F_21 X_15)) (F_21 Y_6))->(((member2052026769e_indi X_15) A_63)->(((member2052026769e_indi Y_6) A_63)->(((eq arrow_1429601828e_indi) X_15) Y_6)))))).
% Axiom fact_372_Pi__mem:(forall (X_14:produc1501160679le_alt) (F_20:(produc1501160679le_alt->Prop)) (A_62:(produc1501160679le_alt->Prop)) (B_51:(produc1501160679le_alt->(Prop->Prop))), (((member377231867_alt_o F_20) ((pi_Pro1701359055_alt_o A_62) B_51))->(((member214075476le_alt X_14) A_62)->((member_o (F_20 X_14)) (B_51 X_14))))).
% Axiom fact_373_Pi__mem:(forall (X_14:arrow_1429601828e_indi) (F_20:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_62:(arrow_1429601828e_indi->Prop)) (B_51:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))), (((member526088951_alt_o F_20) ((pi_Arr1929480907_alt_o A_62) B_51))->(((member2052026769e_indi X_14) A_62)->((member377231867_alt_o (F_20 X_14)) (B_51 X_14))))).
% Axiom fact_374_Pi__mem:(forall (X_14:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_20:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_62:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_51:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))), (((member616898751_alt_o F_20) ((pi_Arr1304755663_alt_o A_62) B_51))->(((member526088951_alt_o X_14) A_62)->((member377231867_alt_o (F_20 X_14)) (B_51 X_14))))).
% Axiom fact_375_Prof__def:(((eq ((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) arrow_734252939e_Prof) ((pi_Arr1929480907_alt_o top_to988227749indi_o) (fun (Uu:arrow_1429601828e_indi)=> arrow_823908191le_Lin))).
% Axiom fact_376_inj__on__id2:(forall (A_61:(nat->Prop)), ((inj_on_nat_nat (fun (X_1:nat)=> X_1)) A_61)).
% Axiom fact_377_funcset__mem:(forall (X_13:produc1501160679le_alt) (F_19:(produc1501160679le_alt->Prop)) (A_60:(produc1501160679le_alt->Prop)) (B_50:(Prop->Prop)), (((member377231867_alt_o F_19) ((pi_Pro1701359055_alt_o A_60) (fun (Uu:produc1501160679le_alt)=> B_50)))->(((member214075476le_alt X_13) A_60)->((member_o (F_19 X_13)) B_50)))).
% Axiom fact_378_funcset__mem:(forall (X_13:arrow_1429601828e_indi) (F_19:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_60:(arrow_1429601828e_indi->Prop)) (B_50:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_19) ((pi_Arr1929480907_alt_o A_60) (fun (Uu:arrow_1429601828e_indi)=> B_50)))->(((member2052026769e_indi X_13) A_60)->((member377231867_alt_o (F_19 X_13)) B_50)))).
% Axiom fact_379_funcset__mem:(forall (X_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_60:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_50:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_19) ((pi_Arr1304755663_alt_o A_60) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_50)))->(((member526088951_alt_o X_13) A_60)->((member377231867_alt_o (F_19 X_13)) B_50)))).
% Axiom fact_380_dictator__def:(forall (F_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (_TPTP_I:arrow_1429601828e_indi), ((iff ((arrow_1212662430ctator F_18) _TPTP_I)) (forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) arrow_734252939e_Prof)->(((eq (produc1501160679le_alt->Prop)) (F_18 X_1)) (X_1 _TPTP_I)))))).
% Axiom fact_381_inj__eq:(forall (X_12:nat) (Y_5:nat) (F_17:(nat->nat)), (((inj_on_nat_nat F_17) top_top_nat_o)->((iff (((eq nat) (F_17 X_12)) (F_17 Y_5))) (((eq nat) X_12) Y_5)))).
% Axiom fact_382_inj__eq:(forall (X_12:arrow_1429601828e_indi) (Y_5:arrow_1429601828e_indi) (F_17:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_17) top_to988227749indi_o)->((iff (((eq nat) (F_17 X_12)) (F_17 Y_5))) (((eq arrow_1429601828e_indi) X_12) Y_5)))).
% Axiom fact_383_injD:(forall (X_11:nat) (Y_4:nat) (F_16:(nat->nat)), (((inj_on_nat_nat F_16) top_top_nat_o)->((((eq nat) (F_16 X_11)) (F_16 Y_4))->(((eq nat) X_11) Y_4)))).
% Axiom fact_384_injD:(forall (X_11:arrow_1429601828e_indi) (Y_4:arrow_1429601828e_indi) (F_16:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_16) top_to988227749indi_o)->((((eq nat) (F_16 X_11)) (F_16 Y_4))->(((eq arrow_1429601828e_indi) X_11) Y_4)))).
% Axiom fact_385_inv__into__f__f:(forall (X_10:nat) (F_15:(nat->nat)) (A_59:(nat->Prop)), (((inj_on_nat_nat F_15) A_59)->(((member_nat X_10) A_59)->(((eq nat) (((hilber195283148at_nat A_59) F_15) (F_15 X_10))) X_10)))).
% Axiom fact_386_inv__into__f__f:(forall (X_10:arrow_1429601828e_indi) (F_15:(arrow_1429601828e_indi->nat)) (A_59:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_15) A_59)->(((member2052026769e_indi X_10) A_59)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat A_59) F_15) (F_15 X_10))) X_10)))).
% Axiom fact_387_inv__into__f__eq:(forall (Y_3:nat) (X_9:nat) (F_14:(nat->nat)) (A_58:(nat->Prop)), (((inj_on_nat_nat F_14) A_58)->(((member_nat X_9) A_58)->((((eq nat) (F_14 X_9)) Y_3)->(((eq nat) (((hilber195283148at_nat A_58) F_14) Y_3)) X_9))))).
% Axiom fact_388_inv__into__f__eq:(forall (Y_3:nat) (X_9:arrow_1429601828e_indi) (F_14:(arrow_1429601828e_indi->nat)) (A_58:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_14) A_58)->(((member2052026769e_indi X_9) A_58)->((((eq nat) (F_14 X_9)) Y_3)->(((eq arrow_1429601828e_indi) (((hilber598459244di_nat A_58) F_14) Y_3)) X_9))))).
% Axiom fact_389_Pi__I:(forall (F_13:(produc1501160679le_alt->Prop)) (B_49:(produc1501160679le_alt->(Prop->Prop))) (A_57:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_57)->((member_o (F_13 X_1)) (B_49 X_1))))->((member377231867_alt_o F_13) ((pi_Pro1701359055_alt_o A_57) B_49)))).
% Axiom fact_390_Pi__I:(forall (F_13:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_49:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_57:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_57)->((member377231867_alt_o (F_13 X_1)) (B_49 X_1))))->((member526088951_alt_o F_13) ((pi_Arr1929480907_alt_o A_57) B_49)))).
% Axiom fact_391_Pi__I:(forall (F_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_49:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_57:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_57)->((member377231867_alt_o (F_13 X_1)) (B_49 X_1))))->((member616898751_alt_o F_13) ((pi_Arr1304755663_alt_o A_57) B_49)))).
% Axiom fact_392_inj__imp__inv__eq:(forall (G_5:(nat->nat)) (F_12:(nat->nat)), (((inj_on_nat_nat F_12) top_top_nat_o)->((forall (X_1:nat), (((eq nat) (F_12 (G_5 X_1))) X_1))->(((eq (nat->nat)) ((hilber195283148at_nat top_top_nat_o) F_12)) G_5)))).
% Axiom fact_393_inj__imp__inv__eq:(forall (G_5:(nat->arrow_1429601828e_indi)) (F_12:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat F_12) top_to988227749indi_o)->((forall (X_1:nat), (((eq nat) (F_12 (G_5 X_1))) X_1))->(((eq (nat->arrow_1429601828e_indi)) ((hilber598459244di_nat top_to988227749indi_o) F_12)) G_5)))).
% Axiom fact_394_less__add__one:(forall (A_56:nat), ((ord_less_nat A_56) ((plus_plus_nat A_56) one_one_nat))).
% Axiom fact_395_add__less__le__mono:(forall (C_28:nat) (D_3:nat) (A_55:nat) (B_48:nat), (((ord_less_nat A_55) B_48)->(((ord_less_eq_nat C_28) D_3)->((ord_less_nat ((plus_plus_nat A_55) C_28)) ((plus_plus_nat B_48) D_3))))).
% Axiom fact_396_add__le__less__mono:(forall (C_27:nat) (D_2:nat) (A_54:nat) (B_47:nat), (((ord_less_eq_nat A_54) B_47)->(((ord_less_nat C_27) D_2)->((ord_less_nat ((plus_plus_nat A_54) C_27)) ((plus_plus_nat B_47) D_2))))).
% Axiom fact_397_injI:(forall (F_11:(nat->nat)), ((forall (X_1:nat) (Y_1:nat), ((((eq nat) (F_11 X_1)) (F_11 Y_1))->(((eq nat) X_1) Y_1)))->((inj_on_nat_nat F_11) top_top_nat_o))).
% Axiom fact_398_injI:(forall (F_11:(arrow_1429601828e_indi->nat)), ((forall (X_1:arrow_1429601828e_indi) (Y_1:arrow_1429601828e_indi), ((((eq nat) (F_11 X_1)) (F_11 Y_1))->(((eq arrow_1429601828e_indi) X_1) Y_1)))->((inj_on978774663di_nat F_11) top_to988227749indi_o))).
% Axiom fact_399_less__fun__def:(forall (F_10:(nat->Prop)) (G_4:(nat->Prop)), ((iff ((ord_less_nat_o F_10) G_4)) ((and ((ord_less_eq_nat_o F_10) G_4)) (((ord_less_eq_nat_o G_4) F_10)->False)))).
% Axiom fact_400_less__fun__def:(forall (F_10:(product_unit->Prop)) (G_4:(product_unit->Prop)), ((iff ((ord_le232288914unit_o F_10) G_4)) ((and ((ord_le1511552390unit_o F_10) G_4)) (((ord_le1511552390unit_o G_4) F_10)->False)))).
% Axiom fact_401_less__fun__def:(forall (F_10:(arrow_1429601828e_indi->Prop)) (G_4:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o F_10) G_4)) ((and ((ord_le1799070453indi_o F_10) G_4)) (((ord_le1799070453indi_o G_4) F_10)->False)))).
% Axiom fact_402_Pi__anti__mono:(forall (B_46:(produc1501160679le_alt->(Prop->Prop))) (A_53:(produc1501160679le_alt->Prop)) (A_52:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_53) A_52)->((ord_le1063113995lt_o_o ((pi_Pro1701359055_alt_o A_52) B_46)) ((pi_Pro1701359055_alt_o A_53) B_46)))).
% Axiom fact_403_Pi__anti__mono:(forall (B_46:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_53:(arrow_1429601828e_indi->Prop)) (A_52:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_53) A_52)->((ord_le1992928527lt_o_o ((pi_Arr1929480907_alt_o A_52) B_46)) ((pi_Arr1929480907_alt_o A_53) B_46)))).
% Axiom fact_404_Pi__anti__mono:(forall (B_46:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_53:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_52:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_53) A_52)->((ord_le134800455lt_o_o ((pi_Arr1304755663_alt_o A_52) B_46)) ((pi_Arr1304755663_alt_o A_53) B_46)))).
% Axiom fact_405_pred__subset__eq2:(forall (R_2:(produc1501160679le_alt->Prop)) (S_2:(produc1501160679le_alt->Prop)), ((iff ((ord_le2080035663_alt_o (fun (X_1:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt)=> ((member214075476le_alt ((produc1347929815le_alt X_1) Y_1)) R_2))) (fun (X_1:arrow_475358991le_alt) (Y_1:arrow_475358991le_alt)=> ((member214075476le_alt ((produc1347929815le_alt X_1) Y_1)) S_2)))) ((ord_le97612146_alt_o R_2) S_2))).
% Axiom fact_406_subset__UNIV:(forall (A_51:((produc1501160679le_alt->Prop)->Prop)), ((ord_le1063113995lt_o_o A_51) top_to1842727771lt_o_o)).
% Axiom fact_407_subset__UNIV:(forall (A_51:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((ord_le134800455lt_o_o A_51) top_to1969627639lt_o_o)).
% Axiom fact_408_subset__UNIV:(forall (A_51:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((ord_le1992928527lt_o_o A_51) top_to2122763103lt_o_o)).
% Axiom fact_409_subset__UNIV:(forall (A_51:(produc1501160679le_alt->Prop)), ((ord_le97612146_alt_o A_51) top_to1841428258_alt_o)).
% Axiom fact_410_subset__UNIV:(forall (A_51:(nat->Prop)), ((ord_less_eq_nat_o A_51) top_top_nat_o)).
% Axiom fact_411_subset__UNIV:(forall (A_51:(product_unit->Prop)), ((ord_le1511552390unit_o A_51) top_to1984820022unit_o)).
% Axiom fact_412_subset__UNIV:(forall (A_51:(arrow_1429601828e_indi->Prop)), ((ord_le1799070453indi_o A_51) top_to988227749indi_o)).
% Axiom fact_413_subset__inj__on:(forall (A_50:(nat->Prop)) (F_9:(nat->nat)) (B_45:(nat->Prop)), (((inj_on_nat_nat F_9) B_45)->(((ord_less_eq_nat_o A_50) B_45)->((inj_on_nat_nat F_9) A_50)))).
% Axiom fact_414_subset__inj__on:(forall (A_50:(arrow_1429601828e_indi->Prop)) (F_9:(arrow_1429601828e_indi->nat)) (B_45:(arrow_1429601828e_indi->Prop)), (((inj_on978774663di_nat F_9) B_45)->(((ord_le1799070453indi_o A_50) B_45)->((inj_on978774663di_nat F_9) A_50)))).
% Axiom fact_415_add__right__imp__eq:(forall (B_44:nat) (A_49:nat) (C_26:nat), ((((eq nat) ((plus_plus_nat B_44) A_49)) ((plus_plus_nat C_26) A_49))->(((eq nat) B_44) C_26))).
% Axiom fact_416_add__imp__eq:(forall (A_48:nat) (B_43:nat) (C_25:nat), ((((eq nat) ((plus_plus_nat A_48) B_43)) ((plus_plus_nat A_48) C_25))->(((eq nat) B_43) C_25))).
% Axiom fact_417_add__left__imp__eq:(forall (A_47:nat) (B_42:nat) (C_24:nat), ((((eq nat) ((plus_plus_nat A_47) B_42)) ((plus_plus_nat A_47) C_24))->(((eq nat) B_42) C_24))).
% Axiom fact_418_add__right__cancel:(forall (B_41:nat) (A_46:nat) (C_23:nat), ((iff (((eq nat) ((plus_plus_nat B_41) A_46)) ((plus_plus_nat C_23) A_46))) (((eq nat) B_41) C_23))).
% Axiom fact_419_add__left__cancel:(forall (A_45:nat) (B_40:nat) (C_22:nat), ((iff (((eq nat) ((plus_plus_nat A_45) B_40)) ((plus_plus_nat A_45) C_22))) (((eq nat) B_40) C_22))).
% Axiom fact_420_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_44:nat) (B_39:nat) (C_21:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_44) B_39)) C_21)) ((plus_plus_nat A_44) ((plus_plus_nat B_39) C_21)))).
% Axiom fact_421_one__reorient:(forall (X_8:nat), ((iff (((eq nat) one_one_nat) X_8)) (((eq nat) X_8) one_one_nat))).
% Axiom fact_422_add__le__imp__le__left:(forall (C_20:nat) (A_43:nat) (B_38:nat), (((ord_less_eq_nat ((plus_plus_nat C_20) A_43)) ((plus_plus_nat C_20) B_38))->((ord_less_eq_nat A_43) B_38))).
% Axiom fact_423_add__le__imp__le__right:(forall (A_42:nat) (C_19:nat) (B_37:nat), (((ord_less_eq_nat ((plus_plus_nat A_42) C_19)) ((plus_plus_nat B_37) C_19))->((ord_less_eq_nat A_42) B_37))).
% Axiom fact_424_add__mono:(forall (C_18:nat) (D_1:nat) (A_41:nat) (B_36:nat), (((ord_less_eq_nat A_41) B_36)->(((ord_less_eq_nat C_18) D_1)->((ord_less_eq_nat ((plus_plus_nat A_41) C_18)) ((plus_plus_nat B_36) D_1))))).
% Axiom fact_425_add__left__mono:(forall (C_17:nat) (A_40:nat) (B_35:nat), (((ord_less_eq_nat A_40) B_35)->((ord_less_eq_nat ((plus_plus_nat C_17) A_40)) ((plus_plus_nat C_17) B_35)))).
% Axiom fact_426_add__right__mono:(forall (C_16:nat) (A_39:nat) (B_34:nat), (((ord_less_eq_nat A_39) B_34)->((ord_less_eq_nat ((plus_plus_nat A_39) C_16)) ((plus_plus_nat B_34) C_16)))).
% Axiom fact_427_add__le__cancel__left:(forall (C_15:nat) (A_38:nat) (B_33:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_15) A_38)) ((plus_plus_nat C_15) B_33))) ((ord_less_eq_nat A_38) B_33))).
% Axiom fact_428_add__le__cancel__right:(forall (A_37:nat) (C_14:nat) (B_32:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_37) C_14)) ((plus_plus_nat B_32) C_14))) ((ord_less_eq_nat A_37) B_32))).
% Axiom fact_429_add__less__imp__less__left:(forall (C_13:nat) (A_36:nat) (B_31:nat), (((ord_less_nat ((plus_plus_nat C_13) A_36)) ((plus_plus_nat C_13) B_31))->((ord_less_nat A_36) B_31))).
% Axiom fact_430_add__less__imp__less__right:(forall (A_35:nat) (C_12:nat) (B_30:nat), (((ord_less_nat ((plus_plus_nat A_35) C_12)) ((plus_plus_nat B_30) C_12))->((ord_less_nat A_35) B_30))).
% Axiom fact_431_add__strict__mono:(forall (C_11:nat) (D:nat) (A_34:nat) (B_29:nat), (((ord_less_nat A_34) B_29)->(((ord_less_nat C_11) D)->((ord_less_nat ((plus_plus_nat A_34) C_11)) ((plus_plus_nat B_29) D))))).
% Axiom fact_432_add__strict__left__mono:(forall (C_10:nat) (A_33:nat) (B_28:nat), (((ord_less_nat A_33) B_28)->((ord_less_nat ((plus_plus_nat C_10) A_33)) ((plus_plus_nat C_10) B_28)))).
% Axiom fact_433_add__strict__right__mono:(forall (C_9:nat) (A_32:nat) (B_27:nat), (((ord_less_nat A_32) B_27)->((ord_less_nat ((plus_plus_nat A_32) C_9)) ((plus_plus_nat B_27) C_9)))).
% Axiom fact_434_add__less__cancel__left:(forall (C_8:nat) (A_31:nat) (B_26:nat), ((iff ((ord_less_nat ((plus_plus_nat C_8) A_31)) ((plus_plus_nat C_8) B_26))) ((ord_less_nat A_31) B_26))).
% Axiom fact_435_add__less__cancel__right:(forall (A_30:nat) (C_7:nat) (B_25:nat), ((iff ((ord_less_nat ((plus_plus_nat A_30) C_7)) ((plus_plus_nat B_25) C_7))) ((ord_less_nat A_30) B_25))).
% Axiom fact_436_le__funI:(forall (F_8:(nat->Prop)) (G_3:(nat->Prop)), ((forall (X_1:nat), ((ord_less_eq_o (F_8 X_1)) (G_3 X_1)))->((ord_less_eq_nat_o F_8) G_3))).
% Axiom fact_437_equalityI:(forall (A_29:(nat->Prop)) (B_24:(nat->Prop)), (((ord_less_eq_nat_o A_29) B_24)->(((ord_less_eq_nat_o B_24) A_29)->(((eq (nat->Prop)) A_29) B_24)))).
% Axiom fact_438_subsetD:(forall (C_6:Prop) (A_28:(Prop->Prop)) (B_23:(Prop->Prop)), (((ord_less_eq_o_o A_28) B_23)->(((member_o C_6) A_28)->((member_o C_6) B_23)))).
% Axiom fact_439_subsetD:(forall (C_6:product_unit) (A_28:(product_unit->Prop)) (B_23:(product_unit->Prop)), (((ord_le1511552390unit_o A_28) B_23)->(((member_Product_unit C_6) A_28)->((member_Product_unit C_6) B_23)))).
% Axiom fact_440_subsetD:(forall (C_6:arrow_1429601828e_indi) (A_28:(arrow_1429601828e_indi->Prop)) (B_23:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_28) B_23)->(((member2052026769e_indi C_6) A_28)->((member2052026769e_indi C_6) B_23)))).
% Axiom fact_441_subsetD:(forall (C_6:nat) (A_28:(nat->Prop)) (B_23:(nat->Prop)), (((ord_less_eq_nat_o A_28) B_23)->(((member_nat C_6) A_28)->((member_nat C_6) B_23)))).
% Axiom fact_442_subsetD:(forall (C_6:(produc1501160679le_alt->Prop)) (A_28:((produc1501160679le_alt->Prop)->Prop)) (B_23:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o A_28) B_23)->(((member377231867_alt_o C_6) A_28)->((member377231867_alt_o C_6) B_23)))).
% Axiom fact_443_subsetD:(forall (C_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_28:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_23:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o A_28) B_23)->(((member616898751_alt_o C_6) A_28)->((member616898751_alt_o C_6) B_23)))).
% Axiom fact_444_subsetD:(forall (C_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_28:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_23:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_28) B_23)->(((member526088951_alt_o C_6) A_28)->((member526088951_alt_o C_6) B_23)))).
% Axiom fact_445_subsetD:(forall (C_6:produc1501160679le_alt) (A_28:(produc1501160679le_alt->Prop)) (B_23:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_28) B_23)->(((member214075476le_alt C_6) A_28)->((member214075476le_alt C_6) B_23)))).
% Axiom fact_446_psubset__eq:(forall (A_27:(nat->Prop)) (B_22:(nat->Prop)), ((iff ((ord_less_nat_o A_27) B_22)) ((and ((ord_less_eq_nat_o A_27) B_22)) (not (((eq (nat->Prop)) A_27) B_22))))).
% Axiom fact_447_psubset__eq:(forall (A_27:(product_unit->Prop)) (B_22:(product_unit->Prop)), ((iff ((ord_le232288914unit_o A_27) B_22)) ((and ((ord_le1511552390unit_o A_27) B_22)) (not (((eq (product_unit->Prop)) A_27) B_22))))).
% Axiom fact_448_psubset__eq:(forall (A_27:(arrow_1429601828e_indi->Prop)) (B_22:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le777687553indi_o A_27) B_22)) ((and ((ord_le1799070453indi_o A_27) B_22)) (not (((eq (arrow_1429601828e_indi->Prop)) A_27) B_22))))).
% Axiom fact_449_subset__iff__psubset__eq:(forall (A_26:(nat->Prop)) (B_21:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_26) B_21)) ((or ((ord_less_nat_o A_26) B_21)) (((eq (nat->Prop)) A_26) B_21)))).
% Axiom fact_450_subset__iff__psubset__eq:(forall (A_26:(product_unit->Prop)) (B_21:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o A_26) B_21)) ((or ((ord_le232288914unit_o A_26) B_21)) (((eq (product_unit->Prop)) A_26) B_21)))).
% Axiom fact_451_subset__iff__psubset__eq:(forall (A_26:(arrow_1429601828e_indi->Prop)) (B_21:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o A_26) B_21)) ((or ((ord_le777687553indi_o A_26) B_21)) (((eq (arrow_1429601828e_indi->Prop)) A_26) B_21)))).
% Axiom fact_452_psubset__imp__subset:(forall (A_25:(nat->Prop)) (B_20:(nat->Prop)), (((ord_less_nat_o A_25) B_20)->((ord_less_eq_nat_o A_25) B_20))).
% Axiom fact_453_psubset__imp__subset:(forall (A_25:(product_unit->Prop)) (B_20:(product_unit->Prop)), (((ord_le232288914unit_o A_25) B_20)->((ord_le1511552390unit_o A_25) B_20))).
% Axiom fact_454_psubset__imp__subset:(forall (A_25:(arrow_1429601828e_indi->Prop)) (B_20:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_25) B_20)->((ord_le1799070453indi_o A_25) B_20))).
% Axiom fact_455_psubset__subset__trans:(forall (C_5:(nat->Prop)) (A_24:(nat->Prop)) (B_19:(nat->Prop)), (((ord_less_nat_o A_24) B_19)->(((ord_less_eq_nat_o B_19) C_5)->((ord_less_nat_o A_24) C_5)))).
% Axiom fact_456_psubset__subset__trans:(forall (C_5:(product_unit->Prop)) (A_24:(product_unit->Prop)) (B_19:(product_unit->Prop)), (((ord_le232288914unit_o A_24) B_19)->(((ord_le1511552390unit_o B_19) C_5)->((ord_le232288914unit_o A_24) C_5)))).
% Axiom fact_457_psubset__subset__trans:(forall (C_5:(arrow_1429601828e_indi->Prop)) (A_24:(arrow_1429601828e_indi->Prop)) (B_19:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_24) B_19)->(((ord_le1799070453indi_o B_19) C_5)->((ord_le777687553indi_o A_24) C_5)))).
% Axiom fact_458_subset__psubset__trans:(forall (C_4:(nat->Prop)) (A_23:(nat->Prop)) (B_18:(nat->Prop)), (((ord_less_eq_nat_o A_23) B_18)->(((ord_less_nat_o B_18) C_4)->((ord_less_nat_o A_23) C_4)))).
% Axiom fact_459_subset__psubset__trans:(forall (C_4:(product_unit->Prop)) (A_23:(product_unit->Prop)) (B_18:(product_unit->Prop)), (((ord_le1511552390unit_o A_23) B_18)->(((ord_le232288914unit_o B_18) C_4)->((ord_le232288914unit_o A_23) C_4)))).
% Axiom fact_460_subset__psubset__trans:(forall (C_4:(arrow_1429601828e_indi->Prop)) (A_23:(arrow_1429601828e_indi->Prop)) (B_18:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_23) B_18)->(((ord_le777687553indi_o B_18) C_4)->((ord_le777687553indi_o A_23) C_4)))).
% Axiom fact_461_equalityE:(forall (A_22:(nat->Prop)) (B_17:(nat->Prop)), ((((eq (nat->Prop)) A_22) B_17)->((((ord_less_eq_nat_o A_22) B_17)->(((ord_less_eq_nat_o B_17) A_22)->False))->False))).
% Axiom fact_462_subset__trans:(forall (C_3:(nat->Prop)) (A_21:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_21) B_16)->(((ord_less_eq_nat_o B_16) C_3)->((ord_less_eq_nat_o A_21) C_3)))).
% Axiom fact_463_set__mp:(forall (X_7:Prop) (A_20:(Prop->Prop)) (B_15:(Prop->Prop)), (((ord_less_eq_o_o A_20) B_15)->(((member_o X_7) A_20)->((member_o X_7) B_15)))).
% Axiom fact_464_set__mp:(forall (X_7:product_unit) (A_20:(product_unit->Prop)) (B_15:(product_unit->Prop)), (((ord_le1511552390unit_o A_20) B_15)->(((member_Product_unit X_7) A_20)->((member_Product_unit X_7) B_15)))).
% Axiom fact_465_set__mp:(forall (X_7:arrow_1429601828e_indi) (A_20:(arrow_1429601828e_indi->Prop)) (B_15:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_20) B_15)->(((member2052026769e_indi X_7) A_20)->((member2052026769e_indi X_7) B_15)))).
% Axiom fact_466_set__mp:(forall (X_7:nat) (A_20:(nat->Prop)) (B_15:(nat->Prop)), (((ord_less_eq_nat_o A_20) B_15)->(((member_nat X_7) A_20)->((member_nat X_7) B_15)))).
% Axiom fact_467_set__mp:(forall (X_7:(produc1501160679le_alt->Prop)) (A_20:((produc1501160679le_alt->Prop)->Prop)) (B_15:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o A_20) B_15)->(((member377231867_alt_o X_7) A_20)->((member377231867_alt_o X_7) B_15)))).
% Axiom fact_468_set__mp:(forall (X_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_20:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_15:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o A_20) B_15)->(((member616898751_alt_o X_7) A_20)->((member616898751_alt_o X_7) B_15)))).
% Axiom fact_469_set__mp:(forall (X_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_20:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_15:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_20) B_15)->(((member526088951_alt_o X_7) A_20)->((member526088951_alt_o X_7) B_15)))).
% Axiom fact_470_set__mp:(forall (X_7:produc1501160679le_alt) (A_20:(produc1501160679le_alt->Prop)) (B_15:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_20) B_15)->(((member214075476le_alt X_7) A_20)->((member214075476le_alt X_7) B_15)))).
% Axiom fact_471_set__rev__mp:(forall (B_14:(Prop->Prop)) (X_6:Prop) (A_19:(Prop->Prop)), (((member_o X_6) A_19)->(((ord_less_eq_o_o A_19) B_14)->((member_o X_6) B_14)))).
% Axiom fact_472_set__rev__mp:(forall (B_14:(product_unit->Prop)) (X_6:product_unit) (A_19:(product_unit->Prop)), (((member_Product_unit X_6) A_19)->(((ord_le1511552390unit_o A_19) B_14)->((member_Product_unit X_6) B_14)))).
% Axiom fact_473_set__rev__mp:(forall (B_14:(arrow_1429601828e_indi->Prop)) (X_6:arrow_1429601828e_indi) (A_19:(arrow_1429601828e_indi->Prop)), (((member2052026769e_indi X_6) A_19)->(((ord_le1799070453indi_o A_19) B_14)->((member2052026769e_indi X_6) B_14)))).
% Axiom fact_474_set__rev__mp:(forall (B_14:(nat->Prop)) (X_6:nat) (A_19:(nat->Prop)), (((member_nat X_6) A_19)->(((ord_less_eq_nat_o A_19) B_14)->((member_nat X_6) B_14)))).
% Axiom fact_475_set__rev__mp:(forall (B_14:((produc1501160679le_alt->Prop)->Prop)) (X_6:(produc1501160679le_alt->Prop)) (A_19:((produc1501160679le_alt->Prop)->Prop)), (((member377231867_alt_o X_6) A_19)->(((ord_le1063113995lt_o_o A_19) B_14)->((member377231867_alt_o X_6) B_14)))).
% Axiom fact_476_set__rev__mp:(forall (B_14:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (X_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_19:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((member616898751_alt_o X_6) A_19)->(((ord_le134800455lt_o_o A_19) B_14)->((member616898751_alt_o X_6) B_14)))).
% Axiom fact_477_set__rev__mp:(forall (B_14:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (X_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_19:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member526088951_alt_o X_6) A_19)->(((ord_le1992928527lt_o_o A_19) B_14)->((member526088951_alt_o X_6) B_14)))).
% Axiom fact_478_set__rev__mp:(forall (B_14:(produc1501160679le_alt->Prop)) (X_6:produc1501160679le_alt) (A_19:(produc1501160679le_alt->Prop)), (((member214075476le_alt X_6) A_19)->(((ord_le97612146_alt_o A_19) B_14)->((member214075476le_alt X_6) B_14)))).
% Axiom fact_479_predicate1D:(forall (X_5:nat) (P_2:(nat->Prop)) (Q_1:(nat->Prop)), (((ord_less_eq_nat_o P_2) Q_1)->((P_2 X_5)->(Q_1 X_5)))).
% Axiom fact_480_in__mono:(forall (X_4:Prop) (A_18:(Prop->Prop)) (B_13:(Prop->Prop)), (((ord_less_eq_o_o A_18) B_13)->(((member_o X_4) A_18)->((member_o X_4) B_13)))).
% Axiom fact_481_in__mono:(forall (X_4:product_unit) (A_18:(product_unit->Prop)) (B_13:(product_unit->Prop)), (((ord_le1511552390unit_o A_18) B_13)->(((member_Product_unit X_4) A_18)->((member_Product_unit X_4) B_13)))).
% Axiom fact_482_in__mono:(forall (X_4:arrow_1429601828e_indi) (A_18:(arrow_1429601828e_indi->Prop)) (B_13:(arrow_1429601828e_indi->Prop)), (((ord_le1799070453indi_o A_18) B_13)->(((member2052026769e_indi X_4) A_18)->((member2052026769e_indi X_4) B_13)))).
% Axiom fact_483_in__mono:(forall (X_4:nat) (A_18:(nat->Prop)) (B_13:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_13)->(((member_nat X_4) A_18)->((member_nat X_4) B_13)))).
% Axiom fact_484_in__mono:(forall (X_4:(produc1501160679le_alt->Prop)) (A_18:((produc1501160679le_alt->Prop)->Prop)) (B_13:((produc1501160679le_alt->Prop)->Prop)), (((ord_le1063113995lt_o_o A_18) B_13)->(((member377231867_alt_o X_4) A_18)->((member377231867_alt_o X_4) B_13)))).
% Axiom fact_485_in__mono:(forall (X_4:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_18:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_13:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le134800455lt_o_o A_18) B_13)->(((member616898751_alt_o X_4) A_18)->((member616898751_alt_o X_4) B_13)))).
% Axiom fact_486_in__mono:(forall (X_4:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_18:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1992928527lt_o_o A_18) B_13)->(((member526088951_alt_o X_4) A_18)->((member526088951_alt_o X_4) B_13)))).
% Axiom fact_487_in__mono:(forall (X_4:produc1501160679le_alt) (A_18:(produc1501160679le_alt->Prop)) (B_13:(produc1501160679le_alt->Prop)), (((ord_le97612146_alt_o A_18) B_13)->(((member214075476le_alt X_4) A_18)->((member214075476le_alt X_4) B_13)))).
% Axiom fact_488_equalityD2:(forall (A_17:(nat->Prop)) (B_12:(nat->Prop)), ((((eq (nat->Prop)) A_17) B_12)->((ord_less_eq_nat_o B_12) A_17))).
% Axiom fact_489_equalityD1:(forall (A_16:(nat->Prop)) (B_11:(nat->Prop)), ((((eq (nat->Prop)) A_16) B_11)->((ord_less_eq_nat_o A_16) B_11))).
% Axiom fact_490_rev__predicate1D:(forall (Q:(nat->Prop)) (P_1:(nat->Prop)) (X_3:nat), ((P_1 X_3)->(((ord_less_eq_nat_o P_1) Q)->(Q X_3)))).
% Axiom fact_491_set__eq__subset:(forall (A_15:(nat->Prop)) (B_10:(nat->Prop)), ((iff (((eq (nat->Prop)) A_15) B_10)) ((and ((ord_less_eq_nat_o A_15) B_10)) ((ord_less_eq_nat_o B_10) A_15)))).
% Axiom fact_492_subset__refl:(forall (A_14:(nat->Prop)), ((ord_less_eq_nat_o A_14) A_14)).
% Axiom fact_493_pred__subset__eq:(forall (R_1:(Prop->Prop)) (S_1:(Prop->Prop)), ((iff ((ord_less_eq_o_o (fun (X_1:Prop)=> ((member_o X_1) R_1))) (fun (X_1:Prop)=> ((member_o X_1) S_1)))) ((ord_less_eq_o_o R_1) S_1))).
% Axiom fact_494_pred__subset__eq:(forall (R_1:(product_unit->Prop)) (S_1:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o (fun (X_1:product_unit)=> ((member_Product_unit X_1) R_1))) (fun (X_1:product_unit)=> ((member_Product_unit X_1) S_1)))) ((ord_le1511552390unit_o R_1) S_1))).
% Axiom fact_495_pred__subset__eq:(forall (R_1:(arrow_1429601828e_indi->Prop)) (S_1:(arrow_1429601828e_indi->Prop)), ((iff ((ord_le1799070453indi_o (fun (X_1:arrow_1429601828e_indi)=> ((member2052026769e_indi X_1) R_1))) (fun (X_1:arrow_1429601828e_indi)=> ((member2052026769e_indi X_1) S_1)))) ((ord_le1799070453indi_o R_1) S_1))).
% Axiom fact_496_pred__subset__eq:(forall (R_1:(nat->Prop)) (S_1:(nat->Prop)), ((iff ((ord_less_eq_nat_o (fun (X_1:nat)=> ((member_nat X_1) R_1))) (fun (X_1:nat)=> ((member_nat X_1) S_1)))) ((ord_less_eq_nat_o R_1) S_1))).
% Axiom fact_497_pred__subset__eq:(forall (R_1:((produc1501160679le_alt->Prop)->Prop)) (S_1:((produc1501160679le_alt->Prop)->Prop)), ((iff ((ord_le1063113995lt_o_o (fun (X_1:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o X_1) R_1))) (fun (X_1:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o X_1) S_1)))) ((ord_le1063113995lt_o_o R_1) S_1))).
% Axiom fact_498_pred__subset__eq:(forall (R_1:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (S_1:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le134800455lt_o_o (fun (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> ((member616898751_alt_o X_1) R_1))) (fun (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop)))=> ((member616898751_alt_o X_1) S_1)))) ((ord_le134800455lt_o_o R_1) S_1))).
% Axiom fact_499_pred__subset__eq:(forall (R_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (S_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((iff ((ord_le1992928527lt_o_o (fun (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> ((member526088951_alt_o X_1) R_1))) (fun (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> ((member526088951_alt_o X_1) S_1)))) ((ord_le1992928527lt_o_o R_1) S_1))).
% Axiom fact_500_pred__subset__eq:(forall (R_1:(produc1501160679le_alt->Prop)) (S_1:(produc1501160679le_alt->Prop)), ((iff ((ord_le97612146_alt_o (fun (X_1:produc1501160679le_alt)=> ((member214075476le_alt X_1) R_1))) (fun (X_1:produc1501160679le_alt)=> ((member214075476le_alt X_1) S_1)))) ((ord_le97612146_alt_o R_1) S_1))).
% Axiom fact_501_Pi__mono:(forall (B_9:(produc1501160679le_alt->(Prop->Prop))) (C_2:(produc1501160679le_alt->(Prop->Prop))) (A_13:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_13)->((ord_less_eq_o_o (B_9 X_1)) (C_2 X_1))))->((ord_le1063113995lt_o_o ((pi_Pro1701359055_alt_o A_13) B_9)) ((pi_Pro1701359055_alt_o A_13) C_2)))).
% Axiom fact_502_Pi__mono:(forall (B_9:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (C_2:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_13:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_13)->((ord_le1063113995lt_o_o (B_9 X_1)) (C_2 X_1))))->((ord_le1992928527lt_o_o ((pi_Arr1929480907_alt_o A_13) B_9)) ((pi_Arr1929480907_alt_o A_13) C_2)))).
% Axiom fact_503_Pi__mono:(forall (B_9:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (C_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_13:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_13)->((ord_le1063113995lt_o_o (B_9 X_1)) (C_2 X_1))))->((ord_le134800455lt_o_o ((pi_Arr1304755663_alt_o A_13) B_9)) ((pi_Arr1304755663_alt_o A_13) C_2)))).
% Axiom fact_504_subsetI:(forall (B_8:(Prop->Prop)) (A_12:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_12)->((member_o X_1) B_8)))->((ord_less_eq_o_o A_12) B_8))).
% Axiom fact_505_subsetI:(forall (B_8:(product_unit->Prop)) (A_12:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_12)->((member_Product_unit X_1) B_8)))->((ord_le1511552390unit_o A_12) B_8))).
% Axiom fact_506_subsetI:(forall (B_8:(arrow_1429601828e_indi->Prop)) (A_12:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_12)->((member2052026769e_indi X_1) B_8)))->((ord_le1799070453indi_o A_12) B_8))).
% Axiom fact_507_subsetI:(forall (B_8:(nat->Prop)) (A_12:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_12)->((member_nat X_1) B_8)))->((ord_less_eq_nat_o A_12) B_8))).
% Axiom fact_508_subsetI:(forall (B_8:((produc1501160679le_alt->Prop)->Prop)) (A_12:((produc1501160679le_alt->Prop)->Prop)), ((forall (X_1:(produc1501160679le_alt->Prop)), (((member377231867_alt_o X_1) A_12)->((member377231867_alt_o X_1) B_8)))->((ord_le1063113995lt_o_o A_12) B_8))).
% Axiom fact_509_subsetI:(forall (B_8:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (A_12:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))), (((member616898751_alt_o X_1) A_12)->((member616898751_alt_o X_1) B_8)))->((ord_le134800455lt_o_o A_12) B_8))).
% Axiom fact_510_subsetI:(forall (B_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (A_12:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_12)->((member526088951_alt_o X_1) B_8)))->((ord_le1992928527lt_o_o A_12) B_8))).
% Axiom fact_511_subsetI:(forall (B_8:(produc1501160679le_alt->Prop)) (A_12:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_12)->((member214075476le_alt X_1) B_8)))->((ord_le97612146_alt_o A_12) B_8))).
% Axiom fact_512_psubsetD:(forall (C_1:Prop) (A_11:(Prop->Prop)) (B_7:(Prop->Prop)), (((ord_less_o_o A_11) B_7)->(((member_o C_1) A_11)->((member_o C_1) B_7)))).
% Axiom fact_513_psubsetD:(forall (C_1:product_unit) (A_11:(product_unit->Prop)) (B_7:(product_unit->Prop)), (((ord_le232288914unit_o A_11) B_7)->(((member_Product_unit C_1) A_11)->((member_Product_unit C_1) B_7)))).
% Axiom fact_514_psubsetD:(forall (C_1:arrow_1429601828e_indi) (A_11:(arrow_1429601828e_indi->Prop)) (B_7:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_11) B_7)->(((member2052026769e_indi C_1) A_11)->((member2052026769e_indi C_1) B_7)))).
% Axiom fact_515_psubsetD:(forall (C_1:nat) (A_11:(nat->Prop)) (B_7:(nat->Prop)), (((ord_less_nat_o A_11) B_7)->(((member_nat C_1) A_11)->((member_nat C_1) B_7)))).
% Axiom fact_516_psubsetD:(forall (C_1:(produc1501160679le_alt->Prop)) (A_11:((produc1501160679le_alt->Prop)->Prop)) (B_7:((produc1501160679le_alt->Prop)->Prop)), (((ord_le910298367lt_o_o A_11) B_7)->(((member377231867_alt_o C_1) A_11)->((member377231867_alt_o C_1) B_7)))).
% Axiom fact_517_psubsetD:(forall (C_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_11:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)) (B_7:(((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))->Prop)), (((ord_le1859604819lt_o_o A_11) B_7)->(((member616898751_alt_o C_1) A_11)->((member616898751_alt_o C_1) B_7)))).
% Axiom fact_518_psubsetD:(forall (C_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_11:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((ord_le157835011lt_o_o A_11) B_7)->(((member526088951_alt_o C_1) A_11)->((member526088951_alt_o C_1) B_7)))).
% Axiom fact_519_psubsetD:(forall (C_1:produc1501160679le_alt) (A_11:(produc1501160679le_alt->Prop)) (B_7:(produc1501160679le_alt->Prop)), (((ord_le988258430_alt_o A_11) B_7)->(((member214075476le_alt C_1) A_11)->((member214075476le_alt C_1) B_7)))).
% Axiom fact_520_psubset__trans:(forall (C:(nat->Prop)) (A_10:(nat->Prop)) (B_6:(nat->Prop)), (((ord_less_nat_o A_10) B_6)->(((ord_less_nat_o B_6) C)->((ord_less_nat_o A_10) C)))).
% Axiom fact_521_psubset__trans:(forall (C:(product_unit->Prop)) (A_10:(product_unit->Prop)) (B_6:(product_unit->Prop)), (((ord_le232288914unit_o A_10) B_6)->(((ord_le232288914unit_o B_6) C)->((ord_le232288914unit_o A_10) C)))).
% Axiom fact_522_psubset__trans:(forall (C:(arrow_1429601828e_indi->Prop)) (A_10:(arrow_1429601828e_indi->Prop)) (B_6:(arrow_1429601828e_indi->Prop)), (((ord_le777687553indi_o A_10) B_6)->(((ord_le777687553indi_o B_6) C)->((ord_le777687553indi_o A_10) C)))).
% Axiom fact_523_in__below:(forall (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt) (L_2:(produc1501160679le_alt->Prop)) (A_9:arrow_475358991le_alt) (B_5:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) A_9) B_5))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((iff ((member214075476le_alt ((produc1347929815le_alt X) Y)) (((arrow_2098199487_below L_2) A_9) B_5))) ((and ((and (not (((eq arrow_475358991le_alt) X) Y))) ((((eq arrow_475358991le_alt) Y) A_9)->((member214075476le_alt ((produc1347929815le_alt X) B_5)) L_2)))) ((not (((eq arrow_475358991le_alt) Y) A_9))->((and ((((eq arrow_475358991le_alt) X) A_9)->((or (((eq arrow_475358991le_alt) Y) B_5)) ((member214075476le_alt ((produc1347929815le_alt B_5) Y)) L_2)))) ((not (((eq arrow_475358991le_alt) X) A_9))->((member214075476le_alt ((produc1347929815le_alt X) Y)) L_2))))))))).
% Axiom fact_524_add__leE:(forall (M_2:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M_2) K)) N)->((((ord_less_eq_nat M_2) N)->(((ord_less_eq_nat K) N)->False))->False))).
% Axiom fact_525_add__leD1:(forall (M_2:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M_2) K)) N)->((ord_less_eq_nat M_2) N))).
% Axiom fact_526_add__leD2:(forall (M_2:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M_2) K)) N)->((ord_less_eq_nat K) N))).
% Axiom fact_527_less__not__refl:(forall (N:nat), (((ord_less_nat N) N)->False)).
% Axiom fact_528_nat__neq__iff:(forall (M_2:nat) (N:nat), ((iff (not (((eq nat) M_2) N))) ((or ((ord_less_nat M_2) N)) ((ord_less_nat N) M_2)))).
% Axiom fact_529_linorder__neqE__nat:(forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))).
% Axiom fact_530_less__irrefl__nat:(forall (N:nat), (((ord_less_nat N) N)->False)).
% Axiom fact_531_less__not__refl2:(forall (N:nat) (M_2:nat), (((ord_less_nat N) M_2)->(not (((eq nat) M_2) N)))).
% Axiom fact_532_less__not__refl3:(forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))).
% Axiom fact_533_nat__less__cases:(forall (P:(nat->(nat->Prop))) (M_2:nat) (N:nat), ((((ord_less_nat M_2) N)->((P N) M_2))->(((((eq nat) M_2) N)->((P N) M_2))->((((ord_less_nat N) M_2)->((P N) M_2))->((P N) M_2))))).
% Axiom fact_534_nat__add__commute:(forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat M_2) N)) ((plus_plus_nat N) M_2))).
% Axiom fact_535_nat__add__left__commute:(forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z)))).
% Axiom fact_536_nat__add__assoc:(forall (M_2:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M_2) N)) K)) ((plus_plus_nat M_2) ((plus_plus_nat N) K)))).
% Axiom fact_537_nat__add__left__cancel:(forall (K:nat) (M_2:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M_2)) ((plus_plus_nat K) N))) (((eq nat) M_2) N))).
% Axiom fact_538_nat__add__right__cancel:(forall (M_2:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M_2) K)) ((plus_plus_nat N) K))) (((eq nat) M_2) N))).
% Axiom fact_539_le__refl:(forall (N:nat), ((ord_less_eq_nat N) N)).
% Axiom fact_540_nat__le__linear:(forall (M_2:nat) (N:nat), ((or ((ord_less_eq_nat M_2) N)) ((ord_less_eq_nat N) M_2))).
% Axiom fact_541_eq__imp__le:(forall (M_2:nat) (N:nat), ((((eq nat) M_2) N)->((ord_less_eq_nat M_2) N))).
% Axiom fact_542_le__trans:(forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->(((ord_less_eq_nat J_1) K)->((ord_less_eq_nat _TPTP_I) K)))).
% Axiom fact_543_le__antisym:(forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->(((ord_less_eq_nat N) M_2)->(((eq nat) M_2) N)))).
% Axiom fact_544_below__Lin:(forall (L_2:(produc1501160679le_alt->Prop)) (X:arrow_475358991le_alt) (Y:arrow_475358991le_alt), ((not (((eq arrow_475358991le_alt) X) Y))->(((member377231867_alt_o L_2) arrow_823908191le_Lin)->((member377231867_alt_o (((arrow_2098199487_below L_2) X) Y)) arrow_823908191le_Lin)))).
% Axiom fact_545_inj__on__add__nat:(forall (K:nat) (N_2:(nat->Prop)), ((inj_on_nat_nat (fun (N_1:nat)=> ((plus_plus_nat N_1) K))) N_2)).
% Axiom fact_546_not__add__less1:(forall (_TPTP_I:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J_1)) _TPTP_I)->False)).
% Axiom fact_547_not__add__less2:(forall (J_1:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J_1) _TPTP_I)) _TPTP_I)->False)).
% Axiom fact_548_nat__add__left__cancel__less:(forall (K:nat) (M_2:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M_2)) ((plus_plus_nat K) N))) ((ord_less_nat M_2) N))).
% Axiom fact_549_trans__less__add1:(forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat _TPTP_I) ((plus_plus_nat J_1) M_2)))).
% Axiom fact_550_trans__less__add2:(forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat _TPTP_I) ((plus_plus_nat M_2) J_1)))).
% Axiom fact_551_add__less__mono1:(forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) K)))).
% Axiom fact_552_add__less__mono:(forall (K:nat) (L:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) L))))).
% Axiom fact_553_less__add__eq__less:(forall (M_2:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M_2) L)) ((plus_plus_nat K) N))->((ord_less_nat M_2) N)))).
% Axiom fact_554_add__lessD1:(forall (_TPTP_I:nat) (J_1:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J_1)) K)->((ord_less_nat _TPTP_I) K))).
% Axiom fact_555_nat__less__le:(forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) N)) ((and ((ord_less_eq_nat M_2) N)) (not (((eq nat) M_2) N))))).
% Axiom fact_556_le__eq__less__or__eq:(forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat M_2) N)) ((or ((ord_less_nat M_2) N)) (((eq nat) M_2) N)))).
% Axiom fact_557_less__imp__le__nat:(forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_eq_nat M_2) N))).
% Axiom fact_558_le__neq__implies__less:(forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((not (((eq nat) M_2) N))->((ord_less_nat M_2) N)))).
% Axiom fact_559_less__or__eq__imp__le:(forall (M_2:nat) (N:nat), (((or ((ord_less_nat M_2) N)) (((eq nat) M_2) N))->((ord_less_eq_nat M_2) N))).
% Axiom fact_560_le__add2:(forall (N:nat) (M_2:nat), ((ord_less_eq_nat N) ((plus_plus_nat M_2) N))).
% Axiom fact_561_le__add1:(forall (N:nat) (M_2:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M_2))).
% Axiom fact_562_le__iff__add:(forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat M_2) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M_2) K_1)))))).
% Axiom fact_563_nat__add__left__cancel__le:(forall (K:nat) (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M_2)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M_2) N))).
% Axiom fact_564_trans__le__add1:(forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J_1) M_2)))).
% Axiom fact_565_trans__le__add2:(forall (M_2:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M_2) J_1)))).
% Axiom fact_566_add__le__mono1:(forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) K)))).
% Axiom fact_567_add__le__mono:(forall (K:nat) (L:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J_1) L))))).
% Axiom fact_568_mono__nat__linear__lb:(forall (M_2:nat) (K:nat) (F:(nat->nat)), ((forall (M:nat) (N_1:nat), (((ord_less_nat M) N_1)->((ord_less_nat (F M)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M_2)) K)) (F ((plus_plus_nat M_2) K))))).
% Axiom fact_569_less__mono__imp__le__mono:(forall (_TPTP_I:nat) (J_1:nat) (F:(nat->nat)), ((forall (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat (F I_1)) (F J))))->(((ord_less_eq_nat _TPTP_I) J_1)->((ord_less_eq_nat (F _TPTP_I)) (F J_1))))).
% Axiom fact_570_termination__basic__simps_I3_J:(forall (Z:nat) (X:nat) (Y:nat), (((ord_less_eq_nat X) Y)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z)))).
% Axiom fact_571_termination__basic__simps_I4_J:(forall (Y:nat) (X:nat) (Z:nat), (((ord_less_eq_nat X) Z)->((ord_less_eq_nat X) ((plus_plus_nat Y) Z)))).
% Axiom fact_572_termination__basic__simps_I2_J:(forall (Y:nat) (X:nat) (Z:nat), (((ord_less_nat X) Z)->((ord_less_nat X) ((plus_plus_nat Y) Z)))).
% Axiom fact_573_termination__basic__simps_I1_J:(forall (Z:nat) (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_nat X) ((plus_plus_nat Y) Z)))).
% Axiom fact_574_termination__basic__simps_I5_J:(forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y))).
% Axiom fact_575_in__rel__def:(forall (R:(produc1501160679le_alt->Prop)) (X_2:arrow_475358991le_alt) (Y_2:arrow_475358991le_alt), ((iff (((in_rel1252994498le_alt R) X_2) Y_2)) ((member214075476le_alt ((produc1347929815le_alt X_2) Y_2)) R))).
% Axiom fact_576_funcsetI:(forall (F_7:(produc1501160679le_alt->Prop)) (B_4:(Prop->Prop)) (A_8:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_8)->((member_o (F_7 X_1)) B_4)))->((member377231867_alt_o F_7) ((pi_Pro1701359055_alt_o A_8) (fun (Uu:produc1501160679le_alt)=> B_4))))).
% Axiom fact_577_funcsetI:(forall (F_7:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_4:((produc1501160679le_alt->Prop)->Prop)) (A_8:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_8)->((member377231867_alt_o (F_7 X_1)) B_4)))->((member526088951_alt_o F_7) ((pi_Arr1929480907_alt_o A_8) (fun (Uu:arrow_1429601828e_indi)=> B_4))))).
% Axiom fact_578_funcsetI:(forall (F_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_4:((produc1501160679le_alt->Prop)->Prop)) (A_8:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_8)->((member377231867_alt_o (F_7 X_1)) B_4)))->((member616898751_alt_o F_7) ((pi_Arr1304755663_alt_o A_8) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_4))))).
% Axiom fact_579_linear__alt:((ex (produc1501160679le_alt->Prop)) (fun (L_1:(produc1501160679le_alt->Prop))=> ((member377231867_alt_o L_1) arrow_823908191le_Lin))).
% Axiom fact_580_Pi__cong:(forall (B_3:(produc1501160679le_alt->(Prop->Prop))) (G_2:(produc1501160679le_alt->Prop)) (F_6:(produc1501160679le_alt->Prop)) (A_7:(produc1501160679le_alt->Prop)), ((forall (W:produc1501160679le_alt), (((member214075476le_alt W) A_7)->((iff (F_6 W)) (G_2 W))))->((iff ((member377231867_alt_o F_6) ((pi_Pro1701359055_alt_o A_7) B_3))) ((member377231867_alt_o G_2) ((pi_Pro1701359055_alt_o A_7) B_3))))).
% Axiom fact_581_Pi__cong:(forall (B_3:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (F_6:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (G_2:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_7:(arrow_1429601828e_indi->Prop)), ((forall (W:arrow_1429601828e_indi), (((member2052026769e_indi W) A_7)->(((eq (produc1501160679le_alt->Prop)) (F_6 W)) (G_2 W))))->((iff ((member526088951_alt_o F_6) ((pi_Arr1929480907_alt_o A_7) B_3))) ((member526088951_alt_o G_2) ((pi_Arr1929480907_alt_o A_7) B_3))))).
% Axiom fact_582_Pi__cong:(forall (B_3:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (F_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (G_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_7:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (W:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o W) A_7)->(((eq (produc1501160679le_alt->Prop)) (F_6 W)) (G_2 W))))->((iff ((member616898751_alt_o F_6) ((pi_Arr1304755663_alt_o A_7) B_3))) ((member616898751_alt_o G_2) ((pi_Arr1304755663_alt_o A_7) B_3))))).
% Axiom fact_583_Pi__I_H:(forall (F_5:(produc1501160679le_alt->Prop)) (B_2:(produc1501160679le_alt->(Prop->Prop))) (A_6:(produc1501160679le_alt->Prop)), ((forall (X_1:produc1501160679le_alt), (((member214075476le_alt X_1) A_6)->((member_o (F_5 X_1)) (B_2 X_1))))->((member377231867_alt_o F_5) ((pi_Pro1701359055_alt_o A_6) B_2)))).
% Axiom fact_584_Pi__I_H:(forall (F_5:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (B_2:(arrow_1429601828e_indi->((produc1501160679le_alt->Prop)->Prop))) (A_6:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_6)->((member377231867_alt_o (F_5 X_1)) (B_2 X_1))))->((member526088951_alt_o F_5) ((pi_Arr1929480907_alt_o A_6) B_2)))).
% Axiom fact_585_Pi__I_H:(forall (F_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (B_2:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->((produc1501160679le_alt->Prop)->Prop))) (A_6:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))), (((member526088951_alt_o X_1) A_6)->((member377231867_alt_o (F_5 X_1)) (B_2 X_1))))->((member616898751_alt_o F_5) ((pi_Arr1304755663_alt_o A_6) B_2)))).
% Axiom fact_586_card__inj:(forall (F_4:(nat->nat)) (A_5:(nat->Prop)) (B_1:(nat->Prop)), (((member_nat_nat F_4) ((pi_nat_nat A_5) (fun (Uu:nat)=> B_1)))->(((inj_on_nat_nat F_4) A_5)->((finite_finite_nat B_1)->((ord_less_eq_nat (finite_card_nat A_5)) (finite_card_nat B_1)))))).
% Axiom fact_587_card__inj:(forall (F_4:(arrow_1429601828e_indi->nat)) (A_5:(arrow_1429601828e_indi->Prop)) (B_1:(nat->Prop)), (((member1315464153di_nat F_4) ((pi_Arr251692973di_nat A_5) (fun (Uu:arrow_1429601828e_indi)=> B_1)))->(((inj_on978774663di_nat F_4) A_5)->((finite_finite_nat B_1)->((ord_less_eq_nat (finite97476818e_indi A_5)) (finite_card_nat B_1)))))).
% Axiom fact_588_card__inj:(forall (F_4:(produc1501160679le_alt->Prop)) (A_5:(produc1501160679le_alt->Prop)) (B_1:(Prop->Prop)), (((member377231867_alt_o F_4) ((pi_Pro1701359055_alt_o A_5) (fun (Uu:produc1501160679le_alt)=> B_1)))->(((inj_on1911943593_alt_o F_4) A_5)->((finite_finite_o B_1)->((ord_less_eq_nat (finite537683861le_alt A_5)) (finite_card_o B_1)))))).
% Axiom fact_589_card__inj:(forall (F_4:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_5:(arrow_1429601828e_indi->Prop)) (B_1:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_4) ((pi_Arr1929480907_alt_o A_5) (fun (Uu:arrow_1429601828e_indi)=> B_1)))->(((inj_on1190919077_alt_o F_4) A_5)->((finite2112685307_alt_o B_1)->((ord_less_eq_nat (finite97476818e_indi A_5)) (finite28306938_alt_o B_1)))))).
% Axiom fact_590_card__inj:(forall (F_4:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_5:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B_1:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_4) ((pi_Arr1304755663_alt_o A_5) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B_1)))->(((inj_on1284293749_alt_o F_4) A_5)->((finite2112685307_alt_o B_1)->((ord_less_eq_nat (finite120663670_alt_o A_5)) (finite28306938_alt_o B_1)))))).
% Axiom fact_591_inj__onI:(forall (F_3:(nat->nat)) (A_4:(nat->Prop)), ((forall (X_1:nat) (Y_1:nat), (((member_nat X_1) A_4)->(((member_nat Y_1) A_4)->((((eq nat) (F_3 X_1)) (F_3 Y_1))->(((eq nat) X_1) Y_1)))))->((inj_on_nat_nat F_3) A_4))).
% Axiom fact_592_inj__onI:(forall (F_3:(arrow_1429601828e_indi->nat)) (A_4:(arrow_1429601828e_indi->Prop)), ((forall (X_1:arrow_1429601828e_indi) (Y_1:arrow_1429601828e_indi), (((member2052026769e_indi X_1) A_4)->(((member2052026769e_indi Y_1) A_4)->((((eq nat) (F_3 X_1)) (F_3 Y_1))->(((eq arrow_1429601828e_indi) X_1) Y_1)))))->((inj_on978774663di_nat F_3) A_4))).
% Axiom fact_593_inj__on__cong:(forall (F_2:(nat->nat)) (G_1:(nat->nat)) (A_2:(nat->Prop)), ((forall (A_3:nat), (((member_nat A_3) A_2)->(((eq nat) (F_2 A_3)) (G_1 A_3))))->((iff ((inj_on_nat_nat F_2) A_2)) ((inj_on_nat_nat G_1) A_2)))).
% Axiom fact_594_inj__on__cong:(forall (F_2:(arrow_1429601828e_indi->nat)) (G_1:(arrow_1429601828e_indi->nat)) (A_2:(arrow_1429601828e_indi->Prop)), ((forall (A_3:arrow_1429601828e_indi), (((member2052026769e_indi A_3) A_2)->(((eq nat) (F_2 A_3)) (G_1 A_3))))->((iff ((inj_on978774663di_nat F_2) A_2)) ((inj_on978774663di_nat G_1) A_2)))).
% Axiom fact_595_finite__indi:(finite664979089e_indi top_to988227749indi_o).
% Axiom fact_596_card__bij:(forall (G:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (F_1:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (A_1:((produc1501160679le_alt->Prop)->Prop)) (B:(arrow_1429601828e_indi->Prop)), (((member304866663e_indi F_1) ((pi_Pro468373057e_indi A_1) (fun (Uu:(produc1501160679le_alt->Prop))=> B)))->(((inj_on1877294875e_indi F_1) A_1)->(((member526088951_alt_o G) ((pi_Arr1929480907_alt_o B) (fun (Uu:arrow_1429601828e_indi)=> A_1)))->(((inj_on1190919077_alt_o G) B)->((finite2112685307_alt_o A_1)->((finite664979089e_indi B)->(((eq nat) (finite28306938_alt_o A_1)) (finite97476818e_indi B))))))))).
% Axiom fact_597_card__bij:(forall (G:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (F_1:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (A_1:((produc1501160679le_alt->Prop)->Prop)) (B:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)), (((member530241719_alt_o F_1) ((pi_Pro763888199_alt_o A_1) (fun (Uu:(produc1501160679le_alt->Prop))=> B)))->(((inj_on743426285_alt_o F_1) A_1)->(((member616898751_alt_o G) ((pi_Arr1304755663_alt_o B) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> A_1)))->(((inj_on1284293749_alt_o G) B)->((finite2112685307_alt_o A_1)->((finite1956767223_alt_o B)->(((eq nat) (finite28306938_alt_o A_1)) (finite120663670_alt_o B))))))))).
% Axiom fact_598_card__bij:(forall (G:(Prop->produc1501160679le_alt)) (F_1:(produc1501160679le_alt->Prop)) (A_1:(produc1501160679le_alt->Prop)) (B:(Prop->Prop)), (((member377231867_alt_o F_1) ((pi_Pro1701359055_alt_o A_1) (fun (Uu:produc1501160679le_alt)=> B)))->(((inj_on1911943593_alt_o F_1) A_1)->(((member492167345le_alt G) ((pi_o_P657324555le_alt B) (fun (Uu:Prop)=> A_1)))->(((inj_on867909093le_alt G) B)->((finite449174868le_alt A_1)->((finite_finite_o B)->(((eq nat) (finite537683861le_alt A_1)) (finite_card_o B))))))))).
% Axiom fact_599_card__bij:(forall (G:((produc1501160679le_alt->Prop)->arrow_1429601828e_indi)) (F_1:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop))) (A_1:(arrow_1429601828e_indi->Prop)) (B:((produc1501160679le_alt->Prop)->Prop)), (((member526088951_alt_o F_1) ((pi_Arr1929480907_alt_o A_1) (fun (Uu:arrow_1429601828e_indi)=> B)))->(((inj_on1190919077_alt_o F_1) A_1)->(((member304866663e_indi G) ((pi_Pro468373057e_indi B) (fun (Uu:(produc1501160679le_alt->Prop))=> A_1)))->(((inj_on1877294875e_indi G) B)->((finite664979089e_indi A_1)->((finite2112685307_alt_o B)->(((eq nat) (finite97476818e_indi A_1)) (finite28306938_alt_o B))))))))).
% Axiom fact_600_card__bij:(forall (G:((produc1501160679le_alt->Prop)->(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))) (F_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->(produc1501160679le_alt->Prop))) (A_1:((arrow_1429601828e_indi->(produc1501160679le_alt->Prop))->Prop)) (B:((produc1501160679le_alt->Prop)->Prop)), (((member616898751_alt_o F_1) ((pi_Arr1304755663_alt_o A_1) (fun (Uu:(arrow_1429601828e_indi->(produc1501160679le_alt->Prop)))=> B)))->(((inj_on1284293749_alt_o F_1) A_1)->(((member530241719_alt_o G) ((pi_Pro763888199_alt_o B) (fun (Uu:(produc1501160679le_alt->Prop))=> A_1)))->(((inj_on743426285_alt_o G) B)->((finite1956767223_alt_o A_1)->((finite2112685307_alt_o B)->(((eq nat) (finite120663670_alt_o A_1)) (finite28306938_alt_o B))))))))).
% Axiom fact_601_finite__Collect__less__nat:(forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_nat N_1) K))))).
% Axiom fact_602_finite__Collect__le__nat:(forall (K:nat), (finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat N_1) K))))).
% Axiom fact_603_card__UNIV__unit:(((eq nat) (finite1949902593t_unit top_to1984820022unit_o)) one_one_nat).
% Axiom fact_604_card__Collect__less__nat:(forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_nat I_1) N))))) N)).
% Axiom fact_605_infinite__UNIV__nat:((finite_finite_nat top_top_nat_o)->False).
% Axiom fact_606_finite__M__bounded__by__nat:(forall (P:(nat->Prop)) (_TPTP_I:nat), (finite_finite_nat (collect_nat (fun (K_1:nat)=> ((and (P K_1)) ((ord_less_nat K_1) _TPTP_I)))))).
% Axiom fact_607_finite__nat__set__iff__bounded__le:(forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_eq_nat X_1) M))))))).
% Axiom fact_608_finite__nat__set__iff__bounded:(forall (N_2:(nat->Prop)), ((iff (finite_finite_nat N_2)) ((ex nat) (fun (M:nat)=> (forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) M))))))).
% Axiom fact_609_finite__less__ub:(forall (U:nat) (F:(nat->nat)), ((forall (N_1:nat), ((ord_less_eq_nat N_1) (F N_1)))->(finite_finite_nat (collect_nat (fun (N_1:nat)=> ((ord_less_eq_nat (F N_1)) U)))))).
% Axiom fact_610_bounded__nat__set__is__finite:(forall (N:nat) (N_2:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) N)))->(finite_finite_nat N_2))).
% Axiom fact_611_less__zeroE:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% Axiom fact_612_le0:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)).
% Axiom fact_613_gr0I:(forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))).
% Axiom fact_614_gr__implies__not0:(forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->(not (((eq nat) N) zero_zero_nat)))).
% Axiom fact_615_less__nat__zero__code:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% Axiom fact_616_neq0__conv:(forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))).
% Axiom fact_617_not__less0:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% Axiom fact_618_plus__nat_Oadd__0:(forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)).
% Axiom fact_619_Nat_Oadd__0__right:(forall (M_2:nat), (((eq nat) ((plus_plus_nat M_2) zero_zero_nat)) M_2)).
% Axiom fact_620_add__is__0:(forall (M_2:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M_2) N)) zero_zero_nat)) ((and (((eq nat) M_2) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))).
% Axiom fact_621_add__eq__self__zero:(forall (M_2:nat) (N:nat), ((((eq nat) ((plus_plus_nat M_2) N)) M_2)->(((eq nat) N) zero_zero_nat))).
% Axiom fact_622_le__0__eq:(forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))).
% Axiom fact_623_less__eq__nat_Osimps_I1_J:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)).
% Axiom fact_624_add__gr__0:(forall (M_2:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M_2) N))) ((or ((ord_less_nat zero_zero_nat) M_2)) ((ord_less_nat zero_zero_nat) N)))).
% Axiom fact_625_ex__least__nat__less:(forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (I_1:nat), (((ord_less_eq_nat I_1) K_1)->((P I_1)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))).
% Axiom fact_626_ex__least__nat__le:(forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (I_1:nat), (((ord_less_nat I_1) K_1)->((P I_1)->False))))) (P K_1))))))).
% Axiom fact_627_less__imp__add__positive:(forall (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat _TPTP_I) K_1)) J_1)))))).
% Axiom fact_628_lessI:(forall (N:nat), ((ord_less_nat N) (suc N))).
% Axiom fact_629_Suc__mono:(forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_nat (suc M_2)) (suc N)))).
% Axiom fact_630_zero__less__Suc:(forall (N:nat), ((ord_less_nat zero_zero_nat) (suc N))).
% Axiom fact_631_Suc__n__not__le__n:(forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False)).
% Axiom fact_632_not__less__eq__eq:(forall (M_2:nat) (N:nat), ((iff (((ord_less_eq_nat M_2) N)->False)) ((ord_less_eq_nat (suc N)) M_2))).
% Axiom fact_633_le__Suc__eq:(forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat M_2) (suc N))) ((or ((ord_less_eq_nat M_2) N)) (((eq nat) M_2) (suc N))))).
% Axiom fact_634_Suc__le__mono:(forall (N:nat) (M_2:nat), ((iff ((ord_less_eq_nat (suc N)) (suc M_2))) ((ord_less_eq_nat N) M_2))).
% Axiom fact_635_le__SucI:(forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((ord_less_eq_nat M_2) (suc N)))).
% Axiom fact_636_le__SucE:(forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) (suc N))->((((ord_less_eq_nat M_2) N)->False)->(((eq nat) M_2) (suc N))))).
% Axiom fact_637_Suc__leD:(forall (M_2:nat) (N:nat), (((ord_less_eq_nat (suc M_2)) N)->((ord_less_eq_nat M_2) N))).
% Axiom fact_638_Suc__inject:(forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y))).
% Axiom fact_639_nat_Oinject:(forall (Nat_3:nat) (Nat_1:nat), ((iff (((eq nat) (suc Nat_3)) (suc Nat_1))) (((eq nat) Nat_3) Nat_1))).
% Axiom fact_640_Suc__n__not__n:(forall (N:nat), (not (((eq nat) (suc N)) N))).
% Axiom fact_641_n__not__Suc__n:(forall (N:nat), (not (((eq nat) N) (suc N)))).
% Axiom fact_642_add__Suc__shift:(forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M_2)) N)) ((plus_plus_nat M_2) (suc N)))).
% Axiom fact_643_add__Suc:(forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat (suc M_2)) N)) (suc ((plus_plus_nat M_2) N)))).
% Axiom fact_644_add__Suc__right:(forall (M_2:nat) (N:nat), (((eq nat) ((plus_plus_nat M_2) (suc N))) (suc ((plus_plus_nat M_2) N)))).
% Axiom fact_645_not__less__eq:(forall (M_2:nat) (N:nat), ((iff (((ord_less_nat M_2) N)->False)) ((ord_less_nat N) (suc M_2)))).
% Axiom fact_646_less__Suc__eq:(forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) (suc N))) ((or ((ord_less_nat M_2) N)) (((eq nat) M_2) N)))).
% Axiom fact_647_Suc__less__eq:(forall (M_2:nat) (N:nat), ((iff ((ord_less_nat (suc M_2)) (suc N))) ((ord_less_nat M_2) N))).
% Axiom fact_648_not__less__less__Suc__eq:(forall (N:nat) (M_2:nat), ((((ord_less_nat N) M_2)->False)->((iff ((ord_less_nat N) (suc M_2))) (((eq nat) N) M_2)))).
% Axiom fact_649_less__antisym:(forall (N:nat) (M_2:nat), ((((ord_less_nat N) M_2)->False)->(((ord_less_nat N) (suc M_2))->(((eq nat) M_2) N)))).
% Axiom fact_650_less__SucI:(forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_nat M_2) (suc N)))).
% Axiom fact_651_Suc__lessI:(forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((not (((eq nat) (suc M_2)) N))->((ord_less_nat (suc M_2)) N)))).
% Axiom fact_652_less__trans__Suc:(forall (K:nat) (_TPTP_I:nat) (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->(((ord_less_nat J_1) K)->((ord_less_nat (suc _TPTP_I)) K)))).
% Axiom fact_653_less__SucE:(forall (M_2:nat) (N:nat), (((ord_less_nat M_2) (suc N))->((((ord_less_nat M_2) N)->False)->(((eq nat) M_2) N)))).
% Axiom fact_654_Suc__lessD:(forall (M_2:nat) (N:nat), (((ord_less_nat (suc M_2)) N)->((ord_less_nat M_2) N))).
% Axiom fact_655_Suc__less__SucD:(forall (M_2:nat) (N:nat), (((ord_less_nat (suc M_2)) (suc N))->((ord_less_nat M_2) N))).
% Axiom fact_656_One__nat__def:(((eq nat) one_one_nat) (suc zero_zero_nat)).
% Axiom fact_657_Suc__le__lessD:(forall (M_2:nat) (N:nat), (((ord_less_eq_nat (suc M_2)) N)->((ord_less_nat M_2) N))).
% Axiom fact_658_le__less__Suc__eq:(forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((iff ((ord_less_nat N) (suc M_2))) (((eq nat) N) M_2)))).
% Axiom fact_659_Suc__leI:(forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ord_less_eq_nat (suc M_2)) N))).
% Axiom fact_660_le__imp__less__Suc:(forall (M_2:nat) (N:nat), (((ord_less_eq_nat M_2) N)->((ord_less_nat M_2) (suc N)))).
% Axiom fact_661_Suc__le__eq:(forall (M_2:nat) (N:nat), ((iff ((ord_less_eq_nat (suc M_2)) N)) ((ord_less_nat M_2) N))).
% Axiom fact_662_less__Suc__eq__le:(forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) (suc N))) ((ord_less_eq_nat M_2) N))).
% Axiom fact_663_less__eq__Suc__le:(forall (N:nat) (M_2:nat), ((iff ((ord_less_nat N) M_2)) ((ord_less_eq_nat (suc N)) M_2))).
% Axiom fact_664_less__iff__Suc__add:(forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M_2) K_1))))))).
% Axiom fact_665_less__add__Suc2:(forall (_TPTP_I:nat) (M_2:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat M_2) _TPTP_I)))).
% Axiom fact_666_less__add__Suc1:(forall (_TPTP_I:nat) (M_2:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat _TPTP_I) M_2)))).
% Axiom fact_667_one__is__add:(forall (M_2:nat) (N:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M_2) N))) ((or ((and (((eq nat) M_2) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M_2) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat)))))).
% Axiom fact_668_add__is__1:(forall (M_2:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M_2) N)) (suc zero_zero_nat))) ((or ((and (((eq nat) M_2) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) ((and (((eq nat) M_2) zero_zero_nat)) (((eq nat) N) (suc zero_zero_nat)))))).
% Axiom fact_669_gr0__conv__Suc:(forall (N:nat), ((iff ((ord_less_nat zero_zero_nat) N)) ((ex nat) (fun (M:nat)=> (((eq nat) N) (suc M)))))).
% Axiom fact_670_less__Suc0:(forall (N:nat), ((iff ((ord_less_nat N) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))).
% Axiom fact_671_less__Suc__eq__0__disj:(forall (M_2:nat) (N:nat), ((iff ((ord_less_nat M_2) (suc N))) ((or (((eq nat) M_2) zero_zero_nat)) ((ex nat) (fun (J:nat)=> ((and (((eq nat) M_2) (suc J))) ((ord_less_nat J) N))))))).
% Axiom fact_672_inj__Suc:(forall (N_2:(nat->Prop)), ((inj_on_nat_nat suc) N_2)).
% Axiom fact_673_Suc__neq__Zero:(forall (M_2:nat), (not (((eq nat) (suc M_2)) zero_zero_nat))).
% Axiom fact_674_Zero__neq__Suc:(forall (M_2:nat), (not (((eq nat) zero_zero_nat) (suc M_2)))).
% Axiom fact_675_nat_Osimps_I3_J:(forall (Nat_2:nat), (not (((eq nat) (suc Nat_2)) zero_zero_nat))).
% Axiom fact_676_Suc__not__Zero:(forall (M_2:nat), (not (((eq nat) (suc M_2)) zero_zero_nat))).
% Axiom fact_677_nat_Osimps_I2_J:(forall (Nat_1:nat), (not (((eq nat) zero_zero_nat) (suc Nat_1)))).
% Axiom fact_678_Zero__not__Suc:(forall (M_2:nat), (not (((eq nat) zero_zero_nat) (suc M_2)))).
% Axiom fact_679_less__eq__Suc__le__raw:(forall (X_1:nat), (((eq (nat->Prop)) (ord_less_nat X_1)) (ord_less_eq_nat (suc X_1)))).
% Axiom fact_680_card__Collect__le__nat:(forall (N:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_eq_nat I_1) N))))) (suc N))).
% Axiom fact_681_card__less__Suc:(forall (_TPTP_I:nat) (M_3:(nat->Prop)), (((member_nat zero_zero_nat) M_3)->(((eq nat) (suc (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_3)) ((ord_less_nat K_1) _TPTP_I))))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_3)) ((ord_less_nat K_1) (suc _TPTP_I))))))))).
% Axiom fact_682_card__less:(forall (_TPTP_I:nat) (M_3:(nat->Prop)), (((member_nat zero_zero_nat) M_3)->(not (((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_3)) ((ord_less_nat K_1) (suc _TPTP_I))))))) zero_zero_nat)))).
% Axiom fact_683_card__less__Suc2:(forall (_TPTP_I:nat) (M_3:(nat->Prop)), ((((member_nat zero_zero_nat) M_3)->False)->(((eq nat) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat (suc K_1)) M_3)) ((ord_less_nat K_1) _TPTP_I)))))) (finite_card_nat (collect_nat (fun (K_1:nat)=> ((and ((member_nat K_1) M_3)) ((ord_less_nat K_1) (suc _TPTP_I))))))))).
% Axiom fact_684_inc__induct:(forall (P:(nat->Prop)) (_TPTP_I:nat) (J_1:nat), (((ord_less_eq_nat _TPTP_I) J_1)->((P J_1)->((forall (I_1:nat), (((ord_less_nat I_1) J_1)->((P (suc I_1))->(P I_1))))->(P _TPTP_I))))).
% Axiom fact_685_less__imp__Suc__add:(forall (M_2:nat) (N:nat), (((ord_less_nat M_2) N)->((ex nat) (fun (K_1:nat)=> (((eq nat) N) (suc ((plus_plus_nat M_2) K_1))))))).
% Axiom fact_686_gr0__implies__Suc:(forall (N:nat), (((ord_less_nat zero_zero_nat) N)->((ex nat) (fun (M:nat)=> (((eq nat) N) (suc M)))))).
% Axiom fact_687_Suc__eq__plus1__left:(forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat one_one_nat) N))).
% Axiom fact_688_Suc__eq__plus1:(forall (N:nat), (((eq nat) (suc N)) ((plus_plus_nat N) one_one_nat))).
% Axiom fact_689_Suc__le__D:(forall (N:nat) (M_1:nat), (((ord_less_eq_nat (suc N)) M_1)->((ex nat) (fun (M:nat)=> (((eq nat) M_1) (suc M)))))).
% Axiom fact_690_lessE:(forall (_TPTP_I:nat) (K:nat), (((ord_less_nat _TPTP_I) K)->((not (((eq nat) K) (suc _TPTP_I)))->((forall (J:nat), (((ord_less_nat _TPTP_I) J)->(not (((eq nat) K) (suc J)))))->False)))).
% Axiom fact_691_Suc__lessE:(forall (_TPTP_I:nat) (K:nat), (((ord_less_nat (suc _TPTP_I)) K)->((forall (J:nat), (((ord_less_nat _TPTP_I) J)->(not (((eq nat) K) (suc J)))))->False))).
% Axiom fact_692_not0__implies__Suc:(forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ex nat) (fun (M:nat)=> (((eq nat) N) (suc M)))))).
% Axiom fact_693_nat_Oexhaust:(forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat:nat), (not (((eq nat) Y) (suc Nat))))->False))).
% Axiom fact_694_zero__induct:(forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N_1:nat), ((P (suc N_1))->(P N_1)))->(P zero_zero_nat)))).
% Axiom fact_695_nat__induct:(forall (N:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N_1:nat), ((P N_1)->(P (suc N_1))))->(P N)))).
% Axiom fact_696_surjh:(((eq (nat->Prop)) ((image_484224243di_nat h) top_to988227749indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite97476818e_indi top_to988227749indi_o))).
% Axiom fact_697_finite__atLeastLessThan:(forall (L:nat) (U:nat), (finite_finite_nat ((ord_at4362885an_nat L) U))).
% Axiom fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123:((forall (H:(arrow_1429601828e_indi->nat)), (((inj_on978774663di_nat H) top_to988227749indi_o)->(not (((eq (nat->Prop)) ((image_484224243di_nat H) top_to988227749indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite97476818e_indi top_to988227749indi_o))))))->False).
% Axiom fact_699_subset__card__intvl__is__intvl:(forall (A:(nat->Prop)) (K:nat), (((ord_less_eq_nat_o A) ((ord_at4362885an_nat K) ((plus_plus_nat K) (finite_card_nat A))))->(((eq (nat->Prop)) A) ((ord_at4362885an_nat K) ((plus_plus_nat K) (finite_card_nat A)))))).
% Axiom help_If_1_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_:(forall (X:(produc1501160679le_alt->Prop)) (Y:(produc1501160679le_alt->Prop)), (((eq (produc1501160679le_alt->Prop)) (((if_Pro1561232536_alt_o True) X) Y)) X)).
% Axiom help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_:(forall (X:(produc1501160679le_alt->Prop)) (Y:(produc1501160679le_alt->Prop)), (((eq (produc1501160679le_alt->Prop)) (((if_Pro1561232536_alt_o False) X) Y)) Y)).
% Axiom help_If_3_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_:(forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))).
% Trying to prove ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))
% Found fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto:((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))
% Found fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto as proof of ((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))
% Found (x0 fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) as proof of ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))
% Found (fun (x0:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))))=> (x0 fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)) as proof of ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))
% Found (fun (x:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (x0:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))))=> (x0 fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)) as proof of ((((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))
% Found (fun (x:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (x0:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))))=> (x0 fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)) as proof of ((((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))->((((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))))
% Found (and_rect00 (fun (x:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (x0:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))))=> (x0 fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto))) as proof of ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))
% Found ((and_rect0 ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))) (fun (x:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (x0:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))))=> (x0 fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto))) as proof of ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))
% Found (((fun (P:Type) (x:((((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))->((((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))) (fun (x:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (x0:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))))=> (x0 fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto))) as proof of ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))
% Found (((fun (P:Type) (x:((((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))->((((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))) (fun (x:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (x0:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))))=> (x0 fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto))) as proof of ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))
% Got proof (((fun (P:Type) (x:((((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))->((((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))) (fun (x:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (x0:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))))=> (x0 fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)))
% Time elapsed = 5.489963s
% node=121 cost=858.000000 depth=8
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (((fun (P:Type) (x:((((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))->((((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))) (fun (x:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e)))))))) (x0:(((member214075476le_alt ((produc1347929815le_alt c) d)) (f (fun (I_1:arrow_1429601828e_indi)=> (((if_Pro1561232536_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_55669061_mktop (p I_1)) e)) (((if_Pro1561232536_alt_o (((eq nat) (h I_1)) n)) (((arrow_789600939_above (p I_1)) c) e)) ((arrow_2054445623_mkbot (p I_1)) e))))))->((member214075476le_alt ((produc1347929815le_alt c) d)) (f p))))=> (x0 fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------