cocATP---0.2.0.THM-Prf.s

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SCT171^3 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n104.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 13:29:47 EDT 2014

% Result   : Theorem 13.62s
% Output   : Proof 13.62s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SCT171^3 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n104.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 08:30:21 CDT 2014
% % CPUTime  : 13.62 
% 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 0x1a46950>, <kernel.Type object at 0x19e7d88>) of role type named ty_ty_tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt
% Using role type
% Declaring arrow_1389031998le_alt:Type
% FOF formula (<kernel.Constant object at 0x1a46f80>, <kernel.Type object at 0x19e7d88>) of role type named ty_ty_tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi
% Using role type
% Declaring arrow_1196572341e_indi:Type
% FOF formula (<kernel.Constant object at 0x1a46878>, <kernel.Type object at 0x19e7c68>) of role type named ty_ty_tc__Nat__Onat
% Using role type
% Declaring nat:Type
% FOF formula (<kernel.Constant object at 0x1a46908>, <kernel.Type object at 0x19e7d88>) of role type named ty_ty_tc__Product____Type__Ounit
% Using role type
% Declaring product_unit:Type
% FOF formula (<kernel.Constant object at 0x1a46f80>, <kernel.Type object at 0x19e7e60>) of role type named ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_Mtc__Arrow__
% Using role type
% Declaring produc1572197287le_alt:Type
% FOF formula (<kernel.Constant object at 0x1a46f80>, <kernel.DependentProduct object at 0x19e7b48>) of role type named sy_c_All
% Using role type
% Declaring all:((produc1572197287le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x1a46f80>, <kernel.DependentProduct object at 0x19e7a28>) of role type named sy_c_Arrow__Order__Mirabelle__piyeccggrh_OIIA
% Using role type
% Declaring arrow_1955289568le_IIA:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x19e7cb0>, <kernel.DependentProduct object at 0x19e7e18>) of role type named sy_c_Arrow__Order__Mirabelle__piyeccggrh_OLin
% Using role type
% Declaring arrow_1982173296le_Lin:((produc1572197287le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x19e7b90>, <kernel.DependentProduct object at 0x19e7b48>) of role type named sy_c_Arrow__Order__Mirabelle__piyeccggrh_OProf
% Using role type
% Declaring arrow_1647925946e_Prof:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x19e7ef0>, <kernel.DependentProduct object at 0x19e7a28>) of role type named sy_c_Arrow__Order__Mirabelle__piyeccggrh_Oabove
% Using role type
% Declaring arrow_556571452_above:((produc1572197287le_alt->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->(produc1572197287le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0x19e7e18>, <kernel.DependentProduct object at 0x19e78c0>) of role type named sy_c_Arrow__Order__Mirabelle__piyeccggrh_Obelow
% Using role type
% Declaring arrow_1865170000_below:((produc1572197287le_alt->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->(produc1572197287le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0x19e77e8>, <kernel.DependentProduct object at 0x19e78c0>) of role type named sy_c_Arrow__Order__Mirabelle__piyeccggrh_Odictator
% Using role type
% Declaring arrow_968343245ctator:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))
% FOF formula (<kernel.Constant object at 0x19e7638>, <kernel.DependentProduct object at 0x19e7b48>) of role type named sy_c_Arrow__Order__Mirabelle__piyeccggrh_Omkbot
% Using role type
% Declaring arrow_1821416136_mkbot:((produc1572197287le_alt->Prop)->(arrow_1389031998le_alt->(produc1572197287le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7a70>, <kernel.DependentProduct object at 0x19e7cb0>) of role type named sy_c_Arrow__Order__Mirabelle__piyeccggrh_Omktop
% Using role type
% Declaring arrow_1970123222_mktop:((produc1572197287le_alt->Prop)->(arrow_1389031998le_alt->(produc1572197287le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7ef0>, <kernel.DependentProduct object at 0x19e78c0>) of role type named sy_c_Arrow__Order__Mirabelle__piyeccggrh_Ounanimity
% Using role type
% Declaring arrow_1282657667nimity:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x19e7b90>, <kernel.DependentProduct object at 0x19e7488>) of role type named sy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_000tc__Nat__Onat_000tc__Na
% Using role type
% Declaring big_co387207925at_nat:((nat->nat)->((nat->Prop)->nat))
% FOF formula (<kernel.Constant object at 0x19e7b48>, <kernel.DependentProduct object at 0x19e7cb0>) of role type named sy_c_Finite__Set_Ocard_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi
% Using role type
% Declaring finite2011930979e_indi:((arrow_1196572341e_indi->Prop)->nat)
% FOF formula (<kernel.Constant object at 0x19e7560>, <kernel.DependentProduct object at 0x19e77e8>) 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 0x19e7368>, <kernel.DependentProduct object at 0x19e74d0>) 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 0x19e7a70>, <kernel.DependentProduct object at 0x19e78c0>) of role type named sy_c_Finite__Set_Ofinite_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi
% Using role type
% Declaring finite431949602e_indi:((arrow_1196572341e_indi->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x19e7ef0>, <kernel.DependentProduct object at 0x19e74d0>) 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 0x19e7b90>, <kernel.DependentProduct object at 0x19e7290>) of role type named sy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000tc_
% Using role type
% Declaring inj_on1505595958di_nat:((arrow_1196572341e_indi->nat)->((arrow_1196572341e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e7248>, <kernel.DependentProduct object at 0x19e7128>) 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 0x19e71b8>, <kernel.DependentProduct object at 0x19e7200>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__O
% Using role type
% Declaring pi_Arr1865419731lt_o_o:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7a70>, <kernel.DependentProduct object at 0x19e7200>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__O_001
% Using role type
% Declaring pi_Arr470535441e_indi:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e74d0>, <kernel.DependentProduct object at 0x19e7200>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__O_002
% Using role type
% Declaring pi_Arr2096782767t_unit:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7b90>, <kernel.DependentProduct object at 0x19e7950>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M
% Using role type
% Declaring pi_Arr1196397536_alt_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7098>, <kernel.DependentProduct object at 0x19e7248>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_003
% Using role type
% Declaring pi_Arr1709554855lt_o_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7a70>, <kernel.DependentProduct object at 0x19e7170>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_004
% Using role type
% Declaring pi_Arr272777533e_indi:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e74d0>, <kernel.DependentProduct object at 0x19e7ef0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_005
% Using role type
% Declaring pi_Arr509685723t_unit:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7b90>, <kernel.DependentProduct object at 0x19e77a0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggr
% Using role type
% Declaring pi_Pro386796690lt_o_o:(((produc1572197287le_alt->Prop)->Prop)->(((produc1572197287le_alt->Prop)->(Prop->Prop))->(((produc1572197287le_alt->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7098>, <kernel.DependentProduct object at 0x19e74d0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggr_006
% Using role type
% Declaring pi_Pro2039443474e_indi:(((produc1572197287le_alt->Prop)->Prop)->(((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))->(((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7758>, <kernel.DependentProduct object at 0x19e7b90>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggr_007
% Using role type
% Declaring pi_Pro30504752t_unit:(((produc1572197287le_alt->Prop)->Prop)->(((produc1572197287le_alt->Prop)->(product_unit->Prop))->(((produc1572197287le_alt->Prop)->product_unit)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e75a8>, <kernel.DependentProduct object at 0x19e7908>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyecc
% Using role type
% Declaring pi_o_A1994447367_alt_o:((Prop->Prop)->((Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))->((Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7098>, <kernel.DependentProduct object at 0x19e7b90>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__
% Using role type
% Declaring pi_o_A1479825007_alt_o:((Prop->Prop)->((Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))->((Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7758>, <kernel.DependentProduct object at 0x19e73f8>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____pi
% Using role type
% Declaring pi_o_P1417870404_alt_o:((Prop->Prop)->((Prop->((produc1572197287le_alt->Prop)->Prop))->((Prop->(produc1572197287le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x19e75a8>, <kernel.DependentProduct object at 0x19e73f8>) 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 0x19e7098>, <kernel.DependentProduct object at 0x19e73f8>) of role type named sy_c_FuncSet_OPi_000_Eo_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg
% Using role type
% Declaring pi_o_P728361163le_alt:((Prop->Prop)->((Prop->(produc1572197287le_alt->Prop))->((Prop->produc1572197287le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7758>, <kernel.DependentProduct object at 0x19e79e0>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000_062
% Using role type
% Declaring pi_Arr583278353_alt_o:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))->((arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7440>, <kernel.DependentProduct object at 0x19e79e0>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000_062_008
% Using role type
% Declaring pi_Arr456308197_alt_o:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))->((arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7ab8>, <kernel.DependentProduct object at 0x19e75a8>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000_062_009
% Using role type
% Declaring pi_Arr1309696186_alt_o:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7998>, <kernel.DependentProduct object at 0x19e7440>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000tc__
% Using role type
% Declaring pi_Arr778514268di_nat:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->(nat->Prop))->((arrow_1196572341e_indi->nat)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e70e0>, <kernel.DependentProduct object at 0x19e7ab8>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000tc___010
% Using role type
% Declaring pi_Arr1762714837le_alt:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((arrow_1196572341e_indi->produc1572197287le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7bd8>, <kernel.DependentProduct object at 0x19e7c20>) 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 0x19e72d8>, <kernel.DependentProduct object at 0x19e7998>) of role type named sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____piyeccgg
% Using role type
% Declaring pi_nat986275508e_indi:((nat->Prop)->((nat->(arrow_1196572341e_indi->Prop))->((nat->arrow_1196572341e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e75a8>, <kernel.DependentProduct object at 0x19e7998>) 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 0x19e7ab8>, <kernel.DependentProduct object at 0x19e99e0>) of role type named sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000_062_I_062_Itc__Arrow____Order
% Using role type
% Declaring pi_Pro443817391_alt_o:((product_unit->Prop)->((product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))->((product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x19e79e0>, <kernel.DependentProduct object at 0x19e75a8>) of role type named sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000_062_Itc__Arrow____Order____Mi
% Using role type
% Declaring pi_Pro1959068871_alt_o:((product_unit->Prop)->((product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))->((product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7998>, <kernel.DependentProduct object at 0x19e93b0>) of role type named sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000_062_Itc__prod_Itc__Arrow____O
% Using role type
% Declaring pi_Pro29851292_alt_o:((product_unit->Prop)->((product_unit->((produc1572197287le_alt->Prop)->Prop))->((product_unit->(produc1572197287le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0x19e75a8>, <kernel.DependentProduct object at 0x19e93b0>) 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 0x19e79e0>, <kernel.DependentProduct object at 0x19e99e0>) of role type named sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__prod_Itc__Arrow____Order__
% Using role type
% Declaring pi_Pro772884595le_alt:((product_unit->Prop)->((product_unit->(produc1572197287le_alt->Prop))->((product_unit->produc1572197287le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e75a8>, <kernel.DependentProduct object at 0x19e93b0>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oal
% Using role type
% Declaring pi_Pro418549519_alt_o:((produc1572197287le_alt->Prop)->((produc1572197287le_alt->(Prop->Prop))->((produc1572197287le_alt->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e79e0>, <kernel.DependentProduct object at 0x19e93f8>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oal_011
% Using role type
% Declaring pi_Pro1246947541e_indi:((produc1572197287le_alt->Prop)->((produc1572197287le_alt->(arrow_1196572341e_indi->Prop))->((produc1572197287le_alt->arrow_1196572341e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7998>, <kernel.DependentProduct object at 0x19e9170>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oal_012
% Using role type
% Declaring pi_Pro926528371t_unit:((produc1572197287le_alt->Prop)->((produc1572197287le_alt->(product_unit->Prop))->((produc1572197287le_alt->product_unit)->Prop)))
% FOF formula (<kernel.Constant object at 0x19e7998>, <kernel.Constant object at 0x19e9170>) 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 0x19e96c8>, <kernel.DependentProduct object at 0x19c94d0>) 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 0x19e93f8>, <kernel.DependentProduct object at 0x19c95f0>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat
% Using role type
% Declaring times_times_nat:(nat->(nat->nat))
% FOF formula (<kernel.Constant object at 0x19e96c8>, <kernel.Constant object at 0x19c9248>) 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 0x19e93f8>, <kernel.DependentProduct object at 0x19c9440>) of role type named sy_c_HOL_Obool_Obool__size
% Using role type
% Declaring bool_size:(Prop->nat)
% FOF formula (<kernel.Constant object at 0x19e9170>, <kernel.DependentProduct object at 0x19c9560>) of role type named sy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____piyeccggrh
% Using role type
% Declaring hilber1125280539di_nat:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->nat)->(nat->arrow_1196572341e_indi)))
% FOF formula (<kernel.Constant object at 0x19e9170>, <kernel.DependentProduct object at 0x19c91b8>) 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 0x19c94d0>, <kernel.DependentProduct object at 0x19c9440>) of role type named sy_c_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_M
% Using role type
% Declaring if_Pro278423000_alt_o:(Prop->((produc1572197287le_alt->Prop)->((produc1572197287le_alt->Prop)->(produc1572197287le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0x19c90e0>, <kernel.DependentProduct object at 0x19c9440>) of role type named sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Nat__Onat_M_Eo_J
% Using role type
% Declaring semila848761471_nat_o:((nat->Prop)->((nat->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x19c95f0>, <kernel.DependentProduct object at 0x19e8ef0>) of role type named sy_c_Nat_OSuc
% Using role type
% Declaring suc:(nat->nat)
% FOF formula (<kernel.Constant object at 0x19c9908>, <kernel.DependentProduct object at 0x19e8ab8>) of role type named sy_c_Nat_Onat_Onat__case_000_Eo
% Using role type
% Declaring nat_case_o:(Prop->((nat->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x19c9320>, <kernel.DependentProduct object at 0x19e8ef0>) of role type named sy_c_Nat_Onat_Onat__size
% Using role type
% Declaring nat_size:(nat->nat)
% FOF formula (<kernel.Constant object at 0x19c9908>, <kernel.DependentProduct object at 0x19e8dd0>) of role type named sy_c_Nat_Osize__class_Osize_000tc__Nat__Onat
% Using role type
% Declaring size_size_nat:(nat->nat)
% FOF formula (<kernel.Constant object at 0x19c95f0>, <kernel.DependentProduct object at 0x19e8ea8>) 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_le1382328578lt_o_o:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19c9908>, <kernel.DependentProduct object at 0x19e8c20>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__Arrow____Order____Mirabelle_
% Using role type
% Declaring ord_le914873172lt_o_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19c95f0>, <kernel.DependentProduct object at 0x19e8dd0>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__prod_Itc__Arrow____Order____
% Using role type
% Declaring ord_le874404799lt_o_o:(((produc1572197287le_alt->Prop)->Prop)->(((produc1572197287le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19c9908>, <kernel.DependentProduct object at 0x19e8e60>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__Arrow____Order____Mirabelle____piy
% Using role type
% Declaring ord_le1339521307_alt_o:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x19c9908>, <kernel.DependentProduct object at 0x19e8050>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__Arrow____Order____Mirabelle____piy_013
% Using role type
% Declaring ord_le1991507760indi_o:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e8d88>, <kernel.DependentProduct object at 0x19e8b48>) 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 0x19e8ea8>, <kernel.DependentProduct object at 0x19e8cf8>) 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 0x19e8ef0>, <kernel.DependentProduct object at 0x19e8b48>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__prod_Itc__Arrow____Order____Mirabe
% Using role type
% Declaring ord_le1852932542_alt_o:((produc1572197287le_alt->Prop)->((produc1572197287le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e8b00>, <kernel.DependentProduct object at 0x19e8d88>) 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 0x19e8ea8>, <kernel.DependentProduct object at 0x15f1908>) 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 0x19e8b48>, <kernel.DependentProduct object at 0x15f18c0>) 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_le1805007862lt_o_o:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e8ef0>, <kernel.DependentProduct object at 0x15f17e8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Arrow____Order____Mirabe
% Using role type
% Declaring ord_le602483040lt_o_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e8ea8>, <kernel.DependentProduct object at 0x15f1950>) 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_le1027220427lt_o_o:(((produc1572197287le_alt->Prop)->Prop)->(((produc1572197287le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e8b48>, <kernel.DependentProduct object at 0x15f1758>) 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 0x19e8050>, <kernel.DependentProduct object at 0x15f18c0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Arrow____Order____Mirabelle___
% Using role type
% Declaring ord_le1463467535_alt_o:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x19e8b48>, <kernel.DependentProduct object at 0x15f1710>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Arrow____Order____Mirabelle____014
% Using role type
% Declaring ord_le1423491573_alt_o:((arrow_1389031998le_alt->Prop)->((arrow_1389031998le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e8050>, <kernel.DependentProduct object at 0x15f16c8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Arrow____Order____Mirabelle____015
% Using role type
% Declaring ord_le865407012indi_o:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e8050>, <kernel.DependentProduct object at 0x15f1638>) 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 0x15f1878>, <kernel.DependentProduct object at 0x15f1680>) 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 0x15f1758>, <kernel.DependentProduct object at 0x15f15a8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__prod_Itc__Arrow____Order____Mi
% Using role type
% Declaring ord_le962286258_alt_o:((produc1572197287le_alt->Prop)->((produc1572197287le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f18c0>, <kernel.DependentProduct object at 0x15f16c8>) 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 0x15f1878>, <kernel.DependentProduct object at 0x15f1680>) 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 0x15f15a8>, <kernel.DependentProduct object at 0x15f1518>) 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_to1492351398lt_o_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x15f16c8>, <kernel.DependentProduct object at 0x15f1878>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__Arrow____Order____Mirabelle__
% Using role type
% Declaring top_to732317616lt_o_o:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0x15f15f0>, <kernel.DependentProduct object at 0x15f1680>) 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_to1806834203lt_o_o:((produc1572197287le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x15f1518>, <kernel.DependentProduct object at 0x15f1878>) 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 0x15f16c8>, <kernel.DependentProduct object at 0x15f1680>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____piye
% Using role type
% Declaring top_to1627321279_alt_o:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x15f1488>, <kernel.DependentProduct object at 0x15f1440>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____piye_016
% Using role type
% Declaring top_to54564308indi_o:(arrow_1196572341e_indi->Prop)
% FOF formula (<kernel.Constant object at 0x15f14d0>, <kernel.DependentProduct object at 0x15f13f8>) 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 0x15f1680>, <kernel.DependentProduct object at 0x15f19e0>) 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 0x15f1440>, <kernel.DependentProduct object at 0x15f1a28>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__Arrow____Order____Mirabel
% Using role type
% Declaring top_to558618722_alt_o:(produc1572197287le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x15f13f8>, <kernel.Sort object at 0x14d7ea8>) 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 0x15f1560>, <kernel.DependentProduct object at 0x15f1680>) of role type named sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_
% Using role type
% Declaring produc897867031le_alt:(arrow_1389031998le_alt->(arrow_1389031998le_alt->produc1572197287le_alt))
% FOF formula (<kernel.Constant object at 0x15f15f0>, <kernel.DependentProduct object at 0x15f1b00>) of role type named sy_c_SetInterval_Oord__class_OatLeastAtMost_000tc__Nat__Onat
% Using role type
% Declaring ord_at238088361st_nat:(nat->(nat->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x15f1440>, <kernel.DependentProduct object at 0x15f19e0>) 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 0x15f1680>, <kernel.DependentProduct object at 0x15f1c20>) of role type named sy_c_SetInterval_Oord__class_OatLeast_000tc__Nat__Onat
% Using role type
% Declaring ord_atLeast_nat:(nat->(nat->Prop))
% FOF formula (<kernel.Constant object at 0x15f1b00>, <kernel.DependentProduct object at 0x15f1a70>) of role type named sy_c_SetInterval_Oord__class_OgreaterThanAtMost_000tc__Nat__Onat
% Using role type
% Declaring ord_gr375877188st_nat:(nat->(nat->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x15f19e0>, <kernel.DependentProduct object at 0x15f1bd8>) of role type named sy_c_SetInterval_Oord__class_OgreaterThanLessThan_000tc__Nat__Onat
% Using role type
% Declaring ord_gr660468384an_nat:(nat->(nat->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x15f1c20>, <kernel.DependentProduct object at 0x15f1cf8>) of role type named sy_c_SetInterval_Oord__class_OgreaterThan_000tc__Nat__Onat
% Using role type
% Declaring ord_greaterThan_nat:(nat->(nat->Prop))
% FOF formula (<kernel.Constant object at 0x15f1a70>, <kernel.DependentProduct object at 0x15f1b48>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__
% Using role type
% Declaring collec670126350_alt_o:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x15f1bd8>, <kernel.DependentProduct object at 0x15f19e0>) of role type named sy_c_Set_OCollect_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_
% Using role type
% Declaring collec979749928_alt_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0x15f1d40>, <kernel.DependentProduct object at 0x15f1e18>) of role type named sy_c_Set_OCollect_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg
% Using role type
% Declaring collec958969213_alt_o:(((produc1572197287le_alt->Prop)->Prop)->((produc1572197287le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1c20>, <kernel.DependentProduct object at 0x15f1b00>) of role type named sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi
% Using role type
% Declaring collec1936859488e_indi:((arrow_1196572341e_indi->Prop)->(arrow_1196572341e_indi->Prop))
% FOF formula (<kernel.Constant object at 0x15f1908>, <kernel.DependentProduct object at 0x15f1c20>) 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 0x15f1cb0>, <kernel.DependentProduct object at 0x15f1e18>) 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 0x15f1b00>, <kernel.DependentProduct object at 0x15f1908>) of role type named sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa
% Using role type
% Declaring collec940901970le_alt:((produc1572197287le_alt->Prop)->(produc1572197287le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x15f1a70>, <kernel.DependentProduct object at 0x15f1f38>) of role type named sy_c_Set_Oimage_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_000tc__N
% Using role type
% Declaring image_1011045538di_nat:((arrow_1196572341e_indi->nat)->((arrow_1196572341e_indi->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x15f1c20>, <kernel.DependentProduct object at 0x15f1fc8>) of role type named sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Nat__Onat
% Using role type
% Declaring image_nat_nat:((nat->nat)->((nat->Prop)->(nat->Prop)))
% FOF formula (<kernel.Constant object at 0x15f1ea8>, <kernel.DependentProduct object at 0x15f1a70>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__
% Using role type
% Declaring member1346253567lt_o_o:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1908>, <kernel.DependentProduct object at 0x15f1c20>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh___017
% Using role type
% Declaring member1539010427e_indi:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->(((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1cb0>, <kernel.DependentProduct object at 0x15f1ea8>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh___018
% Using role type
% Declaring member1043380889t_unit:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)->(((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1f38>, <kernel.DependentProduct object at 0x19e10e0>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_
% Using role type
% Declaring member1425217232_alt_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1a70>, <kernel.DependentProduct object at 0x19e1098>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi__019
% Using role type
% Declaring member1696373143lt_o_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1c20>, <kernel.DependentProduct object at 0x19e1128>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi__020
% Using role type
% Declaring member1186582243e_indi:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1f38>, <kernel.DependentProduct object at 0x19e1050>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi__021
% Using role type
% Declaring member1537523201t_unit:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1a70>, <kernel.DependentProduct object at 0x19e1128>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg
% Using role type
% Declaring member1925470338lt_o_o:(((produc1572197287le_alt->Prop)->Prop)->((((produc1572197287le_alt->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1f38>, <kernel.DependentProduct object at 0x19e1050>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg_022
% Using role type
% Declaring member1830244024e_indi:(((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)->((((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1c20>, <kernel.DependentProduct object at 0x19e1248>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccgg_023
% Using role type
% Declaring member1092867670t_unit:(((produc1572197287le_alt->Prop)->product_unit)->((((produc1572197287le_alt->Prop)->product_unit)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1f38>, <kernel.DependentProduct object at 0x19e1050>) of role type named sy_c_member_000_062_I_Eo_M_062_I_062_Itc__Arrow____Order____Mirabelle____piyeccg
% Using role type
% Declaring member161783341_alt_o:((Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->(((Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x15f1f38>, <kernel.DependentProduct object at 0x19e1170>) of role type named sy_c_member_000_062_I_Eo_M_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__O
% Using role type
% Declaring member984757343_alt_o:((Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->(((Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e1200>, <kernel.DependentProduct object at 0x19e13f8>) of role type named sy_c_member_000_062_I_Eo_M_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piy
% Using role type
% Declaring member1495989556_alt_o:((Prop->(produc1572197287le_alt->Prop))->(((Prop->(produc1572197287le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e12d8>, <kernel.DependentProduct object at 0x19e1290>) 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 0x19e11b8>, <kernel.DependentProduct object at 0x19e13f8>) of role type named sy_c_member_000_062_I_Eo_Mtc__prod_Itc__Arrow____Order____Mirabelle____piyeccggr
% Using role type
% Declaring member1158049649le_alt:((Prop->produc1572197287le_alt)->(((Prop->produc1572197287le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e1200>, <kernel.DependentProduct object at 0x19e1368>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_062_
% Using role type
% Declaring member1521294075_alt_o:((arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->(((arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e1320>, <kernel.DependentProduct object at 0x19e1518>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_062__024
% Using role type
% Declaring member2071265553_alt_o:((arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->(((arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e12d8>, <kernel.DependentProduct object at 0x19e1518>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_M_062__025
% Using role type
% Declaring member822980838_alt_o:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e1440>, <kernel.DependentProduct object at 0x19e15a8>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_Mtc__N
% Using role type
% Declaring member1842285448di_nat:((arrow_1196572341e_indi->nat)->(((arrow_1196572341e_indi->nat)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e13b0>, <kernel.DependentProduct object at 0x19e13f8>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oindi_Mtc__p
% Using role type
% Declaring member232085823le_alt:((arrow_1196572341e_indi->produc1572197287le_alt)->(((arrow_1196572341e_indi->produc1572197287le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e1050>, <kernel.DependentProduct object at 0x19e1560>) 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 0x19e11b8>, <kernel.DependentProduct object at 0x19e15f0>) of role type named sy_c_member_000_062_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle____piyeccggr
% Using role type
% Declaring member1113138010e_indi:((nat->arrow_1196572341e_indi)->(((nat->arrow_1196572341e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e12d8>, <kernel.DependentProduct object at 0x19e1440>) 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 0x19e1518>, <kernel.DependentProduct object at 0x19e1050>) of role type named sy_c_member_000_062_Itc__Product____Type__Ounit_M_062_I_062_Itc__Arrow____Order_
% Using role type
% Declaring member1888392857_alt_o:((product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->(((product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e13b0>, <kernel.DependentProduct object at 0x19e1758>) of role type named sy_c_member_000_062_Itc__Product____Type__Ounit_M_062_Itc__Arrow____Order____Mir
% Using role type
% Declaring member2021528307_alt_o:((product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->(((product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e11b8>, <kernel.DependentProduct object at 0x19e1758>) of role type named sy_c_member_000_062_Itc__Product____Type__Ounit_M_062_Itc__prod_Itc__Arrow____Or
% Using role type
% Declaring member1295651272_alt_o:((product_unit->(produc1572197287le_alt->Prop))->(((product_unit->(produc1572197287le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e1560>, <kernel.DependentProduct object at 0x19e17e8>) 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 0x19e1680>, <kernel.DependentProduct object at 0x19e1440>) of role type named sy_c_member_000_062_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow____Order___
% Using role type
% Declaring member1161214429le_alt:((product_unit->produc1572197287le_alt)->(((product_unit->produc1572197287le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e16c8>, <kernel.DependentProduct object at 0x19e17a0>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa
% Using role type
% Declaring member1241905979_alt_o:((produc1572197287le_alt->Prop)->(((produc1572197287le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e12d8>, <kernel.DependentProduct object at 0x19e1830>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa_026
% Using role type
% Declaring member1074431551e_indi:((produc1572197287le_alt->arrow_1196572341e_indi)->(((produc1572197287le_alt->arrow_1196572341e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e11b8>, <kernel.DependentProduct object at 0x19e1560>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oa_027
% Using role type
% Declaring member44534621t_unit:((produc1572197287le_alt->product_unit)->(((produc1572197287le_alt->product_unit)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e1758>, <kernel.DependentProduct object at 0x19e16c8>) 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 0x19e12d8>, <kernel.DependentProduct object at 0x19e1908>) of role type named sy_c_member_000tc__Arrow____Order____Mirabelle____piyeccggrh__Oindi
% Using role type
% Declaring member1818997282e_indi:(arrow_1196572341e_indi->((arrow_1196572341e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e1248>, <kernel.DependentProduct object at 0x19e1998>) 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 0x19e11b8>, <kernel.DependentProduct object at 0x19e12d8>) 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 0x19e1908>, <kernel.DependentProduct object at 0x19e19e0>) of role type named sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh__Oalt_Mtc
% Using role type
% Declaring member285112084le_alt:(produc1572197287le_alt->((produc1572197287le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x19e16c8>, <kernel.DependentProduct object at 0x19e17a0>) of role type named sy_v_F
% Using role type
% Declaring f:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x19e12d8>, <kernel.DependentProduct object at 0x19e1758>) of role type named sy_v_Lab____
% Using role type
% Declaring lab:(produc1572197287le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x19e11b8>, <kernel.DependentProduct object at 0x19e1a28>) of role type named sy_v_Lba____
% Using role type
% Declaring lba:(produc1572197287le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x19e17a0>, <kernel.DependentProduct object at 0x19e19e0>) of role type named sy_v_P____
% Using role type
% Declaring p:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x19e1758>, <kernel.Constant object at 0x19e19e0>) of role type named sy_v_a____
% Using role type
% Declaring a:arrow_1389031998le_alt
% FOF formula (<kernel.Constant object at 0x19e11b8>, <kernel.Constant object at 0x19e19e0>) of role type named sy_v_b____
% Using role type
% Declaring b:arrow_1389031998le_alt
% FOF formula (<kernel.Constant object at 0x19e17a0>, <kernel.Constant object at 0x19e19e0>) of role type named sy_v_c____
% Using role type
% Declaring c:arrow_1389031998le_alt
% FOF formula (<kernel.Constant object at 0x19e1758>, <kernel.Constant object at 0x19e19e0>) of role type named sy_v_d____
% Using role type
% Declaring d:arrow_1389031998le_alt
% FOF formula (<kernel.Constant object at 0x19e11b8>, <kernel.Constant object at 0x19e19e0>) of role type named sy_v_e____
% Using role type
% Declaring e:arrow_1389031998le_alt
% FOF formula (<kernel.Constant object at 0x19e17a0>, <kernel.DependentProduct object at 0x19e1c68>) of role type named sy_v_h____
% Using role type
% Declaring h:(arrow_1196572341e_indi->nat)
% FOF formula (<kernel.Constant object at 0x19e1b90>, <kernel.Constant object at 0x19e1c68>) of role type named sy_v_n____
% Using role type
% Declaring n:nat
% FOF formula (arrow_1955289568le_IIA f) of role axiom named fact_0_assms_I3_J
% A new axiom: (arrow_1955289568le_IIA f)
% FOF formula (arrow_1282657667nimity f) of role axiom named fact_1_u
% A new axiom: (arrow_1282657667nimity f)
% FOF formula (not (((eq arrow_1389031998le_alt) c) d)) of role axiom named fact_2__096c_A_126_061_Ad_096
% A new axiom: (not (((eq arrow_1389031998le_alt) c) d))
% FOF formula ((member822980838_alt_o p) arrow_1647925946e_Prof) of role axiom named fact_3__096P_A_058_AProf_096
% A new axiom: ((member822980838_alt_o p) arrow_1647925946e_Prof)
% FOF formula (forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (Z:arrow_1389031998le_alt), ((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) ((arrow_1821416136_mkbot L_2) Z))) ((and ((and (not (((eq arrow_1389031998le_alt) Y) Z))) ((((eq arrow_1389031998le_alt) X) Z)->(not (((eq arrow_1389031998le_alt) X) Y))))) ((not (((eq arrow_1389031998le_alt) X) Z))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2))))) of role axiom named fact_4_in__mkbot
% A new axiom: (forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (Z:arrow_1389031998le_alt), ((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) ((arrow_1821416136_mkbot L_2) Z))) ((and ((and (not (((eq arrow_1389031998le_alt) Y) Z))) ((((eq arrow_1389031998le_alt) X) Z)->(not (((eq arrow_1389031998le_alt) X) Y))))) ((not (((eq arrow_1389031998le_alt) X) Z))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2)))))
% FOF formula (forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (Z:arrow_1389031998le_alt), ((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) ((arrow_1970123222_mktop L_2) Z))) ((and ((and (not (((eq arrow_1389031998le_alt) X) Z))) ((((eq arrow_1389031998le_alt) Y) Z)->(not (((eq arrow_1389031998le_alt) X) Y))))) ((not (((eq arrow_1389031998le_alt) Y) Z))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2))))) of role axiom named fact_5_in__mktop
% A new axiom: (forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (Z:arrow_1389031998le_alt), ((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) ((arrow_1970123222_mktop L_2) Z))) ((and ((and (not (((eq arrow_1389031998le_alt) X) Z))) ((((eq arrow_1389031998le_alt) Y) Z)->(not (((eq arrow_1389031998le_alt) X) Y))))) ((not (((eq arrow_1389031998le_alt) Y) Z))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2)))))
% FOF formula (forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_91:arrow_1389031998le_alt) (B_72:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) A_91) B_72))->((not (((eq arrow_1389031998le_alt) A_90) B_72))->((not (((eq arrow_1389031998le_alt) B_71) A_91))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (f P_8))))))))))) of role axiom named fact_6__C2_C
% A new axiom: (forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_91:arrow_1389031998le_alt) (B_72:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) A_91) B_72))->((not (((eq arrow_1389031998le_alt) A_90) B_72))->((not (((eq arrow_1389031998le_alt) B_71) A_91))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (f P_8)))))))))))
% FOF formula (forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_91:arrow_1389031998le_alt) (B_72:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) A_91) B_72))->((not (((eq arrow_1389031998le_alt) A_90) B_72))->((not (((eq arrow_1389031998le_alt) B_71) A_91))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (P_8 I_1))))->(((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))->((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (f P_8))))))))))) of role axiom named fact_7__C1_C
% A new axiom: (forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_91:arrow_1389031998le_alt) (B_72:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) A_91) B_72))->((not (((eq arrow_1389031998le_alt) A_90) B_72))->((not (((eq arrow_1389031998le_alt) B_71) A_91))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (P_8 I_1))))->(((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))->((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (f P_8)))))))))))
% FOF formula (forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (C_42:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) B_71) C_42))->((not (((eq arrow_1389031998le_alt) A_90) C_42))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt B_71) C_42)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt B_71) C_42)) (f P_8)))))))))) of role axiom named fact_8__C4_C
% A new axiom: (forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (C_42:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) B_71) C_42))->((not (((eq arrow_1389031998le_alt) A_90) C_42))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt B_71) C_42)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt B_71) C_42)) (f P_8))))))))))
% FOF formula (forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_91:arrow_1389031998le_alt) (B_72:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) A_91) B_72))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (f P_8))))))))) of role axiom named fact_9_pairwise__neutrality
% A new axiom: (forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_91:arrow_1389031998le_alt) (B_72:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) A_91) B_72))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (f P_8)))))))))
% FOF formula (forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt B_71) A_90)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt B_71) A_90)) (f P_8)))))))) of role axiom named fact_10__C3_C
% A new axiom: (forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt B_71) A_90)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt B_71) A_90)) (f P_8))))))))
% FOF formula (forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt c) d)) (p I_1))) ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) d)) ((arrow_1970123222_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) d)) (((arrow_556571452_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member285112084le_alt ((produc897867031le_alt c) d)) ((arrow_1821416136_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_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt c) d)) (p I_1))) ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) d)) ((arrow_1970123222_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) d)) (((arrow_556571452_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member285112084le_alt ((produc897867031le_alt c) d)) ((arrow_1821416136_mkbot (p I_1)) e))))))))
% FOF formula ((member285112084le_alt ((produc897867031le_alt c) d)) (p (((hilber1125280539di_nat top_to54564308indi_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: ((member285112084le_alt ((produc897867031le_alt c) d)) (p (((hilber1125280539di_nat top_to54564308indi_o) h) n)))
% FOF formula ((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_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: ((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))
% FOF formula ((iff ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))) ((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))) of role axiom named fact_14_PW
% A new axiom: ((iff ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))) ((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))
% FOF formula (forall (P_6:(produc1572197287le_alt->Prop)), ((iff (all P_6)) (forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), (P_6 ((produc897867031le_alt A_76) B_60))))) of role axiom named fact_15_split__paired__All
% A new axiom: (forall (P_6:(produc1572197287le_alt->Prop)), ((iff (all P_6)) (forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), (P_6 ((produc897867031le_alt A_76) B_60)))))
% FOF formula ((member822980838_alt_o (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))) arrow_1647925946e_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: ((member822980838_alt_o (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))) arrow_1647925946e_Prof)
% FOF formula ((member285112084le_alt ((produc897867031le_alt c) e)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_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: ((member285112084le_alt ((produc897867031le_alt c) e)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))
% FOF formula ((member285112084le_alt ((produc897867031le_alt e) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_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: ((member285112084le_alt ((produc897867031le_alt e) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))
% FOF formula ((ord_less_nat n) (finite2011930979e_indi top_to54564308indi_o)) of role axiom named fact_19_n_I1_J
% A new axiom: ((ord_less_nat n) (finite2011930979e_indi top_to54564308indi_o))
% FOF formula ((inj_on1505595958di_nat h) top_to54564308indi_o) of role axiom named fact_20_injh
% A new axiom: ((inj_on1505595958di_nat h) top_to54564308indi_o)
% FOF formula (forall (A_89:arrow_1389031998le_alt) (B_70:arrow_1389031998le_alt) (A_88:arrow_1389031998le_alt) (B_69:arrow_1389031998le_alt), ((((eq produc1572197287le_alt) ((produc897867031le_alt A_89) B_70)) ((produc897867031le_alt A_88) B_69))->(((((eq arrow_1389031998le_alt) A_89) A_88)->(not (((eq arrow_1389031998le_alt) B_70) B_69)))->False))) of role axiom named fact_21_Pair__inject
% A new axiom: (forall (A_89:arrow_1389031998le_alt) (B_70:arrow_1389031998le_alt) (A_88:arrow_1389031998le_alt) (B_69:arrow_1389031998le_alt), ((((eq produc1572197287le_alt) ((produc897867031le_alt A_89) B_70)) ((produc897867031le_alt A_88) B_69))->(((((eq arrow_1389031998le_alt) A_89) A_88)->(not (((eq arrow_1389031998le_alt) B_70) B_69)))->False)))
% FOF formula (forall (A_87:arrow_1389031998le_alt) (B_68:arrow_1389031998le_alt) (A_86:arrow_1389031998le_alt) (B_67:arrow_1389031998le_alt), ((iff (((eq produc1572197287le_alt) ((produc897867031le_alt A_87) B_68)) ((produc897867031le_alt A_86) B_67))) ((and (((eq arrow_1389031998le_alt) A_87) A_86)) (((eq arrow_1389031998le_alt) B_68) B_67)))) of role axiom named fact_22_Pair__eq
% A new axiom: (forall (A_87:arrow_1389031998le_alt) (B_68:arrow_1389031998le_alt) (A_86:arrow_1389031998le_alt) (B_67:arrow_1389031998le_alt), ((iff (((eq produc1572197287le_alt) ((produc897867031le_alt A_87) B_68)) ((produc897867031le_alt A_86) B_67))) ((and (((eq arrow_1389031998le_alt) A_87) A_86)) (((eq arrow_1389031998le_alt) B_68) B_67))))
% FOF formula (forall (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((iff (arrow_1955289568le_IIA F_31)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(forall (Xa:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o Xa) arrow_1647925946e_Prof)->(forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), ((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (X_1 I_1))) ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (Xa I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 X_1))) ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 Xa))))))))))) of role axiom named fact_23_IIA__def
% A new axiom: (forall (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((iff (arrow_1955289568le_IIA F_31)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(forall (Xa:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o Xa) arrow_1647925946e_Prof)->(forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), ((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (X_1 I_1))) ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (Xa I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 X_1))) ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 Xa)))))))))))
% FOF formula (forall (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((iff (arrow_1282657667nimity F_31)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), ((forall (I_1:arrow_1196572341e_indi), ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (X_1 I_1)))->((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 X_1)))))))) of role axiom named fact_24_unanimity__def
% A new axiom: (forall (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((iff (arrow_1282657667nimity F_31)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), ((forall (I_1:arrow_1196572341e_indi), ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (X_1 I_1)))->((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 X_1))))))))
% FOF formula (forall (X_69:(produc1572197287le_alt->Prop)), (top_to1806834203lt_o_o X_69)) of role axiom named fact_25_top1I
% A new axiom: (forall (X_69:(produc1572197287le_alt->Prop)), (top_to1806834203lt_o_o X_69))
% FOF formula (forall (X_69:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (top_to732317616lt_o_o X_69)) of role axiom named fact_26_top1I
% A new axiom: (forall (X_69:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (top_to732317616lt_o_o X_69))
% FOF formula (forall (X_69:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (top_to1492351398lt_o_o X_69)) of role axiom named fact_27_top1I
% A new axiom: (forall (X_69:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (top_to1492351398lt_o_o X_69))
% FOF formula (forall (X_69:produc1572197287le_alt), (top_to558618722_alt_o X_69)) of role axiom named fact_28_top1I
% A new axiom: (forall (X_69:produc1572197287le_alt), (top_to558618722_alt_o X_69))
% FOF formula (forall (X_69:arrow_1196572341e_indi), (top_to54564308indi_o X_69)) of role axiom named fact_29_top1I
% A new axiom: (forall (X_69:arrow_1196572341e_indi), (top_to54564308indi_o X_69))
% FOF formula (forall (X_69:nat), (top_top_nat_o X_69)) of role axiom named fact_30_top1I
% A new axiom: (forall (X_69:nat), (top_top_nat_o X_69))
% FOF formula (forall (X_69:product_unit), (top_to1984820022unit_o X_69)) of role axiom named fact_31_top1I
% A new axiom: (forall (X_69:product_unit), (top_to1984820022unit_o X_69))
% FOF formula (forall (X_68:Prop), ((member_o X_68) top_top_o_o)) of role axiom named fact_32_UNIV__I
% A new axiom: (forall (X_68:Prop), ((member_o X_68) top_top_o_o))
% FOF formula (forall (X_68:arrow_1196572341e_indi), ((member1818997282e_indi X_68) top_to54564308indi_o)) of role axiom named fact_33_UNIV__I
% A new axiom: (forall (X_68:arrow_1196572341e_indi), ((member1818997282e_indi X_68) top_to54564308indi_o))
% FOF formula (forall (X_68:product_unit), ((member_Product_unit X_68) top_to1984820022unit_o)) of role axiom named fact_34_UNIV__I
% A new axiom: (forall (X_68:product_unit), ((member_Product_unit X_68) top_to1984820022unit_o))
% FOF formula (forall (X_68:produc1572197287le_alt), ((member285112084le_alt X_68) top_to558618722_alt_o)) of role axiom named fact_35_UNIV__I
% A new axiom: (forall (X_68:produc1572197287le_alt), ((member285112084le_alt X_68) top_to558618722_alt_o))
% FOF formula (forall (X_68:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((member822980838_alt_o X_68) top_to732317616lt_o_o)) of role axiom named fact_36_UNIV__I
% A new axiom: (forall (X_68:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((member822980838_alt_o X_68) top_to732317616lt_o_o))
% FOF formula (forall (X_68:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((member1425217232_alt_o X_68) top_to1492351398lt_o_o)) of role axiom named fact_37_UNIV__I
% A new axiom: (forall (X_68:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((member1425217232_alt_o X_68) top_to1492351398lt_o_o))
% FOF formula (forall (X_68:(produc1572197287le_alt->Prop)), ((member1241905979_alt_o X_68) top_to1806834203lt_o_o)) of role axiom named fact_38_UNIV__I
% A new axiom: (forall (X_68:(produc1572197287le_alt->Prop)), ((member1241905979_alt_o X_68) top_to1806834203lt_o_o))
% FOF formula (forall (X_68:nat), ((member_nat X_68) top_top_nat_o)) of role axiom named fact_39_UNIV__I
% A new axiom: (forall (X_68:nat), ((member_nat X_68) top_top_nat_o))
% FOF formula (forall (X_67:Prop), ((member_o X_67) top_top_o_o)) of role axiom named fact_40_iso__tuple__UNIV__I
% A new axiom: (forall (X_67:Prop), ((member_o X_67) top_top_o_o))
% FOF formula (forall (X_67:arrow_1196572341e_indi), ((member1818997282e_indi X_67) top_to54564308indi_o)) of role axiom named fact_41_iso__tuple__UNIV__I
% A new axiom: (forall (X_67:arrow_1196572341e_indi), ((member1818997282e_indi X_67) top_to54564308indi_o))
% FOF formula (forall (X_67:product_unit), ((member_Product_unit X_67) top_to1984820022unit_o)) of role axiom named fact_42_iso__tuple__UNIV__I
% A new axiom: (forall (X_67:product_unit), ((member_Product_unit X_67) top_to1984820022unit_o))
% FOF formula (forall (X_67:produc1572197287le_alt), ((member285112084le_alt X_67) top_to558618722_alt_o)) of role axiom named fact_43_iso__tuple__UNIV__I
% A new axiom: (forall (X_67:produc1572197287le_alt), ((member285112084le_alt X_67) top_to558618722_alt_o))
% FOF formula (forall (X_67:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((member822980838_alt_o X_67) top_to732317616lt_o_o)) of role axiom named fact_44_iso__tuple__UNIV__I
% A new axiom: (forall (X_67:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((member822980838_alt_o X_67) top_to732317616lt_o_o))
% FOF formula (forall (X_67:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((member1425217232_alt_o X_67) top_to1492351398lt_o_o)) of role axiom named fact_45_iso__tuple__UNIV__I
% A new axiom: (forall (X_67:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((member1425217232_alt_o X_67) top_to1492351398lt_o_o))
% FOF formula (forall (X_67:(produc1572197287le_alt->Prop)), ((member1241905979_alt_o X_67) top_to1806834203lt_o_o)) of role axiom named fact_46_iso__tuple__UNIV__I
% A new axiom: (forall (X_67:(produc1572197287le_alt->Prop)), ((member1241905979_alt_o X_67) top_to1806834203lt_o_o))
% FOF formula (forall (X_67:nat), ((member_nat X_67) top_top_nat_o)) of role axiom named fact_47_iso__tuple__UNIV__I
% A new axiom: (forall (X_67:nat), ((member_nat X_67) top_top_nat_o))
% FOF formula (forall (X_66:(produc1572197287le_alt->Prop)), ((iff (top_to1806834203lt_o_o X_66)) top_top_o)) of role axiom named fact_48_top__apply
% A new axiom: (forall (X_66:(produc1572197287le_alt->Prop)), ((iff (top_to1806834203lt_o_o X_66)) top_top_o))
% FOF formula (forall (X_66:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((iff (top_to732317616lt_o_o X_66)) top_top_o)) of role axiom named fact_49_top__apply
% A new axiom: (forall (X_66:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((iff (top_to732317616lt_o_o X_66)) top_top_o))
% FOF formula (forall (X_66:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((iff (top_to1492351398lt_o_o X_66)) top_top_o)) of role axiom named fact_50_top__apply
% A new axiom: (forall (X_66:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((iff (top_to1492351398lt_o_o X_66)) top_top_o))
% FOF formula (forall (X_66:produc1572197287le_alt), ((iff (top_to558618722_alt_o X_66)) top_top_o)) of role axiom named fact_51_top__apply
% A new axiom: (forall (X_66:produc1572197287le_alt), ((iff (top_to558618722_alt_o X_66)) top_top_o))
% FOF formula (forall (X_66:arrow_1196572341e_indi), ((iff (top_to54564308indi_o X_66)) top_top_o)) of role axiom named fact_52_top__apply
% A new axiom: (forall (X_66:arrow_1196572341e_indi), ((iff (top_to54564308indi_o X_66)) top_top_o))
% FOF formula (forall (X_66:nat), ((iff (top_top_nat_o X_66)) top_top_o)) of role axiom named fact_53_top__apply
% A new axiom: (forall (X_66:nat), ((iff (top_top_nat_o X_66)) top_top_o))
% FOF formula (forall (X_66:product_unit), ((iff (top_to1984820022unit_o X_66)) top_top_o)) of role axiom named fact_54_top__apply
% A new axiom: (forall (X_66:product_unit), ((iff (top_to1984820022unit_o X_66)) top_top_o))
% FOF formula (forall (A_85:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o top_to1806834203lt_o_o) A_85)->False)) of role axiom named fact_55_not__top__less
% A new axiom: (forall (A_85:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o top_to1806834203lt_o_o) A_85)->False))
% FOF formula (forall (A_85:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o top_to732317616lt_o_o) A_85)->False)) of role axiom named fact_56_not__top__less
% A new axiom: (forall (A_85:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o top_to732317616lt_o_o) A_85)->False))
% FOF formula (forall (A_85:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o top_to1492351398lt_o_o) A_85)->False)) of role axiom named fact_57_not__top__less
% A new axiom: (forall (A_85:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o top_to1492351398lt_o_o) A_85)->False))
% FOF formula (forall (A_85:Prop), (((ord_less_o top_top_o) A_85)->False)) of role axiom named fact_58_not__top__less
% A new axiom: (forall (A_85:Prop), (((ord_less_o top_top_o) A_85)->False))
% FOF formula (forall (A_85:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o top_to558618722_alt_o) A_85)->False)) of role axiom named fact_59_not__top__less
% A new axiom: (forall (A_85:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o top_to558618722_alt_o) A_85)->False))
% FOF formula (forall (A_85:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o top_to54564308indi_o) A_85)->False)) of role axiom named fact_60_not__top__less
% A new axiom: (forall (A_85:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o top_to54564308indi_o) A_85)->False))
% FOF formula (forall (A_85:(nat->Prop)), (((ord_less_nat_o top_top_nat_o) A_85)->False)) of role axiom named fact_61_not__top__less
% A new axiom: (forall (A_85:(nat->Prop)), (((ord_less_nat_o top_top_nat_o) A_85)->False))
% FOF formula (forall (A_85:(product_unit->Prop)), (((ord_le232288914unit_o top_to1984820022unit_o) A_85)->False)) of role axiom named fact_62_not__top__less
% A new axiom: (forall (A_85:(product_unit->Prop)), (((ord_le232288914unit_o top_to1984820022unit_o) A_85)->False))
% FOF formula (forall (A_84:((produc1572197287le_alt->Prop)->Prop)), ((iff (not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_84) top_to1806834203lt_o_o))) ((ord_le874404799lt_o_o A_84) top_to1806834203lt_o_o))) of role axiom named fact_63_less__top
% A new axiom: (forall (A_84:((produc1572197287le_alt->Prop)->Prop)), ((iff (not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_84) top_to1806834203lt_o_o))) ((ord_le874404799lt_o_o A_84) top_to1806834203lt_o_o)))
% FOF formula (forall (A_84:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff (not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_84) top_to732317616lt_o_o))) ((ord_le914873172lt_o_o A_84) top_to732317616lt_o_o))) of role axiom named fact_64_less__top
% A new axiom: (forall (A_84:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff (not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_84) top_to732317616lt_o_o))) ((ord_le914873172lt_o_o A_84) top_to732317616lt_o_o)))
% FOF formula (forall (A_84:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff (not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_84) top_to1492351398lt_o_o))) ((ord_le1382328578lt_o_o A_84) top_to1492351398lt_o_o))) of role axiom named fact_65_less__top
% A new axiom: (forall (A_84:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff (not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_84) top_to1492351398lt_o_o))) ((ord_le1382328578lt_o_o A_84) top_to1492351398lt_o_o)))
% FOF formula (forall (A_84:Prop), ((iff (((iff A_84) top_top_o)->False)) ((ord_less_o A_84) top_top_o))) of role axiom named fact_66_less__top
% A new axiom: (forall (A_84:Prop), ((iff (((iff A_84) top_top_o)->False)) ((ord_less_o A_84) top_top_o)))
% FOF formula (forall (A_84:(produc1572197287le_alt->Prop)), ((iff (not (((eq (produc1572197287le_alt->Prop)) A_84) top_to558618722_alt_o))) ((ord_le1852932542_alt_o A_84) top_to558618722_alt_o))) of role axiom named fact_67_less__top
% A new axiom: (forall (A_84:(produc1572197287le_alt->Prop)), ((iff (not (((eq (produc1572197287le_alt->Prop)) A_84) top_to558618722_alt_o))) ((ord_le1852932542_alt_o A_84) top_to558618722_alt_o)))
% FOF formula (forall (A_84:(arrow_1196572341e_indi->Prop)), ((iff (not (((eq (arrow_1196572341e_indi->Prop)) A_84) top_to54564308indi_o))) ((ord_le1991507760indi_o A_84) top_to54564308indi_o))) of role axiom named fact_68_less__top
% A new axiom: (forall (A_84:(arrow_1196572341e_indi->Prop)), ((iff (not (((eq (arrow_1196572341e_indi->Prop)) A_84) top_to54564308indi_o))) ((ord_le1991507760indi_o A_84) top_to54564308indi_o)))
% FOF formula (forall (A_84:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_84) top_top_nat_o))) ((ord_less_nat_o A_84) top_top_nat_o))) of role axiom named fact_69_less__top
% A new axiom: (forall (A_84:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_84) top_top_nat_o))) ((ord_less_nat_o A_84) top_top_nat_o)))
% FOF formula (forall (A_84:(product_unit->Prop)), ((iff (not (((eq (product_unit->Prop)) A_84) top_to1984820022unit_o))) ((ord_le232288914unit_o A_84) top_to1984820022unit_o))) of role axiom named fact_70_less__top
% A new axiom: (forall (A_84:(product_unit->Prop)), ((iff (not (((eq (product_unit->Prop)) A_84) top_to1984820022unit_o))) ((ord_le232288914unit_o A_84) top_to1984820022unit_o)))
% FOF formula ((member1425217232_alt_o f) ((pi_Arr1196397536_alt_o arrow_1647925946e_Prof) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> arrow_1982173296le_Lin))) of role axiom named fact_71_assms_I1_J
% A new axiom: ((member1425217232_alt_o f) ((pi_Arr1196397536_alt_o arrow_1647925946e_Prof) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> arrow_1982173296le_Lin)))
% FOF formula ((iff ((member285112084le_alt ((produc897867031le_alt e) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_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 ((member285112084le_alt ((produc897867031le_alt e) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) lab) lba)))))
% FOF formula (forall (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (_TPTP_I:arrow_1196572341e_indi), ((iff ((arrow_968343245ctator F_31) _TPTP_I)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(((eq (produc1572197287le_alt->Prop)) (F_31 X_1)) (X_1 _TPTP_I)))))) of role axiom named fact_73_dictator__def
% A new axiom: (forall (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (_TPTP_I:arrow_1196572341e_indi), ((iff ((arrow_968343245ctator F_31) _TPTP_I)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(((eq (produc1572197287le_alt->Prop)) (F_31 X_1)) (X_1 _TPTP_I))))))
% FOF formula ((member1241905979_alt_o lab) arrow_1982173296le_Lin) of role axiom named fact_74__096Lab_A_058_ALin_096
% A new axiom: ((member1241905979_alt_o lab) arrow_1982173296le_Lin)
% FOF formula ((member1241905979_alt_o lba) arrow_1982173296le_Lin) of role axiom named fact_75__096Lba_A_058_ALin_096
% A new axiom: ((member1241905979_alt_o lba) arrow_1982173296le_Lin)
% FOF formula (not (((eq arrow_1389031998le_alt) a) b)) of role axiom named fact_76__096a_A_126_061_Ab_096
% A new axiom: (not (((eq arrow_1389031998le_alt) a) b))
% FOF formula ((member285112084le_alt ((produc897867031le_alt a) b)) lab) of role axiom named fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096
% A new axiom: ((member285112084le_alt ((produc897867031le_alt a) b)) lab)
% FOF formula ((member285112084le_alt ((produc897867031le_alt b) a)) lba) of role axiom named fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096
% A new axiom: ((member285112084le_alt ((produc897867031le_alt b) a)) lba)
% FOF formula (((member285112084le_alt ((produc897867031le_alt a) b)) lba)->False) of role axiom named fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096
% A new axiom: (((member285112084le_alt ((produc897867031le_alt a) b)) lba)->False)
% FOF formula (((member285112084le_alt ((produc897867031le_alt b) a)) lab)->False) of role axiom named fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096
% A new axiom: (((member285112084le_alt ((produc897867031le_alt b) a)) lab)->False)
% FOF formula (forall (N_1:nat), ((member822980838_alt_o (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) N_1)) lab) lba))) arrow_1647925946e_Prof)) of role axiom named fact_81_PiProf
% A new axiom: (forall (N_1:nat), ((member822980838_alt_o (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) N_1)) lab) lba))) arrow_1647925946e_Prof))
% FOF formula ((forall (Lab:(produc1572197287le_alt->Prop)), (((member285112084le_alt ((produc897867031le_alt a) b)) Lab)->(((member1241905979_alt_o Lab) arrow_1982173296le_Lin)->False)))->False) of role axiom named fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_
% A new axiom: ((forall (Lab:(produc1572197287le_alt->Prop)), (((member285112084le_alt ((produc897867031le_alt a) b)) Lab)->(((member1241905979_alt_o Lab) arrow_1982173296le_Lin)->False)))->False)
% FOF formula ((forall (Lba:(produc1572197287le_alt->Prop)), (((member285112084le_alt ((produc897867031le_alt b) a)) Lba)->(((member1241905979_alt_o Lba) arrow_1982173296le_Lin)->False)))->False) of role axiom named fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_
% A new axiom: ((forall (Lba:(produc1572197287le_alt->Prop)), (((member285112084le_alt ((produc897867031le_alt b) a)) Lba)->(((member1241905979_alt_o Lba) arrow_1982173296le_Lin)->False)))->False)
% FOF formula (forall (I_1:arrow_1196572341e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt e) d)) ((arrow_1970123222_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt e) d)) (((arrow_556571452_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member285112084le_alt ((produc897867031le_alt e) d)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt b) a)) lab))) ((((ord_less_nat (h I_1)) n)->False)->((member285112084le_alt ((produc897867031le_alt b) a)) lba))))) of role axiom named fact_84__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_1196572341e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt e) d)) ((arrow_1970123222_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt e) d)) (((arrow_556571452_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member285112084le_alt ((produc897867031le_alt e) d)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt b) a)) lab))) ((((ord_less_nat (h I_1)) n)->False)->((member285112084le_alt ((produc897867031le_alt b) a)) lba)))))
% FOF formula (forall (M:nat), (((ord_less_eq_nat M) n)->((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) M)) lab) lba)))))) of role axiom named fact_85_n_I2_J
% A new axiom: (forall (M:nat), (((ord_less_eq_nat M) n)->((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) M)) lab) lba))))))
% FOF formula (forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((not (((eq arrow_1389031998le_alt) X) Y))->((iff (((member285112084le_alt ((produc897867031le_alt X) Y)) L_2)->False)) ((member285112084le_alt ((produc897867031le_alt Y) X)) L_2))))) of role axiom named fact_86_notin__Lin__iff
% A new axiom: (forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((not (((eq arrow_1389031998le_alt) X) Y))->((iff (((member285112084le_alt ((produc897867031le_alt X) Y)) L_2)->False)) ((member285112084le_alt ((produc897867031le_alt Y) X)) L_2)))))
% FOF formula (forall (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->(((member285112084le_alt ((produc897867031le_alt A_73) B_58)) L_2)->(((member285112084le_alt ((produc897867031le_alt B_58) A_73)) L_2)->False)))) of role axiom named fact_87_Lin__irrefl
% A new axiom: (forall (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->(((member285112084le_alt ((produc897867031le_alt A_73) B_58)) L_2)->(((member285112084le_alt ((produc897867031le_alt B_58) A_73)) L_2)->False))))
% FOF formula (forall (X:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o ((arrow_1970123222_mktop L_2) X)) arrow_1982173296le_Lin))) of role axiom named fact_88_mktop__Lin
% A new axiom: (forall (X:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o ((arrow_1970123222_mktop L_2) X)) arrow_1982173296le_Lin)))
% FOF formula (forall (X:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o ((arrow_1821416136_mkbot L_2) X)) arrow_1982173296le_Lin))) of role axiom named fact_89_mkbot__Lin
% A new axiom: (forall (X:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o ((arrow_1821416136_mkbot L_2) X)) arrow_1982173296le_Lin)))
% FOF formula (forall (L_2:(produc1572197287le_alt->Prop)) (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) X) Y))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o (((arrow_556571452_above L_2) X) Y)) arrow_1982173296le_Lin)))) of role axiom named fact_90_above__Lin
% A new axiom: (forall (L_2:(produc1572197287le_alt->Prop)) (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) X) Y))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o (((arrow_556571452_above L_2) X) Y)) arrow_1982173296le_Lin))))
% FOF formula (forall (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member822980838_alt_o (fun (P_5:arrow_1196572341e_indi)=> L_2)) arrow_1647925946e_Prof))) of role axiom named fact_91_const__Lin__Prof
% A new axiom: (forall (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member822980838_alt_o (fun (P_5:arrow_1196572341e_indi)=> L_2)) arrow_1647925946e_Prof)))
% FOF formula (forall (X_65:nat) (Y_49:nat), ((((ord_less_nat X_65) Y_49)->False)->((not (((eq nat) X_65) Y_49))->((ord_less_nat Y_49) X_65)))) of role axiom named fact_92_linorder__cases
% A new axiom: (forall (X_65:nat) (Y_49:nat), ((((ord_less_nat X_65) Y_49)->False)->((not (((eq nat) X_65) Y_49))->((ord_less_nat Y_49) X_65))))
% FOF formula (forall (X_64:(nat->Prop)) (Y_48:(nat->Prop)), (((ord_less_nat_o X_64) Y_48)->(((ord_less_nat_o Y_48) X_64)->False))) of role axiom named fact_93_order__less__asym
% A new axiom: (forall (X_64:(nat->Prop)) (Y_48:(nat->Prop)), (((ord_less_nat_o X_64) Y_48)->(((ord_less_nat_o Y_48) X_64)->False)))
% FOF formula (forall (X_64:(product_unit->Prop)) (Y_48:(product_unit->Prop)), (((ord_le232288914unit_o X_64) Y_48)->(((ord_le232288914unit_o Y_48) X_64)->False))) of role axiom named fact_94_order__less__asym
% A new axiom: (forall (X_64:(product_unit->Prop)) (Y_48:(product_unit->Prop)), (((ord_le232288914unit_o X_64) Y_48)->(((ord_le232288914unit_o Y_48) X_64)->False)))
% FOF formula (forall (X_64:(arrow_1196572341e_indi->Prop)) (Y_48:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_64) Y_48)->(((ord_le1991507760indi_o Y_48) X_64)->False))) of role axiom named fact_95_order__less__asym
% A new axiom: (forall (X_64:(arrow_1196572341e_indi->Prop)) (Y_48:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_64) Y_48)->(((ord_le1991507760indi_o Y_48) X_64)->False)))
% FOF formula (forall (X_64:nat) (Y_48:nat), (((ord_less_nat X_64) Y_48)->(((ord_less_nat Y_48) X_64)->False))) of role axiom named fact_96_order__less__asym
% A new axiom: (forall (X_64:nat) (Y_48:nat), (((ord_less_nat X_64) Y_48)->(((ord_less_nat Y_48) X_64)->False)))
% FOF formula (forall (Z_8:(nat->Prop)) (Y_47:(nat->Prop)) (X_63:(nat->Prop)), (((ord_less_nat_o Y_47) X_63)->(((ord_less_nat_o Z_8) Y_47)->((ord_less_nat_o Z_8) X_63)))) of role axiom named fact_97_xt1_I10_J
% A new axiom: (forall (Z_8:(nat->Prop)) (Y_47:(nat->Prop)) (X_63:(nat->Prop)), (((ord_less_nat_o Y_47) X_63)->(((ord_less_nat_o Z_8) Y_47)->((ord_less_nat_o Z_8) X_63))))
% FOF formula (forall (Z_8:(product_unit->Prop)) (Y_47:(product_unit->Prop)) (X_63:(product_unit->Prop)), (((ord_le232288914unit_o Y_47) X_63)->(((ord_le232288914unit_o Z_8) Y_47)->((ord_le232288914unit_o Z_8) X_63)))) of role axiom named fact_98_xt1_I10_J
% A new axiom: (forall (Z_8:(product_unit->Prop)) (Y_47:(product_unit->Prop)) (X_63:(product_unit->Prop)), (((ord_le232288914unit_o Y_47) X_63)->(((ord_le232288914unit_o Z_8) Y_47)->((ord_le232288914unit_o Z_8) X_63))))
% FOF formula (forall (Z_8:(arrow_1196572341e_indi->Prop)) (Y_47:(arrow_1196572341e_indi->Prop)) (X_63:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_47) X_63)->(((ord_le1991507760indi_o Z_8) Y_47)->((ord_le1991507760indi_o Z_8) X_63)))) of role axiom named fact_99_xt1_I10_J
% A new axiom: (forall (Z_8:(arrow_1196572341e_indi->Prop)) (Y_47:(arrow_1196572341e_indi->Prop)) (X_63:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_47) X_63)->(((ord_le1991507760indi_o Z_8) Y_47)->((ord_le1991507760indi_o Z_8) X_63))))
% FOF formula (forall (Z_8:nat) (Y_47:nat) (X_63:nat), (((ord_less_nat Y_47) X_63)->(((ord_less_nat Z_8) Y_47)->((ord_less_nat Z_8) X_63)))) of role axiom named fact_100_xt1_I10_J
% A new axiom: (forall (Z_8:nat) (Y_47:nat) (X_63:nat), (((ord_less_nat Y_47) X_63)->(((ord_less_nat Z_8) Y_47)->((ord_less_nat Z_8) X_63))))
% FOF formula (forall (Z_7:(nat->Prop)) (X_62:(nat->Prop)) (Y_46:(nat->Prop)), (((ord_less_nat_o X_62) Y_46)->(((ord_less_nat_o Y_46) Z_7)->((ord_less_nat_o X_62) Z_7)))) of role axiom named fact_101_order__less__trans
% A new axiom: (forall (Z_7:(nat->Prop)) (X_62:(nat->Prop)) (Y_46:(nat->Prop)), (((ord_less_nat_o X_62) Y_46)->(((ord_less_nat_o Y_46) Z_7)->((ord_less_nat_o X_62) Z_7))))
% FOF formula (forall (Z_7:(product_unit->Prop)) (X_62:(product_unit->Prop)) (Y_46:(product_unit->Prop)), (((ord_le232288914unit_o X_62) Y_46)->(((ord_le232288914unit_o Y_46) Z_7)->((ord_le232288914unit_o X_62) Z_7)))) of role axiom named fact_102_order__less__trans
% A new axiom: (forall (Z_7:(product_unit->Prop)) (X_62:(product_unit->Prop)) (Y_46:(product_unit->Prop)), (((ord_le232288914unit_o X_62) Y_46)->(((ord_le232288914unit_o Y_46) Z_7)->((ord_le232288914unit_o X_62) Z_7))))
% FOF formula (forall (Z_7:(arrow_1196572341e_indi->Prop)) (X_62:(arrow_1196572341e_indi->Prop)) (Y_46:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_62) Y_46)->(((ord_le1991507760indi_o Y_46) Z_7)->((ord_le1991507760indi_o X_62) Z_7)))) of role axiom named fact_103_order__less__trans
% A new axiom: (forall (Z_7:(arrow_1196572341e_indi->Prop)) (X_62:(arrow_1196572341e_indi->Prop)) (Y_46:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_62) Y_46)->(((ord_le1991507760indi_o Y_46) Z_7)->((ord_le1991507760indi_o X_62) Z_7))))
% FOF formula (forall (Z_7:nat) (X_62:nat) (Y_46:nat), (((ord_less_nat X_62) Y_46)->(((ord_less_nat Y_46) Z_7)->((ord_less_nat X_62) Z_7)))) of role axiom named fact_104_order__less__trans
% A new axiom: (forall (Z_7:nat) (X_62:nat) (Y_46:nat), (((ord_less_nat X_62) Y_46)->(((ord_less_nat Y_46) Z_7)->((ord_less_nat X_62) Z_7))))
% FOF formula (forall (C_41:(nat->Prop)) (B_66:(nat->Prop)) (A_83:(nat->Prop)), (((ord_less_nat_o B_66) A_83)->((((eq (nat->Prop)) B_66) C_41)->((ord_less_nat_o C_41) A_83)))) of role axiom named fact_105_xt1_I2_J
% A new axiom: (forall (C_41:(nat->Prop)) (B_66:(nat->Prop)) (A_83:(nat->Prop)), (((ord_less_nat_o B_66) A_83)->((((eq (nat->Prop)) B_66) C_41)->((ord_less_nat_o C_41) A_83))))
% FOF formula (forall (C_41:(product_unit->Prop)) (B_66:(product_unit->Prop)) (A_83:(product_unit->Prop)), (((ord_le232288914unit_o B_66) A_83)->((((eq (product_unit->Prop)) B_66) C_41)->((ord_le232288914unit_o C_41) A_83)))) of role axiom named fact_106_xt1_I2_J
% A new axiom: (forall (C_41:(product_unit->Prop)) (B_66:(product_unit->Prop)) (A_83:(product_unit->Prop)), (((ord_le232288914unit_o B_66) A_83)->((((eq (product_unit->Prop)) B_66) C_41)->((ord_le232288914unit_o C_41) A_83))))
% FOF formula (forall (C_41:(arrow_1196572341e_indi->Prop)) (B_66:(arrow_1196572341e_indi->Prop)) (A_83:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_66) A_83)->((((eq (arrow_1196572341e_indi->Prop)) B_66) C_41)->((ord_le1991507760indi_o C_41) A_83)))) of role axiom named fact_107_xt1_I2_J
% A new axiom: (forall (C_41:(arrow_1196572341e_indi->Prop)) (B_66:(arrow_1196572341e_indi->Prop)) (A_83:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_66) A_83)->((((eq (arrow_1196572341e_indi->Prop)) B_66) C_41)->((ord_le1991507760indi_o C_41) A_83))))
% FOF formula (forall (C_41:nat) (B_66:nat) (A_83:nat), (((ord_less_nat B_66) A_83)->((((eq nat) B_66) C_41)->((ord_less_nat C_41) A_83)))) of role axiom named fact_108_xt1_I2_J
% A new axiom: (forall (C_41:nat) (B_66:nat) (A_83:nat), (((ord_less_nat B_66) A_83)->((((eq nat) B_66) C_41)->((ord_less_nat C_41) A_83))))
% FOF formula (forall (C_40:(nat->Prop)) (A_82:(nat->Prop)) (B_65:(nat->Prop)), (((ord_less_nat_o A_82) B_65)->((((eq (nat->Prop)) B_65) C_40)->((ord_less_nat_o A_82) C_40)))) of role axiom named fact_109_ord__less__eq__trans
% A new axiom: (forall (C_40:(nat->Prop)) (A_82:(nat->Prop)) (B_65:(nat->Prop)), (((ord_less_nat_o A_82) B_65)->((((eq (nat->Prop)) B_65) C_40)->((ord_less_nat_o A_82) C_40))))
% FOF formula (forall (C_40:(product_unit->Prop)) (A_82:(product_unit->Prop)) (B_65:(product_unit->Prop)), (((ord_le232288914unit_o A_82) B_65)->((((eq (product_unit->Prop)) B_65) C_40)->((ord_le232288914unit_o A_82) C_40)))) of role axiom named fact_110_ord__less__eq__trans
% A new axiom: (forall (C_40:(product_unit->Prop)) (A_82:(product_unit->Prop)) (B_65:(product_unit->Prop)), (((ord_le232288914unit_o A_82) B_65)->((((eq (product_unit->Prop)) B_65) C_40)->((ord_le232288914unit_o A_82) C_40))))
% FOF formula (forall (C_40:(arrow_1196572341e_indi->Prop)) (A_82:(arrow_1196572341e_indi->Prop)) (B_65:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_82) B_65)->((((eq (arrow_1196572341e_indi->Prop)) B_65) C_40)->((ord_le1991507760indi_o A_82) C_40)))) of role axiom named fact_111_ord__less__eq__trans
% A new axiom: (forall (C_40:(arrow_1196572341e_indi->Prop)) (A_82:(arrow_1196572341e_indi->Prop)) (B_65:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_82) B_65)->((((eq (arrow_1196572341e_indi->Prop)) B_65) C_40)->((ord_le1991507760indi_o A_82) C_40))))
% FOF formula (forall (C_40:nat) (A_82:nat) (B_65:nat), (((ord_less_nat A_82) B_65)->((((eq nat) B_65) C_40)->((ord_less_nat A_82) C_40)))) of role axiom named fact_112_ord__less__eq__trans
% A new axiom: (forall (C_40:nat) (A_82:nat) (B_65:nat), (((ord_less_nat A_82) B_65)->((((eq nat) B_65) C_40)->((ord_less_nat A_82) C_40))))
% FOF formula (forall (C_39:(nat->Prop)) (A_81:(nat->Prop)) (B_64:(nat->Prop)), ((((eq (nat->Prop)) A_81) B_64)->(((ord_less_nat_o C_39) B_64)->((ord_less_nat_o C_39) A_81)))) of role axiom named fact_113_xt1_I1_J
% A new axiom: (forall (C_39:(nat->Prop)) (A_81:(nat->Prop)) (B_64:(nat->Prop)), ((((eq (nat->Prop)) A_81) B_64)->(((ord_less_nat_o C_39) B_64)->((ord_less_nat_o C_39) A_81))))
% FOF formula (forall (C_39:(product_unit->Prop)) (A_81:(product_unit->Prop)) (B_64:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_81) B_64)->(((ord_le232288914unit_o C_39) B_64)->((ord_le232288914unit_o C_39) A_81)))) of role axiom named fact_114_xt1_I1_J
% A new axiom: (forall (C_39:(product_unit->Prop)) (A_81:(product_unit->Prop)) (B_64:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_81) B_64)->(((ord_le232288914unit_o C_39) B_64)->((ord_le232288914unit_o C_39) A_81))))
% FOF formula (forall (C_39:(arrow_1196572341e_indi->Prop)) (A_81:(arrow_1196572341e_indi->Prop)) (B_64:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_81) B_64)->(((ord_le1991507760indi_o C_39) B_64)->((ord_le1991507760indi_o C_39) A_81)))) of role axiom named fact_115_xt1_I1_J
% A new axiom: (forall (C_39:(arrow_1196572341e_indi->Prop)) (A_81:(arrow_1196572341e_indi->Prop)) (B_64:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_81) B_64)->(((ord_le1991507760indi_o C_39) B_64)->((ord_le1991507760indi_o C_39) A_81))))
% FOF formula (forall (C_39:nat) (A_81:nat) (B_64:nat), ((((eq nat) A_81) B_64)->(((ord_less_nat C_39) B_64)->((ord_less_nat C_39) A_81)))) of role axiom named fact_116_xt1_I1_J
% A new axiom: (forall (C_39:nat) (A_81:nat) (B_64:nat), ((((eq nat) A_81) B_64)->(((ord_less_nat C_39) B_64)->((ord_less_nat C_39) A_81))))
% FOF formula (forall (C_38:(nat->Prop)) (A_80:(nat->Prop)) (B_63:(nat->Prop)), ((((eq (nat->Prop)) A_80) B_63)->(((ord_less_nat_o B_63) C_38)->((ord_less_nat_o A_80) C_38)))) of role axiom named fact_117_ord__eq__less__trans
% A new axiom: (forall (C_38:(nat->Prop)) (A_80:(nat->Prop)) (B_63:(nat->Prop)), ((((eq (nat->Prop)) A_80) B_63)->(((ord_less_nat_o B_63) C_38)->((ord_less_nat_o A_80) C_38))))
% FOF formula (forall (C_38:(product_unit->Prop)) (A_80:(product_unit->Prop)) (B_63:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_80) B_63)->(((ord_le232288914unit_o B_63) C_38)->((ord_le232288914unit_o A_80) C_38)))) of role axiom named fact_118_ord__eq__less__trans
% A new axiom: (forall (C_38:(product_unit->Prop)) (A_80:(product_unit->Prop)) (B_63:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_80) B_63)->(((ord_le232288914unit_o B_63) C_38)->((ord_le232288914unit_o A_80) C_38))))
% FOF formula (forall (C_38:(arrow_1196572341e_indi->Prop)) (A_80:(arrow_1196572341e_indi->Prop)) (B_63:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_80) B_63)->(((ord_le1991507760indi_o B_63) C_38)->((ord_le1991507760indi_o A_80) C_38)))) of role axiom named fact_119_ord__eq__less__trans
% A new axiom: (forall (C_38:(arrow_1196572341e_indi->Prop)) (A_80:(arrow_1196572341e_indi->Prop)) (B_63:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_80) B_63)->(((ord_le1991507760indi_o B_63) C_38)->((ord_le1991507760indi_o A_80) C_38))))
% FOF formula (forall (C_38:nat) (A_80:nat) (B_63:nat), ((((eq nat) A_80) B_63)->(((ord_less_nat B_63) C_38)->((ord_less_nat A_80) C_38)))) of role axiom named fact_120_ord__eq__less__trans
% A new axiom: (forall (C_38:nat) (A_80:nat) (B_63:nat), ((((eq nat) A_80) B_63)->(((ord_less_nat B_63) C_38)->((ord_less_nat A_80) C_38))))
% FOF formula (forall (B_62:(nat->Prop)) (A_79:(nat->Prop)), (((ord_less_nat_o B_62) A_79)->(((ord_less_nat_o A_79) B_62)->False))) of role axiom named fact_121_xt1_I9_J
% A new axiom: (forall (B_62:(nat->Prop)) (A_79:(nat->Prop)), (((ord_less_nat_o B_62) A_79)->(((ord_less_nat_o A_79) B_62)->False)))
% FOF formula (forall (B_62:(product_unit->Prop)) (A_79:(product_unit->Prop)), (((ord_le232288914unit_o B_62) A_79)->(((ord_le232288914unit_o A_79) B_62)->False))) of role axiom named fact_122_xt1_I9_J
% A new axiom: (forall (B_62:(product_unit->Prop)) (A_79:(product_unit->Prop)), (((ord_le232288914unit_o B_62) A_79)->(((ord_le232288914unit_o A_79) B_62)->False)))
% FOF formula (forall (B_62:(arrow_1196572341e_indi->Prop)) (A_79:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_62) A_79)->(((ord_le1991507760indi_o A_79) B_62)->False))) of role axiom named fact_123_xt1_I9_J
% A new axiom: (forall (B_62:(arrow_1196572341e_indi->Prop)) (A_79:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_62) A_79)->(((ord_le1991507760indi_o A_79) B_62)->False)))
% FOF formula (forall (B_62:nat) (A_79:nat), (((ord_less_nat B_62) A_79)->(((ord_less_nat A_79) B_62)->False))) of role axiom named fact_124_xt1_I9_J
% A new axiom: (forall (B_62:nat) (A_79:nat), (((ord_less_nat B_62) A_79)->(((ord_less_nat A_79) B_62)->False)))
% FOF formula (forall (A_78:(nat->Prop)) (B_61:(nat->Prop)), (((ord_less_nat_o A_78) B_61)->(((ord_less_nat_o B_61) A_78)->False))) of role axiom named fact_125_order__less__asym_H
% A new axiom: (forall (A_78:(nat->Prop)) (B_61:(nat->Prop)), (((ord_less_nat_o A_78) B_61)->(((ord_less_nat_o B_61) A_78)->False)))
% FOF formula (forall (A_78:(product_unit->Prop)) (B_61:(product_unit->Prop)), (((ord_le232288914unit_o A_78) B_61)->(((ord_le232288914unit_o B_61) A_78)->False))) of role axiom named fact_126_order__less__asym_H
% A new axiom: (forall (A_78:(product_unit->Prop)) (B_61:(product_unit->Prop)), (((ord_le232288914unit_o A_78) B_61)->(((ord_le232288914unit_o B_61) A_78)->False)))
% FOF formula (forall (A_78:(arrow_1196572341e_indi->Prop)) (B_61:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_78) B_61)->(((ord_le1991507760indi_o B_61) A_78)->False))) of role axiom named fact_127_order__less__asym_H
% A new axiom: (forall (A_78:(arrow_1196572341e_indi->Prop)) (B_61:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_78) B_61)->(((ord_le1991507760indi_o B_61) A_78)->False)))
% FOF formula (forall (A_78:nat) (B_61:nat), (((ord_less_nat A_78) B_61)->(((ord_less_nat B_61) A_78)->False))) of role axiom named fact_128_order__less__asym_H
% A new axiom: (forall (A_78:nat) (B_61:nat), (((ord_less_nat A_78) B_61)->(((ord_less_nat B_61) A_78)->False)))
% FOF formula (forall (P_4:Prop) (X_61:(nat->Prop)) (Y_45:(nat->Prop)), (((ord_less_nat_o X_61) Y_45)->(((ord_less_nat_o Y_45) X_61)->P_4))) of role axiom named fact_129_order__less__imp__triv
% A new axiom: (forall (P_4:Prop) (X_61:(nat->Prop)) (Y_45:(nat->Prop)), (((ord_less_nat_o X_61) Y_45)->(((ord_less_nat_o Y_45) X_61)->P_4)))
% FOF formula (forall (P_4:Prop) (X_61:(product_unit->Prop)) (Y_45:(product_unit->Prop)), (((ord_le232288914unit_o X_61) Y_45)->(((ord_le232288914unit_o Y_45) X_61)->P_4))) of role axiom named fact_130_order__less__imp__triv
% A new axiom: (forall (P_4:Prop) (X_61:(product_unit->Prop)) (Y_45:(product_unit->Prop)), (((ord_le232288914unit_o X_61) Y_45)->(((ord_le232288914unit_o Y_45) X_61)->P_4)))
% FOF formula (forall (P_4:Prop) (X_61:(arrow_1196572341e_indi->Prop)) (Y_45:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_61) Y_45)->(((ord_le1991507760indi_o Y_45) X_61)->P_4))) of role axiom named fact_131_order__less__imp__triv
% A new axiom: (forall (P_4:Prop) (X_61:(arrow_1196572341e_indi->Prop)) (Y_45:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_61) Y_45)->(((ord_le1991507760indi_o Y_45) X_61)->P_4)))
% FOF formula (forall (P_4:Prop) (X_61:nat) (Y_45:nat), (((ord_less_nat X_61) Y_45)->(((ord_less_nat Y_45) X_61)->P_4))) of role axiom named fact_132_order__less__imp__triv
% A new axiom: (forall (P_4:Prop) (X_61:nat) (Y_45:nat), (((ord_less_nat X_61) Y_45)->(((ord_less_nat Y_45) X_61)->P_4)))
% FOF formula (forall (X_60:(nat->Prop)) (Y_44:(nat->Prop)), (((ord_less_nat_o X_60) Y_44)->(not (((eq (nat->Prop)) Y_44) X_60)))) of role axiom named fact_133_order__less__imp__not__eq2
% A new axiom: (forall (X_60:(nat->Prop)) (Y_44:(nat->Prop)), (((ord_less_nat_o X_60) Y_44)->(not (((eq (nat->Prop)) Y_44) X_60))))
% 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)) Y_44) X_60)))) of role axiom named fact_134_order__less__imp__not__eq2
% 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)) Y_44) X_60))))
% FOF formula (forall (X_60:(arrow_1196572341e_indi->Prop)) (Y_44:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_60) Y_44)->(not (((eq (arrow_1196572341e_indi->Prop)) Y_44) X_60)))) of role axiom named fact_135_order__less__imp__not__eq2
% A new axiom: (forall (X_60:(arrow_1196572341e_indi->Prop)) (Y_44:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_60) Y_44)->(not (((eq (arrow_1196572341e_indi->Prop)) Y_44) X_60))))
% FOF formula (forall (X_60:nat) (Y_44:nat), (((ord_less_nat X_60) Y_44)->(not (((eq nat) Y_44) X_60)))) of role axiom named fact_136_order__less__imp__not__eq2
% A new axiom: (forall (X_60:nat) (Y_44:nat), (((ord_less_nat X_60) Y_44)->(not (((eq nat) Y_44) X_60))))
% FOF formula (forall (X_59:(nat->Prop)) (Y_43:(nat->Prop)), (((ord_less_nat_o X_59) Y_43)->(not (((eq (nat->Prop)) X_59) Y_43)))) of role axiom named fact_137_order__less__imp__not__eq
% A new axiom: (forall (X_59:(nat->Prop)) (Y_43:(nat->Prop)), (((ord_less_nat_o X_59) Y_43)->(not (((eq (nat->Prop)) X_59) Y_43))))
% FOF formula (forall (X_59:(product_unit->Prop)) (Y_43:(product_unit->Prop)), (((ord_le232288914unit_o X_59) Y_43)->(not (((eq (product_unit->Prop)) X_59) Y_43)))) of role axiom named fact_138_order__less__imp__not__eq
% A new axiom: (forall (X_59:(product_unit->Prop)) (Y_43:(product_unit->Prop)), (((ord_le232288914unit_o X_59) Y_43)->(not (((eq (product_unit->Prop)) X_59) Y_43))))
% FOF formula (forall (X_59:(arrow_1196572341e_indi->Prop)) (Y_43:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_59) Y_43)->(not (((eq (arrow_1196572341e_indi->Prop)) X_59) Y_43)))) of role axiom named fact_139_order__less__imp__not__eq
% A new axiom: (forall (X_59:(arrow_1196572341e_indi->Prop)) (Y_43:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_59) Y_43)->(not (((eq (arrow_1196572341e_indi->Prop)) X_59) Y_43))))
% FOF formula (forall (X_59:nat) (Y_43:nat), (((ord_less_nat X_59) Y_43)->(not (((eq nat) X_59) Y_43)))) of role axiom named fact_140_order__less__imp__not__eq
% A new axiom: (forall (X_59:nat) (Y_43:nat), (((ord_less_nat X_59) Y_43)->(not (((eq nat) X_59) Y_43))))
% 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_141_order__less__imp__not__less
% 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_142_order__less__imp__not__less
% 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_1196572341e_indi->Prop)) (Y_42:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_58) Y_42)->(((ord_le1991507760indi_o Y_42) X_58)->False))) of role axiom named fact_143_order__less__imp__not__less
% A new axiom: (forall (X_58:(arrow_1196572341e_indi->Prop)) (Y_42:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_58) Y_42)->(((ord_le1991507760indi_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_144_order__less__imp__not__less
% 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)->(((ord_less_nat_o Y_41) X_57)->False))) of role axiom named fact_145_order__less__not__sym
% A new axiom: (forall (X_57:(nat->Prop)) (Y_41:(nat->Prop)), (((ord_less_nat_o X_57) Y_41)->(((ord_less_nat_o Y_41) X_57)->False)))
% FOF formula (forall (X_57:(product_unit->Prop)) (Y_41:(product_unit->Prop)), (((ord_le232288914unit_o X_57) Y_41)->(((ord_le232288914unit_o Y_41) X_57)->False))) of role axiom named fact_146_order__less__not__sym
% A new axiom: (forall (X_57:(product_unit->Prop)) (Y_41:(product_unit->Prop)), (((ord_le232288914unit_o X_57) Y_41)->(((ord_le232288914unit_o Y_41) X_57)->False)))
% FOF formula (forall (X_57:(arrow_1196572341e_indi->Prop)) (Y_41:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_57) Y_41)->(((ord_le1991507760indi_o Y_41) X_57)->False))) of role axiom named fact_147_order__less__not__sym
% A new axiom: (forall (X_57:(arrow_1196572341e_indi->Prop)) (Y_41:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_57) Y_41)->(((ord_le1991507760indi_o Y_41) X_57)->False)))
% FOF formula (forall (X_57:nat) (Y_41:nat), (((ord_less_nat X_57) Y_41)->(((ord_less_nat Y_41) X_57)->False))) of role axiom named fact_148_order__less__not__sym
% A new axiom: (forall (X_57:nat) (Y_41:nat), (((ord_less_nat X_57) Y_41)->(((ord_less_nat Y_41) X_57)->False)))
% FOF formula (forall (X_56:(nat->Prop)) (Y_40:(nat->Prop)), (((ord_less_nat_o X_56) Y_40)->(not (((eq (nat->Prop)) X_56) Y_40)))) of role axiom named fact_149_less__imp__neq
% A new axiom: (forall (X_56:(nat->Prop)) (Y_40:(nat->Prop)), (((ord_less_nat_o X_56) Y_40)->(not (((eq (nat->Prop)) X_56) Y_40))))
% FOF formula (forall (X_56:(product_unit->Prop)) (Y_40:(product_unit->Prop)), (((ord_le232288914unit_o X_56) Y_40)->(not (((eq (product_unit->Prop)) X_56) Y_40)))) of role axiom named fact_150_less__imp__neq
% A new axiom: (forall (X_56:(product_unit->Prop)) (Y_40:(product_unit->Prop)), (((ord_le232288914unit_o X_56) Y_40)->(not (((eq (product_unit->Prop)) X_56) Y_40))))
% FOF formula (forall (X_56:(arrow_1196572341e_indi->Prop)) (Y_40:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_56) Y_40)->(not (((eq (arrow_1196572341e_indi->Prop)) X_56) Y_40)))) of role axiom named fact_151_less__imp__neq
% A new axiom: (forall (X_56:(arrow_1196572341e_indi->Prop)) (Y_40:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_56) Y_40)->(not (((eq (arrow_1196572341e_indi->Prop)) X_56) Y_40))))
% FOF formula (forall (X_56:nat) (Y_40:nat), (((ord_less_nat X_56) Y_40)->(not (((eq nat) X_56) Y_40)))) of role axiom named fact_152_less__imp__neq
% A new axiom: (forall (X_56:nat) (Y_40:nat), (((ord_less_nat X_56) Y_40)->(not (((eq nat) X_56) Y_40))))
% FOF formula (forall (X_55:nat) (Y_39:nat), ((not (((eq nat) X_55) Y_39))->((((ord_less_nat X_55) Y_39)->False)->((ord_less_nat Y_39) X_55)))) of role axiom named fact_153_linorder__neqE
% A new axiom: (forall (X_55:nat) (Y_39:nat), ((not (((eq nat) X_55) Y_39))->((((ord_less_nat X_55) Y_39)->False)->((ord_less_nat Y_39) X_55))))
% FOF formula (forall (Y_38:nat) (X_54:nat), ((((ord_less_nat Y_38) X_54)->False)->((iff (((ord_less_nat X_54) Y_38)->False)) (((eq nat) X_54) Y_38)))) of role axiom named fact_154_linorder__antisym__conv3
% A new axiom: (forall (Y_38:nat) (X_54:nat), ((((ord_less_nat Y_38) X_54)->False)->((iff (((ord_less_nat X_54) Y_38)->False)) (((eq nat) X_54) Y_38))))
% FOF formula (forall (X_53:nat) (Y_37:nat), ((or ((or ((ord_less_nat X_53) Y_37)) (((eq nat) X_53) Y_37))) ((ord_less_nat Y_37) X_53))) of role axiom named fact_155_linorder__less__linear
% A new axiom: (forall (X_53:nat) (Y_37:nat), ((or ((or ((ord_less_nat X_53) Y_37)) (((eq nat) X_53) Y_37))) ((ord_less_nat Y_37) X_53)))
% FOF formula (forall (X_52:nat) (Y_36:nat), ((iff (((ord_less_nat X_52) Y_36)->False)) ((or ((ord_less_nat Y_36) X_52)) (((eq nat) X_52) Y_36)))) of role axiom named fact_156_not__less__iff__gr__or__eq
% A new axiom: (forall (X_52:nat) (Y_36:nat), ((iff (((ord_less_nat X_52) Y_36)->False)) ((or ((ord_less_nat Y_36) X_52)) (((eq nat) X_52) Y_36))))
% FOF formula (forall (X_51:nat) (Y_35:nat), ((iff (not (((eq nat) X_51) Y_35))) ((or ((ord_less_nat X_51) Y_35)) ((ord_less_nat Y_35) X_51)))) of role axiom named fact_157_linorder__neq__iff
% A new axiom: (forall (X_51:nat) (Y_35:nat), ((iff (not (((eq nat) X_51) Y_35))) ((or ((ord_less_nat X_51) Y_35)) ((ord_less_nat Y_35) X_51))))
% FOF formula (forall (X_50:(nat->Prop)), (((ord_less_nat_o X_50) X_50)->False)) of role axiom named fact_158_order__less__irrefl
% A new axiom: (forall (X_50:(nat->Prop)), (((ord_less_nat_o X_50) X_50)->False))
% FOF formula (forall (X_50:(product_unit->Prop)), (((ord_le232288914unit_o X_50) X_50)->False)) of role axiom named fact_159_order__less__irrefl
% A new axiom: (forall (X_50:(product_unit->Prop)), (((ord_le232288914unit_o X_50) X_50)->False))
% FOF formula (forall (X_50:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_50) X_50)->False)) of role axiom named fact_160_order__less__irrefl
% A new axiom: (forall (X_50:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_50) X_50)->False))
% FOF formula (forall (X_50:nat), (((ord_less_nat X_50) X_50)->False)) of role axiom named fact_161_order__less__irrefl
% A new axiom: (forall (X_50:nat), (((ord_less_nat X_50) X_50)->False))
% FOF formula (forall (X_49:arrow_1196572341e_indi) (A_77:(arrow_1196572341e_indi->Prop)), ((iff ((member1818997282e_indi X_49) A_77)) (A_77 X_49))) of role axiom named fact_162_mem__def
% A new axiom: (forall (X_49:arrow_1196572341e_indi) (A_77:(arrow_1196572341e_indi->Prop)), ((iff ((member1818997282e_indi X_49) A_77)) (A_77 X_49)))
% FOF formula (forall (X_49:Prop) (A_77:(Prop->Prop)), ((iff ((member_o X_49) A_77)) (A_77 X_49))) of role axiom named fact_163_mem__def
% A new axiom: (forall (X_49:Prop) (A_77:(Prop->Prop)), ((iff ((member_o X_49) A_77)) (A_77 X_49)))
% FOF formula (forall (X_49:product_unit) (A_77:(product_unit->Prop)), ((iff ((member_Product_unit X_49) A_77)) (A_77 X_49))) of role axiom named fact_164_mem__def
% A new axiom: (forall (X_49:product_unit) (A_77:(product_unit->Prop)), ((iff ((member_Product_unit X_49) A_77)) (A_77 X_49)))
% FOF formula (forall (X_49:produc1572197287le_alt) (A_77:(produc1572197287le_alt->Prop)), ((iff ((member285112084le_alt X_49) A_77)) (A_77 X_49))) of role axiom named fact_165_mem__def
% A new axiom: (forall (X_49:produc1572197287le_alt) (A_77:(produc1572197287le_alt->Prop)), ((iff ((member285112084le_alt X_49) A_77)) (A_77 X_49)))
% FOF formula (forall (X_49:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_77:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((member822980838_alt_o X_49) A_77)) (A_77 X_49))) of role axiom named fact_166_mem__def
% A new axiom: (forall (X_49:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_77:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((member822980838_alt_o X_49) A_77)) (A_77 X_49)))
% FOF formula (forall (X_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_77:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((member1425217232_alt_o X_49) A_77)) (A_77 X_49))) of role axiom named fact_167_mem__def
% A new axiom: (forall (X_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_77:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((member1425217232_alt_o X_49) A_77)) (A_77 X_49)))
% FOF formula (forall (X_49:(produc1572197287le_alt->Prop)) (A_77:((produc1572197287le_alt->Prop)->Prop)), ((iff ((member1241905979_alt_o X_49) A_77)) (A_77 X_49))) of role axiom named fact_168_mem__def
% A new axiom: (forall (X_49:(produc1572197287le_alt->Prop)) (A_77:((produc1572197287le_alt->Prop)->Prop)), ((iff ((member1241905979_alt_o X_49) A_77)) (A_77 X_49)))
% FOF formula (forall (X_49:nat) (A_77:(nat->Prop)), ((iff ((member_nat X_49) A_77)) (A_77 X_49))) of role axiom named fact_169_mem__def
% A new axiom: (forall (X_49:nat) (A_77:(nat->Prop)), ((iff ((member_nat X_49) A_77)) (A_77 X_49)))
% FOF formula (forall (P_3:(product_unit->Prop)), (((eq (product_unit->Prop)) (collect_Product_unit P_3)) P_3)) of role axiom named fact_170_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_1196572341e_indi->Prop)), (((eq (arrow_1196572341e_indi->Prop)) (collec1936859488e_indi P_3)) P_3)) of role axiom named fact_171_Collect__def
% A new axiom: (forall (P_3:(arrow_1196572341e_indi->Prop)), (((eq (arrow_1196572341e_indi->Prop)) (collec1936859488e_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_172_Collect__def
% A new axiom: (forall (P_3:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_3)) P_3))
% FOF formula (((eq ((produc1572197287le_alt->Prop)->Prop)) top_to1806834203lt_o_o) (collec958969213_alt_o (fun (X_1:(produc1572197287le_alt->Prop))=> True))) of role axiom named fact_173_UNIV__def
% A new axiom: (((eq ((produc1572197287le_alt->Prop)->Prop)) top_to1806834203lt_o_o) (collec958969213_alt_o (fun (X_1:(produc1572197287le_alt->Prop))=> True)))
% FOF formula (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) top_to732317616lt_o_o) (collec979749928_alt_o (fun (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> True))) of role axiom named fact_174_UNIV__def
% A new axiom: (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) top_to732317616lt_o_o) (collec979749928_alt_o (fun (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> True)))
% FOF formula (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) top_to1492351398lt_o_o) (collec670126350_alt_o (fun (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> True))) of role axiom named fact_175_UNIV__def
% A new axiom: (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) top_to1492351398lt_o_o) (collec670126350_alt_o (fun (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> True)))
% FOF formula (((eq (produc1572197287le_alt->Prop)) top_to558618722_alt_o) (collec940901970le_alt (fun (X_1:produc1572197287le_alt)=> True))) of role axiom named fact_176_UNIV__def
% A new axiom: (((eq (produc1572197287le_alt->Prop)) top_to558618722_alt_o) (collec940901970le_alt (fun (X_1:produc1572197287le_alt)=> True)))
% FOF formula (((eq (arrow_1196572341e_indi->Prop)) top_to54564308indi_o) (collec1936859488e_indi (fun (X_1:arrow_1196572341e_indi)=> True))) of role axiom named fact_177_UNIV__def
% A new axiom: (((eq (arrow_1196572341e_indi->Prop)) top_to54564308indi_o) (collec1936859488e_indi (fun (X_1:arrow_1196572341e_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_178_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_179_UNIV__def
% A new axiom: (((eq (nat->Prop)) top_top_nat_o) (collect_nat (fun (X_1:nat)=> True)))
% FOF formula (forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_73) B_58))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) (((arrow_556571452_above L_2) A_73) B_58))) ((and ((and (not (((eq arrow_1389031998le_alt) X) Y))) ((((eq arrow_1389031998le_alt) X) B_58)->((member285112084le_alt ((produc897867031le_alt A_73) Y)) L_2)))) ((not (((eq arrow_1389031998le_alt) X) B_58))->((and ((((eq arrow_1389031998le_alt) Y) B_58)->((or (((eq arrow_1389031998le_alt) X) A_73)) ((member285112084le_alt ((produc897867031le_alt X) A_73)) L_2)))) ((not (((eq arrow_1389031998le_alt) Y) B_58))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2))))))))) of role axiom named fact_180_in__above
% A new axiom: (forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_73) B_58))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) (((arrow_556571452_above L_2) A_73) B_58))) ((and ((and (not (((eq arrow_1389031998le_alt) X) Y))) ((((eq arrow_1389031998le_alt) X) B_58)->((member285112084le_alt ((produc897867031le_alt A_73) Y)) L_2)))) ((not (((eq arrow_1389031998le_alt) X) B_58))->((and ((((eq arrow_1389031998le_alt) Y) B_58)->((or (((eq arrow_1389031998le_alt) X) A_73)) ((member285112084le_alt ((produc897867031le_alt X) A_73)) L_2)))) ((not (((eq arrow_1389031998le_alt) Y) B_58))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2)))))))))
% FOF formula (forall (S_3:(produc1572197287le_alt->Prop)) (R_2:(produc1572197287le_alt->Prop)), ((iff (forall (X_1:arrow_1389031998le_alt) (Xa:arrow_1389031998le_alt), ((iff ((member285112084le_alt ((produc897867031le_alt X_1) Xa)) R_2)) ((member285112084le_alt ((produc897867031le_alt X_1) Xa)) S_3)))) (((eq (produc1572197287le_alt->Prop)) R_2) S_3))) of role axiom named fact_181_pred__equals__eq2
% A new axiom: (forall (S_3:(produc1572197287le_alt->Prop)) (R_2:(produc1572197287le_alt->Prop)), ((iff (forall (X_1:arrow_1389031998le_alt) (Xa:arrow_1389031998le_alt), ((iff ((member285112084le_alt ((produc897867031le_alt X_1) Xa)) R_2)) ((member285112084le_alt ((produc897867031le_alt X_1) Xa)) S_3)))) (((eq (produc1572197287le_alt->Prop)) R_2) S_3)))
% FOF formula (forall (_TPTP_I:arrow_1196572341e_indi) (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o F_31) ((pi_Arr1196397536_alt_o arrow_1647925946e_Prof) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> arrow_1982173296le_Lin)))->((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_76) B_60))->(((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (X_1 _TPTP_I))->((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 X_1)))))))->((arrow_968343245ctator F_31) _TPTP_I)))) of role axiom named fact_182_dictatorI
% A new axiom: (forall (_TPTP_I:arrow_1196572341e_indi) (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o F_31) ((pi_Arr1196397536_alt_o arrow_1647925946e_Prof) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> arrow_1982173296le_Lin)))->((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_76) B_60))->(((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (X_1 _TPTP_I))->((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 X_1)))))))->((arrow_968343245ctator F_31) _TPTP_I))))
% FOF formula ((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba)))) of role axiom named fact_183_n_I3_J
% A new axiom: ((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba))))
% FOF formula ((iff ((member285112084le_alt ((produc897867031le_alt c) e)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba))))) of role axiom named fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am
% A new axiom: ((iff ((member285112084le_alt ((produc897867031le_alt c) e)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba)))))
% FOF formula (forall (I_1:arrow_1196572341e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) e)) ((arrow_1970123222_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) e)) (((arrow_556571452_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member285112084le_alt ((produc897867031le_alt c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->((member285112084le_alt ((produc897867031le_alt a) b)) lab))) ((((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->False)->((member285112084le_alt ((produc897867031le_alt a) b)) lba))))) of role axiom named fact_185__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_1196572341e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) e)) ((arrow_1970123222_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) e)) (((arrow_556571452_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member285112084le_alt ((produc897867031le_alt c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->((member285112084le_alt ((produc897867031le_alt a) b)) lab))) ((((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->False)->((member285112084le_alt ((produc897867031le_alt a) b)) lba)))))
% FOF formula (forall (X_48:arrow_1196572341e_indi) (Y_34:nat) (F_30:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_30) top_to54564308indi_o)->((((eq nat) (F_30 X_48)) Y_34)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat top_to54564308indi_o) F_30) Y_34)) X_48)))) of role axiom named fact_186_inv__f__eq
% A new axiom: (forall (X_48:arrow_1196572341e_indi) (Y_34:nat) (F_30:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_30) top_to54564308indi_o)->((((eq nat) (F_30 X_48)) Y_34)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat top_to54564308indi_o) F_30) Y_34)) X_48))))
% FOF formula (forall (X_48:nat) (Y_34:nat) (F_30:(nat->nat)), (((inj_on_nat_nat F_30) top_top_nat_o)->((((eq nat) (F_30 X_48)) Y_34)->(((eq nat) (((hilber195283148at_nat top_top_nat_o) F_30) Y_34)) X_48)))) of role axiom named fact_187_inv__f__eq
% A new axiom: (forall (X_48:nat) (Y_34:nat) (F_30:(nat->nat)), (((inj_on_nat_nat F_30) top_top_nat_o)->((((eq nat) (F_30 X_48)) Y_34)->(((eq nat) (((hilber195283148at_nat top_top_nat_o) F_30) Y_34)) X_48))))
% FOF formula (forall (X_47:arrow_1196572341e_indi) (F_29:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_29) top_to54564308indi_o)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat top_to54564308indi_o) F_29) (F_29 X_47))) X_47))) of role axiom named fact_188_inv__f__f
% A new axiom: (forall (X_47:arrow_1196572341e_indi) (F_29:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_29) top_to54564308indi_o)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat top_to54564308indi_o) F_29) (F_29 X_47))) X_47)))
% FOF formula (forall (X_47: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_47))) X_47))) of role axiom named fact_189_inv__f__f
% A new axiom: (forall (X_47: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_47))) X_47)))
% FOF formula (forall (X_46:produc1572197287le_alt) (F_28:(produc1572197287le_alt->Prop)) (A_75:(produc1572197287le_alt->Prop)) (B_59:(produc1572197287le_alt->(Prop->Prop))), (((member1241905979_alt_o F_28) ((pi_Pro418549519_alt_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member285112084le_alt X_46) A_75)->False)))) of role axiom named fact_190_PiE
% A new axiom: (forall (X_46:produc1572197287le_alt) (F_28:(produc1572197287le_alt->Prop)) (A_75:(produc1572197287le_alt->Prop)) (B_59:(produc1572197287le_alt->(Prop->Prop))), (((member1241905979_alt_o F_28) ((pi_Pro418549519_alt_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member285112084le_alt X_46) A_75)->False))))
% FOF formula (forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->produc1572197287le_alt)) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member232085823le_alt F_28) ((pi_Arr1762714837le_alt A_75) B_59))->((((member285112084le_alt (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False)))) of role axiom named fact_191_PiE
% A new axiom: (forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->produc1572197287le_alt)) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member232085823le_alt F_28) ((pi_Arr1762714837le_alt A_75) B_59))->((((member285112084le_alt (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False))))
% FOF formula (forall (X_46:Prop) (F_28:(Prop->produc1572197287le_alt)) (A_75:(Prop->Prop)) (B_59:(Prop->(produc1572197287le_alt->Prop))), (((member1158049649le_alt F_28) ((pi_o_P728361163le_alt A_75) B_59))->((((member285112084le_alt (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False)))) of role axiom named fact_192_PiE
% A new axiom: (forall (X_46:Prop) (F_28:(Prop->produc1572197287le_alt)) (A_75:(Prop->Prop)) (B_59:(Prop->(produc1572197287le_alt->Prop))), (((member1158049649le_alt F_28) ((pi_o_P728361163le_alt A_75) B_59))->((((member285112084le_alt (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False))))
% FOF formula (forall (X_46:product_unit) (F_28:(product_unit->produc1572197287le_alt)) (A_75:(product_unit->Prop)) (B_59:(product_unit->(produc1572197287le_alt->Prop))), (((member1161214429le_alt F_28) ((pi_Pro772884595le_alt A_75) B_59))->((((member285112084le_alt (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False)))) of role axiom named fact_193_PiE
% A new axiom: (forall (X_46:product_unit) (F_28:(product_unit->produc1572197287le_alt)) (A_75:(product_unit->Prop)) (B_59:(product_unit->(produc1572197287le_alt->Prop))), (((member1161214429le_alt F_28) ((pi_Pro772884595le_alt A_75) B_59))->((((member285112084le_alt (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False))))
% FOF formula (forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2071265553_alt_o F_28) ((pi_Arr456308197_alt_o A_75) B_59))->((((member822980838_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False)))) of role axiom named fact_194_PiE
% A new axiom: (forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2071265553_alt_o F_28) ((pi_Arr456308197_alt_o A_75) B_59))->((((member822980838_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False))))
% FOF formula (forall (X_46:Prop) (F_28:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_75:(Prop->Prop)) (B_59:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member984757343_alt_o F_28) ((pi_o_A1479825007_alt_o A_75) B_59))->((((member822980838_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False)))) of role axiom named fact_195_PiE
% A new axiom: (forall (X_46:Prop) (F_28:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_75:(Prop->Prop)) (B_59:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member984757343_alt_o F_28) ((pi_o_A1479825007_alt_o A_75) B_59))->((((member822980838_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False))))
% FOF formula (forall (X_46:product_unit) (F_28:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_75:(product_unit->Prop)) (B_59:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2021528307_alt_o F_28) ((pi_Pro1959068871_alt_o A_75) B_59))->((((member822980838_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False)))) of role axiom named fact_196_PiE
% A new axiom: (forall (X_46:product_unit) (F_28:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_75:(product_unit->Prop)) (B_59:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2021528307_alt_o F_28) ((pi_Pro1959068871_alt_o A_75) B_59))->((((member822980838_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False))))
% FOF formula (forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1521294075_alt_o F_28) ((pi_Arr583278353_alt_o A_75) B_59))->((((member1425217232_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False)))) of role axiom named fact_197_PiE
% A new axiom: (forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1521294075_alt_o F_28) ((pi_Arr583278353_alt_o A_75) B_59))->((((member1425217232_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False))))
% FOF formula (forall (X_46:Prop) (F_28:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_75:(Prop->Prop)) (B_59:(Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member161783341_alt_o F_28) ((pi_o_A1994447367_alt_o A_75) B_59))->((((member1425217232_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False)))) of role axiom named fact_198_PiE
% A new axiom: (forall (X_46:Prop) (F_28:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_75:(Prop->Prop)) (B_59:(Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member161783341_alt_o F_28) ((pi_o_A1994447367_alt_o A_75) B_59))->((((member1425217232_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False))))
% FOF formula (forall (X_46:product_unit) (F_28:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_75:(product_unit->Prop)) (B_59:(product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1888392857_alt_o F_28) ((pi_Pro443817391_alt_o A_75) B_59))->((((member1425217232_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False)))) of role axiom named fact_199_PiE
% A new axiom: (forall (X_46:product_unit) (F_28:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_75:(product_unit->Prop)) (B_59:(product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1888392857_alt_o F_28) ((pi_Pro443817391_alt_o A_75) B_59))->((((member1425217232_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False))))
% FOF formula (forall (X_46:Prop) (F_28:(Prop->(produc1572197287le_alt->Prop))) (A_75:(Prop->Prop)) (B_59:(Prop->((produc1572197287le_alt->Prop)->Prop))), (((member1495989556_alt_o F_28) ((pi_o_P1417870404_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False)))) of role axiom named fact_200_PiE
% A new axiom: (forall (X_46:Prop) (F_28:(Prop->(produc1572197287le_alt->Prop))) (A_75:(Prop->Prop)) (B_59:(Prop->((produc1572197287le_alt->Prop)->Prop))), (((member1495989556_alt_o F_28) ((pi_o_P1417870404_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False))))
% FOF formula (forall (X_46:product_unit) (F_28:(product_unit->(produc1572197287le_alt->Prop))) (A_75:(product_unit->Prop)) (B_59:(product_unit->((produc1572197287le_alt->Prop)->Prop))), (((member1295651272_alt_o F_28) ((pi_Pro29851292_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False)))) of role axiom named fact_201_PiE
% A new axiom: (forall (X_46:product_unit) (F_28:(product_unit->(produc1572197287le_alt->Prop))) (A_75:(product_unit->Prop)) (B_59:(product_unit->((produc1572197287le_alt->Prop)->Prop))), (((member1295651272_alt_o F_28) ((pi_Pro29851292_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False))))
% FOF formula (forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->nat)) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->(nat->Prop))), (((member1842285448di_nat F_28) ((pi_Arr778514268di_nat A_75) B_59))->((((member_nat (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False)))) of role axiom named fact_202_PiE
% A new axiom: (forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->nat)) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->(nat->Prop))), (((member1842285448di_nat F_28) ((pi_Arr778514268di_nat A_75) B_59))->((((member_nat (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False))))
% FOF formula (forall (X_46:Prop) (F_28:(Prop->nat)) (A_75:(Prop->Prop)) (B_59:(Prop->(nat->Prop))), (((member_o_nat F_28) ((pi_o_nat A_75) B_59))->((((member_nat (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False)))) of role axiom named fact_203_PiE
% A new axiom: (forall (X_46:Prop) (F_28:(Prop->nat)) (A_75:(Prop->Prop)) (B_59:(Prop->(nat->Prop))), (((member_o_nat F_28) ((pi_o_nat A_75) B_59))->((((member_nat (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False))))
% FOF formula (forall (X_46:product_unit) (F_28:(product_unit->nat)) (A_75:(product_unit->Prop)) (B_59:(product_unit->(nat->Prop))), (((member1827227242it_nat F_28) ((pi_Product_unit_nat A_75) B_59))->((((member_nat (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False)))) of role axiom named fact_204_PiE
% A new axiom: (forall (X_46:product_unit) (F_28:(product_unit->nat)) (A_75:(product_unit->Prop)) (B_59:(product_unit->(nat->Prop))), (((member1827227242it_nat F_28) ((pi_Product_unit_nat A_75) B_59))->((((member_nat (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False))))
% FOF formula (forall (X_46:produc1572197287le_alt) (F_28:(produc1572197287le_alt->arrow_1196572341e_indi)) (A_75:(produc1572197287le_alt->Prop)) (B_59:(produc1572197287le_alt->(arrow_1196572341e_indi->Prop))), (((member1074431551e_indi F_28) ((pi_Pro1246947541e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member285112084le_alt X_46) A_75)->False)))) of role axiom named fact_205_PiE
% A new axiom: (forall (X_46:produc1572197287le_alt) (F_28:(produc1572197287le_alt->arrow_1196572341e_indi)) (A_75:(produc1572197287le_alt->Prop)) (B_59:(produc1572197287le_alt->(arrow_1196572341e_indi->Prop))), (((member1074431551e_indi F_28) ((pi_Pro1246947541e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member285112084le_alt X_46) A_75)->False))))
% FOF formula (forall (X_46:produc1572197287le_alt) (F_28:(produc1572197287le_alt->product_unit)) (A_75:(produc1572197287le_alt->Prop)) (B_59:(produc1572197287le_alt->(product_unit->Prop))), (((member44534621t_unit F_28) ((pi_Pro926528371t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member285112084le_alt X_46) A_75)->False)))) of role axiom named fact_206_PiE
% A new axiom: (forall (X_46:produc1572197287le_alt) (F_28:(produc1572197287le_alt->product_unit)) (A_75:(produc1572197287le_alt->Prop)) (B_59:(produc1572197287le_alt->(product_unit->Prop))), (((member44534621t_unit F_28) ((pi_Pro926528371t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member285112084le_alt X_46) A_75)->False))))
% FOF formula (forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1186582243e_indi F_28) ((pi_Arr272777533e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False)))) of role axiom named fact_207_PiE
% A new axiom: (forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1186582243e_indi F_28) ((pi_Arr272777533e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False))))
% FOF formula (forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1696373143lt_o_o F_28) ((pi_Arr1709554855lt_o_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False)))) of role axiom named fact_208_PiE
% A new axiom: (forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1696373143lt_o_o F_28) ((pi_Arr1709554855lt_o_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False))))
% FOF formula (forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1537523201t_unit F_28) ((pi_Arr509685723t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False)))) of role axiom named fact_209_PiE
% A new axiom: (forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1537523201t_unit F_28) ((pi_Arr509685723t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False))))
% FOF formula (forall (X_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_75:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_59:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1539010427e_indi F_28) ((pi_Arr470535441e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member1425217232_alt_o X_46) A_75)->False)))) of role axiom named fact_210_PiE
% A new axiom: (forall (X_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_75:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_59:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1539010427e_indi F_28) ((pi_Arr470535441e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member1425217232_alt_o X_46) A_75)->False))))
% FOF formula (forall (X_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_75:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_59:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1346253567lt_o_o F_28) ((pi_Arr1865419731lt_o_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member1425217232_alt_o X_46) A_75)->False)))) of role axiom named fact_211_PiE
% A new axiom: (forall (X_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_75:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_59:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1346253567lt_o_o F_28) ((pi_Arr1865419731lt_o_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member1425217232_alt_o X_46) A_75)->False))))
% FOF formula (forall (X_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (A_75:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_59:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1043380889t_unit F_28) ((pi_Arr2096782767t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member1425217232_alt_o X_46) A_75)->False)))) of role axiom named fact_212_PiE
% A new axiom: (forall (X_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (A_75:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_59:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1043380889t_unit F_28) ((pi_Arr2096782767t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member1425217232_alt_o X_46) A_75)->False))))
% FOF formula (forall (X_46:(produc1572197287le_alt->Prop)) (F_28:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (A_75:((produc1572197287le_alt->Prop)->Prop)) (B_59:((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))), (((member1830244024e_indi F_28) ((pi_Pro2039443474e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member1241905979_alt_o X_46) A_75)->False)))) of role axiom named fact_213_PiE
% A new axiom: (forall (X_46:(produc1572197287le_alt->Prop)) (F_28:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (A_75:((produc1572197287le_alt->Prop)->Prop)) (B_59:((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))), (((member1830244024e_indi F_28) ((pi_Pro2039443474e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member1241905979_alt_o X_46) A_75)->False))))
% FOF formula (forall (X_46:(produc1572197287le_alt->Prop)) (F_28:((produc1572197287le_alt->Prop)->Prop)) (A_75:((produc1572197287le_alt->Prop)->Prop)) (B_59:((produc1572197287le_alt->Prop)->(Prop->Prop))), (((member1925470338lt_o_o F_28) ((pi_Pro386796690lt_o_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member1241905979_alt_o X_46) A_75)->False)))) of role axiom named fact_214_PiE
% A new axiom: (forall (X_46:(produc1572197287le_alt->Prop)) (F_28:((produc1572197287le_alt->Prop)->Prop)) (A_75:((produc1572197287le_alt->Prop)->Prop)) (B_59:((produc1572197287le_alt->Prop)->(Prop->Prop))), (((member1925470338lt_o_o F_28) ((pi_Pro386796690lt_o_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member1241905979_alt_o X_46) A_75)->False))))
% FOF formula (forall (X_46:(produc1572197287le_alt->Prop)) (F_28:((produc1572197287le_alt->Prop)->product_unit)) (A_75:((produc1572197287le_alt->Prop)->Prop)) (B_59:((produc1572197287le_alt->Prop)->(product_unit->Prop))), (((member1092867670t_unit F_28) ((pi_Pro30504752t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member1241905979_alt_o X_46) A_75)->False)))) of role axiom named fact_215_PiE
% A new axiom: (forall (X_46:(produc1572197287le_alt->Prop)) (F_28:((produc1572197287le_alt->Prop)->product_unit)) (A_75:((produc1572197287le_alt->Prop)->Prop)) (B_59:((produc1572197287le_alt->Prop)->(product_unit->Prop))), (((member1092867670t_unit F_28) ((pi_Pro30504752t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member1241905979_alt_o X_46) A_75)->False))))
% FOF formula (forall (X_46:nat) (F_28:(nat->arrow_1196572341e_indi)) (A_75:(nat->Prop)) (B_59:(nat->(arrow_1196572341e_indi->Prop))), (((member1113138010e_indi F_28) ((pi_nat986275508e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member_nat X_46) A_75)->False)))) of role axiom named fact_216_PiE
% A new axiom: (forall (X_46:nat) (F_28:(nat->arrow_1196572341e_indi)) (A_75:(nat->Prop)) (B_59:(nat->(arrow_1196572341e_indi->Prop))), (((member1113138010e_indi F_28) ((pi_nat986275508e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member_nat X_46) A_75)->False))))
% FOF formula (forall (X_46:nat) (F_28:(nat->Prop)) (A_75:(nat->Prop)) (B_59:(nat->(Prop->Prop))), (((member_nat_o F_28) ((pi_nat_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member_nat X_46) A_75)->False)))) of role axiom named fact_217_PiE
% A new axiom: (forall (X_46:nat) (F_28:(nat->Prop)) (A_75:(nat->Prop)) (B_59:(nat->(Prop->Prop))), (((member_nat_o F_28) ((pi_nat_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member_nat X_46) A_75)->False))))
% FOF formula (forall (X_46:nat) (F_28:(nat->product_unit)) (A_75:(nat->Prop)) (B_59:(nat->(product_unit->Prop))), (((member616671224t_unit F_28) ((pi_nat_Product_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member_nat X_46) A_75)->False)))) of role axiom named fact_218_PiE
% A new axiom: (forall (X_46:nat) (F_28:(nat->product_unit)) (A_75:(nat->Prop)) (B_59:(nat->(product_unit->Prop))), (((member616671224t_unit F_28) ((pi_nat_Product_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member_nat X_46) A_75)->False))))
% FOF formula (forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))), (((member1425217232_alt_o F_28) ((pi_Arr1196397536_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False)))) of role axiom named fact_219_PiE
% A new axiom: (forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))), (((member1425217232_alt_o F_28) ((pi_Arr1196397536_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False))))
% FOF formula (forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))), (((member822980838_alt_o F_28) ((pi_Arr1309696186_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False)))) of role axiom named fact_220_PiE
% A new axiom: (forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))), (((member822980838_alt_o F_28) ((pi_Arr1309696186_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False))))
% FOF formula (forall (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_73) B_58))->((ex (produc1572197287le_alt->Prop)) (fun (X_1:(produc1572197287le_alt->Prop))=> ((and ((member1241905979_alt_o X_1) arrow_1982173296le_Lin)) ((member285112084le_alt ((produc897867031le_alt A_73) B_58)) X_1)))))) of role axiom named fact_221_complete__Lin
% A new axiom: (forall (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_73) B_58))->((ex (produc1572197287le_alt->Prop)) (fun (X_1:(produc1572197287le_alt->Prop))=> ((and ((member1241905979_alt_o X_1) arrow_1982173296le_Lin)) ((member285112084le_alt ((produc897867031le_alt A_73) B_58)) X_1))))))
% FOF formula (forall (A_74:(produc1572197287le_alt->Prop)), (((eq ((produc1572197287le_alt->Prop)->Prop)) ((pi_Pro418549519_alt_o A_74) (fun (Uu:produc1572197287le_alt)=> top_top_o_o))) top_to1806834203lt_o_o)) of role axiom named fact_222_Pi__UNIV
% A new axiom: (forall (A_74:(produc1572197287le_alt->Prop)), (((eq ((produc1572197287le_alt->Prop)->Prop)) ((pi_Pro418549519_alt_o A_74) (fun (Uu:produc1572197287le_alt)=> top_top_o_o))) top_to1806834203lt_o_o))
% FOF formula (forall (A_74:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) ((pi_Arr1196397536_alt_o A_74) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> top_to1806834203lt_o_o))) top_to1492351398lt_o_o)) of role axiom named fact_223_Pi__UNIV
% A new axiom: (forall (A_74:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) ((pi_Arr1196397536_alt_o A_74) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> top_to1806834203lt_o_o))) top_to1492351398lt_o_o))
% FOF formula (forall (A_74:(arrow_1196572341e_indi->Prop)), (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) ((pi_Arr1309696186_alt_o A_74) (fun (Uu:arrow_1196572341e_indi)=> top_to1806834203lt_o_o))) top_to732317616lt_o_o)) of role axiom named fact_224_Pi__UNIV
% A new axiom: (forall (A_74:(arrow_1196572341e_indi->Prop)), (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) ((pi_Arr1309696186_alt_o A_74) (fun (Uu:arrow_1196572341e_indi)=> top_to1806834203lt_o_o))) top_to732317616lt_o_o))
% FOF formula (forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_73) B_58))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) (((arrow_1865170000_below L_2) A_73) B_58))) ((and ((and (not (((eq arrow_1389031998le_alt) X) Y))) ((((eq arrow_1389031998le_alt) Y) A_73)->((member285112084le_alt ((produc897867031le_alt X) B_58)) L_2)))) ((not (((eq arrow_1389031998le_alt) Y) A_73))->((and ((((eq arrow_1389031998le_alt) X) A_73)->((or (((eq arrow_1389031998le_alt) Y) B_58)) ((member285112084le_alt ((produc897867031le_alt B_58) Y)) L_2)))) ((not (((eq arrow_1389031998le_alt) X) A_73))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2))))))))) of role axiom named fact_225_in__below
% A new axiom: (forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_73) B_58))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) (((arrow_1865170000_below L_2) A_73) B_58))) ((and ((and (not (((eq arrow_1389031998le_alt) X) Y))) ((((eq arrow_1389031998le_alt) Y) A_73)->((member285112084le_alt ((produc897867031le_alt X) B_58)) L_2)))) ((not (((eq arrow_1389031998le_alt) Y) A_73))->((and ((((eq arrow_1389031998le_alt) X) A_73)->((or (((eq arrow_1389031998le_alt) Y) B_58)) ((member285112084le_alt ((produc897867031le_alt B_58) Y)) L_2)))) ((not (((eq arrow_1389031998le_alt) X) A_73))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2)))))))))
% FOF formula (forall (X_45:((produc1572197287le_alt->Prop)->Prop)), ((ord_le1027220427lt_o_o X_45) X_45)) of role axiom named fact_226_order__refl
% A new axiom: (forall (X_45:((produc1572197287le_alt->Prop)->Prop)), ((ord_le1027220427lt_o_o X_45) X_45))
% FOF formula (forall (X_45:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((ord_le1805007862lt_o_o X_45) X_45)) of role axiom named fact_227_order__refl
% A new axiom: (forall (X_45:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((ord_le1805007862lt_o_o X_45) X_45))
% FOF formula (forall (X_45:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((ord_le602483040lt_o_o X_45) X_45)) of role axiom named fact_228_order__refl
% A new axiom: (forall (X_45:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((ord_le602483040lt_o_o X_45) X_45))
% FOF formula (forall (X_45:(produc1572197287le_alt->Prop)), ((ord_le962286258_alt_o X_45) X_45)) of role axiom named fact_229_order__refl
% A new axiom: (forall (X_45:(produc1572197287le_alt->Prop)), ((ord_le962286258_alt_o X_45) X_45))
% FOF formula (forall (X_45:Prop), ((ord_less_eq_o X_45) X_45)) of role axiom named fact_230_order__refl
% A new axiom: (forall (X_45:Prop), ((ord_less_eq_o X_45) X_45))
% FOF formula (forall (X_45:(arrow_1196572341e_indi->Prop)), ((ord_le865407012indi_o X_45) X_45)) of role axiom named fact_231_order__refl
% A new axiom: (forall (X_45:(arrow_1196572341e_indi->Prop)), ((ord_le865407012indi_o X_45) X_45))
% FOF formula (forall (X_45:(product_unit->Prop)), ((ord_le1511552390unit_o X_45) X_45)) of role axiom named fact_232_order__refl
% A new axiom: (forall (X_45:(product_unit->Prop)), ((ord_le1511552390unit_o X_45) X_45))
% FOF formula (forall (X_45:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((ord_le1463467535_alt_o X_45) X_45)) of role axiom named fact_233_order__refl
% A new axiom: (forall (X_45:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((ord_le1463467535_alt_o X_45) X_45))
% FOF formula (forall (X_45:nat), ((ord_less_eq_nat X_45) X_45)) of role axiom named fact_234_order__refl
% A new axiom: (forall (X_45:nat), ((ord_less_eq_nat X_45) X_45))
% FOF formula (forall (X_45:(nat->Prop)), ((ord_less_eq_nat_o X_45) X_45)) of role axiom named fact_235_order__refl
% A new axiom: (forall (X_45:(nat->Prop)), ((ord_less_eq_nat_o X_45) X_45))
% FOF formula ((ex nat) (fun (N:nat)=> ((and ((and ((ord_less_nat N) (finite2011930979e_indi top_to54564308indi_o))) (forall (M:nat), (((ord_less_eq_nat M) N)->((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) M)) lab) lba)))))))) ((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N) one_one_nat))) lab) lba))))))) of role axiom named fact_236__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:nat)=> ((and ((and ((ord_less_nat N) (finite2011930979e_indi top_to54564308indi_o))) (forall (M:nat), (((ord_less_eq_nat M) N)->((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) M)) lab) lba)))))))) ((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N) one_one_nat))) lab) lba)))))))
% FOF formula ((forall (N:nat), (((ord_less_nat N) (finite2011930979e_indi top_to54564308indi_o))->((forall (M:nat), (((ord_less_eq_nat M) N)->((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) M)) lab) lba))))))->(((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N) one_one_nat))) lab) lba))))->False))))->False) of role axiom named fact_237__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:nat), (((ord_less_nat N) (finite2011930979e_indi top_to54564308indi_o))->((forall (M:nat), (((ord_less_eq_nat M) N)->((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) M)) lab) lba))))))->(((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N) one_one_nat))) lab) lba))))->False))))->False)
% FOF formula (forall (X_44:nat) (Y_33:nat), ((((ord_less_eq_nat X_44) Y_33)->False)->((ord_less_eq_nat Y_33) X_44))) of role axiom named fact_238_linorder__le__cases
% A new axiom: (forall (X_44:nat) (Y_33:nat), ((((ord_less_eq_nat X_44) Y_33)->False)->((ord_less_eq_nat Y_33) X_44)))
% FOF formula (forall (X_43:(produc1572197287le_alt->Prop)) (F_27:((produc1572197287le_alt->Prop)->Prop)) (G_5:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))) of role axiom named fact_239_le__funE
% A new axiom: (forall (X_43:(produc1572197287le_alt->Prop)) (F_27:((produc1572197287le_alt->Prop)->Prop)) (G_5:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43))))
% FOF formula (forall (X_43:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_27:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))) of role axiom named fact_240_le__funE
% A new axiom: (forall (X_43:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_27:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43))))
% FOF formula (forall (X_43:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_27:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))) of role axiom named fact_241_le__funE
% A new axiom: (forall (X_43:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_27:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43))))
% FOF formula (forall (X_43:produc1572197287le_alt) (F_27:(produc1572197287le_alt->Prop)) (G_5:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))) of role axiom named fact_242_le__funE
% A new axiom: (forall (X_43:produc1572197287le_alt) (F_27:(produc1572197287le_alt->Prop)) (G_5:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43))))
% FOF formula (forall (X_43:arrow_1196572341e_indi) (F_27:(arrow_1196572341e_indi->Prop)) (G_5:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))) of role axiom named fact_243_le__funE
% A new axiom: (forall (X_43:arrow_1196572341e_indi) (F_27:(arrow_1196572341e_indi->Prop)) (G_5:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43))))
% FOF formula (forall (X_43:product_unit) (F_27:(product_unit->Prop)) (G_5:(product_unit->Prop)), (((ord_le1511552390unit_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))) of role axiom named fact_244_le__funE
% A new axiom: (forall (X_43:product_unit) (F_27:(product_unit->Prop)) (G_5:(product_unit->Prop)), (((ord_le1511552390unit_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43))))
% FOF formula (forall (X_43:arrow_1389031998le_alt) (F_27:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o F_27) G_5)->((ord_le1423491573_alt_o (F_27 X_43)) (G_5 X_43)))) of role axiom named fact_245_le__funE
% A new axiom: (forall (X_43:arrow_1389031998le_alt) (F_27:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o F_27) G_5)->((ord_le1423491573_alt_o (F_27 X_43)) (G_5 X_43))))
% FOF formula (forall (X_43:nat) (F_27:(nat->Prop)) (G_5:(nat->Prop)), (((ord_less_eq_nat_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))) of role axiom named fact_246_le__funE
% A new axiom: (forall (X_43:nat) (F_27:(nat->Prop)) (G_5:(nat->Prop)), (((ord_less_eq_nat_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43))))
% FOF formula (forall (Z_6:((produc1572197287le_alt->Prop)->Prop)) (Y_32:((produc1572197287le_alt->Prop)->Prop)) (X_42:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_32) X_42)->(((ord_le1027220427lt_o_o Z_6) Y_32)->((ord_le1027220427lt_o_o Z_6) X_42)))) of role axiom named fact_247_xt1_I6_J
% A new axiom: (forall (Z_6:((produc1572197287le_alt->Prop)->Prop)) (Y_32:((produc1572197287le_alt->Prop)->Prop)) (X_42:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_32) X_42)->(((ord_le1027220427lt_o_o Z_6) Y_32)->((ord_le1027220427lt_o_o Z_6) X_42))))
% FOF formula (forall (Z_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_32:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_42:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_32) X_42)->(((ord_le1805007862lt_o_o Z_6) Y_32)->((ord_le1805007862lt_o_o Z_6) X_42)))) of role axiom named fact_248_xt1_I6_J
% A new axiom: (forall (Z_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_32:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_42:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_32) X_42)->(((ord_le1805007862lt_o_o Z_6) Y_32)->((ord_le1805007862lt_o_o Z_6) X_42))))
% FOF formula (forall (Z_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_32:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_42:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_32) X_42)->(((ord_le602483040lt_o_o Z_6) Y_32)->((ord_le602483040lt_o_o Z_6) X_42)))) of role axiom named fact_249_xt1_I6_J
% A new axiom: (forall (Z_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_32:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_42:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_32) X_42)->(((ord_le602483040lt_o_o Z_6) Y_32)->((ord_le602483040lt_o_o Z_6) X_42))))
% FOF formula (forall (Z_6:(produc1572197287le_alt->Prop)) (Y_32:(produc1572197287le_alt->Prop)) (X_42:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_32) X_42)->(((ord_le962286258_alt_o Z_6) Y_32)->((ord_le962286258_alt_o Z_6) X_42)))) of role axiom named fact_250_xt1_I6_J
% A new axiom: (forall (Z_6:(produc1572197287le_alt->Prop)) (Y_32:(produc1572197287le_alt->Prop)) (X_42:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_32) X_42)->(((ord_le962286258_alt_o Z_6) Y_32)->((ord_le962286258_alt_o Z_6) X_42))))
% FOF formula (forall (Z_6:Prop) (Y_32:Prop) (X_42:Prop), (((ord_less_eq_o Y_32) X_42)->(((ord_less_eq_o Z_6) Y_32)->((ord_less_eq_o Z_6) X_42)))) of role axiom named fact_251_xt1_I6_J
% A new axiom: (forall (Z_6:Prop) (Y_32:Prop) (X_42:Prop), (((ord_less_eq_o Y_32) X_42)->(((ord_less_eq_o Z_6) Y_32)->((ord_less_eq_o Z_6) X_42))))
% FOF formula (forall (Z_6:(arrow_1196572341e_indi->Prop)) (Y_32:(arrow_1196572341e_indi->Prop)) (X_42:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_32) X_42)->(((ord_le865407012indi_o Z_6) Y_32)->((ord_le865407012indi_o Z_6) X_42)))) of role axiom named fact_252_xt1_I6_J
% A new axiom: (forall (Z_6:(arrow_1196572341e_indi->Prop)) (Y_32:(arrow_1196572341e_indi->Prop)) (X_42:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_32) X_42)->(((ord_le865407012indi_o Z_6) Y_32)->((ord_le865407012indi_o Z_6) X_42))))
% FOF formula (forall (Z_6:(product_unit->Prop)) (Y_32:(product_unit->Prop)) (X_42:(product_unit->Prop)), (((ord_le1511552390unit_o Y_32) X_42)->(((ord_le1511552390unit_o Z_6) Y_32)->((ord_le1511552390unit_o Z_6) X_42)))) of role axiom named fact_253_xt1_I6_J
% A new axiom: (forall (Z_6:(product_unit->Prop)) (Y_32:(product_unit->Prop)) (X_42:(product_unit->Prop)), (((ord_le1511552390unit_o Y_32) X_42)->(((ord_le1511552390unit_o Z_6) Y_32)->((ord_le1511552390unit_o Z_6) X_42))))
% FOF formula (forall (Z_6:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_32:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_42:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_32) X_42)->(((ord_le1463467535_alt_o Z_6) Y_32)->((ord_le1463467535_alt_o Z_6) X_42)))) of role axiom named fact_254_xt1_I6_J
% A new axiom: (forall (Z_6:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_32:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_42:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_32) X_42)->(((ord_le1463467535_alt_o Z_6) Y_32)->((ord_le1463467535_alt_o Z_6) X_42))))
% FOF formula (forall (Z_6:nat) (Y_32:nat) (X_42:nat), (((ord_less_eq_nat Y_32) X_42)->(((ord_less_eq_nat Z_6) Y_32)->((ord_less_eq_nat Z_6) X_42)))) of role axiom named fact_255_xt1_I6_J
% A new axiom: (forall (Z_6:nat) (Y_32:nat) (X_42:nat), (((ord_less_eq_nat Y_32) X_42)->(((ord_less_eq_nat Z_6) Y_32)->((ord_less_eq_nat Z_6) X_42))))
% FOF formula (forall (Z_6:(nat->Prop)) (Y_32:(nat->Prop)) (X_42:(nat->Prop)), (((ord_less_eq_nat_o Y_32) X_42)->(((ord_less_eq_nat_o Z_6) Y_32)->((ord_less_eq_nat_o Z_6) X_42)))) of role axiom named fact_256_xt1_I6_J
% A new axiom: (forall (Z_6:(nat->Prop)) (Y_32:(nat->Prop)) (X_42:(nat->Prop)), (((ord_less_eq_nat_o Y_32) X_42)->(((ord_less_eq_nat_o Z_6) Y_32)->((ord_less_eq_nat_o Z_6) X_42))))
% FOF formula (forall (Y_31:((produc1572197287le_alt->Prop)->Prop)) (X_41:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_31) X_41)->(((ord_le1027220427lt_o_o X_41) Y_31)->(((eq ((produc1572197287le_alt->Prop)->Prop)) X_41) Y_31)))) of role axiom named fact_257_xt1_I5_J
% A new axiom: (forall (Y_31:((produc1572197287le_alt->Prop)->Prop)) (X_41:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_31) X_41)->(((ord_le1027220427lt_o_o X_41) Y_31)->(((eq ((produc1572197287le_alt->Prop)->Prop)) X_41) Y_31))))
% FOF formula (forall (Y_31:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_41:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_31) X_41)->(((ord_le1805007862lt_o_o X_41) Y_31)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_41) Y_31)))) of role axiom named fact_258_xt1_I5_J
% A new axiom: (forall (Y_31:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_41:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_31) X_41)->(((ord_le1805007862lt_o_o X_41) Y_31)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_41) Y_31))))
% FOF formula (forall (Y_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_41:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_31) X_41)->(((ord_le602483040lt_o_o X_41) Y_31)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_41) Y_31)))) of role axiom named fact_259_xt1_I5_J
% A new axiom: (forall (Y_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_41:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_31) X_41)->(((ord_le602483040lt_o_o X_41) Y_31)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_41) Y_31))))
% FOF formula (forall (Y_31:(produc1572197287le_alt->Prop)) (X_41:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_31) X_41)->(((ord_le962286258_alt_o X_41) Y_31)->(((eq (produc1572197287le_alt->Prop)) X_41) Y_31)))) of role axiom named fact_260_xt1_I5_J
% A new axiom: (forall (Y_31:(produc1572197287le_alt->Prop)) (X_41:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_31) X_41)->(((ord_le962286258_alt_o X_41) Y_31)->(((eq (produc1572197287le_alt->Prop)) X_41) Y_31))))
% FOF formula (forall (Y_31:Prop) (X_41:Prop), (((ord_less_eq_o Y_31) X_41)->(((ord_less_eq_o X_41) Y_31)->((iff X_41) Y_31)))) of role axiom named fact_261_xt1_I5_J
% A new axiom: (forall (Y_31:Prop) (X_41:Prop), (((ord_less_eq_o Y_31) X_41)->(((ord_less_eq_o X_41) Y_31)->((iff X_41) Y_31))))
% FOF formula (forall (Y_31:(arrow_1196572341e_indi->Prop)) (X_41:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_31) X_41)->(((ord_le865407012indi_o X_41) Y_31)->(((eq (arrow_1196572341e_indi->Prop)) X_41) Y_31)))) of role axiom named fact_262_xt1_I5_J
% A new axiom: (forall (Y_31:(arrow_1196572341e_indi->Prop)) (X_41:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_31) X_41)->(((ord_le865407012indi_o X_41) Y_31)->(((eq (arrow_1196572341e_indi->Prop)) X_41) Y_31))))
% FOF formula (forall (Y_31:(product_unit->Prop)) (X_41:(product_unit->Prop)), (((ord_le1511552390unit_o Y_31) X_41)->(((ord_le1511552390unit_o X_41) Y_31)->(((eq (product_unit->Prop)) X_41) Y_31)))) of role axiom named fact_263_xt1_I5_J
% A new axiom: (forall (Y_31:(product_unit->Prop)) (X_41:(product_unit->Prop)), (((ord_le1511552390unit_o Y_31) X_41)->(((ord_le1511552390unit_o X_41) Y_31)->(((eq (product_unit->Prop)) X_41) Y_31))))
% FOF formula (forall (Y_31:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_41:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_31) X_41)->(((ord_le1463467535_alt_o X_41) Y_31)->(((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_41) Y_31)))) of role axiom named fact_264_xt1_I5_J
% A new axiom: (forall (Y_31:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_41:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_31) X_41)->(((ord_le1463467535_alt_o X_41) Y_31)->(((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_41) Y_31))))
% FOF formula (forall (Y_31:nat) (X_41:nat), (((ord_less_eq_nat Y_31) X_41)->(((ord_less_eq_nat X_41) Y_31)->(((eq nat) X_41) Y_31)))) of role axiom named fact_265_xt1_I5_J
% A new axiom: (forall (Y_31:nat) (X_41:nat), (((ord_less_eq_nat Y_31) X_41)->(((ord_less_eq_nat X_41) Y_31)->(((eq nat) X_41) Y_31))))
% FOF formula (forall (Y_31:(nat->Prop)) (X_41:(nat->Prop)), (((ord_less_eq_nat_o Y_31) X_41)->(((ord_less_eq_nat_o X_41) Y_31)->(((eq (nat->Prop)) X_41) Y_31)))) of role axiom named fact_266_xt1_I5_J
% A new axiom: (forall (Y_31:(nat->Prop)) (X_41:(nat->Prop)), (((ord_less_eq_nat_o Y_31) X_41)->(((ord_less_eq_nat_o X_41) Y_31)->(((eq (nat->Prop)) X_41) Y_31))))
% FOF formula (forall (Z_5:((produc1572197287le_alt->Prop)->Prop)) (X_40:((produc1572197287le_alt->Prop)->Prop)) (Y_30:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_40) Y_30)->(((ord_le1027220427lt_o_o Y_30) Z_5)->((ord_le1027220427lt_o_o X_40) Z_5)))) of role axiom named fact_267_order__trans
% A new axiom: (forall (Z_5:((produc1572197287le_alt->Prop)->Prop)) (X_40:((produc1572197287le_alt->Prop)->Prop)) (Y_30:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_40) Y_30)->(((ord_le1027220427lt_o_o Y_30) Z_5)->((ord_le1027220427lt_o_o X_40) Z_5))))
% FOF formula (forall (Z_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_40:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_40) Y_30)->(((ord_le1805007862lt_o_o Y_30) Z_5)->((ord_le1805007862lt_o_o X_40) Z_5)))) of role axiom named fact_268_order__trans
% A new axiom: (forall (Z_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_40:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_40) Y_30)->(((ord_le1805007862lt_o_o Y_30) Z_5)->((ord_le1805007862lt_o_o X_40) Z_5))))
% FOF formula (forall (Z_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_40:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_40) Y_30)->(((ord_le602483040lt_o_o Y_30) Z_5)->((ord_le602483040lt_o_o X_40) Z_5)))) of role axiom named fact_269_order__trans
% A new axiom: (forall (Z_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_40:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_40) Y_30)->(((ord_le602483040lt_o_o Y_30) Z_5)->((ord_le602483040lt_o_o X_40) Z_5))))
% FOF formula (forall (Z_5:(produc1572197287le_alt->Prop)) (X_40:(produc1572197287le_alt->Prop)) (Y_30:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_40) Y_30)->(((ord_le962286258_alt_o Y_30) Z_5)->((ord_le962286258_alt_o X_40) Z_5)))) of role axiom named fact_270_order__trans
% A new axiom: (forall (Z_5:(produc1572197287le_alt->Prop)) (X_40:(produc1572197287le_alt->Prop)) (Y_30:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_40) Y_30)->(((ord_le962286258_alt_o Y_30) Z_5)->((ord_le962286258_alt_o X_40) Z_5))))
% FOF formula (forall (Z_5:Prop) (X_40:Prop) (Y_30:Prop), (((ord_less_eq_o X_40) Y_30)->(((ord_less_eq_o Y_30) Z_5)->((ord_less_eq_o X_40) Z_5)))) of role axiom named fact_271_order__trans
% A new axiom: (forall (Z_5:Prop) (X_40:Prop) (Y_30:Prop), (((ord_less_eq_o X_40) Y_30)->(((ord_less_eq_o Y_30) Z_5)->((ord_less_eq_o X_40) Z_5))))
% FOF formula (forall (Z_5:(arrow_1196572341e_indi->Prop)) (X_40:(arrow_1196572341e_indi->Prop)) (Y_30:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_40) Y_30)->(((ord_le865407012indi_o Y_30) Z_5)->((ord_le865407012indi_o X_40) Z_5)))) of role axiom named fact_272_order__trans
% A new axiom: (forall (Z_5:(arrow_1196572341e_indi->Prop)) (X_40:(arrow_1196572341e_indi->Prop)) (Y_30:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_40) Y_30)->(((ord_le865407012indi_o Y_30) Z_5)->((ord_le865407012indi_o X_40) Z_5))))
% FOF formula (forall (Z_5:(product_unit->Prop)) (X_40:(product_unit->Prop)) (Y_30:(product_unit->Prop)), (((ord_le1511552390unit_o X_40) Y_30)->(((ord_le1511552390unit_o Y_30) Z_5)->((ord_le1511552390unit_o X_40) Z_5)))) of role axiom named fact_273_order__trans
% A new axiom: (forall (Z_5:(product_unit->Prop)) (X_40:(product_unit->Prop)) (Y_30:(product_unit->Prop)), (((ord_le1511552390unit_o X_40) Y_30)->(((ord_le1511552390unit_o Y_30) Z_5)->((ord_le1511552390unit_o X_40) Z_5))))
% FOF formula (forall (Z_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_40:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_40) Y_30)->(((ord_le1463467535_alt_o Y_30) Z_5)->((ord_le1463467535_alt_o X_40) Z_5)))) of role axiom named fact_274_order__trans
% A new axiom: (forall (Z_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_40:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_40) Y_30)->(((ord_le1463467535_alt_o Y_30) Z_5)->((ord_le1463467535_alt_o X_40) Z_5))))
% FOF formula (forall (Z_5:nat) (X_40:nat) (Y_30:nat), (((ord_less_eq_nat X_40) Y_30)->(((ord_less_eq_nat Y_30) Z_5)->((ord_less_eq_nat X_40) Z_5)))) of role axiom named fact_275_order__trans
% A new axiom: (forall (Z_5:nat) (X_40:nat) (Y_30:nat), (((ord_less_eq_nat X_40) Y_30)->(((ord_less_eq_nat Y_30) Z_5)->((ord_less_eq_nat X_40) Z_5))))
% FOF formula (forall (Z_5:(nat->Prop)) (X_40:(nat->Prop)) (Y_30:(nat->Prop)), (((ord_less_eq_nat_o X_40) Y_30)->(((ord_less_eq_nat_o Y_30) Z_5)->((ord_less_eq_nat_o X_40) Z_5)))) of role axiom named fact_276_order__trans
% A new axiom: (forall (Z_5:(nat->Prop)) (X_40:(nat->Prop)) (Y_30:(nat->Prop)), (((ord_less_eq_nat_o X_40) Y_30)->(((ord_less_eq_nat_o Y_30) Z_5)->((ord_less_eq_nat_o X_40) Z_5))))
% FOF formula (forall (X_39:((produc1572197287le_alt->Prop)->Prop)) (Y_29:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_39) Y_29)->(((ord_le1027220427lt_o_o Y_29) X_39)->(((eq ((produc1572197287le_alt->Prop)->Prop)) X_39) Y_29)))) of role axiom named fact_277_order__antisym
% A new axiom: (forall (X_39:((produc1572197287le_alt->Prop)->Prop)) (Y_29:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_39) Y_29)->(((ord_le1027220427lt_o_o Y_29) X_39)->(((eq ((produc1572197287le_alt->Prop)->Prop)) X_39) Y_29))))
% FOF formula (forall (X_39:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_29:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_39) Y_29)->(((ord_le1805007862lt_o_o Y_29) X_39)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_39) Y_29)))) of role axiom named fact_278_order__antisym
% A new axiom: (forall (X_39:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_29:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_39) Y_29)->(((ord_le1805007862lt_o_o Y_29) X_39)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_39) Y_29))))
% FOF formula (forall (X_39:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_29:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_39) Y_29)->(((ord_le602483040lt_o_o Y_29) X_39)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_39) Y_29)))) of role axiom named fact_279_order__antisym
% A new axiom: (forall (X_39:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_29:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_39) Y_29)->(((ord_le602483040lt_o_o Y_29) X_39)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_39) Y_29))))
% FOF formula (forall (X_39:(produc1572197287le_alt->Prop)) (Y_29:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_39) Y_29)->(((ord_le962286258_alt_o Y_29) X_39)->(((eq (produc1572197287le_alt->Prop)) X_39) Y_29)))) of role axiom named fact_280_order__antisym
% A new axiom: (forall (X_39:(produc1572197287le_alt->Prop)) (Y_29:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_39) Y_29)->(((ord_le962286258_alt_o Y_29) X_39)->(((eq (produc1572197287le_alt->Prop)) X_39) Y_29))))
% FOF formula (forall (X_39:Prop) (Y_29:Prop), (((ord_less_eq_o X_39) Y_29)->(((ord_less_eq_o Y_29) X_39)->((iff X_39) Y_29)))) of role axiom named fact_281_order__antisym
% A new axiom: (forall (X_39:Prop) (Y_29:Prop), (((ord_less_eq_o X_39) Y_29)->(((ord_less_eq_o Y_29) X_39)->((iff X_39) Y_29))))
% FOF formula (forall (X_39:(arrow_1196572341e_indi->Prop)) (Y_29:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_39) Y_29)->(((ord_le865407012indi_o Y_29) X_39)->(((eq (arrow_1196572341e_indi->Prop)) X_39) Y_29)))) of role axiom named fact_282_order__antisym
% A new axiom: (forall (X_39:(arrow_1196572341e_indi->Prop)) (Y_29:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_39) Y_29)->(((ord_le865407012indi_o Y_29) X_39)->(((eq (arrow_1196572341e_indi->Prop)) X_39) Y_29))))
% FOF formula (forall (X_39:(product_unit->Prop)) (Y_29:(product_unit->Prop)), (((ord_le1511552390unit_o X_39) Y_29)->(((ord_le1511552390unit_o Y_29) X_39)->(((eq (product_unit->Prop)) X_39) Y_29)))) of role axiom named fact_283_order__antisym
% A new axiom: (forall (X_39:(product_unit->Prop)) (Y_29:(product_unit->Prop)), (((ord_le1511552390unit_o X_39) Y_29)->(((ord_le1511552390unit_o Y_29) X_39)->(((eq (product_unit->Prop)) X_39) Y_29))))
% FOF formula (forall (X_39:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_29:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_39) Y_29)->(((ord_le1463467535_alt_o Y_29) X_39)->(((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_39) Y_29)))) of role axiom named fact_284_order__antisym
% A new axiom: (forall (X_39:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_29:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_39) Y_29)->(((ord_le1463467535_alt_o Y_29) X_39)->(((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_39) Y_29))))
% FOF formula (forall (X_39:nat) (Y_29:nat), (((ord_less_eq_nat X_39) Y_29)->(((ord_less_eq_nat Y_29) X_39)->(((eq nat) X_39) Y_29)))) of role axiom named fact_285_order__antisym
% A new axiom: (forall (X_39:nat) (Y_29:nat), (((ord_less_eq_nat X_39) Y_29)->(((ord_less_eq_nat Y_29) X_39)->(((eq nat) X_39) Y_29))))
% FOF formula (forall (X_39:(nat->Prop)) (Y_29:(nat->Prop)), (((ord_less_eq_nat_o X_39) Y_29)->(((ord_less_eq_nat_o Y_29) X_39)->(((eq (nat->Prop)) X_39) Y_29)))) of role axiom named fact_286_order__antisym
% A new axiom: (forall (X_39:(nat->Prop)) (Y_29:(nat->Prop)), (((ord_less_eq_nat_o X_39) Y_29)->(((ord_less_eq_nat_o Y_29) X_39)->(((eq (nat->Prop)) X_39) Y_29))))
% FOF formula (forall (C_37:((produc1572197287le_alt->Prop)->Prop)) (B_57:((produc1572197287le_alt->Prop)->Prop)) (A_72:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_57) A_72)->((((eq ((produc1572197287le_alt->Prop)->Prop)) B_57) C_37)->((ord_le1027220427lt_o_o C_37) A_72)))) of role axiom named fact_287_xt1_I4_J
% A new axiom: (forall (C_37:((produc1572197287le_alt->Prop)->Prop)) (B_57:((produc1572197287le_alt->Prop)->Prop)) (A_72:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_57) A_72)->((((eq ((produc1572197287le_alt->Prop)->Prop)) B_57) C_37)->((ord_le1027220427lt_o_o C_37) A_72))))
% FOF formula (forall (C_37:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_72:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_57) A_72)->((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) B_57) C_37)->((ord_le1805007862lt_o_o C_37) A_72)))) of role axiom named fact_288_xt1_I4_J
% A new axiom: (forall (C_37:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_72:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_57) A_72)->((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) B_57) C_37)->((ord_le1805007862lt_o_o C_37) A_72))))
% FOF formula (forall (C_37:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_72:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_57) A_72)->((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) B_57) C_37)->((ord_le602483040lt_o_o C_37) A_72)))) of role axiom named fact_289_xt1_I4_J
% A new axiom: (forall (C_37:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_72:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_57) A_72)->((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) B_57) C_37)->((ord_le602483040lt_o_o C_37) A_72))))
% FOF formula (forall (C_37:(produc1572197287le_alt->Prop)) (B_57:(produc1572197287le_alt->Prop)) (A_72:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_57) A_72)->((((eq (produc1572197287le_alt->Prop)) B_57) C_37)->((ord_le962286258_alt_o C_37) A_72)))) of role axiom named fact_290_xt1_I4_J
% A new axiom: (forall (C_37:(produc1572197287le_alt->Prop)) (B_57:(produc1572197287le_alt->Prop)) (A_72:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_57) A_72)->((((eq (produc1572197287le_alt->Prop)) B_57) C_37)->((ord_le962286258_alt_o C_37) A_72))))
% FOF formula (forall (C_37:Prop) (B_57:Prop) (A_72:Prop), (((ord_less_eq_o B_57) A_72)->(((iff B_57) C_37)->((ord_less_eq_o C_37) A_72)))) of role axiom named fact_291_xt1_I4_J
% A new axiom: (forall (C_37:Prop) (B_57:Prop) (A_72:Prop), (((ord_less_eq_o B_57) A_72)->(((iff B_57) C_37)->((ord_less_eq_o C_37) A_72))))
% FOF formula (forall (C_37:(arrow_1196572341e_indi->Prop)) (B_57:(arrow_1196572341e_indi->Prop)) (A_72:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_57) A_72)->((((eq (arrow_1196572341e_indi->Prop)) B_57) C_37)->((ord_le865407012indi_o C_37) A_72)))) of role axiom named fact_292_xt1_I4_J
% A new axiom: (forall (C_37:(arrow_1196572341e_indi->Prop)) (B_57:(arrow_1196572341e_indi->Prop)) (A_72:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_57) A_72)->((((eq (arrow_1196572341e_indi->Prop)) B_57) C_37)->((ord_le865407012indi_o C_37) A_72))))
% FOF formula (forall (C_37:(product_unit->Prop)) (B_57:(product_unit->Prop)) (A_72:(product_unit->Prop)), (((ord_le1511552390unit_o B_57) A_72)->((((eq (product_unit->Prop)) B_57) C_37)->((ord_le1511552390unit_o C_37) A_72)))) of role axiom named fact_293_xt1_I4_J
% A new axiom: (forall (C_37:(product_unit->Prop)) (B_57:(product_unit->Prop)) (A_72:(product_unit->Prop)), (((ord_le1511552390unit_o B_57) A_72)->((((eq (product_unit->Prop)) B_57) C_37)->((ord_le1511552390unit_o C_37) A_72))))
% FOF formula (forall (C_37:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_57:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_72:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_57) A_72)->((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) B_57) C_37)->((ord_le1463467535_alt_o C_37) A_72)))) of role axiom named fact_294_xt1_I4_J
% A new axiom: (forall (C_37:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_57:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_72:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_57) A_72)->((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) B_57) C_37)->((ord_le1463467535_alt_o C_37) A_72))))
% FOF formula (forall (C_37:nat) (B_57:nat) (A_72:nat), (((ord_less_eq_nat B_57) A_72)->((((eq nat) B_57) C_37)->((ord_less_eq_nat C_37) A_72)))) of role axiom named fact_295_xt1_I4_J
% A new axiom: (forall (C_37:nat) (B_57:nat) (A_72:nat), (((ord_less_eq_nat B_57) A_72)->((((eq nat) B_57) C_37)->((ord_less_eq_nat C_37) A_72))))
% FOF formula (forall (C_37:(nat->Prop)) (B_57:(nat->Prop)) (A_72:(nat->Prop)), (((ord_less_eq_nat_o B_57) A_72)->((((eq (nat->Prop)) B_57) C_37)->((ord_less_eq_nat_o C_37) A_72)))) of role axiom named fact_296_xt1_I4_J
% A new axiom: (forall (C_37:(nat->Prop)) (B_57:(nat->Prop)) (A_72:(nat->Prop)), (((ord_less_eq_nat_o B_57) A_72)->((((eq (nat->Prop)) B_57) C_37)->((ord_less_eq_nat_o C_37) A_72))))
% FOF formula (forall (C_36:((produc1572197287le_alt->Prop)->Prop)) (A_71:((produc1572197287le_alt->Prop)->Prop)) (B_56:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_71) B_56)->((((eq ((produc1572197287le_alt->Prop)->Prop)) B_56) C_36)->((ord_le1027220427lt_o_o A_71) C_36)))) of role axiom named fact_297_ord__le__eq__trans
% A new axiom: (forall (C_36:((produc1572197287le_alt->Prop)->Prop)) (A_71:((produc1572197287le_alt->Prop)->Prop)) (B_56:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_71) B_56)->((((eq ((produc1572197287le_alt->Prop)->Prop)) B_56) C_36)->((ord_le1027220427lt_o_o A_71) C_36))))
% FOF formula (forall (C_36:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_71:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_56:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_71) B_56)->((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) B_56) C_36)->((ord_le1805007862lt_o_o A_71) C_36)))) of role axiom named fact_298_ord__le__eq__trans
% A new axiom: (forall (C_36:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_71:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_56:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_71) B_56)->((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) B_56) C_36)->((ord_le1805007862lt_o_o A_71) C_36))))
% FOF formula (forall (C_36:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_71:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_56:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_71) B_56)->((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) B_56) C_36)->((ord_le602483040lt_o_o A_71) C_36)))) of role axiom named fact_299_ord__le__eq__trans
% A new axiom: (forall (C_36:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_71:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_56:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_71) B_56)->((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) B_56) C_36)->((ord_le602483040lt_o_o A_71) C_36))))
% FOF formula (forall (C_36:(produc1572197287le_alt->Prop)) (A_71:(produc1572197287le_alt->Prop)) (B_56:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_71) B_56)->((((eq (produc1572197287le_alt->Prop)) B_56) C_36)->((ord_le962286258_alt_o A_71) C_36)))) of role axiom named fact_300_ord__le__eq__trans
% A new axiom: (forall (C_36:(produc1572197287le_alt->Prop)) (A_71:(produc1572197287le_alt->Prop)) (B_56:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_71) B_56)->((((eq (produc1572197287le_alt->Prop)) B_56) C_36)->((ord_le962286258_alt_o A_71) C_36))))
% FOF formula (forall (C_36:Prop) (A_71:Prop) (B_56:Prop), (((ord_less_eq_o A_71) B_56)->(((iff B_56) C_36)->((ord_less_eq_o A_71) C_36)))) of role axiom named fact_301_ord__le__eq__trans
% A new axiom: (forall (C_36:Prop) (A_71:Prop) (B_56:Prop), (((ord_less_eq_o A_71) B_56)->(((iff B_56) C_36)->((ord_less_eq_o A_71) C_36))))
% FOF formula (forall (C_36:(arrow_1196572341e_indi->Prop)) (A_71:(arrow_1196572341e_indi->Prop)) (B_56:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_71) B_56)->((((eq (arrow_1196572341e_indi->Prop)) B_56) C_36)->((ord_le865407012indi_o A_71) C_36)))) of role axiom named fact_302_ord__le__eq__trans
% A new axiom: (forall (C_36:(arrow_1196572341e_indi->Prop)) (A_71:(arrow_1196572341e_indi->Prop)) (B_56:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_71) B_56)->((((eq (arrow_1196572341e_indi->Prop)) B_56) C_36)->((ord_le865407012indi_o A_71) C_36))))
% FOF formula (forall (C_36:(product_unit->Prop)) (A_71:(product_unit->Prop)) (B_56:(product_unit->Prop)), (((ord_le1511552390unit_o A_71) B_56)->((((eq (product_unit->Prop)) B_56) C_36)->((ord_le1511552390unit_o A_71) C_36)))) of role axiom named fact_303_ord__le__eq__trans
% A new axiom: (forall (C_36:(product_unit->Prop)) (A_71:(product_unit->Prop)) (B_56:(product_unit->Prop)), (((ord_le1511552390unit_o A_71) B_56)->((((eq (product_unit->Prop)) B_56) C_36)->((ord_le1511552390unit_o A_71) C_36))))
% FOF formula (forall (C_36:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_71:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_56:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_71) B_56)->((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) B_56) C_36)->((ord_le1463467535_alt_o A_71) C_36)))) of role axiom named fact_304_ord__le__eq__trans
% A new axiom: (forall (C_36:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_71:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_56:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_71) B_56)->((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) B_56) C_36)->((ord_le1463467535_alt_o A_71) C_36))))
% FOF formula (forall (C_36:nat) (A_71:nat) (B_56:nat), (((ord_less_eq_nat A_71) B_56)->((((eq nat) B_56) C_36)->((ord_less_eq_nat A_71) C_36)))) of role axiom named fact_305_ord__le__eq__trans
% A new axiom: (forall (C_36:nat) (A_71:nat) (B_56:nat), (((ord_less_eq_nat A_71) B_56)->((((eq nat) B_56) C_36)->((ord_less_eq_nat A_71) C_36))))
% FOF formula (forall (C_36:(nat->Prop)) (A_71:(nat->Prop)) (B_56:(nat->Prop)), (((ord_less_eq_nat_o A_71) B_56)->((((eq (nat->Prop)) B_56) C_36)->((ord_less_eq_nat_o A_71) C_36)))) of role axiom named fact_306_ord__le__eq__trans
% A new axiom: (forall (C_36:(nat->Prop)) (A_71:(nat->Prop)) (B_56:(nat->Prop)), (((ord_less_eq_nat_o A_71) B_56)->((((eq (nat->Prop)) B_56) C_36)->((ord_less_eq_nat_o A_71) C_36))))
% FOF formula (forall (C_35:((produc1572197287le_alt->Prop)->Prop)) (A_70:((produc1572197287le_alt->Prop)->Prop)) (B_55:((produc1572197287le_alt->Prop)->Prop)), ((((eq ((produc1572197287le_alt->Prop)->Prop)) A_70) B_55)->(((ord_le1027220427lt_o_o C_35) B_55)->((ord_le1027220427lt_o_o C_35) A_70)))) of role axiom named fact_307_xt1_I3_J
% A new axiom: (forall (C_35:((produc1572197287le_alt->Prop)->Prop)) (A_70:((produc1572197287le_alt->Prop)->Prop)) (B_55:((produc1572197287le_alt->Prop)->Prop)), ((((eq ((produc1572197287le_alt->Prop)->Prop)) A_70) B_55)->(((ord_le1027220427lt_o_o C_35) B_55)->((ord_le1027220427lt_o_o C_35) A_70))))
% FOF formula (forall (C_35:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_70:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_70) B_55)->(((ord_le1805007862lt_o_o C_35) B_55)->((ord_le1805007862lt_o_o C_35) A_70)))) of role axiom named fact_308_xt1_I3_J
% A new axiom: (forall (C_35:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_70:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_70) B_55)->(((ord_le1805007862lt_o_o C_35) B_55)->((ord_le1805007862lt_o_o C_35) A_70))))
% FOF formula (forall (C_35:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_70:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_70) B_55)->(((ord_le602483040lt_o_o C_35) B_55)->((ord_le602483040lt_o_o C_35) A_70)))) of role axiom named fact_309_xt1_I3_J
% A new axiom: (forall (C_35:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_70:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_70) B_55)->(((ord_le602483040lt_o_o C_35) B_55)->((ord_le602483040lt_o_o C_35) A_70))))
% FOF formula (forall (C_35:(produc1572197287le_alt->Prop)) (A_70:(produc1572197287le_alt->Prop)) (B_55:(produc1572197287le_alt->Prop)), ((((eq (produc1572197287le_alt->Prop)) A_70) B_55)->(((ord_le962286258_alt_o C_35) B_55)->((ord_le962286258_alt_o C_35) A_70)))) of role axiom named fact_310_xt1_I3_J
% A new axiom: (forall (C_35:(produc1572197287le_alt->Prop)) (A_70:(produc1572197287le_alt->Prop)) (B_55:(produc1572197287le_alt->Prop)), ((((eq (produc1572197287le_alt->Prop)) A_70) B_55)->(((ord_le962286258_alt_o C_35) B_55)->((ord_le962286258_alt_o C_35) A_70))))
% FOF formula (forall (C_35:Prop) (B_55:Prop) (A_70:Prop), (((iff A_70) B_55)->(((ord_less_eq_o C_35) B_55)->((ord_less_eq_o C_35) A_70)))) of role axiom named fact_311_xt1_I3_J
% A new axiom: (forall (C_35:Prop) (B_55:Prop) (A_70:Prop), (((iff A_70) B_55)->(((ord_less_eq_o C_35) B_55)->((ord_less_eq_o C_35) A_70))))
% FOF formula (forall (C_35:(arrow_1196572341e_indi->Prop)) (A_70:(arrow_1196572341e_indi->Prop)) (B_55:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_70) B_55)->(((ord_le865407012indi_o C_35) B_55)->((ord_le865407012indi_o C_35) A_70)))) of role axiom named fact_312_xt1_I3_J
% A new axiom: (forall (C_35:(arrow_1196572341e_indi->Prop)) (A_70:(arrow_1196572341e_indi->Prop)) (B_55:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_70) B_55)->(((ord_le865407012indi_o C_35) B_55)->((ord_le865407012indi_o C_35) A_70))))
% FOF formula (forall (C_35:(product_unit->Prop)) (A_70:(product_unit->Prop)) (B_55:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_70) B_55)->(((ord_le1511552390unit_o C_35) B_55)->((ord_le1511552390unit_o C_35) A_70)))) of role axiom named fact_313_xt1_I3_J
% A new axiom: (forall (C_35:(product_unit->Prop)) (A_70:(product_unit->Prop)) (B_55:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_70) B_55)->(((ord_le1511552390unit_o C_35) B_55)->((ord_le1511552390unit_o C_35) A_70))))
% FOF formula (forall (C_35:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_70:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_55:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_70) B_55)->(((ord_le1463467535_alt_o C_35) B_55)->((ord_le1463467535_alt_o C_35) A_70)))) of role axiom named fact_314_xt1_I3_J
% A new axiom: (forall (C_35:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_70:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_55:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_70) B_55)->(((ord_le1463467535_alt_o C_35) B_55)->((ord_le1463467535_alt_o C_35) A_70))))
% FOF formula (forall (C_35:nat) (A_70:nat) (B_55:nat), ((((eq nat) A_70) B_55)->(((ord_less_eq_nat C_35) B_55)->((ord_less_eq_nat C_35) A_70)))) of role axiom named fact_315_xt1_I3_J
% A new axiom: (forall (C_35:nat) (A_70:nat) (B_55:nat), ((((eq nat) A_70) B_55)->(((ord_less_eq_nat C_35) B_55)->((ord_less_eq_nat C_35) A_70))))
% FOF formula (forall (C_35:(nat->Prop)) (A_70:(nat->Prop)) (B_55:(nat->Prop)), ((((eq (nat->Prop)) A_70) B_55)->(((ord_less_eq_nat_o C_35) B_55)->((ord_less_eq_nat_o C_35) A_70)))) of role axiom named fact_316_xt1_I3_J
% A new axiom: (forall (C_35:(nat->Prop)) (A_70:(nat->Prop)) (B_55:(nat->Prop)), ((((eq (nat->Prop)) A_70) B_55)->(((ord_less_eq_nat_o C_35) B_55)->((ord_less_eq_nat_o C_35) A_70))))
% FOF formula (forall (C_34:((produc1572197287le_alt->Prop)->Prop)) (A_69:((produc1572197287le_alt->Prop)->Prop)) (B_54:((produc1572197287le_alt->Prop)->Prop)), ((((eq ((produc1572197287le_alt->Prop)->Prop)) A_69) B_54)->(((ord_le1027220427lt_o_o B_54) C_34)->((ord_le1027220427lt_o_o A_69) C_34)))) of role axiom named fact_317_ord__eq__le__trans
% A new axiom: (forall (C_34:((produc1572197287le_alt->Prop)->Prop)) (A_69:((produc1572197287le_alt->Prop)->Prop)) (B_54:((produc1572197287le_alt->Prop)->Prop)), ((((eq ((produc1572197287le_alt->Prop)->Prop)) A_69) B_54)->(((ord_le1027220427lt_o_o B_54) C_34)->((ord_le1027220427lt_o_o A_69) C_34))))
% FOF formula (forall (C_34:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_69:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_54:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_69) B_54)->(((ord_le1805007862lt_o_o B_54) C_34)->((ord_le1805007862lt_o_o A_69) C_34)))) of role axiom named fact_318_ord__eq__le__trans
% A new axiom: (forall (C_34:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_69:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_54:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_69) B_54)->(((ord_le1805007862lt_o_o B_54) C_34)->((ord_le1805007862lt_o_o A_69) C_34))))
% FOF formula (forall (C_34:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_69:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_54:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_69) B_54)->(((ord_le602483040lt_o_o B_54) C_34)->((ord_le602483040lt_o_o A_69) C_34)))) of role axiom named fact_319_ord__eq__le__trans
% A new axiom: (forall (C_34:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_69:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_54:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_69) B_54)->(((ord_le602483040lt_o_o B_54) C_34)->((ord_le602483040lt_o_o A_69) C_34))))
% FOF formula (forall (C_34:(produc1572197287le_alt->Prop)) (A_69:(produc1572197287le_alt->Prop)) (B_54:(produc1572197287le_alt->Prop)), ((((eq (produc1572197287le_alt->Prop)) A_69) B_54)->(((ord_le962286258_alt_o B_54) C_34)->((ord_le962286258_alt_o A_69) C_34)))) of role axiom named fact_320_ord__eq__le__trans
% A new axiom: (forall (C_34:(produc1572197287le_alt->Prop)) (A_69:(produc1572197287le_alt->Prop)) (B_54:(produc1572197287le_alt->Prop)), ((((eq (produc1572197287le_alt->Prop)) A_69) B_54)->(((ord_le962286258_alt_o B_54) C_34)->((ord_le962286258_alt_o A_69) C_34))))
% FOF formula (forall (C_34:Prop) (B_54:Prop) (A_69:Prop), (((iff A_69) B_54)->(((ord_less_eq_o B_54) C_34)->((ord_less_eq_o A_69) C_34)))) of role axiom named fact_321_ord__eq__le__trans
% A new axiom: (forall (C_34:Prop) (B_54:Prop) (A_69:Prop), (((iff A_69) B_54)->(((ord_less_eq_o B_54) C_34)->((ord_less_eq_o A_69) C_34))))
% FOF formula (forall (C_34:(arrow_1196572341e_indi->Prop)) (A_69:(arrow_1196572341e_indi->Prop)) (B_54:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_69) B_54)->(((ord_le865407012indi_o B_54) C_34)->((ord_le865407012indi_o A_69) C_34)))) of role axiom named fact_322_ord__eq__le__trans
% A new axiom: (forall (C_34:(arrow_1196572341e_indi->Prop)) (A_69:(arrow_1196572341e_indi->Prop)) (B_54:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_69) B_54)->(((ord_le865407012indi_o B_54) C_34)->((ord_le865407012indi_o A_69) C_34))))
% FOF formula (forall (C_34:(product_unit->Prop)) (A_69:(product_unit->Prop)) (B_54:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_69) B_54)->(((ord_le1511552390unit_o B_54) C_34)->((ord_le1511552390unit_o A_69) C_34)))) of role axiom named fact_323_ord__eq__le__trans
% A new axiom: (forall (C_34:(product_unit->Prop)) (A_69:(product_unit->Prop)) (B_54:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_69) B_54)->(((ord_le1511552390unit_o B_54) C_34)->((ord_le1511552390unit_o A_69) C_34))))
% FOF formula (forall (C_34:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_69:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_54:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_69) B_54)->(((ord_le1463467535_alt_o B_54) C_34)->((ord_le1463467535_alt_o A_69) C_34)))) of role axiom named fact_324_ord__eq__le__trans
% A new axiom: (forall (C_34:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_69:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_54:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_69) B_54)->(((ord_le1463467535_alt_o B_54) C_34)->((ord_le1463467535_alt_o A_69) C_34))))
% FOF formula (forall (C_34:nat) (A_69:nat) (B_54:nat), ((((eq nat) A_69) B_54)->(((ord_less_eq_nat B_54) C_34)->((ord_less_eq_nat A_69) C_34)))) of role axiom named fact_325_ord__eq__le__trans
% A new axiom: (forall (C_34:nat) (A_69:nat) (B_54:nat), ((((eq nat) A_69) B_54)->(((ord_less_eq_nat B_54) C_34)->((ord_less_eq_nat A_69) C_34))))
% FOF formula (forall (C_34:(nat->Prop)) (A_69:(nat->Prop)) (B_54:(nat->Prop)), ((((eq (nat->Prop)) A_69) B_54)->(((ord_less_eq_nat_o B_54) C_34)->((ord_less_eq_nat_o A_69) C_34)))) of role axiom named fact_326_ord__eq__le__trans
% A new axiom: (forall (C_34:(nat->Prop)) (A_69:(nat->Prop)) (B_54:(nat->Prop)), ((((eq (nat->Prop)) A_69) B_54)->(((ord_less_eq_nat_o B_54) C_34)->((ord_less_eq_nat_o A_69) C_34))))
% FOF formula (forall (Y_28:((produc1572197287le_alt->Prop)->Prop)) (X_38:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_28) X_38)->((iff ((ord_le1027220427lt_o_o X_38) Y_28)) (((eq ((produc1572197287le_alt->Prop)->Prop)) X_38) Y_28)))) of role axiom named fact_327_order__antisym__conv
% A new axiom: (forall (Y_28:((produc1572197287le_alt->Prop)->Prop)) (X_38:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_28) X_38)->((iff ((ord_le1027220427lt_o_o X_38) Y_28)) (((eq ((produc1572197287le_alt->Prop)->Prop)) X_38) Y_28))))
% FOF formula (forall (Y_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_38:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_28) X_38)->((iff ((ord_le1805007862lt_o_o X_38) Y_28)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_38) Y_28)))) of role axiom named fact_328_order__antisym__conv
% A new axiom: (forall (Y_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_38:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_28) X_38)->((iff ((ord_le1805007862lt_o_o X_38) Y_28)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_38) Y_28))))
% FOF formula (forall (Y_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_38:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_28) X_38)->((iff ((ord_le602483040lt_o_o X_38) Y_28)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_38) Y_28)))) of role axiom named fact_329_order__antisym__conv
% A new axiom: (forall (Y_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_38:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_28) X_38)->((iff ((ord_le602483040lt_o_o X_38) Y_28)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_38) Y_28))))
% FOF formula (forall (Y_28:(produc1572197287le_alt->Prop)) (X_38:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_28) X_38)->((iff ((ord_le962286258_alt_o X_38) Y_28)) (((eq (produc1572197287le_alt->Prop)) X_38) Y_28)))) of role axiom named fact_330_order__antisym__conv
% A new axiom: (forall (Y_28:(produc1572197287le_alt->Prop)) (X_38:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_28) X_38)->((iff ((ord_le962286258_alt_o X_38) Y_28)) (((eq (produc1572197287le_alt->Prop)) X_38) Y_28))))
% FOF formula (forall (Y_28:Prop) (X_38:Prop), (((ord_less_eq_o Y_28) X_38)->((iff ((ord_less_eq_o X_38) Y_28)) ((iff X_38) Y_28)))) of role axiom named fact_331_order__antisym__conv
% A new axiom: (forall (Y_28:Prop) (X_38:Prop), (((ord_less_eq_o Y_28) X_38)->((iff ((ord_less_eq_o X_38) Y_28)) ((iff X_38) Y_28))))
% FOF formula (forall (Y_28:(arrow_1196572341e_indi->Prop)) (X_38:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_28) X_38)->((iff ((ord_le865407012indi_o X_38) Y_28)) (((eq (arrow_1196572341e_indi->Prop)) X_38) Y_28)))) of role axiom named fact_332_order__antisym__conv
% A new axiom: (forall (Y_28:(arrow_1196572341e_indi->Prop)) (X_38:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_28) X_38)->((iff ((ord_le865407012indi_o X_38) Y_28)) (((eq (arrow_1196572341e_indi->Prop)) X_38) Y_28))))
% FOF formula (forall (Y_28:(product_unit->Prop)) (X_38:(product_unit->Prop)), (((ord_le1511552390unit_o Y_28) X_38)->((iff ((ord_le1511552390unit_o X_38) Y_28)) (((eq (product_unit->Prop)) X_38) Y_28)))) of role axiom named fact_333_order__antisym__conv
% A new axiom: (forall (Y_28:(product_unit->Prop)) (X_38:(product_unit->Prop)), (((ord_le1511552390unit_o Y_28) X_38)->((iff ((ord_le1511552390unit_o X_38) Y_28)) (((eq (product_unit->Prop)) X_38) Y_28))))
% FOF formula (forall (Y_28:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_38:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_28) X_38)->((iff ((ord_le1463467535_alt_o X_38) Y_28)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_38) Y_28)))) of role axiom named fact_334_order__antisym__conv
% A new axiom: (forall (Y_28:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_38:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_28) X_38)->((iff ((ord_le1463467535_alt_o X_38) Y_28)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_38) Y_28))))
% FOF formula (forall (Y_28:nat) (X_38:nat), (((ord_less_eq_nat Y_28) X_38)->((iff ((ord_less_eq_nat X_38) Y_28)) (((eq nat) X_38) Y_28)))) of role axiom named fact_335_order__antisym__conv
% A new axiom: (forall (Y_28:nat) (X_38:nat), (((ord_less_eq_nat Y_28) X_38)->((iff ((ord_less_eq_nat X_38) Y_28)) (((eq nat) X_38) Y_28))))
% FOF formula (forall (Y_28:(nat->Prop)) (X_38:(nat->Prop)), (((ord_less_eq_nat_o Y_28) X_38)->((iff ((ord_less_eq_nat_o X_38) Y_28)) (((eq (nat->Prop)) X_38) Y_28)))) of role axiom named fact_336_order__antisym__conv
% A new axiom: (forall (Y_28:(nat->Prop)) (X_38:(nat->Prop)), (((ord_less_eq_nat_o Y_28) X_38)->((iff ((ord_less_eq_nat_o X_38) Y_28)) (((eq (nat->Prop)) X_38) Y_28))))
% FOF formula (forall (X_37:(produc1572197287le_alt->Prop)) (F_26:((produc1572197287le_alt->Prop)->Prop)) (G_4:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))) of role axiom named fact_337_le__funD
% A new axiom: (forall (X_37:(produc1572197287le_alt->Prop)) (F_26:((produc1572197287le_alt->Prop)->Prop)) (G_4:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37))))
% FOF formula (forall (X_37:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_26:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))) of role axiom named fact_338_le__funD
% A new axiom: (forall (X_37:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_26:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37))))
% FOF formula (forall (X_37:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_26:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))) of role axiom named fact_339_le__funD
% A new axiom: (forall (X_37:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_26:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37))))
% FOF formula (forall (X_37:produc1572197287le_alt) (F_26:(produc1572197287le_alt->Prop)) (G_4:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))) of role axiom named fact_340_le__funD
% A new axiom: (forall (X_37:produc1572197287le_alt) (F_26:(produc1572197287le_alt->Prop)) (G_4:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37))))
% FOF formula (forall (X_37:arrow_1196572341e_indi) (F_26:(arrow_1196572341e_indi->Prop)) (G_4:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))) of role axiom named fact_341_le__funD
% A new axiom: (forall (X_37:arrow_1196572341e_indi) (F_26:(arrow_1196572341e_indi->Prop)) (G_4:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37))))
% FOF formula (forall (X_37:product_unit) (F_26:(product_unit->Prop)) (G_4:(product_unit->Prop)), (((ord_le1511552390unit_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))) of role axiom named fact_342_le__funD
% A new axiom: (forall (X_37:product_unit) (F_26:(product_unit->Prop)) (G_4:(product_unit->Prop)), (((ord_le1511552390unit_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37))))
% FOF formula (forall (X_37:arrow_1389031998le_alt) (F_26:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_4:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o F_26) G_4)->((ord_le1423491573_alt_o (F_26 X_37)) (G_4 X_37)))) of role axiom named fact_343_le__funD
% A new axiom: (forall (X_37:arrow_1389031998le_alt) (F_26:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_4:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o F_26) G_4)->((ord_le1423491573_alt_o (F_26 X_37)) (G_4 X_37))))
% FOF formula (forall (X_37:nat) (F_26:(nat->Prop)) (G_4:(nat->Prop)), (((ord_less_eq_nat_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))) of role axiom named fact_344_le__funD
% A new axiom: (forall (X_37:nat) (F_26:(nat->Prop)) (G_4:(nat->Prop)), (((ord_less_eq_nat_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37))))
% FOF formula (forall (X_36:((produc1572197287le_alt->Prop)->Prop)) (Y_27:((produc1572197287le_alt->Prop)->Prop)), ((((eq ((produc1572197287le_alt->Prop)->Prop)) X_36) Y_27)->((ord_le1027220427lt_o_o X_36) Y_27))) of role axiom named fact_345_order__eq__refl
% A new axiom: (forall (X_36:((produc1572197287le_alt->Prop)->Prop)) (Y_27:((produc1572197287le_alt->Prop)->Prop)), ((((eq ((produc1572197287le_alt->Prop)->Prop)) X_36) Y_27)->((ord_le1027220427lt_o_o X_36) Y_27)))
% FOF formula (forall (X_36:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_27:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_36) Y_27)->((ord_le1805007862lt_o_o X_36) Y_27))) of role axiom named fact_346_order__eq__refl
% A new axiom: (forall (X_36:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_27:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_36) Y_27)->((ord_le1805007862lt_o_o X_36) Y_27)))
% FOF formula (forall (X_36:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_27:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_36) Y_27)->((ord_le602483040lt_o_o X_36) Y_27))) of role axiom named fact_347_order__eq__refl
% A new axiom: (forall (X_36:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_27:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_36) Y_27)->((ord_le602483040lt_o_o X_36) Y_27)))
% FOF formula (forall (X_36:(produc1572197287le_alt->Prop)) (Y_27:(produc1572197287le_alt->Prop)), ((((eq (produc1572197287le_alt->Prop)) X_36) Y_27)->((ord_le962286258_alt_o X_36) Y_27))) of role axiom named fact_348_order__eq__refl
% A new axiom: (forall (X_36:(produc1572197287le_alt->Prop)) (Y_27:(produc1572197287le_alt->Prop)), ((((eq (produc1572197287le_alt->Prop)) X_36) Y_27)->((ord_le962286258_alt_o X_36) Y_27)))
% FOF formula (forall (Y_27:Prop) (X_36:Prop), (((iff X_36) Y_27)->((ord_less_eq_o X_36) Y_27))) of role axiom named fact_349_order__eq__refl
% A new axiom: (forall (Y_27:Prop) (X_36:Prop), (((iff X_36) Y_27)->((ord_less_eq_o X_36) Y_27)))
% FOF formula (forall (X_36:(arrow_1196572341e_indi->Prop)) (Y_27:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) X_36) Y_27)->((ord_le865407012indi_o X_36) Y_27))) of role axiom named fact_350_order__eq__refl
% A new axiom: (forall (X_36:(arrow_1196572341e_indi->Prop)) (Y_27:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) X_36) Y_27)->((ord_le865407012indi_o X_36) Y_27)))
% FOF formula (forall (X_36:(product_unit->Prop)) (Y_27:(product_unit->Prop)), ((((eq (product_unit->Prop)) X_36) Y_27)->((ord_le1511552390unit_o X_36) Y_27))) of role axiom named fact_351_order__eq__refl
% A new axiom: (forall (X_36:(product_unit->Prop)) (Y_27:(product_unit->Prop)), ((((eq (product_unit->Prop)) X_36) Y_27)->((ord_le1511552390unit_o X_36) Y_27)))
% FOF formula (forall (X_36:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_27:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_36) Y_27)->((ord_le1463467535_alt_o X_36) Y_27))) of role axiom named fact_352_order__eq__refl
% A new axiom: (forall (X_36:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_27:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_36) Y_27)->((ord_le1463467535_alt_o X_36) Y_27)))
% FOF formula (forall (X_36:nat) (Y_27:nat), ((((eq nat) X_36) Y_27)->((ord_less_eq_nat X_36) Y_27))) of role axiom named fact_353_order__eq__refl
% A new axiom: (forall (X_36:nat) (Y_27:nat), ((((eq nat) X_36) Y_27)->((ord_less_eq_nat X_36) Y_27)))
% FOF formula (forall (X_36:(nat->Prop)) (Y_27:(nat->Prop)), ((((eq (nat->Prop)) X_36) Y_27)->((ord_less_eq_nat_o X_36) Y_27))) of role axiom named fact_354_order__eq__refl
% A new axiom: (forall (X_36:(nat->Prop)) (Y_27:(nat->Prop)), ((((eq (nat->Prop)) X_36) Y_27)->((ord_less_eq_nat_o X_36) Y_27)))
% FOF formula (forall (X_35:((produc1572197287le_alt->Prop)->Prop)) (Y_26:((produc1572197287le_alt->Prop)->Prop)), ((iff (((eq ((produc1572197287le_alt->Prop)->Prop)) X_35) Y_26)) ((and ((ord_le1027220427lt_o_o X_35) Y_26)) ((ord_le1027220427lt_o_o Y_26) X_35)))) of role axiom named fact_355_order__eq__iff
% A new axiom: (forall (X_35:((produc1572197287le_alt->Prop)->Prop)) (Y_26:((produc1572197287le_alt->Prop)->Prop)), ((iff (((eq ((produc1572197287le_alt->Prop)->Prop)) X_35) Y_26)) ((and ((ord_le1027220427lt_o_o X_35) Y_26)) ((ord_le1027220427lt_o_o Y_26) X_35))))
% FOF formula (forall (X_35:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_26:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_35) Y_26)) ((and ((ord_le1805007862lt_o_o X_35) Y_26)) ((ord_le1805007862lt_o_o Y_26) X_35)))) of role axiom named fact_356_order__eq__iff
% A new axiom: (forall (X_35:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_26:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_35) Y_26)) ((and ((ord_le1805007862lt_o_o X_35) Y_26)) ((ord_le1805007862lt_o_o Y_26) X_35))))
% FOF formula (forall (X_35:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_26:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_35) Y_26)) ((and ((ord_le602483040lt_o_o X_35) Y_26)) ((ord_le602483040lt_o_o Y_26) X_35)))) of role axiom named fact_357_order__eq__iff
% A new axiom: (forall (X_35:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_26:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_35) Y_26)) ((and ((ord_le602483040lt_o_o X_35) Y_26)) ((ord_le602483040lt_o_o Y_26) X_35))))
% FOF formula (forall (X_35:(produc1572197287le_alt->Prop)) (Y_26:(produc1572197287le_alt->Prop)), ((iff (((eq (produc1572197287le_alt->Prop)) X_35) Y_26)) ((and ((ord_le962286258_alt_o X_35) Y_26)) ((ord_le962286258_alt_o Y_26) X_35)))) of role axiom named fact_358_order__eq__iff
% A new axiom: (forall (X_35:(produc1572197287le_alt->Prop)) (Y_26:(produc1572197287le_alt->Prop)), ((iff (((eq (produc1572197287le_alt->Prop)) X_35) Y_26)) ((and ((ord_le962286258_alt_o X_35) Y_26)) ((ord_le962286258_alt_o Y_26) X_35))))
% FOF formula (forall (Y_26:Prop) (X_35:Prop), ((iff ((iff X_35) Y_26)) ((and ((ord_less_eq_o X_35) Y_26)) ((ord_less_eq_o Y_26) X_35)))) of role axiom named fact_359_order__eq__iff
% A new axiom: (forall (Y_26:Prop) (X_35:Prop), ((iff ((iff X_35) Y_26)) ((and ((ord_less_eq_o X_35) Y_26)) ((ord_less_eq_o Y_26) X_35))))
% FOF formula (forall (X_35:(arrow_1196572341e_indi->Prop)) (Y_26:(arrow_1196572341e_indi->Prop)), ((iff (((eq (arrow_1196572341e_indi->Prop)) X_35) Y_26)) ((and ((ord_le865407012indi_o X_35) Y_26)) ((ord_le865407012indi_o Y_26) X_35)))) of role axiom named fact_360_order__eq__iff
% A new axiom: (forall (X_35:(arrow_1196572341e_indi->Prop)) (Y_26:(arrow_1196572341e_indi->Prop)), ((iff (((eq (arrow_1196572341e_indi->Prop)) X_35) Y_26)) ((and ((ord_le865407012indi_o X_35) Y_26)) ((ord_le865407012indi_o Y_26) X_35))))
% FOF formula (forall (X_35:(product_unit->Prop)) (Y_26:(product_unit->Prop)), ((iff (((eq (product_unit->Prop)) X_35) Y_26)) ((and ((ord_le1511552390unit_o X_35) Y_26)) ((ord_le1511552390unit_o Y_26) X_35)))) of role axiom named fact_361_order__eq__iff
% A new axiom: (forall (X_35:(product_unit->Prop)) (Y_26:(product_unit->Prop)), ((iff (((eq (product_unit->Prop)) X_35) Y_26)) ((and ((ord_le1511552390unit_o X_35) Y_26)) ((ord_le1511552390unit_o Y_26) X_35))))
% FOF formula (forall (X_35:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_26:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_35) Y_26)) ((and ((ord_le1463467535_alt_o X_35) Y_26)) ((ord_le1463467535_alt_o Y_26) X_35)))) of role axiom named fact_362_order__eq__iff
% A new axiom: (forall (X_35:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_26:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_35) Y_26)) ((and ((ord_le1463467535_alt_o X_35) Y_26)) ((ord_le1463467535_alt_o Y_26) X_35))))
% FOF formula (forall (X_35:nat) (Y_26:nat), ((iff (((eq nat) X_35) Y_26)) ((and ((ord_less_eq_nat X_35) Y_26)) ((ord_less_eq_nat Y_26) X_35)))) of role axiom named fact_363_order__eq__iff
% A new axiom: (forall (X_35:nat) (Y_26:nat), ((iff (((eq nat) X_35) Y_26)) ((and ((ord_less_eq_nat X_35) Y_26)) ((ord_less_eq_nat Y_26) X_35))))
% FOF formula (forall (X_35:(nat->Prop)) (Y_26:(nat->Prop)), ((iff (((eq (nat->Prop)) X_35) Y_26)) ((and ((ord_less_eq_nat_o X_35) Y_26)) ((ord_less_eq_nat_o Y_26) X_35)))) of role axiom named fact_364_order__eq__iff
% A new axiom: (forall (X_35:(nat->Prop)) (Y_26:(nat->Prop)), ((iff (((eq (nat->Prop)) X_35) Y_26)) ((and ((ord_less_eq_nat_o X_35) Y_26)) ((ord_less_eq_nat_o Y_26) X_35))))
% FOF formula (forall (X_34:nat) (Y_25:nat), ((or ((ord_less_eq_nat X_34) Y_25)) ((ord_less_eq_nat Y_25) X_34))) of role axiom named fact_365_linorder__linear
% A new axiom: (forall (X_34:nat) (Y_25:nat), ((or ((ord_less_eq_nat X_34) Y_25)) ((ord_less_eq_nat Y_25) X_34)))
% FOF formula (forall (F_25:((produc1572197287le_alt->Prop)->Prop)) (G_3:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o F_25) G_3)) (forall (X_1:(produc1572197287le_alt->Prop)), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))) of role axiom named fact_366_le__fun__def
% A new axiom: (forall (F_25:((produc1572197287le_alt->Prop)->Prop)) (G_3:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o F_25) G_3)) (forall (X_1:(produc1572197287le_alt->Prop)), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1)))))
% FOF formula (forall (F_25:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o F_25) G_3)) (forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))) of role axiom named fact_367_le__fun__def
% A new axiom: (forall (F_25:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o F_25) G_3)) (forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1)))))
% FOF formula (forall (F_25:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o F_25) G_3)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))) of role axiom named fact_368_le__fun__def
% A new axiom: (forall (F_25:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o F_25) G_3)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1)))))
% FOF formula (forall (F_25:(produc1572197287le_alt->Prop)) (G_3:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o F_25) G_3)) (forall (X_1:produc1572197287le_alt), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))) of role axiom named fact_369_le__fun__def
% A new axiom: (forall (F_25:(produc1572197287le_alt->Prop)) (G_3:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o F_25) G_3)) (forall (X_1:produc1572197287le_alt), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1)))))
% FOF formula (forall (F_25:(arrow_1196572341e_indi->Prop)) (G_3:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o F_25) G_3)) (forall (X_1:arrow_1196572341e_indi), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))) of role axiom named fact_370_le__fun__def
% A new axiom: (forall (F_25:(arrow_1196572341e_indi->Prop)) (G_3:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o F_25) G_3)) (forall (X_1:arrow_1196572341e_indi), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1)))))
% FOF formula (forall (F_25:(product_unit->Prop)) (G_3:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o F_25) G_3)) (forall (X_1:product_unit), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))) of role axiom named fact_371_le__fun__def
% A new axiom: (forall (F_25:(product_unit->Prop)) (G_3:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o F_25) G_3)) (forall (X_1:product_unit), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1)))))
% FOF formula (forall (F_25:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_3:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1463467535_alt_o F_25) G_3)) (forall (X_1:arrow_1389031998le_alt), ((ord_le1423491573_alt_o (F_25 X_1)) (G_3 X_1))))) of role axiom named fact_372_le__fun__def
% A new axiom: (forall (F_25:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_3:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1463467535_alt_o F_25) G_3)) (forall (X_1:arrow_1389031998le_alt), ((ord_le1423491573_alt_o (F_25 X_1)) (G_3 X_1)))))
% FOF formula (forall (F_25:(nat->Prop)) (G_3:(nat->Prop)), ((iff ((ord_less_eq_nat_o F_25) G_3)) (forall (X_1:nat), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))) of role axiom named fact_373_le__fun__def
% A new axiom: (forall (F_25:(nat->Prop)) (G_3:(nat->Prop)), ((iff ((ord_less_eq_nat_o F_25) G_3)) (forall (X_1:nat), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1)))))
% FOF formula (forall (X_33:nat) (Y_24:nat), ((iff (((ord_less_nat X_33) Y_24)->False)) ((ord_less_eq_nat Y_24) X_33))) of role axiom named fact_374_linorder__not__less
% A new axiom: (forall (X_33:nat) (Y_24:nat), ((iff (((ord_less_nat X_33) Y_24)->False)) ((ord_less_eq_nat Y_24) X_33)))
% FOF formula (forall (X_32:nat) (Y_23:nat), ((iff (((ord_less_eq_nat X_32) Y_23)->False)) ((ord_less_nat Y_23) X_32))) of role axiom named fact_375_linorder__not__le
% A new axiom: (forall (X_32:nat) (Y_23:nat), ((iff (((ord_less_eq_nat X_32) Y_23)->False)) ((ord_less_nat Y_23) X_32)))
% FOF formula (forall (X_31:nat) (Y_22:nat), ((or ((ord_less_eq_nat X_31) Y_22)) ((ord_less_nat Y_22) X_31))) of role axiom named fact_376_linorder__le__less__linear
% A new axiom: (forall (X_31:nat) (Y_22:nat), ((or ((ord_less_eq_nat X_31) Y_22)) ((ord_less_nat Y_22) X_31)))
% 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)) (not (((eq (product_unit->Prop)) X_30) Y_21))))) of role axiom named fact_377_order__less__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)) (not (((eq (product_unit->Prop)) X_30) Y_21)))))
% FOF formula (forall (X_30:(arrow_1196572341e_indi->Prop)) (Y_21:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o X_30) Y_21)) ((and ((ord_le865407012indi_o X_30) Y_21)) (not (((eq (arrow_1196572341e_indi->Prop)) X_30) Y_21))))) of role axiom named fact_378_order__less__le
% A new axiom: (forall (X_30:(arrow_1196572341e_indi->Prop)) (Y_21:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o X_30) Y_21)) ((and ((ord_le865407012indi_o X_30) Y_21)) (not (((eq (arrow_1196572341e_indi->Prop)) X_30) Y_21)))))
% FOF formula (forall (X_30:((produc1572197287le_alt->Prop)->Prop)) (Y_21:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o X_30) Y_21)) ((and ((ord_le1027220427lt_o_o X_30) Y_21)) (not (((eq ((produc1572197287le_alt->Prop)->Prop)) X_30) Y_21))))) of role axiom named fact_379_order__less__le
% A new axiom: (forall (X_30:((produc1572197287le_alt->Prop)->Prop)) (Y_21:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o X_30) Y_21)) ((and ((ord_le1027220427lt_o_o X_30) Y_21)) (not (((eq ((produc1572197287le_alt->Prop)->Prop)) X_30) Y_21)))))
% FOF formula (forall (X_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o X_30) Y_21)) ((and ((ord_le1805007862lt_o_o X_30) Y_21)) (not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_30) Y_21))))) of role axiom named fact_380_order__less__le
% A new axiom: (forall (X_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o X_30) Y_21)) ((and ((ord_le1805007862lt_o_o X_30) Y_21)) (not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_30) Y_21)))))
% FOF formula (forall (X_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o X_30) Y_21)) ((and ((ord_le602483040lt_o_o X_30) Y_21)) (not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_30) Y_21))))) of role axiom named fact_381_order__less__le
% A new axiom: (forall (X_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o X_30) Y_21)) ((and ((ord_le602483040lt_o_o X_30) Y_21)) (not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_30) Y_21)))))
% FOF formula (forall (X_30:(produc1572197287le_alt->Prop)) (Y_21:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o X_30) Y_21)) ((and ((ord_le962286258_alt_o X_30) Y_21)) (not (((eq (produc1572197287le_alt->Prop)) X_30) Y_21))))) of role axiom named fact_382_order__less__le
% A new axiom: (forall (X_30:(produc1572197287le_alt->Prop)) (Y_21:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o X_30) Y_21)) ((and ((ord_le962286258_alt_o X_30) Y_21)) (not (((eq (produc1572197287le_alt->Prop)) X_30) Y_21)))))
% 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)) (((iff X_30) Y_21)->False)))) of role axiom named fact_383_order__less__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)) (((iff X_30) Y_21)->False))))
% FOF formula (forall (X_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1339521307_alt_o X_30) Y_21)) ((and ((ord_le1463467535_alt_o X_30) Y_21)) (not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_30) Y_21))))) of role axiom named fact_384_order__less__le
% A new axiom: (forall (X_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1339521307_alt_o X_30) Y_21)) ((and ((ord_le1463467535_alt_o X_30) Y_21)) (not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_30) Y_21)))))
% 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)) (not (((eq (nat->Prop)) X_30) Y_21))))) of role axiom named fact_385_order__less__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)) (not (((eq (nat->Prop)) X_30) Y_21)))))
% 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)) (not (((eq nat) X_30) Y_21))))) of role axiom named fact_386_order__less__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)) (not (((eq nat) X_30) Y_21)))))
% FOF formula (forall (X_29:(product_unit->Prop)) (Y_20:(product_unit->Prop)), ((iff ((ord_le232288914unit_o X_29) Y_20)) ((and ((ord_le1511552390unit_o X_29) Y_20)) (((ord_le1511552390unit_o Y_20) X_29)->False)))) of role axiom named fact_387_less__le__not__le
% A new axiom: (forall (X_29:(product_unit->Prop)) (Y_20:(product_unit->Prop)), ((iff ((ord_le232288914unit_o X_29) Y_20)) ((and ((ord_le1511552390unit_o X_29) Y_20)) (((ord_le1511552390unit_o Y_20) X_29)->False))))
% FOF formula (forall (X_29:(arrow_1196572341e_indi->Prop)) (Y_20:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o X_29) Y_20)) ((and ((ord_le865407012indi_o X_29) Y_20)) (((ord_le865407012indi_o Y_20) X_29)->False)))) of role axiom named fact_388_less__le__not__le
% A new axiom: (forall (X_29:(arrow_1196572341e_indi->Prop)) (Y_20:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o X_29) Y_20)) ((and ((ord_le865407012indi_o X_29) Y_20)) (((ord_le865407012indi_o Y_20) X_29)->False))))
% FOF formula (forall (X_29:((produc1572197287le_alt->Prop)->Prop)) (Y_20:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o X_29) Y_20)) ((and ((ord_le1027220427lt_o_o X_29) Y_20)) (((ord_le1027220427lt_o_o Y_20) X_29)->False)))) of role axiom named fact_389_less__le__not__le
% A new axiom: (forall (X_29:((produc1572197287le_alt->Prop)->Prop)) (Y_20:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o X_29) Y_20)) ((and ((ord_le1027220427lt_o_o X_29) Y_20)) (((ord_le1027220427lt_o_o Y_20) X_29)->False))))
% FOF formula (forall (X_29:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o X_29) Y_20)) ((and ((ord_le1805007862lt_o_o X_29) Y_20)) (((ord_le1805007862lt_o_o Y_20) X_29)->False)))) of role axiom named fact_390_less__le__not__le
% A new axiom: (forall (X_29:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o X_29) Y_20)) ((and ((ord_le1805007862lt_o_o X_29) Y_20)) (((ord_le1805007862lt_o_o Y_20) X_29)->False))))
% FOF formula (forall (X_29:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o X_29) Y_20)) ((and ((ord_le602483040lt_o_o X_29) Y_20)) (((ord_le602483040lt_o_o Y_20) X_29)->False)))) of role axiom named fact_391_less__le__not__le
% A new axiom: (forall (X_29:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o X_29) Y_20)) ((and ((ord_le602483040lt_o_o X_29) Y_20)) (((ord_le602483040lt_o_o Y_20) X_29)->False))))
% FOF formula (forall (X_29:(produc1572197287le_alt->Prop)) (Y_20:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o X_29) Y_20)) ((and ((ord_le962286258_alt_o X_29) Y_20)) (((ord_le962286258_alt_o Y_20) X_29)->False)))) of role axiom named fact_392_less__le__not__le
% A new axiom: (forall (X_29:(produc1572197287le_alt->Prop)) (Y_20:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o X_29) Y_20)) ((and ((ord_le962286258_alt_o X_29) Y_20)) (((ord_le962286258_alt_o Y_20) X_29)->False))))
% FOF formula (forall (X_29:Prop) (Y_20:Prop), ((iff ((ord_less_o X_29) Y_20)) ((and ((ord_less_eq_o X_29) Y_20)) (((ord_less_eq_o Y_20) X_29)->False)))) of role axiom named fact_393_less__le__not__le
% A new axiom: (forall (X_29:Prop) (Y_20:Prop), ((iff ((ord_less_o X_29) Y_20)) ((and ((ord_less_eq_o X_29) Y_20)) (((ord_less_eq_o Y_20) X_29)->False))))
% FOF formula (forall (X_29:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_20:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1339521307_alt_o X_29) Y_20)) ((and ((ord_le1463467535_alt_o X_29) Y_20)) (((ord_le1463467535_alt_o Y_20) X_29)->False)))) of role axiom named fact_394_less__le__not__le
% A new axiom: (forall (X_29:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_20:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1339521307_alt_o X_29) Y_20)) ((and ((ord_le1463467535_alt_o X_29) Y_20)) (((ord_le1463467535_alt_o Y_20) X_29)->False))))
% FOF formula (forall (X_29:(nat->Prop)) (Y_20:(nat->Prop)), ((iff ((ord_less_nat_o X_29) Y_20)) ((and ((ord_less_eq_nat_o X_29) Y_20)) (((ord_less_eq_nat_o Y_20) X_29)->False)))) of role axiom named fact_395_less__le__not__le
% A new axiom: (forall (X_29:(nat->Prop)) (Y_20:(nat->Prop)), ((iff ((ord_less_nat_o X_29) Y_20)) ((and ((ord_less_eq_nat_o X_29) Y_20)) (((ord_less_eq_nat_o Y_20) X_29)->False))))
% FOF formula (forall (X_29:nat) (Y_20:nat), ((iff ((ord_less_nat X_29) Y_20)) ((and ((ord_less_eq_nat X_29) Y_20)) (((ord_less_eq_nat Y_20) X_29)->False)))) of role axiom named fact_396_less__le__not__le
% A new axiom: (forall (X_29:nat) (Y_20:nat), ((iff ((ord_less_nat X_29) Y_20)) ((and ((ord_less_eq_nat X_29) Y_20)) (((ord_less_eq_nat Y_20) X_29)->False))))
% FOF formula (forall (X_28:(product_unit->Prop)) (Y_19:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o X_28) Y_19)) ((or ((ord_le232288914unit_o X_28) Y_19)) (((eq (product_unit->Prop)) X_28) Y_19)))) of role axiom named fact_397_order__le__less
% A new axiom: (forall (X_28:(product_unit->Prop)) (Y_19:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o X_28) Y_19)) ((or ((ord_le232288914unit_o X_28) Y_19)) (((eq (product_unit->Prop)) X_28) Y_19))))
% FOF formula (forall (X_28:(arrow_1196572341e_indi->Prop)) (Y_19:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o X_28) Y_19)) ((or ((ord_le1991507760indi_o X_28) Y_19)) (((eq (arrow_1196572341e_indi->Prop)) X_28) Y_19)))) of role axiom named fact_398_order__le__less
% A new axiom: (forall (X_28:(arrow_1196572341e_indi->Prop)) (Y_19:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o X_28) Y_19)) ((or ((ord_le1991507760indi_o X_28) Y_19)) (((eq (arrow_1196572341e_indi->Prop)) X_28) Y_19))))
% FOF formula (forall (X_28:((produc1572197287le_alt->Prop)->Prop)) (Y_19:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o X_28) Y_19)) ((or ((ord_le874404799lt_o_o X_28) Y_19)) (((eq ((produc1572197287le_alt->Prop)->Prop)) X_28) Y_19)))) of role axiom named fact_399_order__le__less
% A new axiom: (forall (X_28:((produc1572197287le_alt->Prop)->Prop)) (Y_19:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o X_28) Y_19)) ((or ((ord_le874404799lt_o_o X_28) Y_19)) (((eq ((produc1572197287le_alt->Prop)->Prop)) X_28) Y_19))))
% FOF formula (forall (X_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o X_28) Y_19)) ((or ((ord_le1382328578lt_o_o X_28) Y_19)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_28) Y_19)))) of role axiom named fact_400_order__le__less
% A new axiom: (forall (X_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o X_28) Y_19)) ((or ((ord_le1382328578lt_o_o X_28) Y_19)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_28) Y_19))))
% FOF formula (forall (X_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o X_28) Y_19)) ((or ((ord_le914873172lt_o_o X_28) Y_19)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_28) Y_19)))) of role axiom named fact_401_order__le__less
% A new axiom: (forall (X_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o X_28) Y_19)) ((or ((ord_le914873172lt_o_o X_28) Y_19)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_28) Y_19))))
% FOF formula (forall (X_28:(produc1572197287le_alt->Prop)) (Y_19:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o X_28) Y_19)) ((or ((ord_le1852932542_alt_o X_28) Y_19)) (((eq (produc1572197287le_alt->Prop)) X_28) Y_19)))) of role axiom named fact_402_order__le__less
% A new axiom: (forall (X_28:(produc1572197287le_alt->Prop)) (Y_19:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o X_28) Y_19)) ((or ((ord_le1852932542_alt_o X_28) Y_19)) (((eq (produc1572197287le_alt->Prop)) X_28) Y_19))))
% FOF formula (forall (X_28:Prop) (Y_19:Prop), ((iff ((ord_less_eq_o X_28) Y_19)) ((or ((ord_less_o X_28) Y_19)) ((iff X_28) Y_19)))) of role axiom named fact_403_order__le__less
% A new axiom: (forall (X_28:Prop) (Y_19:Prop), ((iff ((ord_less_eq_o X_28) Y_19)) ((or ((ord_less_o X_28) Y_19)) ((iff X_28) Y_19))))
% FOF formula (forall (X_28:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1463467535_alt_o X_28) Y_19)) ((or ((ord_le1339521307_alt_o X_28) Y_19)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_28) Y_19)))) of role axiom named fact_404_order__le__less
% A new axiom: (forall (X_28:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1463467535_alt_o X_28) Y_19)) ((or ((ord_le1339521307_alt_o X_28) Y_19)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_28) Y_19))))
% FOF formula (forall (X_28:(nat->Prop)) (Y_19:(nat->Prop)), ((iff ((ord_less_eq_nat_o X_28) Y_19)) ((or ((ord_less_nat_o X_28) Y_19)) (((eq (nat->Prop)) X_28) Y_19)))) of role axiom named fact_405_order__le__less
% A new axiom: (forall (X_28:(nat->Prop)) (Y_19:(nat->Prop)), ((iff ((ord_less_eq_nat_o X_28) Y_19)) ((or ((ord_less_nat_o X_28) Y_19)) (((eq (nat->Prop)) X_28) Y_19))))
% FOF formula (forall (X_28:nat) (Y_19:nat), ((iff ((ord_less_eq_nat X_28) Y_19)) ((or ((ord_less_nat X_28) Y_19)) (((eq nat) X_28) Y_19)))) of role axiom named fact_406_order__le__less
% A new axiom: (forall (X_28:nat) (Y_19:nat), ((iff ((ord_less_eq_nat X_28) Y_19)) ((or ((ord_less_nat X_28) Y_19)) (((eq nat) X_28) Y_19))))
% FOF formula (forall (X_27:nat) (Y_18:nat), ((((ord_less_nat X_27) Y_18)->False)->((ord_less_eq_nat Y_18) X_27))) of role axiom named fact_407_leI
% A new axiom: (forall (X_27:nat) (Y_18:nat), ((((ord_less_nat X_27) Y_18)->False)->((ord_less_eq_nat Y_18) X_27)))
% FOF formula (forall (Y_17:nat) (X_26:nat), ((((ord_less_eq_nat Y_17) X_26)->False)->((ord_less_nat X_26) Y_17))) of role axiom named fact_408_not__leE
% A new axiom: (forall (Y_17:nat) (X_26:nat), ((((ord_less_eq_nat Y_17) X_26)->False)->((ord_less_nat X_26) Y_17)))
% FOF formula (forall (X_25:nat) (Y_16:nat), ((((ord_less_nat X_25) Y_16)->False)->((iff ((ord_less_eq_nat X_25) Y_16)) (((eq nat) X_25) Y_16)))) of role axiom named fact_409_linorder__antisym__conv1
% A new axiom: (forall (X_25:nat) (Y_16:nat), ((((ord_less_nat X_25) Y_16)->False)->((iff ((ord_less_eq_nat X_25) Y_16)) (((eq nat) X_25) Y_16))))
% FOF formula (forall (A_68:(product_unit->Prop)) (B_53:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_68) B_53))->(((ord_le1511552390unit_o A_68) B_53)->((ord_le232288914unit_o A_68) B_53)))) of role axiom named fact_410_order__neq__le__trans
% A new axiom: (forall (A_68:(product_unit->Prop)) (B_53:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_68) B_53))->(((ord_le1511552390unit_o A_68) B_53)->((ord_le232288914unit_o A_68) B_53))))
% FOF formula (forall (A_68:(arrow_1196572341e_indi->Prop)) (B_53:(arrow_1196572341e_indi->Prop)), ((not (((eq (arrow_1196572341e_indi->Prop)) A_68) B_53))->(((ord_le865407012indi_o A_68) B_53)->((ord_le1991507760indi_o A_68) B_53)))) of role axiom named fact_411_order__neq__le__trans
% A new axiom: (forall (A_68:(arrow_1196572341e_indi->Prop)) (B_53:(arrow_1196572341e_indi->Prop)), ((not (((eq (arrow_1196572341e_indi->Prop)) A_68) B_53))->(((ord_le865407012indi_o A_68) B_53)->((ord_le1991507760indi_o A_68) B_53))))
% FOF formula (forall (A_68:((produc1572197287le_alt->Prop)->Prop)) (B_53:((produc1572197287le_alt->Prop)->Prop)), ((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_68) B_53))->(((ord_le1027220427lt_o_o A_68) B_53)->((ord_le874404799lt_o_o A_68) B_53)))) of role axiom named fact_412_order__neq__le__trans
% A new axiom: (forall (A_68:((produc1572197287le_alt->Prop)->Prop)) (B_53:((produc1572197287le_alt->Prop)->Prop)), ((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_68) B_53))->(((ord_le1027220427lt_o_o A_68) B_53)->((ord_le874404799lt_o_o A_68) B_53))))
% FOF formula (forall (A_68:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_53:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_68) B_53))->(((ord_le1805007862lt_o_o A_68) B_53)->((ord_le1382328578lt_o_o A_68) B_53)))) of role axiom named fact_413_order__neq__le__trans
% A new axiom: (forall (A_68:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_53:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_68) B_53))->(((ord_le1805007862lt_o_o A_68) B_53)->((ord_le1382328578lt_o_o A_68) B_53))))
% FOF formula (forall (A_68:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_53:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_68) B_53))->(((ord_le602483040lt_o_o A_68) B_53)->((ord_le914873172lt_o_o A_68) B_53)))) of role axiom named fact_414_order__neq__le__trans
% A new axiom: (forall (A_68:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_53:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_68) B_53))->(((ord_le602483040lt_o_o A_68) B_53)->((ord_le914873172lt_o_o A_68) B_53))))
% FOF formula (forall (A_68:(produc1572197287le_alt->Prop)) (B_53:(produc1572197287le_alt->Prop)), ((not (((eq (produc1572197287le_alt->Prop)) A_68) B_53))->(((ord_le962286258_alt_o A_68) B_53)->((ord_le1852932542_alt_o A_68) B_53)))) of role axiom named fact_415_order__neq__le__trans
% A new axiom: (forall (A_68:(produc1572197287le_alt->Prop)) (B_53:(produc1572197287le_alt->Prop)), ((not (((eq (produc1572197287le_alt->Prop)) A_68) B_53))->(((ord_le962286258_alt_o A_68) B_53)->((ord_le1852932542_alt_o A_68) B_53))))
% FOF formula (forall (B_53:Prop) (A_68:Prop), ((((iff A_68) B_53)->False)->(((ord_less_eq_o A_68) B_53)->((ord_less_o A_68) B_53)))) of role axiom named fact_416_order__neq__le__trans
% A new axiom: (forall (B_53:Prop) (A_68:Prop), ((((iff A_68) B_53)->False)->(((ord_less_eq_o A_68) B_53)->((ord_less_o A_68) B_53))))
% FOF formula (forall (A_68:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_53:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_68) B_53))->(((ord_le1463467535_alt_o A_68) B_53)->((ord_le1339521307_alt_o A_68) B_53)))) of role axiom named fact_417_order__neq__le__trans
% A new axiom: (forall (A_68:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_53:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_68) B_53))->(((ord_le1463467535_alt_o A_68) B_53)->((ord_le1339521307_alt_o A_68) B_53))))
% FOF formula (forall (A_68:(nat->Prop)) (B_53:(nat->Prop)), ((not (((eq (nat->Prop)) A_68) B_53))->(((ord_less_eq_nat_o A_68) B_53)->((ord_less_nat_o A_68) B_53)))) of role axiom named fact_418_order__neq__le__trans
% A new axiom: (forall (A_68:(nat->Prop)) (B_53:(nat->Prop)), ((not (((eq (nat->Prop)) A_68) B_53))->(((ord_less_eq_nat_o A_68) B_53)->((ord_less_nat_o A_68) B_53))))
% FOF formula (forall (A_68:nat) (B_53:nat), ((not (((eq nat) A_68) B_53))->(((ord_less_eq_nat A_68) B_53)->((ord_less_nat A_68) B_53)))) of role axiom named fact_419_order__neq__le__trans
% A new axiom: (forall (A_68:nat) (B_53:nat), ((not (((eq nat) A_68) B_53))->(((ord_less_eq_nat A_68) B_53)->((ord_less_nat A_68) B_53))))
% FOF formula (forall (A_67:(product_unit->Prop)) (B_52:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_67) B_52))->(((ord_le1511552390unit_o B_52) A_67)->((ord_le232288914unit_o B_52) A_67)))) of role axiom named fact_420_xt1_I12_J
% A new axiom: (forall (A_67:(product_unit->Prop)) (B_52:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_67) B_52))->(((ord_le1511552390unit_o B_52) A_67)->((ord_le232288914unit_o B_52) A_67))))
% FOF formula (forall (A_67:(arrow_1196572341e_indi->Prop)) (B_52:(arrow_1196572341e_indi->Prop)), ((not (((eq (arrow_1196572341e_indi->Prop)) A_67) B_52))->(((ord_le865407012indi_o B_52) A_67)->((ord_le1991507760indi_o B_52) A_67)))) of role axiom named fact_421_xt1_I12_J
% A new axiom: (forall (A_67:(arrow_1196572341e_indi->Prop)) (B_52:(arrow_1196572341e_indi->Prop)), ((not (((eq (arrow_1196572341e_indi->Prop)) A_67) B_52))->(((ord_le865407012indi_o B_52) A_67)->((ord_le1991507760indi_o B_52) A_67))))
% FOF formula (forall (A_67:((produc1572197287le_alt->Prop)->Prop)) (B_52:((produc1572197287le_alt->Prop)->Prop)), ((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_67) B_52))->(((ord_le1027220427lt_o_o B_52) A_67)->((ord_le874404799lt_o_o B_52) A_67)))) of role axiom named fact_422_xt1_I12_J
% A new axiom: (forall (A_67:((produc1572197287le_alt->Prop)->Prop)) (B_52:((produc1572197287le_alt->Prop)->Prop)), ((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_67) B_52))->(((ord_le1027220427lt_o_o B_52) A_67)->((ord_le874404799lt_o_o B_52) A_67))))
% FOF formula (forall (A_67:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_67) B_52))->(((ord_le1805007862lt_o_o B_52) A_67)->((ord_le1382328578lt_o_o B_52) A_67)))) of role axiom named fact_423_xt1_I12_J
% A new axiom: (forall (A_67:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_67) B_52))->(((ord_le1805007862lt_o_o B_52) A_67)->((ord_le1382328578lt_o_o B_52) A_67))))
% FOF formula (forall (A_67:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_67) B_52))->(((ord_le602483040lt_o_o B_52) A_67)->((ord_le914873172lt_o_o B_52) A_67)))) of role axiom named fact_424_xt1_I12_J
% A new axiom: (forall (A_67:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_67) B_52))->(((ord_le602483040lt_o_o B_52) A_67)->((ord_le914873172lt_o_o B_52) A_67))))
% FOF formula (forall (A_67:(produc1572197287le_alt->Prop)) (B_52:(produc1572197287le_alt->Prop)), ((not (((eq (produc1572197287le_alt->Prop)) A_67) B_52))->(((ord_le962286258_alt_o B_52) A_67)->((ord_le1852932542_alt_o B_52) A_67)))) of role axiom named fact_425_xt1_I12_J
% A new axiom: (forall (A_67:(produc1572197287le_alt->Prop)) (B_52:(produc1572197287le_alt->Prop)), ((not (((eq (produc1572197287le_alt->Prop)) A_67) B_52))->(((ord_le962286258_alt_o B_52) A_67)->((ord_le1852932542_alt_o B_52) A_67))))
% FOF formula (forall (B_52:Prop) (A_67:Prop), ((((iff A_67) B_52)->False)->(((ord_less_eq_o B_52) A_67)->((ord_less_o B_52) A_67)))) of role axiom named fact_426_xt1_I12_J
% A new axiom: (forall (B_52:Prop) (A_67:Prop), ((((iff A_67) B_52)->False)->(((ord_less_eq_o B_52) A_67)->((ord_less_o B_52) A_67))))
% FOF formula (forall (A_67:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_52:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_67) B_52))->(((ord_le1463467535_alt_o B_52) A_67)->((ord_le1339521307_alt_o B_52) A_67)))) of role axiom named fact_427_xt1_I12_J
% A new axiom: (forall (A_67:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_52:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_67) B_52))->(((ord_le1463467535_alt_o B_52) A_67)->((ord_le1339521307_alt_o B_52) A_67))))
% FOF formula (forall (A_67:(nat->Prop)) (B_52:(nat->Prop)), ((not (((eq (nat->Prop)) A_67) B_52))->(((ord_less_eq_nat_o B_52) A_67)->((ord_less_nat_o B_52) A_67)))) of role axiom named fact_428_xt1_I12_J
% A new axiom: (forall (A_67:(nat->Prop)) (B_52:(nat->Prop)), ((not (((eq (nat->Prop)) A_67) B_52))->(((ord_less_eq_nat_o B_52) A_67)->((ord_less_nat_o B_52) A_67))))
% FOF formula (forall (A_67:nat) (B_52:nat), ((not (((eq nat) A_67) B_52))->(((ord_less_eq_nat B_52) A_67)->((ord_less_nat B_52) A_67)))) of role axiom named fact_429_xt1_I12_J
% A new axiom: (forall (A_67:nat) (B_52:nat), ((not (((eq nat) A_67) B_52))->(((ord_less_eq_nat B_52) A_67)->((ord_less_nat B_52) A_67))))
% FOF formula (forall (Y_15:nat) (X_24:nat), (((ord_less_eq_nat Y_15) X_24)->(((ord_less_nat X_24) Y_15)->False))) of role axiom named fact_430_leD
% A new axiom: (forall (Y_15:nat) (X_24:nat), (((ord_less_eq_nat Y_15) X_24)->(((ord_less_nat X_24) Y_15)->False)))
% FOF formula (forall (X_23:(product_unit->Prop)) (Y_14:(product_unit->Prop)), (((ord_le232288914unit_o X_23) Y_14)->((ord_le1511552390unit_o X_23) Y_14))) of role axiom named fact_431_order__less__imp__le
% A new axiom: (forall (X_23:(product_unit->Prop)) (Y_14:(product_unit->Prop)), (((ord_le232288914unit_o X_23) Y_14)->((ord_le1511552390unit_o X_23) Y_14)))
% FOF formula (forall (X_23:(arrow_1196572341e_indi->Prop)) (Y_14:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_23) Y_14)->((ord_le865407012indi_o X_23) Y_14))) of role axiom named fact_432_order__less__imp__le
% A new axiom: (forall (X_23:(arrow_1196572341e_indi->Prop)) (Y_14:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_23) Y_14)->((ord_le865407012indi_o X_23) Y_14)))
% FOF formula (forall (X_23:((produc1572197287le_alt->Prop)->Prop)) (Y_14:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o X_23) Y_14)->((ord_le1027220427lt_o_o X_23) Y_14))) of role axiom named fact_433_order__less__imp__le
% A new axiom: (forall (X_23:((produc1572197287le_alt->Prop)->Prop)) (Y_14:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o X_23) Y_14)->((ord_le1027220427lt_o_o X_23) Y_14)))
% FOF formula (forall (X_23:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o X_23) Y_14)->((ord_le1805007862lt_o_o X_23) Y_14))) of role axiom named fact_434_order__less__imp__le
% A new axiom: (forall (X_23:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o X_23) Y_14)->((ord_le1805007862lt_o_o X_23) Y_14)))
% FOF formula (forall (X_23:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o X_23) Y_14)->((ord_le602483040lt_o_o X_23) Y_14))) of role axiom named fact_435_order__less__imp__le
% A new axiom: (forall (X_23:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o X_23) Y_14)->((ord_le602483040lt_o_o X_23) Y_14)))
% FOF formula (forall (X_23:(produc1572197287le_alt->Prop)) (Y_14:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o X_23) Y_14)->((ord_le962286258_alt_o X_23) Y_14))) of role axiom named fact_436_order__less__imp__le
% A new axiom: (forall (X_23:(produc1572197287le_alt->Prop)) (Y_14:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o X_23) Y_14)->((ord_le962286258_alt_o X_23) Y_14)))
% FOF formula (forall (X_23:Prop) (Y_14:Prop), (((ord_less_o X_23) Y_14)->((ord_less_eq_o X_23) Y_14))) of role axiom named fact_437_order__less__imp__le
% A new axiom: (forall (X_23:Prop) (Y_14:Prop), (((ord_less_o X_23) Y_14)->((ord_less_eq_o X_23) Y_14)))
% FOF formula (forall (X_23:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_14:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o X_23) Y_14)->((ord_le1463467535_alt_o X_23) Y_14))) of role axiom named fact_438_order__less__imp__le
% A new axiom: (forall (X_23:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_14:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o X_23) Y_14)->((ord_le1463467535_alt_o X_23) Y_14)))
% FOF formula (forall (X_23:(nat->Prop)) (Y_14:(nat->Prop)), (((ord_less_nat_o X_23) Y_14)->((ord_less_eq_nat_o X_23) Y_14))) of role axiom named fact_439_order__less__imp__le
% A new axiom: (forall (X_23:(nat->Prop)) (Y_14:(nat->Prop)), (((ord_less_nat_o X_23) Y_14)->((ord_less_eq_nat_o X_23) Y_14)))
% FOF formula (forall (X_23:nat) (Y_14:nat), (((ord_less_nat X_23) Y_14)->((ord_less_eq_nat X_23) Y_14))) of role axiom named fact_440_order__less__imp__le
% A new axiom: (forall (X_23:nat) (Y_14:nat), (((ord_less_nat X_23) Y_14)->((ord_less_eq_nat X_23) Y_14)))
% FOF formula (forall (X_22:nat) (Y_13:nat), (((ord_less_eq_nat X_22) Y_13)->((iff (((ord_less_nat X_22) Y_13)->False)) (((eq nat) X_22) Y_13)))) of role axiom named fact_441_linorder__antisym__conv2
% A new axiom: (forall (X_22:nat) (Y_13:nat), (((ord_less_eq_nat X_22) Y_13)->((iff (((ord_less_nat X_22) Y_13)->False)) (((eq nat) X_22) Y_13))))
% FOF formula (forall (X_21:(product_unit->Prop)) (Y_12:(product_unit->Prop)), (((ord_le1511552390unit_o X_21) Y_12)->((or ((ord_le232288914unit_o X_21) Y_12)) (((eq (product_unit->Prop)) X_21) Y_12)))) of role axiom named fact_442_order__le__imp__less__or__eq
% A new axiom: (forall (X_21:(product_unit->Prop)) (Y_12:(product_unit->Prop)), (((ord_le1511552390unit_o X_21) Y_12)->((or ((ord_le232288914unit_o X_21) Y_12)) (((eq (product_unit->Prop)) X_21) Y_12))))
% FOF formula (forall (X_21:(arrow_1196572341e_indi->Prop)) (Y_12:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_21) Y_12)->((or ((ord_le1991507760indi_o X_21) Y_12)) (((eq (arrow_1196572341e_indi->Prop)) X_21) Y_12)))) of role axiom named fact_443_order__le__imp__less__or__eq
% A new axiom: (forall (X_21:(arrow_1196572341e_indi->Prop)) (Y_12:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_21) Y_12)->((or ((ord_le1991507760indi_o X_21) Y_12)) (((eq (arrow_1196572341e_indi->Prop)) X_21) Y_12))))
% FOF formula (forall (X_21:((produc1572197287le_alt->Prop)->Prop)) (Y_12:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_21) Y_12)->((or ((ord_le874404799lt_o_o X_21) Y_12)) (((eq ((produc1572197287le_alt->Prop)->Prop)) X_21) Y_12)))) of role axiom named fact_444_order__le__imp__less__or__eq
% A new axiom: (forall (X_21:((produc1572197287le_alt->Prop)->Prop)) (Y_12:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_21) Y_12)->((or ((ord_le874404799lt_o_o X_21) Y_12)) (((eq ((produc1572197287le_alt->Prop)->Prop)) X_21) Y_12))))
% FOF formula (forall (X_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_12:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_21) Y_12)->((or ((ord_le1382328578lt_o_o X_21) Y_12)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_21) Y_12)))) of role axiom named fact_445_order__le__imp__less__or__eq
% A new axiom: (forall (X_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_12:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_21) Y_12)->((or ((ord_le1382328578lt_o_o X_21) Y_12)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_21) Y_12))))
% FOF formula (forall (X_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_21) Y_12)->((or ((ord_le914873172lt_o_o X_21) Y_12)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_21) Y_12)))) of role axiom named fact_446_order__le__imp__less__or__eq
% A new axiom: (forall (X_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_21) Y_12)->((or ((ord_le914873172lt_o_o X_21) Y_12)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_21) Y_12))))
% FOF formula (forall (X_21:(produc1572197287le_alt->Prop)) (Y_12:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_21) Y_12)->((or ((ord_le1852932542_alt_o X_21) Y_12)) (((eq (produc1572197287le_alt->Prop)) X_21) Y_12)))) of role axiom named fact_447_order__le__imp__less__or__eq
% A new axiom: (forall (X_21:(produc1572197287le_alt->Prop)) (Y_12:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_21) Y_12)->((or ((ord_le1852932542_alt_o X_21) Y_12)) (((eq (produc1572197287le_alt->Prop)) X_21) Y_12))))
% FOF formula (forall (X_21:Prop) (Y_12:Prop), (((ord_less_eq_o X_21) Y_12)->((or ((ord_less_o X_21) Y_12)) ((iff X_21) Y_12)))) of role axiom named fact_448_order__le__imp__less__or__eq
% A new axiom: (forall (X_21:Prop) (Y_12:Prop), (((ord_less_eq_o X_21) Y_12)->((or ((ord_less_o X_21) Y_12)) ((iff X_21) Y_12))))
% FOF formula (forall (X_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_12:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_21) Y_12)->((or ((ord_le1339521307_alt_o X_21) Y_12)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_21) Y_12)))) of role axiom named fact_449_order__le__imp__less__or__eq
% A new axiom: (forall (X_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_12:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_21) Y_12)->((or ((ord_le1339521307_alt_o X_21) Y_12)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_21) Y_12))))
% FOF formula (forall (X_21:(nat->Prop)) (Y_12:(nat->Prop)), (((ord_less_eq_nat_o X_21) Y_12)->((or ((ord_less_nat_o X_21) Y_12)) (((eq (nat->Prop)) X_21) Y_12)))) of role axiom named fact_450_order__le__imp__less__or__eq
% A new axiom: (forall (X_21:(nat->Prop)) (Y_12:(nat->Prop)), (((ord_less_eq_nat_o X_21) Y_12)->((or ((ord_less_nat_o X_21) Y_12)) (((eq (nat->Prop)) X_21) Y_12))))
% FOF formula (forall (X_21:nat) (Y_12:nat), (((ord_less_eq_nat X_21) Y_12)->((or ((ord_less_nat X_21) Y_12)) (((eq nat) X_21) Y_12)))) of role axiom named fact_451_order__le__imp__less__or__eq
% A new axiom: (forall (X_21:nat) (Y_12:nat), (((ord_less_eq_nat X_21) Y_12)->((or ((ord_less_nat X_21) Y_12)) (((eq nat) X_21) Y_12))))
% FOF formula (forall (A_66:(product_unit->Prop)) (B_51:(product_unit->Prop)), (((ord_le1511552390unit_o A_66) B_51)->((not (((eq (product_unit->Prop)) A_66) B_51))->((ord_le232288914unit_o A_66) B_51)))) of role axiom named fact_452_order__le__neq__trans
% A new axiom: (forall (A_66:(product_unit->Prop)) (B_51:(product_unit->Prop)), (((ord_le1511552390unit_o A_66) B_51)->((not (((eq (product_unit->Prop)) A_66) B_51))->((ord_le232288914unit_o A_66) B_51))))
% FOF formula (forall (A_66:(arrow_1196572341e_indi->Prop)) (B_51:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_66) B_51)->((not (((eq (arrow_1196572341e_indi->Prop)) A_66) B_51))->((ord_le1991507760indi_o A_66) B_51)))) of role axiom named fact_453_order__le__neq__trans
% A new axiom: (forall (A_66:(arrow_1196572341e_indi->Prop)) (B_51:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_66) B_51)->((not (((eq (arrow_1196572341e_indi->Prop)) A_66) B_51))->((ord_le1991507760indi_o A_66) B_51))))
% FOF formula (forall (A_66:((produc1572197287le_alt->Prop)->Prop)) (B_51:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_66) B_51)->((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_66) B_51))->((ord_le874404799lt_o_o A_66) B_51)))) of role axiom named fact_454_order__le__neq__trans
% A new axiom: (forall (A_66:((produc1572197287le_alt->Prop)->Prop)) (B_51:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_66) B_51)->((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_66) B_51))->((ord_le874404799lt_o_o A_66) B_51))))
% FOF formula (forall (A_66:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_51:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_66) B_51)->((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_66) B_51))->((ord_le1382328578lt_o_o A_66) B_51)))) of role axiom named fact_455_order__le__neq__trans
% A new axiom: (forall (A_66:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_51:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_66) B_51)->((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_66) B_51))->((ord_le1382328578lt_o_o A_66) B_51))))
% FOF formula (forall (A_66:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_51:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_66) B_51)->((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_66) B_51))->((ord_le914873172lt_o_o A_66) B_51)))) of role axiom named fact_456_order__le__neq__trans
% A new axiom: (forall (A_66:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_51:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_66) B_51)->((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_66) B_51))->((ord_le914873172lt_o_o A_66) B_51))))
% FOF formula (forall (A_66:(produc1572197287le_alt->Prop)) (B_51:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_66) B_51)->((not (((eq (produc1572197287le_alt->Prop)) A_66) B_51))->((ord_le1852932542_alt_o A_66) B_51)))) of role axiom named fact_457_order__le__neq__trans
% A new axiom: (forall (A_66:(produc1572197287le_alt->Prop)) (B_51:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_66) B_51)->((not (((eq (produc1572197287le_alt->Prop)) A_66) B_51))->((ord_le1852932542_alt_o A_66) B_51))))
% FOF formula (forall (A_66:Prop) (B_51:Prop), (((ord_less_eq_o A_66) B_51)->((((iff A_66) B_51)->False)->((ord_less_o A_66) B_51)))) of role axiom named fact_458_order__le__neq__trans
% A new axiom: (forall (A_66:Prop) (B_51:Prop), (((ord_less_eq_o A_66) B_51)->((((iff A_66) B_51)->False)->((ord_less_o A_66) B_51))))
% FOF formula (forall (A_66:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_51:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_66) B_51)->((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_66) B_51))->((ord_le1339521307_alt_o A_66) B_51)))) of role axiom named fact_459_order__le__neq__trans
% A new axiom: (forall (A_66:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_51:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_66) B_51)->((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_66) B_51))->((ord_le1339521307_alt_o A_66) B_51))))
% FOF formula (forall (A_66:(nat->Prop)) (B_51:(nat->Prop)), (((ord_less_eq_nat_o A_66) B_51)->((not (((eq (nat->Prop)) A_66) B_51))->((ord_less_nat_o A_66) B_51)))) of role axiom named fact_460_order__le__neq__trans
% A new axiom: (forall (A_66:(nat->Prop)) (B_51:(nat->Prop)), (((ord_less_eq_nat_o A_66) B_51)->((not (((eq (nat->Prop)) A_66) B_51))->((ord_less_nat_o A_66) B_51))))
% FOF formula (forall (A_66:nat) (B_51:nat), (((ord_less_eq_nat A_66) B_51)->((not (((eq nat) A_66) B_51))->((ord_less_nat A_66) B_51)))) of role axiom named fact_461_order__le__neq__trans
% A new axiom: (forall (A_66:nat) (B_51:nat), (((ord_less_eq_nat A_66) B_51)->((not (((eq nat) A_66) B_51))->((ord_less_nat A_66) B_51))))
% FOF formula (forall (B_50:(product_unit->Prop)) (A_65:(product_unit->Prop)), (((ord_le1511552390unit_o B_50) A_65)->((not (((eq (product_unit->Prop)) A_65) B_50))->((ord_le232288914unit_o B_50) A_65)))) of role axiom named fact_462_xt1_I11_J
% A new axiom: (forall (B_50:(product_unit->Prop)) (A_65:(product_unit->Prop)), (((ord_le1511552390unit_o B_50) A_65)->((not (((eq (product_unit->Prop)) A_65) B_50))->((ord_le232288914unit_o B_50) A_65))))
% FOF formula (forall (B_50:(arrow_1196572341e_indi->Prop)) (A_65:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_50) A_65)->((not (((eq (arrow_1196572341e_indi->Prop)) A_65) B_50))->((ord_le1991507760indi_o B_50) A_65)))) of role axiom named fact_463_xt1_I11_J
% A new axiom: (forall (B_50:(arrow_1196572341e_indi->Prop)) (A_65:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_50) A_65)->((not (((eq (arrow_1196572341e_indi->Prop)) A_65) B_50))->((ord_le1991507760indi_o B_50) A_65))))
% FOF formula (forall (B_50:((produc1572197287le_alt->Prop)->Prop)) (A_65:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_50) A_65)->((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_65) B_50))->((ord_le874404799lt_o_o B_50) A_65)))) of role axiom named fact_464_xt1_I11_J
% A new axiom: (forall (B_50:((produc1572197287le_alt->Prop)->Prop)) (A_65:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_50) A_65)->((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_65) B_50))->((ord_le874404799lt_o_o B_50) A_65))))
% FOF formula (forall (B_50:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_65:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_50) A_65)->((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_65) B_50))->((ord_le1382328578lt_o_o B_50) A_65)))) of role axiom named fact_465_xt1_I11_J
% A new axiom: (forall (B_50:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_65:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_50) A_65)->((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_65) B_50))->((ord_le1382328578lt_o_o B_50) A_65))))
% FOF formula (forall (B_50:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_65:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_50) A_65)->((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_65) B_50))->((ord_le914873172lt_o_o B_50) A_65)))) of role axiom named fact_466_xt1_I11_J
% A new axiom: (forall (B_50:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_65:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_50) A_65)->((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_65) B_50))->((ord_le914873172lt_o_o B_50) A_65))))
% FOF formula (forall (B_50:(produc1572197287le_alt->Prop)) (A_65:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_50) A_65)->((not (((eq (produc1572197287le_alt->Prop)) A_65) B_50))->((ord_le1852932542_alt_o B_50) A_65)))) of role axiom named fact_467_xt1_I11_J
% A new axiom: (forall (B_50:(produc1572197287le_alt->Prop)) (A_65:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_50) A_65)->((not (((eq (produc1572197287le_alt->Prop)) A_65) B_50))->((ord_le1852932542_alt_o B_50) A_65))))
% FOF formula (forall (B_50:Prop) (A_65:Prop), (((ord_less_eq_o B_50) A_65)->((((iff A_65) B_50)->False)->((ord_less_o B_50) A_65)))) of role axiom named fact_468_xt1_I11_J
% A new axiom: (forall (B_50:Prop) (A_65:Prop), (((ord_less_eq_o B_50) A_65)->((((iff A_65) B_50)->False)->((ord_less_o B_50) A_65))))
% FOF formula (forall (B_50:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_65:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_50) A_65)->((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_65) B_50))->((ord_le1339521307_alt_o B_50) A_65)))) of role axiom named fact_469_xt1_I11_J
% A new axiom: (forall (B_50:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_65:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_50) A_65)->((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_65) B_50))->((ord_le1339521307_alt_o B_50) A_65))))
% FOF formula (forall (B_50:(nat->Prop)) (A_65:(nat->Prop)), (((ord_less_eq_nat_o B_50) A_65)->((not (((eq (nat->Prop)) A_65) B_50))->((ord_less_nat_o B_50) A_65)))) of role axiom named fact_470_xt1_I11_J
% A new axiom: (forall (B_50:(nat->Prop)) (A_65:(nat->Prop)), (((ord_less_eq_nat_o B_50) A_65)->((not (((eq (nat->Prop)) A_65) B_50))->((ord_less_nat_o B_50) A_65))))
% FOF formula (forall (B_50:nat) (A_65:nat), (((ord_less_eq_nat B_50) A_65)->((not (((eq nat) A_65) B_50))->((ord_less_nat B_50) A_65)))) of role axiom named fact_471_xt1_I11_J
% A new axiom: (forall (B_50:nat) (A_65:nat), (((ord_less_eq_nat B_50) A_65)->((not (((eq nat) A_65) B_50))->((ord_less_nat B_50) A_65))))
% FOF formula (forall (Z_4:(product_unit->Prop)) (X_20:(product_unit->Prop)) (Y_11:(product_unit->Prop)), (((ord_le232288914unit_o X_20) Y_11)->(((ord_le1511552390unit_o Y_11) Z_4)->((ord_le232288914unit_o X_20) Z_4)))) of role axiom named fact_472_order__less__le__trans
% A new axiom: (forall (Z_4:(product_unit->Prop)) (X_20:(product_unit->Prop)) (Y_11:(product_unit->Prop)), (((ord_le232288914unit_o X_20) Y_11)->(((ord_le1511552390unit_o Y_11) Z_4)->((ord_le232288914unit_o X_20) Z_4))))
% FOF formula (forall (Z_4:(arrow_1196572341e_indi->Prop)) (X_20:(arrow_1196572341e_indi->Prop)) (Y_11:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_20) Y_11)->(((ord_le865407012indi_o Y_11) Z_4)->((ord_le1991507760indi_o X_20) Z_4)))) of role axiom named fact_473_order__less__le__trans
% A new axiom: (forall (Z_4:(arrow_1196572341e_indi->Prop)) (X_20:(arrow_1196572341e_indi->Prop)) (Y_11:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_20) Y_11)->(((ord_le865407012indi_o Y_11) Z_4)->((ord_le1991507760indi_o X_20) Z_4))))
% FOF formula (forall (Z_4:((produc1572197287le_alt->Prop)->Prop)) (X_20:((produc1572197287le_alt->Prop)->Prop)) (Y_11:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o X_20) Y_11)->(((ord_le1027220427lt_o_o Y_11) Z_4)->((ord_le874404799lt_o_o X_20) Z_4)))) of role axiom named fact_474_order__less__le__trans
% A new axiom: (forall (Z_4:((produc1572197287le_alt->Prop)->Prop)) (X_20:((produc1572197287le_alt->Prop)->Prop)) (Y_11:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o X_20) Y_11)->(((ord_le1027220427lt_o_o Y_11) Z_4)->((ord_le874404799lt_o_o X_20) Z_4))))
% FOF formula (forall (Z_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_11:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o X_20) Y_11)->(((ord_le1805007862lt_o_o Y_11) Z_4)->((ord_le1382328578lt_o_o X_20) Z_4)))) of role axiom named fact_475_order__less__le__trans
% A new axiom: (forall (Z_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_11:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o X_20) Y_11)->(((ord_le1805007862lt_o_o Y_11) Z_4)->((ord_le1382328578lt_o_o X_20) Z_4))))
% FOF formula (forall (Z_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_11:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o X_20) Y_11)->(((ord_le602483040lt_o_o Y_11) Z_4)->((ord_le914873172lt_o_o X_20) Z_4)))) of role axiom named fact_476_order__less__le__trans
% A new axiom: (forall (Z_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_11:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o X_20) Y_11)->(((ord_le602483040lt_o_o Y_11) Z_4)->((ord_le914873172lt_o_o X_20) Z_4))))
% FOF formula (forall (Z_4:(produc1572197287le_alt->Prop)) (X_20:(produc1572197287le_alt->Prop)) (Y_11:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o X_20) Y_11)->(((ord_le962286258_alt_o Y_11) Z_4)->((ord_le1852932542_alt_o X_20) Z_4)))) of role axiom named fact_477_order__less__le__trans
% A new axiom: (forall (Z_4:(produc1572197287le_alt->Prop)) (X_20:(produc1572197287le_alt->Prop)) (Y_11:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o X_20) Y_11)->(((ord_le962286258_alt_o Y_11) Z_4)->((ord_le1852932542_alt_o X_20) Z_4))))
% FOF formula (forall (Z_4:Prop) (X_20:Prop) (Y_11:Prop), (((ord_less_o X_20) Y_11)->(((ord_less_eq_o Y_11) Z_4)->((ord_less_o X_20) Z_4)))) of role axiom named fact_478_order__less__le__trans
% A new axiom: (forall (Z_4:Prop) (X_20:Prop) (Y_11:Prop), (((ord_less_o X_20) Y_11)->(((ord_less_eq_o Y_11) Z_4)->((ord_less_o X_20) Z_4))))
% FOF formula (forall (Z_4:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_20:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_11:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o X_20) Y_11)->(((ord_le1463467535_alt_o Y_11) Z_4)->((ord_le1339521307_alt_o X_20) Z_4)))) of role axiom named fact_479_order__less__le__trans
% A new axiom: (forall (Z_4:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_20:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_11:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o X_20) Y_11)->(((ord_le1463467535_alt_o Y_11) Z_4)->((ord_le1339521307_alt_o X_20) Z_4))))
% FOF formula (forall (Z_4:(nat->Prop)) (X_20:(nat->Prop)) (Y_11:(nat->Prop)), (((ord_less_nat_o X_20) Y_11)->(((ord_less_eq_nat_o Y_11) Z_4)->((ord_less_nat_o X_20) Z_4)))) of role axiom named fact_480_order__less__le__trans
% A new axiom: (forall (Z_4:(nat->Prop)) (X_20:(nat->Prop)) (Y_11:(nat->Prop)), (((ord_less_nat_o X_20) Y_11)->(((ord_less_eq_nat_o Y_11) Z_4)->((ord_less_nat_o X_20) Z_4))))
% FOF formula (forall (Z_4:nat) (X_20:nat) (Y_11:nat), (((ord_less_nat X_20) Y_11)->(((ord_less_eq_nat Y_11) Z_4)->((ord_less_nat X_20) Z_4)))) of role axiom named fact_481_order__less__le__trans
% A new axiom: (forall (Z_4:nat) (X_20:nat) (Y_11:nat), (((ord_less_nat X_20) Y_11)->(((ord_less_eq_nat Y_11) Z_4)->((ord_less_nat X_20) Z_4))))
% FOF formula (forall (Z_3:(product_unit->Prop)) (Y_10:(product_unit->Prop)) (X_19:(product_unit->Prop)), (((ord_le232288914unit_o Y_10) X_19)->(((ord_le1511552390unit_o Z_3) Y_10)->((ord_le232288914unit_o Z_3) X_19)))) of role axiom named fact_482_xt1_I7_J
% A new axiom: (forall (Z_3:(product_unit->Prop)) (Y_10:(product_unit->Prop)) (X_19:(product_unit->Prop)), (((ord_le232288914unit_o Y_10) X_19)->(((ord_le1511552390unit_o Z_3) Y_10)->((ord_le232288914unit_o Z_3) X_19))))
% FOF formula (forall (Z_3:(arrow_1196572341e_indi->Prop)) (Y_10:(arrow_1196572341e_indi->Prop)) (X_19:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_10) X_19)->(((ord_le865407012indi_o Z_3) Y_10)->((ord_le1991507760indi_o Z_3) X_19)))) of role axiom named fact_483_xt1_I7_J
% A new axiom: (forall (Z_3:(arrow_1196572341e_indi->Prop)) (Y_10:(arrow_1196572341e_indi->Prop)) (X_19:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_10) X_19)->(((ord_le865407012indi_o Z_3) Y_10)->((ord_le1991507760indi_o Z_3) X_19))))
% FOF formula (forall (Z_3:((produc1572197287le_alt->Prop)->Prop)) (Y_10:((produc1572197287le_alt->Prop)->Prop)) (X_19:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o Y_10) X_19)->(((ord_le1027220427lt_o_o Z_3) Y_10)->((ord_le874404799lt_o_o Z_3) X_19)))) of role axiom named fact_484_xt1_I7_J
% A new axiom: (forall (Z_3:((produc1572197287le_alt->Prop)->Prop)) (Y_10:((produc1572197287le_alt->Prop)->Prop)) (X_19:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o Y_10) X_19)->(((ord_le1027220427lt_o_o Z_3) Y_10)->((ord_le874404799lt_o_o Z_3) X_19))))
% FOF formula (forall (Z_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o Y_10) X_19)->(((ord_le1805007862lt_o_o Z_3) Y_10)->((ord_le1382328578lt_o_o Z_3) X_19)))) of role axiom named fact_485_xt1_I7_J
% A new axiom: (forall (Z_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o Y_10) X_19)->(((ord_le1805007862lt_o_o Z_3) Y_10)->((ord_le1382328578lt_o_o Z_3) X_19))))
% FOF formula (forall (Z_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_10:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o Y_10) X_19)->(((ord_le602483040lt_o_o Z_3) Y_10)->((ord_le914873172lt_o_o Z_3) X_19)))) of role axiom named fact_486_xt1_I7_J
% A new axiom: (forall (Z_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_10:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o Y_10) X_19)->(((ord_le602483040lt_o_o Z_3) Y_10)->((ord_le914873172lt_o_o Z_3) X_19))))
% FOF formula (forall (Z_3:(produc1572197287le_alt->Prop)) (Y_10:(produc1572197287le_alt->Prop)) (X_19:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o Y_10) X_19)->(((ord_le962286258_alt_o Z_3) Y_10)->((ord_le1852932542_alt_o Z_3) X_19)))) of role axiom named fact_487_xt1_I7_J
% A new axiom: (forall (Z_3:(produc1572197287le_alt->Prop)) (Y_10:(produc1572197287le_alt->Prop)) (X_19:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o Y_10) X_19)->(((ord_le962286258_alt_o Z_3) Y_10)->((ord_le1852932542_alt_o Z_3) X_19))))
% FOF formula (forall (Z_3:Prop) (Y_10:Prop) (X_19:Prop), (((ord_less_o Y_10) X_19)->(((ord_less_eq_o Z_3) Y_10)->((ord_less_o Z_3) X_19)))) of role axiom named fact_488_xt1_I7_J
% A new axiom: (forall (Z_3:Prop) (Y_10:Prop) (X_19:Prop), (((ord_less_o Y_10) X_19)->(((ord_less_eq_o Z_3) Y_10)->((ord_less_o Z_3) X_19))))
% FOF formula (forall (Z_3:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_10:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o Y_10) X_19)->(((ord_le1463467535_alt_o Z_3) Y_10)->((ord_le1339521307_alt_o Z_3) X_19)))) of role axiom named fact_489_xt1_I7_J
% A new axiom: (forall (Z_3:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_10:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o Y_10) X_19)->(((ord_le1463467535_alt_o Z_3) Y_10)->((ord_le1339521307_alt_o Z_3) X_19))))
% FOF formula (forall (Z_3:(nat->Prop)) (Y_10:(nat->Prop)) (X_19:(nat->Prop)), (((ord_less_nat_o Y_10) X_19)->(((ord_less_eq_nat_o Z_3) Y_10)->((ord_less_nat_o Z_3) X_19)))) of role axiom named fact_490_xt1_I7_J
% A new axiom: (forall (Z_3:(nat->Prop)) (Y_10:(nat->Prop)) (X_19:(nat->Prop)), (((ord_less_nat_o Y_10) X_19)->(((ord_less_eq_nat_o Z_3) Y_10)->((ord_less_nat_o Z_3) X_19))))
% FOF formula (forall (Z_3:nat) (Y_10:nat) (X_19:nat), (((ord_less_nat Y_10) X_19)->(((ord_less_eq_nat Z_3) Y_10)->((ord_less_nat Z_3) X_19)))) of role axiom named fact_491_xt1_I7_J
% A new axiom: (forall (Z_3:nat) (Y_10:nat) (X_19:nat), (((ord_less_nat Y_10) X_19)->(((ord_less_eq_nat Z_3) Y_10)->((ord_less_nat Z_3) X_19))))
% FOF formula (forall (Z_2:(product_unit->Prop)) (X_18:(product_unit->Prop)) (Y_9:(product_unit->Prop)), (((ord_le1511552390unit_o X_18) Y_9)->(((ord_le232288914unit_o Y_9) Z_2)->((ord_le232288914unit_o X_18) Z_2)))) of role axiom named fact_492_order__le__less__trans
% A new axiom: (forall (Z_2:(product_unit->Prop)) (X_18:(product_unit->Prop)) (Y_9:(product_unit->Prop)), (((ord_le1511552390unit_o X_18) Y_9)->(((ord_le232288914unit_o Y_9) Z_2)->((ord_le232288914unit_o X_18) Z_2))))
% FOF formula (forall (Z_2:(arrow_1196572341e_indi->Prop)) (X_18:(arrow_1196572341e_indi->Prop)) (Y_9:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_18) Y_9)->(((ord_le1991507760indi_o Y_9) Z_2)->((ord_le1991507760indi_o X_18) Z_2)))) of role axiom named fact_493_order__le__less__trans
% A new axiom: (forall (Z_2:(arrow_1196572341e_indi->Prop)) (X_18:(arrow_1196572341e_indi->Prop)) (Y_9:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_18) Y_9)->(((ord_le1991507760indi_o Y_9) Z_2)->((ord_le1991507760indi_o X_18) Z_2))))
% FOF formula (forall (Z_2:((produc1572197287le_alt->Prop)->Prop)) (X_18:((produc1572197287le_alt->Prop)->Prop)) (Y_9:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_18) Y_9)->(((ord_le874404799lt_o_o Y_9) Z_2)->((ord_le874404799lt_o_o X_18) Z_2)))) of role axiom named fact_494_order__le__less__trans
% A new axiom: (forall (Z_2:((produc1572197287le_alt->Prop)->Prop)) (X_18:((produc1572197287le_alt->Prop)->Prop)) (Y_9:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_18) Y_9)->(((ord_le874404799lt_o_o Y_9) Z_2)->((ord_le874404799lt_o_o X_18) Z_2))))
% FOF formula (forall (Z_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_18:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_9:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_18) Y_9)->(((ord_le1382328578lt_o_o Y_9) Z_2)->((ord_le1382328578lt_o_o X_18) Z_2)))) of role axiom named fact_495_order__le__less__trans
% A new axiom: (forall (Z_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_18:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_9:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_18) Y_9)->(((ord_le1382328578lt_o_o Y_9) Z_2)->((ord_le1382328578lt_o_o X_18) Z_2))))
% FOF formula (forall (Z_2:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_18:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_9:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_18) Y_9)->(((ord_le914873172lt_o_o Y_9) Z_2)->((ord_le914873172lt_o_o X_18) Z_2)))) of role axiom named fact_496_order__le__less__trans
% A new axiom: (forall (Z_2:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_18:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_9:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_18) Y_9)->(((ord_le914873172lt_o_o Y_9) Z_2)->((ord_le914873172lt_o_o X_18) Z_2))))
% FOF formula (forall (Z_2:(produc1572197287le_alt->Prop)) (X_18:(produc1572197287le_alt->Prop)) (Y_9:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_18) Y_9)->(((ord_le1852932542_alt_o Y_9) Z_2)->((ord_le1852932542_alt_o X_18) Z_2)))) of role axiom named fact_497_order__le__less__trans
% A new axiom: (forall (Z_2:(produc1572197287le_alt->Prop)) (X_18:(produc1572197287le_alt->Prop)) (Y_9:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_18) Y_9)->(((ord_le1852932542_alt_o Y_9) Z_2)->((ord_le1852932542_alt_o X_18) Z_2))))
% FOF formula (forall (Z_2:Prop) (X_18:Prop) (Y_9:Prop), (((ord_less_eq_o X_18) Y_9)->(((ord_less_o Y_9) Z_2)->((ord_less_o X_18) Z_2)))) of role axiom named fact_498_order__le__less__trans
% A new axiom: (forall (Z_2:Prop) (X_18:Prop) (Y_9:Prop), (((ord_less_eq_o X_18) Y_9)->(((ord_less_o Y_9) Z_2)->((ord_less_o X_18) Z_2))))
% FOF formula (forall (Z_2:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_18:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_9:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_18) Y_9)->(((ord_le1339521307_alt_o Y_9) Z_2)->((ord_le1339521307_alt_o X_18) Z_2)))) of role axiom named fact_499_order__le__less__trans
% A new axiom: (forall (Z_2:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_18:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_9:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_18) Y_9)->(((ord_le1339521307_alt_o Y_9) Z_2)->((ord_le1339521307_alt_o X_18) Z_2))))
% FOF formula (forall (Z_2:(nat->Prop)) (X_18:(nat->Prop)) (Y_9:(nat->Prop)), (((ord_less_eq_nat_o X_18) Y_9)->(((ord_less_nat_o Y_9) Z_2)->((ord_less_nat_o X_18) Z_2)))) of role axiom named fact_500_order__le__less__trans
% A new axiom: (forall (Z_2:(nat->Prop)) (X_18:(nat->Prop)) (Y_9:(nat->Prop)), (((ord_less_eq_nat_o X_18) Y_9)->(((ord_less_nat_o Y_9) Z_2)->((ord_less_nat_o X_18) Z_2))))
% FOF formula (forall (Z_2:nat) (X_18:nat) (Y_9:nat), (((ord_less_eq_nat X_18) Y_9)->(((ord_less_nat Y_9) Z_2)->((ord_less_nat X_18) Z_2)))) of role axiom named fact_501_order__le__less__trans
% A new axiom: (forall (Z_2:nat) (X_18:nat) (Y_9:nat), (((ord_less_eq_nat X_18) Y_9)->(((ord_less_nat Y_9) Z_2)->((ord_less_nat X_18) Z_2))))
% FOF formula (forall (Z_1:(product_unit->Prop)) (Y_8:(product_unit->Prop)) (X_17:(product_unit->Prop)), (((ord_le1511552390unit_o Y_8) X_17)->(((ord_le232288914unit_o Z_1) Y_8)->((ord_le232288914unit_o Z_1) X_17)))) of role axiom named fact_502_xt1_I8_J
% A new axiom: (forall (Z_1:(product_unit->Prop)) (Y_8:(product_unit->Prop)) (X_17:(product_unit->Prop)), (((ord_le1511552390unit_o Y_8) X_17)->(((ord_le232288914unit_o Z_1) Y_8)->((ord_le232288914unit_o Z_1) X_17))))
% FOF formula (forall (Z_1:(arrow_1196572341e_indi->Prop)) (Y_8:(arrow_1196572341e_indi->Prop)) (X_17:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_8) X_17)->(((ord_le1991507760indi_o Z_1) Y_8)->((ord_le1991507760indi_o Z_1) X_17)))) of role axiom named fact_503_xt1_I8_J
% A new axiom: (forall (Z_1:(arrow_1196572341e_indi->Prop)) (Y_8:(arrow_1196572341e_indi->Prop)) (X_17:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_8) X_17)->(((ord_le1991507760indi_o Z_1) Y_8)->((ord_le1991507760indi_o Z_1) X_17))))
% FOF formula (forall (Z_1:((produc1572197287le_alt->Prop)->Prop)) (Y_8:((produc1572197287le_alt->Prop)->Prop)) (X_17:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_8) X_17)->(((ord_le874404799lt_o_o Z_1) Y_8)->((ord_le874404799lt_o_o Z_1) X_17)))) of role axiom named fact_504_xt1_I8_J
% A new axiom: (forall (Z_1:((produc1572197287le_alt->Prop)->Prop)) (Y_8:((produc1572197287le_alt->Prop)->Prop)) (X_17:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_8) X_17)->(((ord_le874404799lt_o_o Z_1) Y_8)->((ord_le874404799lt_o_o Z_1) X_17))))
% FOF formula (forall (Z_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_17:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_8) X_17)->(((ord_le1382328578lt_o_o Z_1) Y_8)->((ord_le1382328578lt_o_o Z_1) X_17)))) of role axiom named fact_505_xt1_I8_J
% A new axiom: (forall (Z_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_17:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_8) X_17)->(((ord_le1382328578lt_o_o Z_1) Y_8)->((ord_le1382328578lt_o_o Z_1) X_17))))
% FOF formula (forall (Z_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_17:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_8) X_17)->(((ord_le914873172lt_o_o Z_1) Y_8)->((ord_le914873172lt_o_o Z_1) X_17)))) of role axiom named fact_506_xt1_I8_J
% A new axiom: (forall (Z_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_17:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_8) X_17)->(((ord_le914873172lt_o_o Z_1) Y_8)->((ord_le914873172lt_o_o Z_1) X_17))))
% FOF formula (forall (Z_1:(produc1572197287le_alt->Prop)) (Y_8:(produc1572197287le_alt->Prop)) (X_17:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_8) X_17)->(((ord_le1852932542_alt_o Z_1) Y_8)->((ord_le1852932542_alt_o Z_1) X_17)))) of role axiom named fact_507_xt1_I8_J
% A new axiom: (forall (Z_1:(produc1572197287le_alt->Prop)) (Y_8:(produc1572197287le_alt->Prop)) (X_17:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_8) X_17)->(((ord_le1852932542_alt_o Z_1) Y_8)->((ord_le1852932542_alt_o Z_1) X_17))))
% FOF formula (forall (Z_1:Prop) (Y_8:Prop) (X_17:Prop), (((ord_less_eq_o Y_8) X_17)->(((ord_less_o Z_1) Y_8)->((ord_less_o Z_1) X_17)))) of role axiom named fact_508_xt1_I8_J
% A new axiom: (forall (Z_1:Prop) (Y_8:Prop) (X_17:Prop), (((ord_less_eq_o Y_8) X_17)->(((ord_less_o Z_1) Y_8)->((ord_less_o Z_1) X_17))))
% FOF formula (forall (Z_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_8:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_17:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_8) X_17)->(((ord_le1339521307_alt_o Z_1) Y_8)->((ord_le1339521307_alt_o Z_1) X_17)))) of role axiom named fact_509_xt1_I8_J
% A new axiom: (forall (Z_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_8:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_17:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_8) X_17)->(((ord_le1339521307_alt_o Z_1) Y_8)->((ord_le1339521307_alt_o Z_1) X_17))))
% FOF formula (forall (Z_1:(nat->Prop)) (Y_8:(nat->Prop)) (X_17:(nat->Prop)), (((ord_less_eq_nat_o Y_8) X_17)->(((ord_less_nat_o Z_1) Y_8)->((ord_less_nat_o Z_1) X_17)))) of role axiom named fact_510_xt1_I8_J
% A new axiom: (forall (Z_1:(nat->Prop)) (Y_8:(nat->Prop)) (X_17:(nat->Prop)), (((ord_less_eq_nat_o Y_8) X_17)->(((ord_less_nat_o Z_1) Y_8)->((ord_less_nat_o Z_1) X_17))))
% FOF formula (forall (Z_1:nat) (Y_8:nat) (X_17:nat), (((ord_less_eq_nat Y_8) X_17)->(((ord_less_nat Z_1) Y_8)->((ord_less_nat Z_1) X_17)))) of role axiom named fact_511_xt1_I8_J
% A new axiom: (forall (Z_1:nat) (Y_8:nat) (X_17:nat), (((ord_less_eq_nat Y_8) X_17)->(((ord_less_nat Z_1) Y_8)->((ord_less_nat Z_1) X_17))))
% FOF formula (forall (A_64:((produc1572197287le_alt->Prop)->Prop)), ((ord_le1027220427lt_o_o A_64) top_to1806834203lt_o_o)) of role axiom named fact_512_top__greatest
% A new axiom: (forall (A_64:((produc1572197287le_alt->Prop)->Prop)), ((ord_le1027220427lt_o_o A_64) top_to1806834203lt_o_o))
% FOF formula (forall (A_64:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((ord_le602483040lt_o_o A_64) top_to732317616lt_o_o)) of role axiom named fact_513_top__greatest
% A new axiom: (forall (A_64:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((ord_le602483040lt_o_o A_64) top_to732317616lt_o_o))
% FOF formula (forall (A_64:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((ord_le1805007862lt_o_o A_64) top_to1492351398lt_o_o)) of role axiom named fact_514_top__greatest
% A new axiom: (forall (A_64:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((ord_le1805007862lt_o_o A_64) top_to1492351398lt_o_o))
% FOF formula (forall (A_64:Prop), ((ord_less_eq_o A_64) top_top_o)) of role axiom named fact_515_top__greatest
% A new axiom: (forall (A_64:Prop), ((ord_less_eq_o A_64) top_top_o))
% FOF formula (forall (A_64:(produc1572197287le_alt->Prop)), ((ord_le962286258_alt_o A_64) top_to558618722_alt_o)) of role axiom named fact_516_top__greatest
% A new axiom: (forall (A_64:(produc1572197287le_alt->Prop)), ((ord_le962286258_alt_o A_64) top_to558618722_alt_o))
% FOF formula (forall (A_64:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((ord_le1463467535_alt_o A_64) top_to1627321279_alt_o)) of role axiom named fact_517_top__greatest
% A new axiom: (forall (A_64:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((ord_le1463467535_alt_o A_64) top_to1627321279_alt_o))
% FOF formula (forall (A_64:(arrow_1196572341e_indi->Prop)), ((ord_le865407012indi_o A_64) top_to54564308indi_o)) of role axiom named fact_518_top__greatest
% A new axiom: (forall (A_64:(arrow_1196572341e_indi->Prop)), ((ord_le865407012indi_o A_64) top_to54564308indi_o))
% FOF formula (forall (A_64:(nat->Prop)), ((ord_less_eq_nat_o A_64) top_top_nat_o)) of role axiom named fact_519_top__greatest
% A new axiom: (forall (A_64:(nat->Prop)), ((ord_less_eq_nat_o A_64) top_top_nat_o))
% FOF formula (forall (A_64:(product_unit->Prop)), ((ord_le1511552390unit_o A_64) top_to1984820022unit_o)) of role axiom named fact_520_top__greatest
% A new axiom: (forall (A_64:(product_unit->Prop)), ((ord_le1511552390unit_o A_64) top_to1984820022unit_o))
% FOF formula (forall (A_63:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o top_to1806834203lt_o_o) A_63)) (((eq ((produc1572197287le_alt->Prop)->Prop)) A_63) top_to1806834203lt_o_o))) of role axiom named fact_521_top__unique
% A new axiom: (forall (A_63:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o top_to1806834203lt_o_o) A_63)) (((eq ((produc1572197287le_alt->Prop)->Prop)) A_63) top_to1806834203lt_o_o)))
% FOF formula (forall (A_63:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o top_to732317616lt_o_o) A_63)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_63) top_to732317616lt_o_o))) of role axiom named fact_522_top__unique
% A new axiom: (forall (A_63:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o top_to732317616lt_o_o) A_63)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_63) top_to732317616lt_o_o)))
% FOF formula (forall (A_63:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o top_to1492351398lt_o_o) A_63)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_63) top_to1492351398lt_o_o))) of role axiom named fact_523_top__unique
% A new axiom: (forall (A_63:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o top_to1492351398lt_o_o) A_63)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_63) top_to1492351398lt_o_o)))
% FOF formula (forall (A_63:Prop), ((iff ((ord_less_eq_o top_top_o) A_63)) ((iff A_63) top_top_o))) of role axiom named fact_524_top__unique
% A new axiom: (forall (A_63:Prop), ((iff ((ord_less_eq_o top_top_o) A_63)) ((iff A_63) top_top_o)))
% FOF formula (forall (A_63:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o top_to558618722_alt_o) A_63)) (((eq (produc1572197287le_alt->Prop)) A_63) top_to558618722_alt_o))) of role axiom named fact_525_top__unique
% A new axiom: (forall (A_63:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o top_to558618722_alt_o) A_63)) (((eq (produc1572197287le_alt->Prop)) A_63) top_to558618722_alt_o)))
% FOF formula (forall (A_63:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1463467535_alt_o top_to1627321279_alt_o) A_63)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_63) top_to1627321279_alt_o))) of role axiom named fact_526_top__unique
% A new axiom: (forall (A_63:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1463467535_alt_o top_to1627321279_alt_o) A_63)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_63) top_to1627321279_alt_o)))
% FOF formula (forall (A_63:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o top_to54564308indi_o) A_63)) (((eq (arrow_1196572341e_indi->Prop)) A_63) top_to54564308indi_o))) of role axiom named fact_527_top__unique
% A new axiom: (forall (A_63:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o top_to54564308indi_o) A_63)) (((eq (arrow_1196572341e_indi->Prop)) A_63) top_to54564308indi_o)))
% FOF formula (forall (A_63:(nat->Prop)), ((iff ((ord_less_eq_nat_o top_top_nat_o) A_63)) (((eq (nat->Prop)) A_63) top_top_nat_o))) of role axiom named fact_528_top__unique
% A new axiom: (forall (A_63:(nat->Prop)), ((iff ((ord_less_eq_nat_o top_top_nat_o) A_63)) (((eq (nat->Prop)) A_63) top_top_nat_o)))
% FOF formula (forall (A_63:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o top_to1984820022unit_o) A_63)) (((eq (product_unit->Prop)) A_63) top_to1984820022unit_o))) of role axiom named fact_529_top__unique
% A new axiom: (forall (A_63:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o top_to1984820022unit_o) A_63)) (((eq (product_unit->Prop)) A_63) top_to1984820022unit_o)))
% FOF formula (forall (A_62:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o top_to1806834203lt_o_o) A_62)->(((eq ((produc1572197287le_alt->Prop)->Prop)) A_62) top_to1806834203lt_o_o))) of role axiom named fact_530_top__le
% A new axiom: (forall (A_62:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o top_to1806834203lt_o_o) A_62)->(((eq ((produc1572197287le_alt->Prop)->Prop)) A_62) top_to1806834203lt_o_o)))
% FOF formula (forall (A_62:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o top_to732317616lt_o_o) A_62)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_62) top_to732317616lt_o_o))) of role axiom named fact_531_top__le
% A new axiom: (forall (A_62:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o top_to732317616lt_o_o) A_62)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_62) top_to732317616lt_o_o)))
% FOF formula (forall (A_62:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o top_to1492351398lt_o_o) A_62)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_62) top_to1492351398lt_o_o))) of role axiom named fact_532_top__le
% A new axiom: (forall (A_62:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o top_to1492351398lt_o_o) A_62)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_62) top_to1492351398lt_o_o)))
% FOF formula (forall (A_62:Prop), (((ord_less_eq_o top_top_o) A_62)->((iff A_62) top_top_o))) of role axiom named fact_533_top__le
% A new axiom: (forall (A_62:Prop), (((ord_less_eq_o top_top_o) A_62)->((iff A_62) top_top_o)))
% FOF formula (forall (A_62:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o top_to558618722_alt_o) A_62)->(((eq (produc1572197287le_alt->Prop)) A_62) top_to558618722_alt_o))) of role axiom named fact_534_top__le
% A new axiom: (forall (A_62:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o top_to558618722_alt_o) A_62)->(((eq (produc1572197287le_alt->Prop)) A_62) top_to558618722_alt_o)))
% FOF formula (forall (A_62:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o top_to1627321279_alt_o) A_62)->(((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_62) top_to1627321279_alt_o))) of role axiom named fact_535_top__le
% A new axiom: (forall (A_62:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o top_to1627321279_alt_o) A_62)->(((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_62) top_to1627321279_alt_o)))
% FOF formula (forall (A_62:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o top_to54564308indi_o) A_62)->(((eq (arrow_1196572341e_indi->Prop)) A_62) top_to54564308indi_o))) of role axiom named fact_536_top__le
% A new axiom: (forall (A_62:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o top_to54564308indi_o) A_62)->(((eq (arrow_1196572341e_indi->Prop)) A_62) top_to54564308indi_o)))
% FOF formula (forall (A_62:(nat->Prop)), (((ord_less_eq_nat_o top_top_nat_o) A_62)->(((eq (nat->Prop)) A_62) top_top_nat_o))) of role axiom named fact_537_top__le
% A new axiom: (forall (A_62:(nat->Prop)), (((ord_less_eq_nat_o top_top_nat_o) A_62)->(((eq (nat->Prop)) A_62) top_top_nat_o)))
% FOF formula (forall (A_62:(product_unit->Prop)), (((ord_le1511552390unit_o top_to1984820022unit_o) A_62)->(((eq (product_unit->Prop)) A_62) top_to1984820022unit_o))) of role axiom named fact_538_top__le
% A new axiom: (forall (A_62:(product_unit->Prop)), (((ord_le1511552390unit_o top_to1984820022unit_o) A_62)->(((eq (product_unit->Prop)) A_62) top_to1984820022unit_o)))
% FOF formula (forall (F_24:(arrow_1196572341e_indi->nat)) (A_61:(arrow_1196572341e_indi->Prop)), ((iff ((inj_on1505595958di_nat F_24) A_61)) (forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_61)->(forall (Xa:arrow_1196572341e_indi), (((member1818997282e_indi Xa) A_61)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq arrow_1196572341e_indi) X_1) Xa)))))))) of role axiom named fact_539_inj__on__def
% A new axiom: (forall (F_24:(arrow_1196572341e_indi->nat)) (A_61:(arrow_1196572341e_indi->Prop)), ((iff ((inj_on1505595958di_nat F_24) A_61)) (forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_61)->(forall (Xa:arrow_1196572341e_indi), (((member1818997282e_indi Xa) A_61)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq arrow_1196572341e_indi) X_1) Xa))))))))
% FOF formula (forall (F_24:(nat->nat)) (A_61:(nat->Prop)), ((iff ((inj_on_nat_nat F_24) A_61)) (forall (X_1:nat), (((member_nat X_1) A_61)->(forall (Xa:nat), (((member_nat Xa) A_61)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq nat) X_1) Xa)))))))) of role axiom named fact_540_inj__on__def
% A new axiom: (forall (F_24:(nat->nat)) (A_61:(nat->Prop)), ((iff ((inj_on_nat_nat F_24) A_61)) (forall (X_1:nat), (((member_nat X_1) A_61)->(forall (Xa:nat), (((member_nat Xa) A_61)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq nat) X_1) Xa))))))))
% FOF formula (forall (X_16:arrow_1196572341e_indi) (Y_7:arrow_1196572341e_indi) (F_23:(arrow_1196572341e_indi->nat)) (A_60:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_23) A_60)->((not (((eq arrow_1196572341e_indi) X_16) Y_7))->(((member1818997282e_indi X_16) A_60)->(((member1818997282e_indi Y_7) A_60)->(not (((eq nat) (F_23 X_16)) (F_23 Y_7)))))))) of role axiom named fact_541_inj__on__contraD
% A new axiom: (forall (X_16:arrow_1196572341e_indi) (Y_7:arrow_1196572341e_indi) (F_23:(arrow_1196572341e_indi->nat)) (A_60:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_23) A_60)->((not (((eq arrow_1196572341e_indi) X_16) Y_7))->(((member1818997282e_indi X_16) A_60)->(((member1818997282e_indi Y_7) A_60)->(not (((eq nat) (F_23 X_16)) (F_23 Y_7))))))))
% FOF formula (forall (X_16:nat) (Y_7:nat) (F_23:(nat->nat)) (A_60:(nat->Prop)), (((inj_on_nat_nat F_23) A_60)->((not (((eq nat) X_16) Y_7))->(((member_nat X_16) A_60)->(((member_nat Y_7) A_60)->(not (((eq nat) (F_23 X_16)) (F_23 Y_7)))))))) of role axiom named fact_542_inj__on__contraD
% A new axiom: (forall (X_16:nat) (Y_7:nat) (F_23:(nat->nat)) (A_60:(nat->Prop)), (((inj_on_nat_nat F_23) A_60)->((not (((eq nat) X_16) Y_7))->(((member_nat X_16) A_60)->(((member_nat Y_7) A_60)->(not (((eq nat) (F_23 X_16)) (F_23 Y_7))))))))
% FOF formula (forall (Y_6:arrow_1196572341e_indi) (X_15:arrow_1196572341e_indi) (F_22:(arrow_1196572341e_indi->nat)) (A_59:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_22) A_59)->(((member1818997282e_indi X_15) A_59)->(((member1818997282e_indi Y_6) A_59)->((iff (((eq nat) (F_22 X_15)) (F_22 Y_6))) (((eq arrow_1196572341e_indi) X_15) Y_6)))))) of role axiom named fact_543_inj__on__iff
% A new axiom: (forall (Y_6:arrow_1196572341e_indi) (X_15:arrow_1196572341e_indi) (F_22:(arrow_1196572341e_indi->nat)) (A_59:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_22) A_59)->(((member1818997282e_indi X_15) A_59)->(((member1818997282e_indi Y_6) A_59)->((iff (((eq nat) (F_22 X_15)) (F_22 Y_6))) (((eq arrow_1196572341e_indi) X_15) Y_6))))))
% FOF formula (forall (Y_6:nat) (X_15:nat) (F_22:(nat->nat)) (A_59:(nat->Prop)), (((inj_on_nat_nat F_22) A_59)->(((member_nat X_15) A_59)->(((member_nat Y_6) A_59)->((iff (((eq nat) (F_22 X_15)) (F_22 Y_6))) (((eq nat) X_15) Y_6)))))) of role axiom named fact_544_inj__on__iff
% A new axiom: (forall (Y_6:nat) (X_15:nat) (F_22:(nat->nat)) (A_59:(nat->Prop)), (((inj_on_nat_nat F_22) A_59)->(((member_nat X_15) A_59)->(((member_nat Y_6) A_59)->((iff (((eq nat) (F_22 X_15)) (F_22 Y_6))) (((eq nat) X_15) Y_6))))))
% FOF formula (forall (X_14:arrow_1196572341e_indi) (Y_5:arrow_1196572341e_indi) (F_21:(arrow_1196572341e_indi->nat)) (A_58:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_21) A_58)->((((eq nat) (F_21 X_14)) (F_21 Y_5))->(((member1818997282e_indi X_14) A_58)->(((member1818997282e_indi Y_5) A_58)->(((eq arrow_1196572341e_indi) X_14) Y_5)))))) of role axiom named fact_545_inj__onD
% A new axiom: (forall (X_14:arrow_1196572341e_indi) (Y_5:arrow_1196572341e_indi) (F_21:(arrow_1196572341e_indi->nat)) (A_58:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_21) A_58)->((((eq nat) (F_21 X_14)) (F_21 Y_5))->(((member1818997282e_indi X_14) A_58)->(((member1818997282e_indi Y_5) A_58)->(((eq arrow_1196572341e_indi) X_14) Y_5))))))
% FOF formula (forall (X_14:nat) (Y_5:nat) (F_21:(nat->nat)) (A_58:(nat->Prop)), (((inj_on_nat_nat F_21) A_58)->((((eq nat) (F_21 X_14)) (F_21 Y_5))->(((member_nat X_14) A_58)->(((member_nat Y_5) A_58)->(((eq nat) X_14) Y_5)))))) of role axiom named fact_546_inj__onD
% A new axiom: (forall (X_14:nat) (Y_5:nat) (F_21:(nat->nat)) (A_58:(nat->Prop)), (((inj_on_nat_nat F_21) A_58)->((((eq nat) (F_21 X_14)) (F_21 Y_5))->(((member_nat X_14) A_58)->(((member_nat Y_5) A_58)->(((eq nat) X_14) Y_5))))))
% FOF formula (forall (X_13:produc1572197287le_alt) (F_20:(produc1572197287le_alt->Prop)) (A_57:(produc1572197287le_alt->Prop)) (B_49:(produc1572197287le_alt->(Prop->Prop))), (((member1241905979_alt_o F_20) ((pi_Pro418549519_alt_o A_57) B_49))->(((member285112084le_alt X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_547_Pi__mem
% A new axiom: (forall (X_13:produc1572197287le_alt) (F_20:(produc1572197287le_alt->Prop)) (A_57:(produc1572197287le_alt->Prop)) (B_49:(produc1572197287le_alt->(Prop->Prop))), (((member1241905979_alt_o F_20) ((pi_Pro418549519_alt_o A_57) B_49))->(((member285112084le_alt X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:produc1572197287le_alt) (F_20:(produc1572197287le_alt->arrow_1196572341e_indi)) (A_57:(produc1572197287le_alt->Prop)) (B_49:(produc1572197287le_alt->(arrow_1196572341e_indi->Prop))), (((member1074431551e_indi F_20) ((pi_Pro1246947541e_indi A_57) B_49))->(((member285112084le_alt X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_548_Pi__mem
% A new axiom: (forall (X_13:produc1572197287le_alt) (F_20:(produc1572197287le_alt->arrow_1196572341e_indi)) (A_57:(produc1572197287le_alt->Prop)) (B_49:(produc1572197287le_alt->(arrow_1196572341e_indi->Prop))), (((member1074431551e_indi F_20) ((pi_Pro1246947541e_indi A_57) B_49))->(((member285112084le_alt X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:produc1572197287le_alt) (F_20:(produc1572197287le_alt->product_unit)) (A_57:(produc1572197287le_alt->Prop)) (B_49:(produc1572197287le_alt->(product_unit->Prop))), (((member44534621t_unit F_20) ((pi_Pro926528371t_unit A_57) B_49))->(((member285112084le_alt X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_549_Pi__mem
% A new axiom: (forall (X_13:produc1572197287le_alt) (F_20:(produc1572197287le_alt->product_unit)) (A_57:(produc1572197287le_alt->Prop)) (B_49:(produc1572197287le_alt->(product_unit->Prop))), (((member44534621t_unit F_20) ((pi_Pro926528371t_unit A_57) B_49))->(((member285112084le_alt X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1186582243e_indi F_20) ((pi_Arr272777533e_indi A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_550_Pi__mem
% A new axiom: (forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1186582243e_indi F_20) ((pi_Arr272777533e_indi A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1696373143lt_o_o F_20) ((pi_Arr1709554855lt_o_o A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_551_Pi__mem
% A new axiom: (forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1696373143lt_o_o F_20) ((pi_Arr1709554855lt_o_o A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1537523201t_unit F_20) ((pi_Arr509685723t_unit A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_552_Pi__mem
% A new axiom: (forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1537523201t_unit F_20) ((pi_Arr509685723t_unit A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_49:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1539010427e_indi F_20) ((pi_Arr470535441e_indi A_57) B_49))->(((member1425217232_alt_o X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_553_Pi__mem
% A new axiom: (forall (X_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_49:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1539010427e_indi F_20) ((pi_Arr470535441e_indi A_57) B_49))->(((member1425217232_alt_o X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_49:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1346253567lt_o_o F_20) ((pi_Arr1865419731lt_o_o A_57) B_49))->(((member1425217232_alt_o X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_554_Pi__mem
% A new axiom: (forall (X_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_49:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1346253567lt_o_o F_20) ((pi_Arr1865419731lt_o_o A_57) B_49))->(((member1425217232_alt_o X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (A_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_49:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1043380889t_unit F_20) ((pi_Arr2096782767t_unit A_57) B_49))->(((member1425217232_alt_o X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_555_Pi__mem
% A new axiom: (forall (X_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (A_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_49:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1043380889t_unit F_20) ((pi_Arr2096782767t_unit A_57) B_49))->(((member1425217232_alt_o X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:(produc1572197287le_alt->Prop)) (F_20:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (A_57:((produc1572197287le_alt->Prop)->Prop)) (B_49:((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))), (((member1830244024e_indi F_20) ((pi_Pro2039443474e_indi A_57) B_49))->(((member1241905979_alt_o X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_556_Pi__mem
% A new axiom: (forall (X_13:(produc1572197287le_alt->Prop)) (F_20:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (A_57:((produc1572197287le_alt->Prop)->Prop)) (B_49:((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))), (((member1830244024e_indi F_20) ((pi_Pro2039443474e_indi A_57) B_49))->(((member1241905979_alt_o X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:(produc1572197287le_alt->Prop)) (F_20:((produc1572197287le_alt->Prop)->Prop)) (A_57:((produc1572197287le_alt->Prop)->Prop)) (B_49:((produc1572197287le_alt->Prop)->(Prop->Prop))), (((member1925470338lt_o_o F_20) ((pi_Pro386796690lt_o_o A_57) B_49))->(((member1241905979_alt_o X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_557_Pi__mem
% A new axiom: (forall (X_13:(produc1572197287le_alt->Prop)) (F_20:((produc1572197287le_alt->Prop)->Prop)) (A_57:((produc1572197287le_alt->Prop)->Prop)) (B_49:((produc1572197287le_alt->Prop)->(Prop->Prop))), (((member1925470338lt_o_o F_20) ((pi_Pro386796690lt_o_o A_57) B_49))->(((member1241905979_alt_o X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:(produc1572197287le_alt->Prop)) (F_20:((produc1572197287le_alt->Prop)->product_unit)) (A_57:((produc1572197287le_alt->Prop)->Prop)) (B_49:((produc1572197287le_alt->Prop)->(product_unit->Prop))), (((member1092867670t_unit F_20) ((pi_Pro30504752t_unit A_57) B_49))->(((member1241905979_alt_o X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_558_Pi__mem
% A new axiom: (forall (X_13:(produc1572197287le_alt->Prop)) (F_20:((produc1572197287le_alt->Prop)->product_unit)) (A_57:((produc1572197287le_alt->Prop)->Prop)) (B_49:((produc1572197287le_alt->Prop)->(product_unit->Prop))), (((member1092867670t_unit F_20) ((pi_Pro30504752t_unit A_57) B_49))->(((member1241905979_alt_o X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:nat) (F_20:(nat->arrow_1196572341e_indi)) (A_57:(nat->Prop)) (B_49:(nat->(arrow_1196572341e_indi->Prop))), (((member1113138010e_indi F_20) ((pi_nat986275508e_indi A_57) B_49))->(((member_nat X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_559_Pi__mem
% A new axiom: (forall (X_13:nat) (F_20:(nat->arrow_1196572341e_indi)) (A_57:(nat->Prop)) (B_49:(nat->(arrow_1196572341e_indi->Prop))), (((member1113138010e_indi F_20) ((pi_nat986275508e_indi A_57) B_49))->(((member_nat X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:nat) (F_20:(nat->Prop)) (A_57:(nat->Prop)) (B_49:(nat->(Prop->Prop))), (((member_nat_o F_20) ((pi_nat_o A_57) B_49))->(((member_nat X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_560_Pi__mem
% A new axiom: (forall (X_13:nat) (F_20:(nat->Prop)) (A_57:(nat->Prop)) (B_49:(nat->(Prop->Prop))), (((member_nat_o F_20) ((pi_nat_o A_57) B_49))->(((member_nat X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:nat) (F_20:(nat->product_unit)) (A_57:(nat->Prop)) (B_49:(nat->(product_unit->Prop))), (((member616671224t_unit F_20) ((pi_nat_Product_unit A_57) B_49))->(((member_nat X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_561_Pi__mem
% A new axiom: (forall (X_13:nat) (F_20:(nat->product_unit)) (A_57:(nat->Prop)) (B_49:(nat->(product_unit->Prop))), (((member616671224t_unit F_20) ((pi_nat_Product_unit A_57) B_49))->(((member_nat X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->produc1572197287le_alt)) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member232085823le_alt F_20) ((pi_Arr1762714837le_alt A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member285112084le_alt (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_562_Pi__mem
% A new axiom: (forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->produc1572197287le_alt)) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member232085823le_alt F_20) ((pi_Arr1762714837le_alt A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member285112084le_alt (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:Prop) (F_20:(Prop->produc1572197287le_alt)) (A_57:(Prop->Prop)) (B_49:(Prop->(produc1572197287le_alt->Prop))), (((member1158049649le_alt F_20) ((pi_o_P728361163le_alt A_57) B_49))->(((member_o X_13) A_57)->((member285112084le_alt (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_563_Pi__mem
% A new axiom: (forall (X_13:Prop) (F_20:(Prop->produc1572197287le_alt)) (A_57:(Prop->Prop)) (B_49:(Prop->(produc1572197287le_alt->Prop))), (((member1158049649le_alt F_20) ((pi_o_P728361163le_alt A_57) B_49))->(((member_o X_13) A_57)->((member285112084le_alt (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:product_unit) (F_20:(product_unit->produc1572197287le_alt)) (A_57:(product_unit->Prop)) (B_49:(product_unit->(produc1572197287le_alt->Prop))), (((member1161214429le_alt F_20) ((pi_Pro772884595le_alt A_57) B_49))->(((member_Product_unit X_13) A_57)->((member285112084le_alt (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_564_Pi__mem
% A new axiom: (forall (X_13:product_unit) (F_20:(product_unit->produc1572197287le_alt)) (A_57:(product_unit->Prop)) (B_49:(product_unit->(produc1572197287le_alt->Prop))), (((member1161214429le_alt F_20) ((pi_Pro772884595le_alt A_57) B_49))->(((member_Product_unit X_13) A_57)->((member285112084le_alt (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2071265553_alt_o F_20) ((pi_Arr456308197_alt_o A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member822980838_alt_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_565_Pi__mem
% A new axiom: (forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2071265553_alt_o F_20) ((pi_Arr456308197_alt_o A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member822980838_alt_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:Prop) (F_20:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_57:(Prop->Prop)) (B_49:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member984757343_alt_o F_20) ((pi_o_A1479825007_alt_o A_57) B_49))->(((member_o X_13) A_57)->((member822980838_alt_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_566_Pi__mem
% A new axiom: (forall (X_13:Prop) (F_20:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_57:(Prop->Prop)) (B_49:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member984757343_alt_o F_20) ((pi_o_A1479825007_alt_o A_57) B_49))->(((member_o X_13) A_57)->((member822980838_alt_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:product_unit) (F_20:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_57:(product_unit->Prop)) (B_49:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2021528307_alt_o F_20) ((pi_Pro1959068871_alt_o A_57) B_49))->(((member_Product_unit X_13) A_57)->((member822980838_alt_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_567_Pi__mem
% A new axiom: (forall (X_13:product_unit) (F_20:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_57:(product_unit->Prop)) (B_49:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2021528307_alt_o F_20) ((pi_Pro1959068871_alt_o A_57) B_49))->(((member_Product_unit X_13) A_57)->((member822980838_alt_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1521294075_alt_o F_20) ((pi_Arr583278353_alt_o A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member1425217232_alt_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_568_Pi__mem
% A new axiom: (forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1521294075_alt_o F_20) ((pi_Arr583278353_alt_o A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member1425217232_alt_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:Prop) (F_20:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_57:(Prop->Prop)) (B_49:(Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member161783341_alt_o F_20) ((pi_o_A1994447367_alt_o A_57) B_49))->(((member_o X_13) A_57)->((member1425217232_alt_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_569_Pi__mem
% A new axiom: (forall (X_13:Prop) (F_20:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_57:(Prop->Prop)) (B_49:(Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member161783341_alt_o F_20) ((pi_o_A1994447367_alt_o A_57) B_49))->(((member_o X_13) A_57)->((member1425217232_alt_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:product_unit) (F_20:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_57:(product_unit->Prop)) (B_49:(product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1888392857_alt_o F_20) ((pi_Pro443817391_alt_o A_57) B_49))->(((member_Product_unit X_13) A_57)->((member1425217232_alt_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_570_Pi__mem
% A new axiom: (forall (X_13:product_unit) (F_20:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_57:(product_unit->Prop)) (B_49:(product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1888392857_alt_o F_20) ((pi_Pro443817391_alt_o A_57) B_49))->(((member_Product_unit X_13) A_57)->((member1425217232_alt_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:Prop) (F_20:(Prop->(produc1572197287le_alt->Prop))) (A_57:(Prop->Prop)) (B_49:(Prop->((produc1572197287le_alt->Prop)->Prop))), (((member1495989556_alt_o F_20) ((pi_o_P1417870404_alt_o A_57) B_49))->(((member_o X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_571_Pi__mem
% A new axiom: (forall (X_13:Prop) (F_20:(Prop->(produc1572197287le_alt->Prop))) (A_57:(Prop->Prop)) (B_49:(Prop->((produc1572197287le_alt->Prop)->Prop))), (((member1495989556_alt_o F_20) ((pi_o_P1417870404_alt_o A_57) B_49))->(((member_o X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:product_unit) (F_20:(product_unit->(produc1572197287le_alt->Prop))) (A_57:(product_unit->Prop)) (B_49:(product_unit->((produc1572197287le_alt->Prop)->Prop))), (((member1295651272_alt_o F_20) ((pi_Pro29851292_alt_o A_57) B_49))->(((member_Product_unit X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_572_Pi__mem
% A new axiom: (forall (X_13:product_unit) (F_20:(product_unit->(produc1572197287le_alt->Prop))) (A_57:(product_unit->Prop)) (B_49:(product_unit->((produc1572197287le_alt->Prop)->Prop))), (((member1295651272_alt_o F_20) ((pi_Pro29851292_alt_o A_57) B_49))->(((member_Product_unit X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->nat)) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->(nat->Prop))), (((member1842285448di_nat F_20) ((pi_Arr778514268di_nat A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member_nat (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_573_Pi__mem
% A new axiom: (forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->nat)) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->(nat->Prop))), (((member1842285448di_nat F_20) ((pi_Arr778514268di_nat A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member_nat (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:Prop) (F_20:(Prop->nat)) (A_57:(Prop->Prop)) (B_49:(Prop->(nat->Prop))), (((member_o_nat F_20) ((pi_o_nat A_57) B_49))->(((member_o X_13) A_57)->((member_nat (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_574_Pi__mem
% A new axiom: (forall (X_13:Prop) (F_20:(Prop->nat)) (A_57:(Prop->Prop)) (B_49:(Prop->(nat->Prop))), (((member_o_nat F_20) ((pi_o_nat A_57) B_49))->(((member_o X_13) A_57)->((member_nat (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:product_unit) (F_20:(product_unit->nat)) (A_57:(product_unit->Prop)) (B_49:(product_unit->(nat->Prop))), (((member1827227242it_nat F_20) ((pi_Product_unit_nat A_57) B_49))->(((member_Product_unit X_13) A_57)->((member_nat (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_575_Pi__mem
% A new axiom: (forall (X_13:product_unit) (F_20:(product_unit->nat)) (A_57:(product_unit->Prop)) (B_49:(product_unit->(nat->Prop))), (((member1827227242it_nat F_20) ((pi_Product_unit_nat A_57) B_49))->(((member_Product_unit X_13) A_57)->((member_nat (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))), (((member1425217232_alt_o F_20) ((pi_Arr1196397536_alt_o A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_576_Pi__mem
% A new axiom: (forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))), (((member1425217232_alt_o F_20) ((pi_Arr1196397536_alt_o A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))), (((member822980838_alt_o F_20) ((pi_Arr1309696186_alt_o A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13))))) of role axiom named fact_577_Pi__mem
% A new axiom: (forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))), (((member822980838_alt_o F_20) ((pi_Arr1309696186_alt_o A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13)))))
% FOF formula (forall (L_2:(produc1572197287le_alt->Prop)) (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) X) Y))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o (((arrow_1865170000_below L_2) X) Y)) arrow_1982173296le_Lin)))) of role axiom named fact_578_below__Lin
% A new axiom: (forall (L_2:(produc1572197287le_alt->Prop)) (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) X) Y))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o (((arrow_1865170000_below L_2) X) Y)) arrow_1982173296le_Lin))))
% FOF formula (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) arrow_1647925946e_Prof) ((pi_Arr1309696186_alt_o top_to54564308indi_o) (fun (Uu:arrow_1196572341e_indi)=> arrow_1982173296le_Lin))) of role axiom named fact_579_Prof__def
% A new axiom: (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) arrow_1647925946e_Prof) ((pi_Arr1309696186_alt_o top_to54564308indi_o) (fun (Uu:arrow_1196572341e_indi)=> arrow_1982173296le_Lin)))
% FOF formula (forall (A_56:(nat->Prop)), ((inj_on_nat_nat (fun (X_1:nat)=> X_1)) A_56)) of role axiom named fact_580_inj__on__id2
% A new axiom: (forall (A_56:(nat->Prop)), ((inj_on_nat_nat (fun (X_1:nat)=> X_1)) A_56))
% FOF formula (forall (X_12:produc1572197287le_alt) (F_19:(produc1572197287le_alt->Prop)) (A_55:(produc1572197287le_alt->Prop)) (B_48:(Prop->Prop)), (((member1241905979_alt_o F_19) ((pi_Pro418549519_alt_o A_55) (fun (Uu:produc1572197287le_alt)=> B_48)))->(((member285112084le_alt X_12) A_55)->((member_o (F_19 X_12)) B_48)))) of role axiom named fact_581_funcset__mem
% A new axiom: (forall (X_12:produc1572197287le_alt) (F_19:(produc1572197287le_alt->Prop)) (A_55:(produc1572197287le_alt->Prop)) (B_48:(Prop->Prop)), (((member1241905979_alt_o F_19) ((pi_Pro418549519_alt_o A_55) (fun (Uu:produc1572197287le_alt)=> B_48)))->(((member285112084le_alt X_12) A_55)->((member_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:produc1572197287le_alt) (F_19:(produc1572197287le_alt->arrow_1196572341e_indi)) (A_55:(produc1572197287le_alt->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1074431551e_indi F_19) ((pi_Pro1246947541e_indi A_55) (fun (Uu:produc1572197287le_alt)=> B_48)))->(((member285112084le_alt X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48)))) of role axiom named fact_582_funcset__mem
% A new axiom: (forall (X_12:produc1572197287le_alt) (F_19:(produc1572197287le_alt->arrow_1196572341e_indi)) (A_55:(produc1572197287le_alt->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1074431551e_indi F_19) ((pi_Pro1246947541e_indi A_55) (fun (Uu:produc1572197287le_alt)=> B_48)))->(((member285112084le_alt X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:produc1572197287le_alt) (F_19:(produc1572197287le_alt->product_unit)) (A_55:(produc1572197287le_alt->Prop)) (B_48:(product_unit->Prop)), (((member44534621t_unit F_19) ((pi_Pro926528371t_unit A_55) (fun (Uu:produc1572197287le_alt)=> B_48)))->(((member285112084le_alt X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48)))) of role axiom named fact_583_funcset__mem
% A new axiom: (forall (X_12:produc1572197287le_alt) (F_19:(produc1572197287le_alt->product_unit)) (A_55:(produc1572197287le_alt->Prop)) (B_48:(product_unit->Prop)), (((member44534621t_unit F_19) ((pi_Pro926528371t_unit A_55) (fun (Uu:produc1572197287le_alt)=> B_48)))->(((member285112084le_alt X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1186582243e_indi F_19) ((pi_Arr272777533e_indi A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48)))) of role axiom named fact_584_funcset__mem
% A new axiom: (forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1186582243e_indi F_19) ((pi_Arr272777533e_indi A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:(Prop->Prop)), (((member1696373143lt_o_o F_19) ((pi_Arr1709554855lt_o_o A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member_o (F_19 X_12)) B_48)))) of role axiom named fact_585_funcset__mem
% A new axiom: (forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:(Prop->Prop)), (((member1696373143lt_o_o F_19) ((pi_Arr1709554855lt_o_o A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:(product_unit->Prop)), (((member1537523201t_unit F_19) ((pi_Arr509685723t_unit A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48)))) of role axiom named fact_586_funcset__mem
% A new axiom: (forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:(product_unit->Prop)), (((member1537523201t_unit F_19) ((pi_Arr509685723t_unit A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1539010427e_indi F_19) ((pi_Arr470535441e_indi A_55) (fun (Uu:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> B_48)))->(((member1425217232_alt_o X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48)))) of role axiom named fact_587_funcset__mem
% A new axiom: (forall (X_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1539010427e_indi F_19) ((pi_Arr470535441e_indi A_55) (fun (Uu:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> B_48)))->(((member1425217232_alt_o X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_48:(Prop->Prop)), (((member1346253567lt_o_o F_19) ((pi_Arr1865419731lt_o_o A_55) (fun (Uu:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> B_48)))->(((member1425217232_alt_o X_12) A_55)->((member_o (F_19 X_12)) B_48)))) of role axiom named fact_588_funcset__mem
% A new axiom: (forall (X_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_48:(Prop->Prop)), (((member1346253567lt_o_o F_19) ((pi_Arr1865419731lt_o_o A_55) (fun (Uu:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> B_48)))->(((member1425217232_alt_o X_12) A_55)->((member_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (A_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_48:(product_unit->Prop)), (((member1043380889t_unit F_19) ((pi_Arr2096782767t_unit A_55) (fun (Uu:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> B_48)))->(((member1425217232_alt_o X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48)))) of role axiom named fact_589_funcset__mem
% A new axiom: (forall (X_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (A_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_48:(product_unit->Prop)), (((member1043380889t_unit F_19) ((pi_Arr2096782767t_unit A_55) (fun (Uu:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> B_48)))->(((member1425217232_alt_o X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:(produc1572197287le_alt->Prop)) (F_19:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (A_55:((produc1572197287le_alt->Prop)->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1830244024e_indi F_19) ((pi_Pro2039443474e_indi A_55) (fun (Uu:(produc1572197287le_alt->Prop))=> B_48)))->(((member1241905979_alt_o X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48)))) of role axiom named fact_590_funcset__mem
% A new axiom: (forall (X_12:(produc1572197287le_alt->Prop)) (F_19:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (A_55:((produc1572197287le_alt->Prop)->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1830244024e_indi F_19) ((pi_Pro2039443474e_indi A_55) (fun (Uu:(produc1572197287le_alt->Prop))=> B_48)))->(((member1241905979_alt_o X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:(produc1572197287le_alt->Prop)) (F_19:((produc1572197287le_alt->Prop)->Prop)) (A_55:((produc1572197287le_alt->Prop)->Prop)) (B_48:(Prop->Prop)), (((member1925470338lt_o_o F_19) ((pi_Pro386796690lt_o_o A_55) (fun (Uu:(produc1572197287le_alt->Prop))=> B_48)))->(((member1241905979_alt_o X_12) A_55)->((member_o (F_19 X_12)) B_48)))) of role axiom named fact_591_funcset__mem
% A new axiom: (forall (X_12:(produc1572197287le_alt->Prop)) (F_19:((produc1572197287le_alt->Prop)->Prop)) (A_55:((produc1572197287le_alt->Prop)->Prop)) (B_48:(Prop->Prop)), (((member1925470338lt_o_o F_19) ((pi_Pro386796690lt_o_o A_55) (fun (Uu:(produc1572197287le_alt->Prop))=> B_48)))->(((member1241905979_alt_o X_12) A_55)->((member_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:(produc1572197287le_alt->Prop)) (F_19:((produc1572197287le_alt->Prop)->product_unit)) (A_55:((produc1572197287le_alt->Prop)->Prop)) (B_48:(product_unit->Prop)), (((member1092867670t_unit F_19) ((pi_Pro30504752t_unit A_55) (fun (Uu:(produc1572197287le_alt->Prop))=> B_48)))->(((member1241905979_alt_o X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48)))) of role axiom named fact_592_funcset__mem
% A new axiom: (forall (X_12:(produc1572197287le_alt->Prop)) (F_19:((produc1572197287le_alt->Prop)->product_unit)) (A_55:((produc1572197287le_alt->Prop)->Prop)) (B_48:(product_unit->Prop)), (((member1092867670t_unit F_19) ((pi_Pro30504752t_unit A_55) (fun (Uu:(produc1572197287le_alt->Prop))=> B_48)))->(((member1241905979_alt_o X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:nat) (F_19:(nat->arrow_1196572341e_indi)) (A_55:(nat->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1113138010e_indi F_19) ((pi_nat986275508e_indi A_55) (fun (Uu:nat)=> B_48)))->(((member_nat X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48)))) of role axiom named fact_593_funcset__mem
% A new axiom: (forall (X_12:nat) (F_19:(nat->arrow_1196572341e_indi)) (A_55:(nat->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1113138010e_indi F_19) ((pi_nat986275508e_indi A_55) (fun (Uu:nat)=> B_48)))->(((member_nat X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:nat) (F_19:(nat->Prop)) (A_55:(nat->Prop)) (B_48:(Prop->Prop)), (((member_nat_o F_19) ((pi_nat_o A_55) (fun (Uu:nat)=> B_48)))->(((member_nat X_12) A_55)->((member_o (F_19 X_12)) B_48)))) of role axiom named fact_594_funcset__mem
% A new axiom: (forall (X_12:nat) (F_19:(nat->Prop)) (A_55:(nat->Prop)) (B_48:(Prop->Prop)), (((member_nat_o F_19) ((pi_nat_o A_55) (fun (Uu:nat)=> B_48)))->(((member_nat X_12) A_55)->((member_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:nat) (F_19:(nat->product_unit)) (A_55:(nat->Prop)) (B_48:(product_unit->Prop)), (((member616671224t_unit F_19) ((pi_nat_Product_unit A_55) (fun (Uu:nat)=> B_48)))->(((member_nat X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48)))) of role axiom named fact_595_funcset__mem
% A new axiom: (forall (X_12:nat) (F_19:(nat->product_unit)) (A_55:(nat->Prop)) (B_48:(product_unit->Prop)), (((member616671224t_unit F_19) ((pi_nat_Product_unit A_55) (fun (Uu:nat)=> B_48)))->(((member_nat X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->produc1572197287le_alt)) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:(produc1572197287le_alt->Prop)), (((member232085823le_alt F_19) ((pi_Arr1762714837le_alt A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member285112084le_alt (F_19 X_12)) B_48)))) of role axiom named fact_596_funcset__mem
% A new axiom: (forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->produc1572197287le_alt)) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:(produc1572197287le_alt->Prop)), (((member232085823le_alt F_19) ((pi_Arr1762714837le_alt A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member285112084le_alt (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:Prop) (F_19:(Prop->produc1572197287le_alt)) (A_55:(Prop->Prop)) (B_48:(produc1572197287le_alt->Prop)), (((member1158049649le_alt F_19) ((pi_o_P728361163le_alt A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member285112084le_alt (F_19 X_12)) B_48)))) of role axiom named fact_597_funcset__mem
% A new axiom: (forall (X_12:Prop) (F_19:(Prop->produc1572197287le_alt)) (A_55:(Prop->Prop)) (B_48:(produc1572197287le_alt->Prop)), (((member1158049649le_alt F_19) ((pi_o_P728361163le_alt A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member285112084le_alt (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:product_unit) (F_19:(product_unit->produc1572197287le_alt)) (A_55:(product_unit->Prop)) (B_48:(produc1572197287le_alt->Prop)), (((member1161214429le_alt F_19) ((pi_Pro772884595le_alt A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member285112084le_alt (F_19 X_12)) B_48)))) of role axiom named fact_598_funcset__mem
% A new axiom: (forall (X_12:product_unit) (F_19:(product_unit->produc1572197287le_alt)) (A_55:(product_unit->Prop)) (B_48:(produc1572197287le_alt->Prop)), (((member1161214429le_alt F_19) ((pi_Pro772884595le_alt A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member285112084le_alt (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member2071265553_alt_o F_19) ((pi_Arr456308197_alt_o A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member822980838_alt_o (F_19 X_12)) B_48)))) of role axiom named fact_599_funcset__mem
% A new axiom: (forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member2071265553_alt_o F_19) ((pi_Arr456308197_alt_o A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member822980838_alt_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:Prop) (F_19:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_55:(Prop->Prop)) (B_48:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member984757343_alt_o F_19) ((pi_o_A1479825007_alt_o A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member822980838_alt_o (F_19 X_12)) B_48)))) of role axiom named fact_600_funcset__mem
% A new axiom: (forall (X_12:Prop) (F_19:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_55:(Prop->Prop)) (B_48:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member984757343_alt_o F_19) ((pi_o_A1479825007_alt_o A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member822980838_alt_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:product_unit) (F_19:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_55:(product_unit->Prop)) (B_48:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member2021528307_alt_o F_19) ((pi_Pro1959068871_alt_o A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member822980838_alt_o (F_19 X_12)) B_48)))) of role axiom named fact_601_funcset__mem
% A new axiom: (forall (X_12:product_unit) (F_19:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_55:(product_unit->Prop)) (B_48:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member2021528307_alt_o F_19) ((pi_Pro1959068871_alt_o A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member822980838_alt_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member1521294075_alt_o F_19) ((pi_Arr583278353_alt_o A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member1425217232_alt_o (F_19 X_12)) B_48)))) of role axiom named fact_602_funcset__mem
% A new axiom: (forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member1521294075_alt_o F_19) ((pi_Arr583278353_alt_o A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member1425217232_alt_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:Prop) (F_19:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_55:(Prop->Prop)) (B_48:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member161783341_alt_o F_19) ((pi_o_A1994447367_alt_o A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member1425217232_alt_o (F_19 X_12)) B_48)))) of role axiom named fact_603_funcset__mem
% A new axiom: (forall (X_12:Prop) (F_19:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_55:(Prop->Prop)) (B_48:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member161783341_alt_o F_19) ((pi_o_A1994447367_alt_o A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member1425217232_alt_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:product_unit) (F_19:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_55:(product_unit->Prop)) (B_48:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member1888392857_alt_o F_19) ((pi_Pro443817391_alt_o A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member1425217232_alt_o (F_19 X_12)) B_48)))) of role axiom named fact_604_funcset__mem
% A new axiom: (forall (X_12:product_unit) (F_19:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_55:(product_unit->Prop)) (B_48:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member1888392857_alt_o F_19) ((pi_Pro443817391_alt_o A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member1425217232_alt_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:Prop) (F_19:(Prop->(produc1572197287le_alt->Prop))) (A_55:(Prop->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member1495989556_alt_o F_19) ((pi_o_P1417870404_alt_o A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48)))) of role axiom named fact_605_funcset__mem
% A new axiom: (forall (X_12:Prop) (F_19:(Prop->(produc1572197287le_alt->Prop))) (A_55:(Prop->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member1495989556_alt_o F_19) ((pi_o_P1417870404_alt_o A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:product_unit) (F_19:(product_unit->(produc1572197287le_alt->Prop))) (A_55:(product_unit->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member1295651272_alt_o F_19) ((pi_Pro29851292_alt_o A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48)))) of role axiom named fact_606_funcset__mem
% A new axiom: (forall (X_12:product_unit) (F_19:(product_unit->(produc1572197287le_alt->Prop))) (A_55:(product_unit->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member1295651272_alt_o F_19) ((pi_Pro29851292_alt_o A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->nat)) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:(nat->Prop)), (((member1842285448di_nat F_19) ((pi_Arr778514268di_nat A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member_nat (F_19 X_12)) B_48)))) of role axiom named fact_607_funcset__mem
% A new axiom: (forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->nat)) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:(nat->Prop)), (((member1842285448di_nat F_19) ((pi_Arr778514268di_nat A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member_nat (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:Prop) (F_19:(Prop->nat)) (A_55:(Prop->Prop)) (B_48:(nat->Prop)), (((member_o_nat F_19) ((pi_o_nat A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member_nat (F_19 X_12)) B_48)))) of role axiom named fact_608_funcset__mem
% A new axiom: (forall (X_12:Prop) (F_19:(Prop->nat)) (A_55:(Prop->Prop)) (B_48:(nat->Prop)), (((member_o_nat F_19) ((pi_o_nat A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member_nat (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:product_unit) (F_19:(product_unit->nat)) (A_55:(product_unit->Prop)) (B_48:(nat->Prop)), (((member1827227242it_nat F_19) ((pi_Product_unit_nat A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member_nat (F_19 X_12)) B_48)))) of role axiom named fact_609_funcset__mem
% A new axiom: (forall (X_12:product_unit) (F_19:(product_unit->nat)) (A_55:(product_unit->Prop)) (B_48:(nat->Prop)), (((member1827227242it_nat F_19) ((pi_Product_unit_nat A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member_nat (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member1425217232_alt_o F_19) ((pi_Arr1196397536_alt_o A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48)))) of role axiom named fact_610_funcset__mem
% A new axiom: (forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member1425217232_alt_o F_19) ((pi_Arr1196397536_alt_o A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member822980838_alt_o F_19) ((pi_Arr1309696186_alt_o A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48)))) of role axiom named fact_611_funcset__mem
% A new axiom: (forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member822980838_alt_o F_19) ((pi_Arr1309696186_alt_o A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48))))
% FOF formula (forall (X_11:arrow_1196572341e_indi) (Y_4:arrow_1196572341e_indi) (F_18:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_18) top_to54564308indi_o)->((iff (((eq nat) (F_18 X_11)) (F_18 Y_4))) (((eq arrow_1196572341e_indi) X_11) Y_4)))) of role axiom named fact_612_inj__eq
% A new axiom: (forall (X_11:arrow_1196572341e_indi) (Y_4:arrow_1196572341e_indi) (F_18:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_18) top_to54564308indi_o)->((iff (((eq nat) (F_18 X_11)) (F_18 Y_4))) (((eq arrow_1196572341e_indi) X_11) Y_4))))
% FOF formula (forall (X_11:nat) (Y_4:nat) (F_18:(nat->nat)), (((inj_on_nat_nat F_18) top_top_nat_o)->((iff (((eq nat) (F_18 X_11)) (F_18 Y_4))) (((eq nat) X_11) Y_4)))) of role axiom named fact_613_inj__eq
% A new axiom: (forall (X_11:nat) (Y_4:nat) (F_18:(nat->nat)), (((inj_on_nat_nat F_18) top_top_nat_o)->((iff (((eq nat) (F_18 X_11)) (F_18 Y_4))) (((eq nat) X_11) Y_4))))
% FOF formula (forall (X_10:arrow_1196572341e_indi) (Y_3:arrow_1196572341e_indi) (F_17:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_17) top_to54564308indi_o)->((((eq nat) (F_17 X_10)) (F_17 Y_3))->(((eq arrow_1196572341e_indi) X_10) Y_3)))) of role axiom named fact_614_injD
% A new axiom: (forall (X_10:arrow_1196572341e_indi) (Y_3:arrow_1196572341e_indi) (F_17:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_17) top_to54564308indi_o)->((((eq nat) (F_17 X_10)) (F_17 Y_3))->(((eq arrow_1196572341e_indi) X_10) Y_3))))
% FOF formula (forall (X_10:nat) (Y_3:nat) (F_17:(nat->nat)), (((inj_on_nat_nat F_17) top_top_nat_o)->((((eq nat) (F_17 X_10)) (F_17 Y_3))->(((eq nat) X_10) Y_3)))) of role axiom named fact_615_injD
% A new axiom: (forall (X_10:nat) (Y_3:nat) (F_17:(nat->nat)), (((inj_on_nat_nat F_17) top_top_nat_o)->((((eq nat) (F_17 X_10)) (F_17 Y_3))->(((eq nat) X_10) Y_3))))
% FOF formula (forall (X_9:arrow_1196572341e_indi) (F_16:(arrow_1196572341e_indi->nat)) (A_54:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_16) A_54)->(((member1818997282e_indi X_9) A_54)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat A_54) F_16) (F_16 X_9))) X_9)))) of role axiom named fact_616_inv__into__f__f
% A new axiom: (forall (X_9:arrow_1196572341e_indi) (F_16:(arrow_1196572341e_indi->nat)) (A_54:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_16) A_54)->(((member1818997282e_indi X_9) A_54)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat A_54) F_16) (F_16 X_9))) X_9))))
% FOF formula (forall (X_9:nat) (F_16:(nat->nat)) (A_54:(nat->Prop)), (((inj_on_nat_nat F_16) A_54)->(((member_nat X_9) A_54)->(((eq nat) (((hilber195283148at_nat A_54) F_16) (F_16 X_9))) X_9)))) of role axiom named fact_617_inv__into__f__f
% A new axiom: (forall (X_9:nat) (F_16:(nat->nat)) (A_54:(nat->Prop)), (((inj_on_nat_nat F_16) A_54)->(((member_nat X_9) A_54)->(((eq nat) (((hilber195283148at_nat A_54) F_16) (F_16 X_9))) X_9))))
% FOF formula (forall (Y_2:nat) (X_8:arrow_1196572341e_indi) (F_15:(arrow_1196572341e_indi->nat)) (A_53:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_15) A_53)->(((member1818997282e_indi X_8) A_53)->((((eq nat) (F_15 X_8)) Y_2)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat A_53) F_15) Y_2)) X_8))))) of role axiom named fact_618_inv__into__f__eq
% A new axiom: (forall (Y_2:nat) (X_8:arrow_1196572341e_indi) (F_15:(arrow_1196572341e_indi->nat)) (A_53:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_15) A_53)->(((member1818997282e_indi X_8) A_53)->((((eq nat) (F_15 X_8)) Y_2)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat A_53) F_15) Y_2)) X_8)))))
% FOF formula (forall (Y_2:nat) (X_8:nat) (F_15:(nat->nat)) (A_53:(nat->Prop)), (((inj_on_nat_nat F_15) A_53)->(((member_nat X_8) A_53)->((((eq nat) (F_15 X_8)) Y_2)->(((eq nat) (((hilber195283148at_nat A_53) F_15) Y_2)) X_8))))) of role axiom named fact_619_inv__into__f__eq
% A new axiom: (forall (Y_2:nat) (X_8:nat) (F_15:(nat->nat)) (A_53:(nat->Prop)), (((inj_on_nat_nat F_15) A_53)->(((member_nat X_8) A_53)->((((eq nat) (F_15 X_8)) Y_2)->(((eq nat) (((hilber195283148at_nat A_53) F_15) Y_2)) X_8)))))
% FOF formula (forall (F_14:(produc1572197287le_alt->arrow_1196572341e_indi)) (B_47:(produc1572197287le_alt->(arrow_1196572341e_indi->Prop))) (A_52:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), (((member285112084le_alt X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1074431551e_indi F_14) ((pi_Pro1246947541e_indi A_52) B_47)))) of role axiom named fact_620_Pi__I
% A new axiom: (forall (F_14:(produc1572197287le_alt->arrow_1196572341e_indi)) (B_47:(produc1572197287le_alt->(arrow_1196572341e_indi->Prop))) (A_52:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), (((member285112084le_alt X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1074431551e_indi F_14) ((pi_Pro1246947541e_indi A_52) B_47))))
% FOF formula (forall (F_14:(produc1572197287le_alt->product_unit)) (B_47:(produc1572197287le_alt->(product_unit->Prop))) (A_52:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), (((member285112084le_alt X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member44534621t_unit F_14) ((pi_Pro926528371t_unit A_52) B_47)))) of role axiom named fact_621_Pi__I
% A new axiom: (forall (F_14:(produc1572197287le_alt->product_unit)) (B_47:(produc1572197287le_alt->(product_unit->Prop))) (A_52:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), (((member285112084le_alt X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member44534621t_unit F_14) ((pi_Pro926528371t_unit A_52) B_47))))
% FOF formula (forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1186582243e_indi F_14) ((pi_Arr272777533e_indi A_52) B_47)))) of role axiom named fact_622_Pi__I
% A new axiom: (forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1186582243e_indi F_14) ((pi_Arr272777533e_indi A_52) B_47))))
% FOF formula (forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1696373143lt_o_o F_14) ((pi_Arr1709554855lt_o_o A_52) B_47)))) of role axiom named fact_623_Pi__I
% A new axiom: (forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1696373143lt_o_o F_14) ((pi_Arr1709554855lt_o_o A_52) B_47))))
% FOF formula (forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member1537523201t_unit F_14) ((pi_Arr509685723t_unit A_52) B_47)))) of role axiom named fact_624_Pi__I
% A new axiom: (forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member1537523201t_unit F_14) ((pi_Arr509685723t_unit A_52) B_47))))
% FOF formula (forall (F_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (B_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))) (A_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1539010427e_indi F_14) ((pi_Arr470535441e_indi A_52) B_47)))) of role axiom named fact_625_Pi__I
% A new axiom: (forall (F_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (B_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))) (A_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1539010427e_indi F_14) ((pi_Arr470535441e_indi A_52) B_47))))
% FOF formula (forall (F_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))) (A_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1346253567lt_o_o F_14) ((pi_Arr1865419731lt_o_o A_52) B_47)))) of role axiom named fact_626_Pi__I
% A new axiom: (forall (F_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))) (A_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1346253567lt_o_o F_14) ((pi_Arr1865419731lt_o_o A_52) B_47))))
% FOF formula (forall (F_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (B_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))) (A_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member1043380889t_unit F_14) ((pi_Arr2096782767t_unit A_52) B_47)))) of role axiom named fact_627_Pi__I
% A new axiom: (forall (F_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (B_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))) (A_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member1043380889t_unit F_14) ((pi_Arr2096782767t_unit A_52) B_47))))
% FOF formula (forall (F_14:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (B_47:((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))) (A_52:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1830244024e_indi F_14) ((pi_Pro2039443474e_indi A_52) B_47)))) of role axiom named fact_628_Pi__I
% A new axiom: (forall (F_14:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (B_47:((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))) (A_52:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1830244024e_indi F_14) ((pi_Pro2039443474e_indi A_52) B_47))))
% FOF formula (forall (F_14:((produc1572197287le_alt->Prop)->Prop)) (B_47:((produc1572197287le_alt->Prop)->(Prop->Prop))) (A_52:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1925470338lt_o_o F_14) ((pi_Pro386796690lt_o_o A_52) B_47)))) of role axiom named fact_629_Pi__I
% A new axiom: (forall (F_14:((produc1572197287le_alt->Prop)->Prop)) (B_47:((produc1572197287le_alt->Prop)->(Prop->Prop))) (A_52:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1925470338lt_o_o F_14) ((pi_Pro386796690lt_o_o A_52) B_47))))
% FOF formula (forall (F_14:((produc1572197287le_alt->Prop)->product_unit)) (B_47:((produc1572197287le_alt->Prop)->(product_unit->Prop))) (A_52:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member1092867670t_unit F_14) ((pi_Pro30504752t_unit A_52) B_47)))) of role axiom named fact_630_Pi__I
% A new axiom: (forall (F_14:((produc1572197287le_alt->Prop)->product_unit)) (B_47:((produc1572197287le_alt->Prop)->(product_unit->Prop))) (A_52:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member1092867670t_unit F_14) ((pi_Pro30504752t_unit A_52) B_47))))
% FOF formula (forall (F_14:(nat->arrow_1196572341e_indi)) (B_47:(nat->(arrow_1196572341e_indi->Prop))) (A_52:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1113138010e_indi F_14) ((pi_nat986275508e_indi A_52) B_47)))) of role axiom named fact_631_Pi__I
% A new axiom: (forall (F_14:(nat->arrow_1196572341e_indi)) (B_47:(nat->(arrow_1196572341e_indi->Prop))) (A_52:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1113138010e_indi F_14) ((pi_nat986275508e_indi A_52) B_47))))
% FOF formula (forall (F_14:(nat->Prop)) (B_47:(nat->(Prop->Prop))) (A_52:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member_nat_o F_14) ((pi_nat_o A_52) B_47)))) of role axiom named fact_632_Pi__I
% A new axiom: (forall (F_14:(nat->Prop)) (B_47:(nat->(Prop->Prop))) (A_52:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member_nat_o F_14) ((pi_nat_o A_52) B_47))))
% FOF formula (forall (F_14:(nat->product_unit)) (B_47:(nat->(product_unit->Prop))) (A_52:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member616671224t_unit F_14) ((pi_nat_Product_unit A_52) B_47)))) of role axiom named fact_633_Pi__I
% A new axiom: (forall (F_14:(nat->product_unit)) (B_47:(nat->(product_unit->Prop))) (A_52:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member616671224t_unit F_14) ((pi_nat_Product_unit A_52) B_47))))
% FOF formula (forall (F_14:(arrow_1196572341e_indi->produc1572197287le_alt)) (B_47:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member285112084le_alt (F_14 X_1)) (B_47 X_1))))->((member232085823le_alt F_14) ((pi_Arr1762714837le_alt A_52) B_47)))) of role axiom named fact_634_Pi__I
% A new axiom: (forall (F_14:(arrow_1196572341e_indi->produc1572197287le_alt)) (B_47:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member285112084le_alt (F_14 X_1)) (B_47 X_1))))->((member232085823le_alt F_14) ((pi_Arr1762714837le_alt A_52) B_47))))
% FOF formula (forall (F_14:(Prop->produc1572197287le_alt)) (B_47:(Prop->(produc1572197287le_alt->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member285112084le_alt (F_14 X_1)) (B_47 X_1))))->((member1158049649le_alt F_14) ((pi_o_P728361163le_alt A_52) B_47)))) of role axiom named fact_635_Pi__I
% A new axiom: (forall (F_14:(Prop->produc1572197287le_alt)) (B_47:(Prop->(produc1572197287le_alt->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member285112084le_alt (F_14 X_1)) (B_47 X_1))))->((member1158049649le_alt F_14) ((pi_o_P728361163le_alt A_52) B_47))))
% FOF formula (forall (F_14:(product_unit->produc1572197287le_alt)) (B_47:(product_unit->(produc1572197287le_alt->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member285112084le_alt (F_14 X_1)) (B_47 X_1))))->((member1161214429le_alt F_14) ((pi_Pro772884595le_alt A_52) B_47)))) of role axiom named fact_636_Pi__I
% A new axiom: (forall (F_14:(product_unit->produc1572197287le_alt)) (B_47:(product_unit->(produc1572197287le_alt->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member285112084le_alt (F_14 X_1)) (B_47 X_1))))->((member1161214429le_alt F_14) ((pi_Pro772884595le_alt A_52) B_47))))
% FOF formula (forall (F_14:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (B_47:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member822980838_alt_o (F_14 X_1)) (B_47 X_1))))->((member2071265553_alt_o F_14) ((pi_Arr456308197_alt_o A_52) B_47)))) of role axiom named fact_637_Pi__I
% A new axiom: (forall (F_14:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (B_47:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member822980838_alt_o (F_14 X_1)) (B_47 X_1))))->((member2071265553_alt_o F_14) ((pi_Arr456308197_alt_o A_52) B_47))))
% FOF formula (forall (F_14:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (B_47:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member822980838_alt_o (F_14 X_1)) (B_47 X_1))))->((member984757343_alt_o F_14) ((pi_o_A1479825007_alt_o A_52) B_47)))) of role axiom named fact_638_Pi__I
% A new axiom: (forall (F_14:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (B_47:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member822980838_alt_o (F_14 X_1)) (B_47 X_1))))->((member984757343_alt_o F_14) ((pi_o_A1479825007_alt_o A_52) B_47))))
% FOF formula (forall (F_14:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (B_47:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member822980838_alt_o (F_14 X_1)) (B_47 X_1))))->((member2021528307_alt_o F_14) ((pi_Pro1959068871_alt_o A_52) B_47)))) of role axiom named fact_639_Pi__I
% A new axiom: (forall (F_14:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (B_47:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member822980838_alt_o (F_14 X_1)) (B_47 X_1))))->((member2021528307_alt_o F_14) ((pi_Pro1959068871_alt_o A_52) B_47))))
% FOF formula (forall (F_14:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (B_47:(arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member1425217232_alt_o (F_14 X_1)) (B_47 X_1))))->((member1521294075_alt_o F_14) ((pi_Arr583278353_alt_o A_52) B_47)))) of role axiom named fact_640_Pi__I
% A new axiom: (forall (F_14:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (B_47:(arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member1425217232_alt_o (F_14 X_1)) (B_47 X_1))))->((member1521294075_alt_o F_14) ((pi_Arr583278353_alt_o A_52) B_47))))
% FOF formula (forall (F_14:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (B_47:(Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member1425217232_alt_o (F_14 X_1)) (B_47 X_1))))->((member161783341_alt_o F_14) ((pi_o_A1994447367_alt_o A_52) B_47)))) of role axiom named fact_641_Pi__I
% A new axiom: (forall (F_14:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (B_47:(Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member1425217232_alt_o (F_14 X_1)) (B_47 X_1))))->((member161783341_alt_o F_14) ((pi_o_A1994447367_alt_o A_52) B_47))))
% FOF formula (forall (F_14:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (B_47:(product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member1425217232_alt_o (F_14 X_1)) (B_47 X_1))))->((member1888392857_alt_o F_14) ((pi_Pro443817391_alt_o A_52) B_47)))) of role axiom named fact_642_Pi__I
% A new axiom: (forall (F_14:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (B_47:(product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member1425217232_alt_o (F_14 X_1)) (B_47 X_1))))->((member1888392857_alt_o F_14) ((pi_Pro443817391_alt_o A_52) B_47))))
% FOF formula (forall (F_14:(Prop->(produc1572197287le_alt->Prop))) (B_47:(Prop->((produc1572197287le_alt->Prop)->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member1495989556_alt_o F_14) ((pi_o_P1417870404_alt_o A_52) B_47)))) of role axiom named fact_643_Pi__I
% A new axiom: (forall (F_14:(Prop->(produc1572197287le_alt->Prop))) (B_47:(Prop->((produc1572197287le_alt->Prop)->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member1495989556_alt_o F_14) ((pi_o_P1417870404_alt_o A_52) B_47))))
% FOF formula (forall (F_14:(product_unit->(produc1572197287le_alt->Prop))) (B_47:(product_unit->((produc1572197287le_alt->Prop)->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member1295651272_alt_o F_14) ((pi_Pro29851292_alt_o A_52) B_47)))) of role axiom named fact_644_Pi__I
% A new axiom: (forall (F_14:(product_unit->(produc1572197287le_alt->Prop))) (B_47:(product_unit->((produc1572197287le_alt->Prop)->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member1295651272_alt_o F_14) ((pi_Pro29851292_alt_o A_52) B_47))))
% FOF formula (forall (F_14:(arrow_1196572341e_indi->nat)) (B_47:(arrow_1196572341e_indi->(nat->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member_nat (F_14 X_1)) (B_47 X_1))))->((member1842285448di_nat F_14) ((pi_Arr778514268di_nat A_52) B_47)))) of role axiom named fact_645_Pi__I
% A new axiom: (forall (F_14:(arrow_1196572341e_indi->nat)) (B_47:(arrow_1196572341e_indi->(nat->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member_nat (F_14 X_1)) (B_47 X_1))))->((member1842285448di_nat F_14) ((pi_Arr778514268di_nat A_52) B_47))))
% FOF formula (forall (F_14:(Prop->nat)) (B_47:(Prop->(nat->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member_nat (F_14 X_1)) (B_47 X_1))))->((member_o_nat F_14) ((pi_o_nat A_52) B_47)))) of role axiom named fact_646_Pi__I
% A new axiom: (forall (F_14:(Prop->nat)) (B_47:(Prop->(nat->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member_nat (F_14 X_1)) (B_47 X_1))))->((member_o_nat F_14) ((pi_o_nat A_52) B_47))))
% FOF formula (forall (F_14:(product_unit->nat)) (B_47:(product_unit->(nat->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member_nat (F_14 X_1)) (B_47 X_1))))->((member1827227242it_nat F_14) ((pi_Product_unit_nat A_52) B_47)))) of role axiom named fact_647_Pi__I
% A new axiom: (forall (F_14:(product_unit->nat)) (B_47:(product_unit->(nat->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member_nat (F_14 X_1)) (B_47 X_1))))->((member1827227242it_nat F_14) ((pi_Product_unit_nat A_52) B_47))))
% FOF formula (forall (F_14:(produc1572197287le_alt->Prop)) (B_47:(produc1572197287le_alt->(Prop->Prop))) (A_52:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), (((member285112084le_alt X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1241905979_alt_o F_14) ((pi_Pro418549519_alt_o A_52) B_47)))) of role axiom named fact_648_Pi__I
% A new axiom: (forall (F_14:(produc1572197287le_alt->Prop)) (B_47:(produc1572197287le_alt->(Prop->Prop))) (A_52:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), (((member285112084le_alt X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1241905979_alt_o F_14) ((pi_Pro418549519_alt_o A_52) B_47))))
% FOF formula (forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member1425217232_alt_o F_14) ((pi_Arr1196397536_alt_o A_52) B_47)))) of role axiom named fact_649_Pi__I
% A new axiom: (forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member1425217232_alt_o F_14) ((pi_Arr1196397536_alt_o A_52) B_47))))
% FOF formula (forall (F_14:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (B_47:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member822980838_alt_o F_14) ((pi_Arr1309696186_alt_o A_52) B_47)))) of role axiom named fact_650_Pi__I
% A new axiom: (forall (F_14:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (B_47:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member822980838_alt_o F_14) ((pi_Arr1309696186_alt_o A_52) B_47))))
% FOF formula (forall (G_2:(nat->arrow_1196572341e_indi)) (F_13:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_13) top_to54564308indi_o)->((forall (X_1:nat), (((eq nat) (F_13 (G_2 X_1))) X_1))->(((eq (nat->arrow_1196572341e_indi)) ((hilber1125280539di_nat top_to54564308indi_o) F_13)) G_2)))) of role axiom named fact_651_inj__imp__inv__eq
% A new axiom: (forall (G_2:(nat->arrow_1196572341e_indi)) (F_13:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_13) top_to54564308indi_o)->((forall (X_1:nat), (((eq nat) (F_13 (G_2 X_1))) X_1))->(((eq (nat->arrow_1196572341e_indi)) ((hilber1125280539di_nat top_to54564308indi_o) F_13)) G_2))))
% FOF formula (forall (G_2:(nat->nat)) (F_13:(nat->nat)), (((inj_on_nat_nat F_13) top_top_nat_o)->((forall (X_1:nat), (((eq nat) (F_13 (G_2 X_1))) X_1))->(((eq (nat->nat)) ((hilber195283148at_nat top_top_nat_o) F_13)) G_2)))) of role axiom named fact_652_inj__imp__inv__eq
% A new axiom: (forall (G_2:(nat->nat)) (F_13:(nat->nat)), (((inj_on_nat_nat F_13) top_top_nat_o)->((forall (X_1:nat), (((eq nat) (F_13 (G_2 X_1))) X_1))->(((eq (nat->nat)) ((hilber195283148at_nat top_top_nat_o) F_13)) G_2))))
% FOF formula (forall (A_51:nat), ((ord_less_nat A_51) ((plus_plus_nat A_51) one_one_nat))) of role axiom named fact_653_less__add__one
% A new axiom: (forall (A_51:nat), ((ord_less_nat A_51) ((plus_plus_nat A_51) one_one_nat)))
% FOF formula (forall (C_33:nat) (D_3:nat) (A_50:nat) (B_46:nat), (((ord_less_nat A_50) B_46)->(((ord_less_eq_nat C_33) D_3)->((ord_less_nat ((plus_plus_nat A_50) C_33)) ((plus_plus_nat B_46) D_3))))) of role axiom named fact_654_add__less__le__mono
% A new axiom: (forall (C_33:nat) (D_3:nat) (A_50:nat) (B_46:nat), (((ord_less_nat A_50) B_46)->(((ord_less_eq_nat C_33) D_3)->((ord_less_nat ((plus_plus_nat A_50) C_33)) ((plus_plus_nat B_46) D_3)))))
% FOF formula (forall (C_32:nat) (D_2:nat) (A_49:nat) (B_45:nat), (((ord_less_eq_nat A_49) B_45)->(((ord_less_nat C_32) D_2)->((ord_less_nat ((plus_plus_nat A_49) C_32)) ((plus_plus_nat B_45) D_2))))) of role axiom named fact_655_add__le__less__mono
% A new axiom: (forall (C_32:nat) (D_2:nat) (A_49:nat) (B_45:nat), (((ord_less_eq_nat A_49) B_45)->(((ord_less_nat C_32) D_2)->((ord_less_nat ((plus_plus_nat A_49) C_32)) ((plus_plus_nat B_45) D_2)))))
% FOF formula (forall (F_12:(arrow_1196572341e_indi->nat)), ((forall (X_1:arrow_1196572341e_indi) (Y_1:arrow_1196572341e_indi), ((((eq nat) (F_12 X_1)) (F_12 Y_1))->(((eq arrow_1196572341e_indi) X_1) Y_1)))->((inj_on1505595958di_nat F_12) top_to54564308indi_o))) of role axiom named fact_656_injI
% A new axiom: (forall (F_12:(arrow_1196572341e_indi->nat)), ((forall (X_1:arrow_1196572341e_indi) (Y_1:arrow_1196572341e_indi), ((((eq nat) (F_12 X_1)) (F_12 Y_1))->(((eq arrow_1196572341e_indi) X_1) Y_1)))->((inj_on1505595958di_nat F_12) top_to54564308indi_o)))
% FOF formula (forall (F_12:(nat->nat)), ((forall (X_1:nat) (Y_1:nat), ((((eq nat) (F_12 X_1)) (F_12 Y_1))->(((eq nat) X_1) Y_1)))->((inj_on_nat_nat F_12) top_top_nat_o))) of role axiom named fact_657_injI
% A new axiom: (forall (F_12:(nat->nat)), ((forall (X_1:nat) (Y_1:nat), ((((eq nat) (F_12 X_1)) (F_12 Y_1))->(((eq nat) X_1) Y_1)))->((inj_on_nat_nat F_12) top_top_nat_o)))
% FOF formula (forall (C_31:(nat->Prop)) (F_11:((nat->Prop)->(nat->Prop))) (B_44:(nat->Prop)) (A_48:(nat->Prop)), (((ord_less_nat_o B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48)))))) of role axiom named fact_658_xt5
% A new axiom: (forall (C_31:(nat->Prop)) (F_11:((nat->Prop)->(nat->Prop))) (B_44:(nat->Prop)) (A_48:(nat->Prop)), (((ord_less_nat_o B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:(nat->Prop)) (F_11:((product_unit->Prop)->(nat->Prop))) (B_44:(product_unit->Prop)) (A_48:(product_unit->Prop)), (((ord_le232288914unit_o B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48)))))) of role axiom named fact_659_xt5
% A new axiom: (forall (C_31:(nat->Prop)) (F_11:((product_unit->Prop)->(nat->Prop))) (B_44:(product_unit->Prop)) (A_48:(product_unit->Prop)), (((ord_le232288914unit_o B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:(nat->Prop)) (F_11:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_44:(arrow_1196572341e_indi->Prop)) (A_48:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48)))))) of role axiom named fact_660_xt5
% A new axiom: (forall (C_31:(nat->Prop)) (F_11:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_44:(arrow_1196572341e_indi->Prop)) (A_48:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:(nat->Prop)) (F_11:(nat->(nat->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48)))))) of role axiom named fact_661_xt5
% A new axiom: (forall (C_31:(nat->Prop)) (F_11:(nat->(nat->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:(product_unit->Prop)) (F_11:(nat->(product_unit->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1511552390unit_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le232288914unit_o (F_11 Y_1)) (F_11 X_1))))->((ord_le232288914unit_o C_31) (F_11 A_48)))))) of role axiom named fact_662_xt5
% A new axiom: (forall (C_31:(product_unit->Prop)) (F_11:(nat->(product_unit->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1511552390unit_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le232288914unit_o (F_11 Y_1)) (F_11 X_1))))->((ord_le232288914unit_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:(arrow_1196572341e_indi->Prop)) (F_11:(nat->(arrow_1196572341e_indi->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le865407012indi_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1991507760indi_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1991507760indi_o C_31) (F_11 A_48)))))) of role axiom named fact_663_xt5
% A new axiom: (forall (C_31:(arrow_1196572341e_indi->Prop)) (F_11:(nat->(arrow_1196572341e_indi->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le865407012indi_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1991507760indi_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1991507760indi_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:((produc1572197287le_alt->Prop)->Prop)) (F_11:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1027220427lt_o_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le874404799lt_o_o (F_11 Y_1)) (F_11 X_1))))->((ord_le874404799lt_o_o C_31) (F_11 A_48)))))) of role axiom named fact_664_xt5
% A new axiom: (forall (C_31:((produc1572197287le_alt->Prop)->Prop)) (F_11:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1027220427lt_o_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le874404799lt_o_o (F_11 Y_1)) (F_11 X_1))))->((ord_le874404799lt_o_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_11:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1805007862lt_o_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1382328578lt_o_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1382328578lt_o_o C_31) (F_11 A_48)))))) of role axiom named fact_665_xt5
% A new axiom: (forall (C_31:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_11:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1805007862lt_o_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1382328578lt_o_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1382328578lt_o_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_11:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le602483040lt_o_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le914873172lt_o_o (F_11 Y_1)) (F_11 X_1))))->((ord_le914873172lt_o_o C_31) (F_11 A_48)))))) of role axiom named fact_666_xt5
% A new axiom: (forall (C_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_11:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le602483040lt_o_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le914873172lt_o_o (F_11 Y_1)) (F_11 X_1))))->((ord_le914873172lt_o_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:(produc1572197287le_alt->Prop)) (F_11:(nat->(produc1572197287le_alt->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le962286258_alt_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1852932542_alt_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1852932542_alt_o C_31) (F_11 A_48)))))) of role axiom named fact_667_xt5
% A new axiom: (forall (C_31:(produc1572197287le_alt->Prop)) (F_11:(nat->(produc1572197287le_alt->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le962286258_alt_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1852932542_alt_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1852932542_alt_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:Prop) (F_11:(nat->Prop)) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_less_eq_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_o C_31) (F_11 A_48)))))) of role axiom named fact_668_xt5
% A new axiom: (forall (C_31:Prop) (F_11:(nat->Prop)) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_less_eq_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_11:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1463467535_alt_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1339521307_alt_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1339521307_alt_o C_31) (F_11 A_48)))))) of role axiom named fact_669_xt5
% A new axiom: (forall (C_31:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_11:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1463467535_alt_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1339521307_alt_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1339521307_alt_o C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:nat) (F_11:((nat->Prop)->nat)) (B_44:(nat->Prop)) (A_48:(nat->Prop)), (((ord_less_nat_o B_44) A_48)->(((ord_less_eq_nat C_31) (F_11 B_44))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat C_31) (F_11 A_48)))))) of role axiom named fact_670_xt5
% A new axiom: (forall (C_31:nat) (F_11:((nat->Prop)->nat)) (B_44:(nat->Prop)) (A_48:(nat->Prop)), (((ord_less_nat_o B_44) A_48)->(((ord_less_eq_nat C_31) (F_11 B_44))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:nat) (F_11:((product_unit->Prop)->nat)) (B_44:(product_unit->Prop)) (A_48:(product_unit->Prop)), (((ord_le232288914unit_o B_44) A_48)->(((ord_less_eq_nat C_31) (F_11 B_44))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat C_31) (F_11 A_48)))))) of role axiom named fact_671_xt5
% A new axiom: (forall (C_31:nat) (F_11:((product_unit->Prop)->nat)) (B_44:(product_unit->Prop)) (A_48:(product_unit->Prop)), (((ord_le232288914unit_o B_44) A_48)->(((ord_less_eq_nat C_31) (F_11 B_44))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat C_31) (F_11 A_48))))))
% FOF formula (forall (C_31:nat) (F_11:((arrow_1196572341e_indi->Prop)->nat)) (B_44:(arrow_1196572341e_indi->Prop)) (A_48:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_44) A_48)->(((ord_less_eq_nat C_31) (F_11 B_44))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat C_31) (F_11 A_48)))))) of role axiom named fact_672_xt5
% A new axiom: (forall (C_31:nat) (F_11:((arrow_1196572341e_indi->Prop)->nat)) (B_44:(arrow_1196572341e_indi->Prop)) (A_48:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_44) A_48)->(((ord_less_eq_nat C_31) (F_11 B_44))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat C_31) (F_11 A_48))))))
% FOF formula (forall (C_30:(nat->Prop)) (F_10:(nat->(nat->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))) of role axiom named fact_673_xt7
% A new axiom: (forall (C_30:(nat->Prop)) (F_10:(nat->(nat->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(product_unit->Prop)) (F_10:(nat->(product_unit->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le232288914unit_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1511552390unit_o (F_10 Y_1)) (F_10 X_1))))->((ord_le232288914unit_o C_30) (F_10 A_47)))))) of role axiom named fact_674_xt7
% A new axiom: (forall (C_30:(product_unit->Prop)) (F_10:(nat->(product_unit->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le232288914unit_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1511552390unit_o (F_10 Y_1)) (F_10 X_1))))->((ord_le232288914unit_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(arrow_1196572341e_indi->Prop)) (F_10:(nat->(arrow_1196572341e_indi->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1991507760indi_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le865407012indi_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1991507760indi_o C_30) (F_10 A_47)))))) of role axiom named fact_675_xt7
% A new axiom: (forall (C_30:(arrow_1196572341e_indi->Prop)) (F_10:(nat->(arrow_1196572341e_indi->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1991507760indi_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le865407012indi_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1991507760indi_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:((produc1572197287le_alt->Prop)->Prop)) (F_10:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le874404799lt_o_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1027220427lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le874404799lt_o_o C_30) (F_10 A_47)))))) of role axiom named fact_676_xt7
% A new axiom: (forall (C_30:((produc1572197287le_alt->Prop)->Prop)) (F_10:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le874404799lt_o_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1027220427lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le874404799lt_o_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_10:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1382328578lt_o_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1805007862lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1382328578lt_o_o C_30) (F_10 A_47)))))) of role axiom named fact_677_xt7
% A new axiom: (forall (C_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_10:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1382328578lt_o_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1805007862lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1382328578lt_o_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_10:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le914873172lt_o_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le602483040lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le914873172lt_o_o C_30) (F_10 A_47)))))) of role axiom named fact_678_xt7
% A new axiom: (forall (C_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_10:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le914873172lt_o_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le602483040lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le914873172lt_o_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(produc1572197287le_alt->Prop)) (F_10:(nat->(produc1572197287le_alt->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1852932542_alt_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le962286258_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1852932542_alt_o C_30) (F_10 A_47)))))) of role axiom named fact_679_xt7
% A new axiom: (forall (C_30:(produc1572197287le_alt->Prop)) (F_10:(nat->(produc1572197287le_alt->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1852932542_alt_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le962286258_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1852932542_alt_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:Prop) (F_10:(nat->Prop)) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_less_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_o C_30) (F_10 A_47)))))) of role axiom named fact_680_xt7
% A new axiom: (forall (C_30:Prop) (F_10:(nat->Prop)) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_less_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_10:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1339521307_alt_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1463467535_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1339521307_alt_o C_30) (F_10 A_47)))))) of role axiom named fact_681_xt7
% A new axiom: (forall (C_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_10:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1339521307_alt_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1463467535_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1339521307_alt_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(nat->Prop)) (F_10:((nat->Prop)->(nat->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))) of role axiom named fact_682_xt7
% A new axiom: (forall (C_30:(nat->Prop)) (F_10:((nat->Prop)->(nat->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(product_unit->Prop)) (F_10:((nat->Prop)->(product_unit->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le232288914unit_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1511552390unit_o (F_10 Y_1)) (F_10 X_1))))->((ord_le232288914unit_o C_30) (F_10 A_47)))))) of role axiom named fact_683_xt7
% A new axiom: (forall (C_30:(product_unit->Prop)) (F_10:((nat->Prop)->(product_unit->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le232288914unit_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1511552390unit_o (F_10 Y_1)) (F_10 X_1))))->((ord_le232288914unit_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(arrow_1196572341e_indi->Prop)) (F_10:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1991507760indi_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le865407012indi_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1991507760indi_o C_30) (F_10 A_47)))))) of role axiom named fact_684_xt7
% A new axiom: (forall (C_30:(arrow_1196572341e_indi->Prop)) (F_10:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1991507760indi_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le865407012indi_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1991507760indi_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:((produc1572197287le_alt->Prop)->Prop)) (F_10:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le874404799lt_o_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1027220427lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le874404799lt_o_o C_30) (F_10 A_47)))))) of role axiom named fact_685_xt7
% A new axiom: (forall (C_30:((produc1572197287le_alt->Prop)->Prop)) (F_10:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le874404799lt_o_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1027220427lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le874404799lt_o_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_10:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1382328578lt_o_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1805007862lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1382328578lt_o_o C_30) (F_10 A_47)))))) of role axiom named fact_686_xt7
% A new axiom: (forall (C_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_10:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1382328578lt_o_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1805007862lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1382328578lt_o_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_10:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le914873172lt_o_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le602483040lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le914873172lt_o_o C_30) (F_10 A_47)))))) of role axiom named fact_687_xt7
% A new axiom: (forall (C_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_10:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le914873172lt_o_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le602483040lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le914873172lt_o_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(produc1572197287le_alt->Prop)) (F_10:((nat->Prop)->(produc1572197287le_alt->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1852932542_alt_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le962286258_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1852932542_alt_o C_30) (F_10 A_47)))))) of role axiom named fact_688_xt7
% A new axiom: (forall (C_30:(produc1572197287le_alt->Prop)) (F_10:((nat->Prop)->(produc1572197287le_alt->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1852932542_alt_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le962286258_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1852932542_alt_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:Prop) (F_10:((nat->Prop)->Prop)) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_less_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_o C_30) (F_10 A_47)))))) of role axiom named fact_689_xt7
% A new axiom: (forall (C_30:Prop) (F_10:((nat->Prop)->Prop)) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_less_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_10:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1339521307_alt_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1463467535_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1339521307_alt_o C_30) (F_10 A_47)))))) of role axiom named fact_690_xt7
% A new axiom: (forall (C_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_10:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1339521307_alt_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1463467535_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1339521307_alt_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(nat->Prop)) (F_10:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (B_43:((produc1572197287le_alt->Prop)->Prop)) (A_47:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))) of role axiom named fact_691_xt7
% A new axiom: (forall (C_30:(nat->Prop)) (F_10:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (B_43:((produc1572197287le_alt->Prop)->Prop)) (A_47:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(nat->Prop)) (F_10:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_43:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))) of role axiom named fact_692_xt7
% A new axiom: (forall (C_30:(nat->Prop)) (F_10:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_43:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(nat->Prop)) (F_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_43:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))) of role axiom named fact_693_xt7
% A new axiom: (forall (C_30:(nat->Prop)) (F_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_43:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(nat->Prop)) (F_10:((produc1572197287le_alt->Prop)->(nat->Prop))) (B_43:(produc1572197287le_alt->Prop)) (A_47:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))) of role axiom named fact_694_xt7
% A new axiom: (forall (C_30:(nat->Prop)) (F_10:((produc1572197287le_alt->Prop)->(nat->Prop))) (B_43:(produc1572197287le_alt->Prop)) (A_47:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(nat->Prop)) (F_10:(Prop->(nat->Prop))) (B_43:Prop) (A_47:Prop), (((ord_less_eq_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))) of role axiom named fact_695_xt7
% A new axiom: (forall (C_30:(nat->Prop)) (F_10:(Prop->(nat->Prop))) (B_43:Prop) (A_47:Prop), (((ord_less_eq_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(nat->Prop)) (F_10:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_43:(arrow_1196572341e_indi->Prop)) (A_47:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))) of role axiom named fact_696_xt7
% A new axiom: (forall (C_30:(nat->Prop)) (F_10:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_43:(arrow_1196572341e_indi->Prop)) (A_47:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(nat->Prop)) (F_10:((product_unit->Prop)->(nat->Prop))) (B_43:(product_unit->Prop)) (A_47:(product_unit->Prop)), (((ord_le1511552390unit_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))) of role axiom named fact_697_xt7
% A new axiom: (forall (C_30:(nat->Prop)) (F_10:((product_unit->Prop)->(nat->Prop))) (B_43:(product_unit->Prop)) (A_47:(product_unit->Prop)), (((ord_le1511552390unit_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:(nat->Prop)) (F_10:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (B_43:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_47:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))) of role axiom named fact_698_xt7
% A new axiom: (forall (C_30:(nat->Prop)) (F_10:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (B_43:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_47:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:nat) (F_10:(((produc1572197287le_alt->Prop)->Prop)->nat)) (B_43:((produc1572197287le_alt->Prop)->Prop)) (A_47:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))) of role axiom named fact_699_xt7
% A new axiom: (forall (C_30:nat) (F_10:(((produc1572197287le_alt->Prop)->Prop)->nat)) (B_43:((produc1572197287le_alt->Prop)->Prop)) (A_47:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:nat) (F_10:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_43:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))) of role axiom named fact_700_xt7
% A new axiom: (forall (C_30:nat) (F_10:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_43:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:nat) (F_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_43:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))) of role axiom named fact_701_xt7
% A new axiom: (forall (C_30:nat) (F_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_43:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:nat) (F_10:((produc1572197287le_alt->Prop)->nat)) (B_43:(produc1572197287le_alt->Prop)) (A_47:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))) of role axiom named fact_702_xt7
% A new axiom: (forall (C_30:nat) (F_10:((produc1572197287le_alt->Prop)->nat)) (B_43:(produc1572197287le_alt->Prop)) (A_47:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:nat) (F_10:(Prop->nat)) (B_43:Prop) (A_47:Prop), (((ord_less_eq_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))) of role axiom named fact_703_xt7
% A new axiom: (forall (C_30:nat) (F_10:(Prop->nat)) (B_43:Prop) (A_47:Prop), (((ord_less_eq_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:nat) (F_10:((arrow_1196572341e_indi->Prop)->nat)) (B_43:(arrow_1196572341e_indi->Prop)) (A_47:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))) of role axiom named fact_704_xt7
% A new axiom: (forall (C_30:nat) (F_10:((arrow_1196572341e_indi->Prop)->nat)) (B_43:(arrow_1196572341e_indi->Prop)) (A_47:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:nat) (F_10:((product_unit->Prop)->nat)) (B_43:(product_unit->Prop)) (A_47:(product_unit->Prop)), (((ord_le1511552390unit_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))) of role axiom named fact_705_xt7
% A new axiom: (forall (C_30:nat) (F_10:((product_unit->Prop)->nat)) (B_43:(product_unit->Prop)) (A_47:(product_unit->Prop)), (((ord_le1511552390unit_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47))))))
% FOF formula (forall (C_30:nat) (F_10:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (B_43:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_47:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))) of role axiom named fact_706_xt7
% A new axiom: (forall (C_30:nat) (F_10:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (B_43:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_47:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47))))))
% FOF formula (forall (F_9:(product_unit->Prop)) (G_1:(product_unit->Prop)), ((iff ((ord_le232288914unit_o F_9) G_1)) ((and ((ord_le1511552390unit_o F_9) G_1)) (((ord_le1511552390unit_o G_1) F_9)->False)))) of role axiom named fact_707_less__fun__def
% A new axiom: (forall (F_9:(product_unit->Prop)) (G_1:(product_unit->Prop)), ((iff ((ord_le232288914unit_o F_9) G_1)) ((and ((ord_le1511552390unit_o F_9) G_1)) (((ord_le1511552390unit_o G_1) F_9)->False))))
% FOF formula (forall (F_9:(arrow_1196572341e_indi->Prop)) (G_1:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o F_9) G_1)) ((and ((ord_le865407012indi_o F_9) G_1)) (((ord_le865407012indi_o G_1) F_9)->False)))) of role axiom named fact_708_less__fun__def
% A new axiom: (forall (F_9:(arrow_1196572341e_indi->Prop)) (G_1:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o F_9) G_1)) ((and ((ord_le865407012indi_o F_9) G_1)) (((ord_le865407012indi_o G_1) F_9)->False))))
% FOF formula (forall (F_9:((produc1572197287le_alt->Prop)->Prop)) (G_1:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o F_9) G_1)) ((and ((ord_le1027220427lt_o_o F_9) G_1)) (((ord_le1027220427lt_o_o G_1) F_9)->False)))) of role axiom named fact_709_less__fun__def
% A new axiom: (forall (F_9:((produc1572197287le_alt->Prop)->Prop)) (G_1:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o F_9) G_1)) ((and ((ord_le1027220427lt_o_o F_9) G_1)) (((ord_le1027220427lt_o_o G_1) F_9)->False))))
% FOF formula (forall (F_9:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o F_9) G_1)) ((and ((ord_le1805007862lt_o_o F_9) G_1)) (((ord_le1805007862lt_o_o G_1) F_9)->False)))) of role axiom named fact_710_less__fun__def
% A new axiom: (forall (F_9:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o F_9) G_1)) ((and ((ord_le1805007862lt_o_o F_9) G_1)) (((ord_le1805007862lt_o_o G_1) F_9)->False))))
% FOF formula (forall (F_9:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o F_9) G_1)) ((and ((ord_le602483040lt_o_o F_9) G_1)) (((ord_le602483040lt_o_o G_1) F_9)->False)))) of role axiom named fact_711_less__fun__def
% A new axiom: (forall (F_9:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o F_9) G_1)) ((and ((ord_le602483040lt_o_o F_9) G_1)) (((ord_le602483040lt_o_o G_1) F_9)->False))))
% FOF formula (forall (F_9:(produc1572197287le_alt->Prop)) (G_1:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o F_9) G_1)) ((and ((ord_le962286258_alt_o F_9) G_1)) (((ord_le962286258_alt_o G_1) F_9)->False)))) of role axiom named fact_712_less__fun__def
% A new axiom: (forall (F_9:(produc1572197287le_alt->Prop)) (G_1:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o F_9) G_1)) ((and ((ord_le962286258_alt_o F_9) G_1)) (((ord_le962286258_alt_o G_1) F_9)->False))))
% FOF formula (forall (F_9:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1339521307_alt_o F_9) G_1)) ((and ((ord_le1463467535_alt_o F_9) G_1)) (((ord_le1463467535_alt_o G_1) F_9)->False)))) of role axiom named fact_713_less__fun__def
% A new axiom: (forall (F_9:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1339521307_alt_o F_9) G_1)) ((and ((ord_le1463467535_alt_o F_9) G_1)) (((ord_le1463467535_alt_o G_1) F_9)->False))))
% FOF formula (forall (F_9:(nat->Prop)) (G_1:(nat->Prop)), ((iff ((ord_less_nat_o F_9) G_1)) ((and ((ord_less_eq_nat_o F_9) G_1)) (((ord_less_eq_nat_o G_1) F_9)->False)))) of role axiom named fact_714_less__fun__def
% A new axiom: (forall (F_9:(nat->Prop)) (G_1:(nat->Prop)), ((iff ((ord_less_nat_o F_9) G_1)) ((and ((ord_less_eq_nat_o F_9) G_1)) (((ord_less_eq_nat_o G_1) F_9)->False))))
% FOF formula (forall (B_42:(produc1572197287le_alt->(Prop->Prop))) (A_46:(produc1572197287le_alt->Prop)) (A_45:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_46) A_45)->((ord_le1027220427lt_o_o ((pi_Pro418549519_alt_o A_45) B_42)) ((pi_Pro418549519_alt_o A_46) B_42)))) of role axiom named fact_715_Pi__anti__mono
% A new axiom: (forall (B_42:(produc1572197287le_alt->(Prop->Prop))) (A_46:(produc1572197287le_alt->Prop)) (A_45:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_46) A_45)->((ord_le1027220427lt_o_o ((pi_Pro418549519_alt_o A_45) B_42)) ((pi_Pro418549519_alt_o A_46) B_42))))
% FOF formula (forall (B_42:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))) (A_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_45:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_46) A_45)->((ord_le1805007862lt_o_o ((pi_Arr1196397536_alt_o A_45) B_42)) ((pi_Arr1196397536_alt_o A_46) B_42)))) of role axiom named fact_716_Pi__anti__mono
% A new axiom: (forall (B_42:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))) (A_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_45:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_46) A_45)->((ord_le1805007862lt_o_o ((pi_Arr1196397536_alt_o A_45) B_42)) ((pi_Arr1196397536_alt_o A_46) B_42))))
% FOF formula (forall (B_42:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))) (A_46:(arrow_1196572341e_indi->Prop)) (A_45:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_46) A_45)->((ord_le602483040lt_o_o ((pi_Arr1309696186_alt_o A_45) B_42)) ((pi_Arr1309696186_alt_o A_46) B_42)))) of role axiom named fact_717_Pi__anti__mono
% A new axiom: (forall (B_42:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))) (A_46:(arrow_1196572341e_indi->Prop)) (A_45:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_46) A_45)->((ord_le602483040lt_o_o ((pi_Arr1309696186_alt_o A_45) B_42)) ((pi_Arr1309696186_alt_o A_46) B_42))))
% FOF formula (forall (R_1:(produc1572197287le_alt->Prop)) (S_2:(produc1572197287le_alt->Prop)), ((iff ((ord_le1463467535_alt_o (fun (X_1:arrow_1389031998le_alt) (Y_1:arrow_1389031998le_alt)=> ((member285112084le_alt ((produc897867031le_alt X_1) Y_1)) R_1))) (fun (X_1:arrow_1389031998le_alt) (Y_1:arrow_1389031998le_alt)=> ((member285112084le_alt ((produc897867031le_alt X_1) Y_1)) S_2)))) ((ord_le962286258_alt_o R_1) S_2))) of role axiom named fact_718_pred__subset__eq2
% A new axiom: (forall (R_1:(produc1572197287le_alt->Prop)) (S_2:(produc1572197287le_alt->Prop)), ((iff ((ord_le1463467535_alt_o (fun (X_1:arrow_1389031998le_alt) (Y_1:arrow_1389031998le_alt)=> ((member285112084le_alt ((produc897867031le_alt X_1) Y_1)) R_1))) (fun (X_1:arrow_1389031998le_alt) (Y_1:arrow_1389031998le_alt)=> ((member285112084le_alt ((produc897867031le_alt X_1) Y_1)) S_2)))) ((ord_le962286258_alt_o R_1) S_2)))
% FOF formula (forall (A_44:((produc1572197287le_alt->Prop)->Prop)), ((ord_le1027220427lt_o_o A_44) top_to1806834203lt_o_o)) of role axiom named fact_719_subset__UNIV
% A new axiom: (forall (A_44:((produc1572197287le_alt->Prop)->Prop)), ((ord_le1027220427lt_o_o A_44) top_to1806834203lt_o_o))
% FOF formula (forall (A_44:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((ord_le602483040lt_o_o A_44) top_to732317616lt_o_o)) of role axiom named fact_720_subset__UNIV
% A new axiom: (forall (A_44:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((ord_le602483040lt_o_o A_44) top_to732317616lt_o_o))
% FOF formula (forall (A_44:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((ord_le1805007862lt_o_o A_44) top_to1492351398lt_o_o)) of role axiom named fact_721_subset__UNIV
% A new axiom: (forall (A_44:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((ord_le1805007862lt_o_o A_44) top_to1492351398lt_o_o))
% FOF formula (forall (A_44:(produc1572197287le_alt->Prop)), ((ord_le962286258_alt_o A_44) top_to558618722_alt_o)) of role axiom named fact_722_subset__UNIV
% A new axiom: (forall (A_44:(produc1572197287le_alt->Prop)), ((ord_le962286258_alt_o A_44) top_to558618722_alt_o))
% FOF formula (forall (A_44:(arrow_1196572341e_indi->Prop)), ((ord_le865407012indi_o A_44) top_to54564308indi_o)) of role axiom named fact_723_subset__UNIV
% A new axiom: (forall (A_44:(arrow_1196572341e_indi->Prop)), ((ord_le865407012indi_o A_44) top_to54564308indi_o))
% FOF formula (forall (A_44:(nat->Prop)), ((ord_less_eq_nat_o A_44) top_top_nat_o)) of role axiom named fact_724_subset__UNIV
% A new axiom: (forall (A_44:(nat->Prop)), ((ord_less_eq_nat_o A_44) top_top_nat_o))
% FOF formula (forall (A_44:(product_unit->Prop)), ((ord_le1511552390unit_o A_44) top_to1984820022unit_o)) of role axiom named fact_725_subset__UNIV
% A new axiom: (forall (A_44:(product_unit->Prop)), ((ord_le1511552390unit_o A_44) top_to1984820022unit_o))
% FOF formula (forall (A_43:(arrow_1196572341e_indi->Prop)) (F_8:(arrow_1196572341e_indi->nat)) (B_41:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_8) B_41)->(((ord_le865407012indi_o A_43) B_41)->((inj_on1505595958di_nat F_8) A_43)))) of role axiom named fact_726_subset__inj__on
% A new axiom: (forall (A_43:(arrow_1196572341e_indi->Prop)) (F_8:(arrow_1196572341e_indi->nat)) (B_41:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_8) B_41)->(((ord_le865407012indi_o A_43) B_41)->((inj_on1505595958di_nat F_8) A_43))))
% FOF formula (forall (A_43:(nat->Prop)) (F_8:(nat->nat)) (B_41:(nat->Prop)), (((inj_on_nat_nat F_8) B_41)->(((ord_less_eq_nat_o A_43) B_41)->((inj_on_nat_nat F_8) A_43)))) of role axiom named fact_727_subset__inj__on
% A new axiom: (forall (A_43:(nat->Prop)) (F_8:(nat->nat)) (B_41:(nat->Prop)), (((inj_on_nat_nat F_8) B_41)->(((ord_less_eq_nat_o A_43) B_41)->((inj_on_nat_nat F_8) A_43))))
% FOF formula (forall (B_40:nat) (A_42:nat) (C_29:nat), ((((eq nat) ((plus_plus_nat B_40) A_42)) ((plus_plus_nat C_29) A_42))->(((eq nat) B_40) C_29))) of role axiom named fact_728_add__right__imp__eq
% A new axiom: (forall (B_40:nat) (A_42:nat) (C_29:nat), ((((eq nat) ((plus_plus_nat B_40) A_42)) ((plus_plus_nat C_29) A_42))->(((eq nat) B_40) C_29)))
% FOF formula (forall (A_41:nat) (B_39:nat) (C_28:nat), ((((eq nat) ((plus_plus_nat A_41) B_39)) ((plus_plus_nat A_41) C_28))->(((eq nat) B_39) C_28))) of role axiom named fact_729_add__imp__eq
% A new axiom: (forall (A_41:nat) (B_39:nat) (C_28:nat), ((((eq nat) ((plus_plus_nat A_41) B_39)) ((plus_plus_nat A_41) C_28))->(((eq nat) B_39) C_28)))
% FOF formula (forall (A_40:nat) (B_38:nat) (C_27:nat), ((((eq nat) ((plus_plus_nat A_40) B_38)) ((plus_plus_nat A_40) C_27))->(((eq nat) B_38) C_27))) of role axiom named fact_730_add__left__imp__eq
% A new axiom: (forall (A_40:nat) (B_38:nat) (C_27:nat), ((((eq nat) ((plus_plus_nat A_40) B_38)) ((plus_plus_nat A_40) C_27))->(((eq nat) B_38) C_27)))
% FOF formula (forall (B_37:nat) (A_39:nat) (C_26:nat), ((iff (((eq nat) ((plus_plus_nat B_37) A_39)) ((plus_plus_nat C_26) A_39))) (((eq nat) B_37) C_26))) of role axiom named fact_731_add__right__cancel
% A new axiom: (forall (B_37:nat) (A_39:nat) (C_26:nat), ((iff (((eq nat) ((plus_plus_nat B_37) A_39)) ((plus_plus_nat C_26) A_39))) (((eq nat) B_37) C_26)))
% FOF formula (forall (A_38:nat) (B_36:nat) (C_25:nat), ((iff (((eq nat) ((plus_plus_nat A_38) B_36)) ((plus_plus_nat A_38) C_25))) (((eq nat) B_36) C_25))) of role axiom named fact_732_add__left__cancel
% A new axiom: (forall (A_38:nat) (B_36:nat) (C_25:nat), ((iff (((eq nat) ((plus_plus_nat A_38) B_36)) ((plus_plus_nat A_38) C_25))) (((eq nat) B_36) C_25)))
% FOF formula (forall (A_37:nat) (B_35:nat) (C_24:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_37) B_35)) C_24)) ((plus_plus_nat A_37) ((plus_plus_nat B_35) C_24)))) of role axiom named fact_733_ab__semigroup__add__class_Oadd__ac_I1_J
% A new axiom: (forall (A_37:nat) (B_35:nat) (C_24:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_37) B_35)) C_24)) ((plus_plus_nat A_37) ((plus_plus_nat B_35) C_24))))
% FOF formula (forall (X_7:nat), ((iff (((eq nat) one_one_nat) X_7)) (((eq nat) X_7) one_one_nat))) of role axiom named fact_734_one__reorient
% A new axiom: (forall (X_7:nat), ((iff (((eq nat) one_one_nat) X_7)) (((eq nat) X_7) one_one_nat)))
% FOF formula (forall (C_23:nat) (A_36:nat) (B_34:nat), (((ord_less_eq_nat ((plus_plus_nat C_23) A_36)) ((plus_plus_nat C_23) B_34))->((ord_less_eq_nat A_36) B_34))) of role axiom named fact_735_add__le__imp__le__left
% A new axiom: (forall (C_23:nat) (A_36:nat) (B_34:nat), (((ord_less_eq_nat ((plus_plus_nat C_23) A_36)) ((plus_plus_nat C_23) B_34))->((ord_less_eq_nat A_36) B_34)))
% FOF formula (forall (A_35:nat) (C_22:nat) (B_33:nat), (((ord_less_eq_nat ((plus_plus_nat A_35) C_22)) ((plus_plus_nat B_33) C_22))->((ord_less_eq_nat A_35) B_33))) of role axiom named fact_736_add__le__imp__le__right
% A new axiom: (forall (A_35:nat) (C_22:nat) (B_33:nat), (((ord_less_eq_nat ((plus_plus_nat A_35) C_22)) ((plus_plus_nat B_33) C_22))->((ord_less_eq_nat A_35) B_33)))
% FOF formula (forall (C_21:nat) (D_1:nat) (A_34:nat) (B_32:nat), (((ord_less_eq_nat A_34) B_32)->(((ord_less_eq_nat C_21) D_1)->((ord_less_eq_nat ((plus_plus_nat A_34) C_21)) ((plus_plus_nat B_32) D_1))))) of role axiom named fact_737_add__mono
% A new axiom: (forall (C_21:nat) (D_1:nat) (A_34:nat) (B_32:nat), (((ord_less_eq_nat A_34) B_32)->(((ord_less_eq_nat C_21) D_1)->((ord_less_eq_nat ((plus_plus_nat A_34) C_21)) ((plus_plus_nat B_32) D_1)))))
% FOF formula (forall (C_20:nat) (A_33:nat) (B_31:nat), (((ord_less_eq_nat A_33) B_31)->((ord_less_eq_nat ((plus_plus_nat C_20) A_33)) ((plus_plus_nat C_20) B_31)))) of role axiom named fact_738_add__left__mono
% A new axiom: (forall (C_20:nat) (A_33:nat) (B_31:nat), (((ord_less_eq_nat A_33) B_31)->((ord_less_eq_nat ((plus_plus_nat C_20) A_33)) ((plus_plus_nat C_20) B_31))))
% FOF formula (forall (C_19:nat) (A_32:nat) (B_30:nat), (((ord_less_eq_nat A_32) B_30)->((ord_less_eq_nat ((plus_plus_nat A_32) C_19)) ((plus_plus_nat B_30) C_19)))) of role axiom named fact_739_add__right__mono
% A new axiom: (forall (C_19:nat) (A_32:nat) (B_30:nat), (((ord_less_eq_nat A_32) B_30)->((ord_less_eq_nat ((plus_plus_nat A_32) C_19)) ((plus_plus_nat B_30) C_19))))
% FOF formula (forall (C_18:nat) (A_31:nat) (B_29:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_18) A_31)) ((plus_plus_nat C_18) B_29))) ((ord_less_eq_nat A_31) B_29))) of role axiom named fact_740_add__le__cancel__left
% A new axiom: (forall (C_18:nat) (A_31:nat) (B_29:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_18) A_31)) ((plus_plus_nat C_18) B_29))) ((ord_less_eq_nat A_31) B_29)))
% FOF formula (forall (A_30:nat) (C_17:nat) (B_28:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_30) C_17)) ((plus_plus_nat B_28) C_17))) ((ord_less_eq_nat A_30) B_28))) of role axiom named fact_741_add__le__cancel__right
% A new axiom: (forall (A_30:nat) (C_17:nat) (B_28:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_30) C_17)) ((plus_plus_nat B_28) C_17))) ((ord_less_eq_nat A_30) B_28)))
% FOF formula (forall (C_16:nat) (A_29:nat) (B_27:nat), (((ord_less_nat ((plus_plus_nat C_16) A_29)) ((plus_plus_nat C_16) B_27))->((ord_less_nat A_29) B_27))) of role axiom named fact_742_add__less__imp__less__left
% A new axiom: (forall (C_16:nat) (A_29:nat) (B_27:nat), (((ord_less_nat ((plus_plus_nat C_16) A_29)) ((plus_plus_nat C_16) B_27))->((ord_less_nat A_29) B_27)))
% FOF formula (forall (A_28:nat) (C_15:nat) (B_26:nat), (((ord_less_nat ((plus_plus_nat A_28) C_15)) ((plus_plus_nat B_26) C_15))->((ord_less_nat A_28) B_26))) of role axiom named fact_743_add__less__imp__less__right
% A new axiom: (forall (A_28:nat) (C_15:nat) (B_26:nat), (((ord_less_nat ((plus_plus_nat A_28) C_15)) ((plus_plus_nat B_26) C_15))->((ord_less_nat A_28) B_26)))
% FOF formula (forall (C_14:nat) (D:nat) (A_27:nat) (B_25:nat), (((ord_less_nat A_27) B_25)->(((ord_less_nat C_14) D)->((ord_less_nat ((plus_plus_nat A_27) C_14)) ((plus_plus_nat B_25) D))))) of role axiom named fact_744_add__strict__mono
% A new axiom: (forall (C_14:nat) (D:nat) (A_27:nat) (B_25:nat), (((ord_less_nat A_27) B_25)->(((ord_less_nat C_14) D)->((ord_less_nat ((plus_plus_nat A_27) C_14)) ((plus_plus_nat B_25) D)))))
% FOF formula (forall (C_13:nat) (A_26:nat) (B_24:nat), (((ord_less_nat A_26) B_24)->((ord_less_nat ((plus_plus_nat C_13) A_26)) ((plus_plus_nat C_13) B_24)))) of role axiom named fact_745_add__strict__left__mono
% A new axiom: (forall (C_13:nat) (A_26:nat) (B_24:nat), (((ord_less_nat A_26) B_24)->((ord_less_nat ((plus_plus_nat C_13) A_26)) ((plus_plus_nat C_13) B_24))))
% FOF formula (forall (C_12:nat) (A_25:nat) (B_23:nat), (((ord_less_nat A_25) B_23)->((ord_less_nat ((plus_plus_nat A_25) C_12)) ((plus_plus_nat B_23) C_12)))) of role axiom named fact_746_add__strict__right__mono
% A new axiom: (forall (C_12:nat) (A_25:nat) (B_23:nat), (((ord_less_nat A_25) B_23)->((ord_less_nat ((plus_plus_nat A_25) C_12)) ((plus_plus_nat B_23) C_12))))
% FOF formula (forall (C_11:nat) (A_24:nat) (B_22:nat), ((iff ((ord_less_nat ((plus_plus_nat C_11) A_24)) ((plus_plus_nat C_11) B_22))) ((ord_less_nat A_24) B_22))) of role axiom named fact_747_add__less__cancel__left
% A new axiom: (forall (C_11:nat) (A_24:nat) (B_22:nat), ((iff ((ord_less_nat ((plus_plus_nat C_11) A_24)) ((plus_plus_nat C_11) B_22))) ((ord_less_nat A_24) B_22)))
% FOF formula (forall (A_23:nat) (C_10:nat) (B_21:nat), ((iff ((ord_less_nat ((plus_plus_nat A_23) C_10)) ((plus_plus_nat B_21) C_10))) ((ord_less_nat A_23) B_21))) of role axiom named fact_748_add__less__cancel__right
% A new axiom: (forall (A_23:nat) (C_10:nat) (B_21:nat), ((iff ((ord_less_nat ((plus_plus_nat A_23) C_10)) ((plus_plus_nat B_21) C_10))) ((ord_less_nat A_23) B_21)))
% FOF formula (forall (F_7:((produc1572197287le_alt->Prop)->Prop)) (G:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le1027220427lt_o_o F_7) G))) of role axiom named fact_749_le__funI
% A new axiom: (forall (F_7:((produc1572197287le_alt->Prop)->Prop)) (G:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le1027220427lt_o_o F_7) G)))
% FOF formula (forall (F_7:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le1805007862lt_o_o F_7) G))) of role axiom named fact_750_le__funI
% A new axiom: (forall (F_7:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le1805007862lt_o_o F_7) G)))
% FOF formula (forall (F_7:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le602483040lt_o_o F_7) G))) of role axiom named fact_751_le__funI
% A new axiom: (forall (F_7:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le602483040lt_o_o F_7) G)))
% FOF formula (forall (F_7:(produc1572197287le_alt->Prop)) (G:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le962286258_alt_o F_7) G))) of role axiom named fact_752_le__funI
% A new axiom: (forall (F_7:(produc1572197287le_alt->Prop)) (G:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le962286258_alt_o F_7) G)))
% FOF formula (forall (F_7:(arrow_1196572341e_indi->Prop)) (G:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le865407012indi_o F_7) G))) of role axiom named fact_753_le__funI
% A new axiom: (forall (F_7:(arrow_1196572341e_indi->Prop)) (G:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le865407012indi_o F_7) G)))
% FOF formula (forall (F_7:(product_unit->Prop)) (G:(product_unit->Prop)), ((forall (X_1:product_unit), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le1511552390unit_o F_7) G))) of role axiom named fact_754_le__funI
% A new axiom: (forall (F_7:(product_unit->Prop)) (G:(product_unit->Prop)), ((forall (X_1:product_unit), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le1511552390unit_o F_7) G)))
% FOF formula (forall (F_7:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((forall (X_1:arrow_1389031998le_alt), ((ord_le1423491573_alt_o (F_7 X_1)) (G X_1)))->((ord_le1463467535_alt_o F_7) G))) of role axiom named fact_755_le__funI
% A new axiom: (forall (F_7:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((forall (X_1:arrow_1389031998le_alt), ((ord_le1423491573_alt_o (F_7 X_1)) (G X_1)))->((ord_le1463467535_alt_o F_7) G)))
% FOF formula (forall (F_7:(nat->Prop)) (G:(nat->Prop)), ((forall (X_1:nat), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_less_eq_nat_o F_7) G))) of role axiom named fact_756_le__funI
% A new axiom: (forall (F_7:(nat->Prop)) (G:(nat->Prop)), ((forall (X_1:nat), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_less_eq_nat_o F_7) G)))
% FOF formula (forall (C_9:(nat->Prop)) (F_6:((nat->Prop)->(nat->Prop))) (B_20:(nat->Prop)) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_less_nat_o C_9) B_20)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22))))) of role axiom named fact_757_xt6
% A new axiom: (forall (C_9:(nat->Prop)) (F_6:((nat->Prop)->(nat->Prop))) (B_20:(nat->Prop)) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_less_nat_o C_9) B_20)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:(product_unit->Prop)) (F_6:((product_unit->Prop)->(nat->Prop))) (B_20:(product_unit->Prop)) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_le232288914unit_o C_9) B_20)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22))))) of role axiom named fact_758_xt6
% A new axiom: (forall (C_9:(product_unit->Prop)) (F_6:((product_unit->Prop)->(nat->Prop))) (B_20:(product_unit->Prop)) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_le232288914unit_o C_9) B_20)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:(arrow_1196572341e_indi->Prop)) (F_6:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_20:(arrow_1196572341e_indi->Prop)) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_le1991507760indi_o C_9) B_20)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22))))) of role axiom named fact_759_xt6
% A new axiom: (forall (C_9:(arrow_1196572341e_indi->Prop)) (F_6:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_20:(arrow_1196572341e_indi->Prop)) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_le1991507760indi_o C_9) B_20)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:nat) (F_6:(nat->(nat->Prop))) (B_20:nat) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22))))) of role axiom named fact_760_xt6
% A new axiom: (forall (C_9:nat) (F_6:(nat->(nat->Prop))) (B_20:nat) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:nat) (F_6:(nat->(product_unit->Prop))) (B_20:nat) (A_22:(product_unit->Prop)), (((ord_le1511552390unit_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le232288914unit_o (F_6 Y_1)) (F_6 X_1))))->((ord_le232288914unit_o (F_6 C_9)) A_22))))) of role axiom named fact_761_xt6
% A new axiom: (forall (C_9:nat) (F_6:(nat->(product_unit->Prop))) (B_20:nat) (A_22:(product_unit->Prop)), (((ord_le1511552390unit_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le232288914unit_o (F_6 Y_1)) (F_6 X_1))))->((ord_le232288914unit_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:nat) (F_6:(nat->(arrow_1196572341e_indi->Prop))) (B_20:nat) (A_22:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1991507760indi_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1991507760indi_o (F_6 C_9)) A_22))))) of role axiom named fact_762_xt6
% A new axiom: (forall (C_9:nat) (F_6:(nat->(arrow_1196572341e_indi->Prop))) (B_20:nat) (A_22:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1991507760indi_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1991507760indi_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:nat) (F_6:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_20:nat) (A_22:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le874404799lt_o_o (F_6 Y_1)) (F_6 X_1))))->((ord_le874404799lt_o_o (F_6 C_9)) A_22))))) of role axiom named fact_763_xt6
% A new axiom: (forall (C_9:nat) (F_6:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_20:nat) (A_22:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le874404799lt_o_o (F_6 Y_1)) (F_6 X_1))))->((ord_le874404799lt_o_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:nat) (F_6:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_20:nat) (A_22:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1382328578lt_o_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1382328578lt_o_o (F_6 C_9)) A_22))))) of role axiom named fact_764_xt6
% A new axiom: (forall (C_9:nat) (F_6:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_20:nat) (A_22:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1382328578lt_o_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1382328578lt_o_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:nat) (F_6:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_20:nat) (A_22:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le914873172lt_o_o (F_6 Y_1)) (F_6 X_1))))->((ord_le914873172lt_o_o (F_6 C_9)) A_22))))) of role axiom named fact_765_xt6
% A new axiom: (forall (C_9:nat) (F_6:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_20:nat) (A_22:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le914873172lt_o_o (F_6 Y_1)) (F_6 X_1))))->((ord_le914873172lt_o_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:nat) (F_6:(nat->(produc1572197287le_alt->Prop))) (B_20:nat) (A_22:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1852932542_alt_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1852932542_alt_o (F_6 C_9)) A_22))))) of role axiom named fact_766_xt6
% A new axiom: (forall (C_9:nat) (F_6:(nat->(produc1572197287le_alt->Prop))) (B_20:nat) (A_22:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1852932542_alt_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1852932542_alt_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:nat) (F_6:(nat->Prop)) (B_20:nat) (A_22:Prop), (((ord_less_eq_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_o (F_6 C_9)) A_22))))) of role axiom named fact_767_xt6
% A new axiom: (forall (C_9:nat) (F_6:(nat->Prop)) (B_20:nat) (A_22:Prop), (((ord_less_eq_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:nat) (F_6:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_20:nat) (A_22:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1339521307_alt_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1339521307_alt_o (F_6 C_9)) A_22))))) of role axiom named fact_768_xt6
% A new axiom: (forall (C_9:nat) (F_6:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_20:nat) (A_22:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1339521307_alt_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1339521307_alt_o (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:(nat->Prop)) (F_6:((nat->Prop)->nat)) (B_20:(nat->Prop)) (A_22:nat), (((ord_less_eq_nat (F_6 B_20)) A_22)->(((ord_less_nat_o C_9) B_20)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat (F_6 C_9)) A_22))))) of role axiom named fact_769_xt6
% A new axiom: (forall (C_9:(nat->Prop)) (F_6:((nat->Prop)->nat)) (B_20:(nat->Prop)) (A_22:nat), (((ord_less_eq_nat (F_6 B_20)) A_22)->(((ord_less_nat_o C_9) B_20)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:(product_unit->Prop)) (F_6:((product_unit->Prop)->nat)) (B_20:(product_unit->Prop)) (A_22:nat), (((ord_less_eq_nat (F_6 B_20)) A_22)->(((ord_le232288914unit_o C_9) B_20)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat (F_6 C_9)) A_22))))) of role axiom named fact_770_xt6
% A new axiom: (forall (C_9:(product_unit->Prop)) (F_6:((product_unit->Prop)->nat)) (B_20:(product_unit->Prop)) (A_22:nat), (((ord_less_eq_nat (F_6 B_20)) A_22)->(((ord_le232288914unit_o C_9) B_20)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat (F_6 C_9)) A_22)))))
% FOF formula (forall (C_9:(arrow_1196572341e_indi->Prop)) (F_6:((arrow_1196572341e_indi->Prop)->nat)) (B_20:(arrow_1196572341e_indi->Prop)) (A_22:nat), (((ord_less_eq_nat (F_6 B_20)) A_22)->(((ord_le1991507760indi_o C_9) B_20)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat (F_6 C_9)) A_22))))) of role axiom named fact_771_xt6
% A new axiom: (forall (C_9:(arrow_1196572341e_indi->Prop)) (F_6:((arrow_1196572341e_indi->Prop)->nat)) (B_20:(arrow_1196572341e_indi->Prop)) (A_22:nat), (((ord_less_eq_nat (F_6 B_20)) A_22)->(((ord_le1991507760indi_o C_9) B_20)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat (F_6 C_9)) A_22)))))
% FOF formula (forall (C_8:nat) (F_5:(nat->(nat->Prop))) (B_19:nat) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))) of role axiom named fact_772_xt4
% A new axiom: (forall (C_8:nat) (F_5:(nat->(nat->Prop))) (B_19:nat) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:nat) (F_5:(nat->(product_unit->Prop))) (B_19:nat) (A_21:(product_unit->Prop)), (((ord_le232288914unit_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1511552390unit_o (F_5 Y_1)) (F_5 X_1))))->((ord_le232288914unit_o (F_5 C_8)) A_21))))) of role axiom named fact_773_xt4
% A new axiom: (forall (C_8:nat) (F_5:(nat->(product_unit->Prop))) (B_19:nat) (A_21:(product_unit->Prop)), (((ord_le232288914unit_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1511552390unit_o (F_5 Y_1)) (F_5 X_1))))->((ord_le232288914unit_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:nat) (F_5:(nat->(arrow_1196572341e_indi->Prop))) (B_19:nat) (A_21:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le865407012indi_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1991507760indi_o (F_5 C_8)) A_21))))) of role axiom named fact_774_xt4
% A new axiom: (forall (C_8:nat) (F_5:(nat->(arrow_1196572341e_indi->Prop))) (B_19:nat) (A_21:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le865407012indi_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1991507760indi_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:nat) (F_5:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_19:nat) (A_21:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1027220427lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le874404799lt_o_o (F_5 C_8)) A_21))))) of role axiom named fact_775_xt4
% A new axiom: (forall (C_8:nat) (F_5:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_19:nat) (A_21:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1027220427lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le874404799lt_o_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:nat) (F_5:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_19:nat) (A_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1805007862lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1382328578lt_o_o (F_5 C_8)) A_21))))) of role axiom named fact_776_xt4
% A new axiom: (forall (C_8:nat) (F_5:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_19:nat) (A_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1805007862lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1382328578lt_o_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:nat) (F_5:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_19:nat) (A_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le602483040lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le914873172lt_o_o (F_5 C_8)) A_21))))) of role axiom named fact_777_xt4
% A new axiom: (forall (C_8:nat) (F_5:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_19:nat) (A_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le602483040lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le914873172lt_o_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:nat) (F_5:(nat->(produc1572197287le_alt->Prop))) (B_19:nat) (A_21:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le962286258_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1852932542_alt_o (F_5 C_8)) A_21))))) of role axiom named fact_778_xt4
% A new axiom: (forall (C_8:nat) (F_5:(nat->(produc1572197287le_alt->Prop))) (B_19:nat) (A_21:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le962286258_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1852932542_alt_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:nat) (F_5:(nat->Prop)) (B_19:nat) (A_21:Prop), (((ord_less_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_o (F_5 C_8)) A_21))))) of role axiom named fact_779_xt4
% A new axiom: (forall (C_8:nat) (F_5:(nat->Prop)) (B_19:nat) (A_21:Prop), (((ord_less_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:nat) (F_5:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_19:nat) (A_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1463467535_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1339521307_alt_o (F_5 C_8)) A_21))))) of role axiom named fact_780_xt4
% A new axiom: (forall (C_8:nat) (F_5:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_19:nat) (A_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1463467535_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1339521307_alt_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(nat->Prop))) (B_19:(nat->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))) of role axiom named fact_781_xt4
% A new axiom: (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(nat->Prop))) (B_19:(nat->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(product_unit->Prop))) (B_19:(nat->Prop)) (A_21:(product_unit->Prop)), (((ord_le232288914unit_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1511552390unit_o (F_5 Y_1)) (F_5 X_1))))->((ord_le232288914unit_o (F_5 C_8)) A_21))))) of role axiom named fact_782_xt4
% A new axiom: (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(product_unit->Prop))) (B_19:(nat->Prop)) (A_21:(product_unit->Prop)), (((ord_le232288914unit_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1511552390unit_o (F_5 Y_1)) (F_5 X_1))))->((ord_le232288914unit_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (B_19:(nat->Prop)) (A_21:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le865407012indi_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1991507760indi_o (F_5 C_8)) A_21))))) of role axiom named fact_783_xt4
% A new axiom: (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (B_19:(nat->Prop)) (A_21:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le865407012indi_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1991507760indi_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (B_19:(nat->Prop)) (A_21:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1027220427lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le874404799lt_o_o (F_5 C_8)) A_21))))) of role axiom named fact_784_xt4
% A new axiom: (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (B_19:(nat->Prop)) (A_21:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1027220427lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le874404799lt_o_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_19:(nat->Prop)) (A_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1805007862lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1382328578lt_o_o (F_5 C_8)) A_21))))) of role axiom named fact_785_xt4
% A new axiom: (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_19:(nat->Prop)) (A_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1805007862lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1382328578lt_o_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_19:(nat->Prop)) (A_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le602483040lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le914873172lt_o_o (F_5 C_8)) A_21))))) of role axiom named fact_786_xt4
% A new axiom: (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_19:(nat->Prop)) (A_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le602483040lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le914873172lt_o_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(produc1572197287le_alt->Prop))) (B_19:(nat->Prop)) (A_21:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le962286258_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1852932542_alt_o (F_5 C_8)) A_21))))) of role axiom named fact_787_xt4
% A new axiom: (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(produc1572197287le_alt->Prop))) (B_19:(nat->Prop)) (A_21:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le962286258_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1852932542_alt_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->Prop)) (B_19:(nat->Prop)) (A_21:Prop), (((ord_less_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_o (F_5 C_8)) A_21))))) of role axiom named fact_788_xt4
% A new axiom: (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->Prop)) (B_19:(nat->Prop)) (A_21:Prop), (((ord_less_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_19:(nat->Prop)) (A_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1463467535_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1339521307_alt_o (F_5 C_8)) A_21))))) of role axiom named fact_789_xt4
% A new axiom: (forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_19:(nat->Prop)) (A_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1463467535_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1339521307_alt_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:((produc1572197287le_alt->Prop)->Prop)) (F_5:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (B_19:((produc1572197287le_alt->Prop)->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1027220427lt_o_o C_8) B_19)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))) of role axiom named fact_790_xt4
% A new axiom: (forall (C_8:((produc1572197287le_alt->Prop)->Prop)) (F_5:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (B_19:((produc1572197287le_alt->Prop)->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1027220427lt_o_o C_8) B_19)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_5:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1805007862lt_o_o C_8) B_19)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))) of role axiom named fact_791_xt4
% A new axiom: (forall (C_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_5:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1805007862lt_o_o C_8) B_19)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le602483040lt_o_o C_8) B_19)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))) of role axiom named fact_792_xt4
% A new axiom: (forall (C_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le602483040lt_o_o C_8) B_19)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(produc1572197287le_alt->Prop)) (F_5:((produc1572197287le_alt->Prop)->(nat->Prop))) (B_19:(produc1572197287le_alt->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le962286258_alt_o C_8) B_19)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))) of role axiom named fact_793_xt4
% A new axiom: (forall (C_8:(produc1572197287le_alt->Prop)) (F_5:((produc1572197287le_alt->Prop)->(nat->Prop))) (B_19:(produc1572197287le_alt->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le962286258_alt_o C_8) B_19)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:Prop) (F_5:(Prop->(nat->Prop))) (B_19:Prop) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_less_eq_o C_8) B_19)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))) of role axiom named fact_794_xt4
% A new axiom: (forall (C_8:Prop) (F_5:(Prop->(nat->Prop))) (B_19:Prop) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_less_eq_o C_8) B_19)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(arrow_1196572341e_indi->Prop)) (F_5:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_19:(arrow_1196572341e_indi->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le865407012indi_o C_8) B_19)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))) of role axiom named fact_795_xt4
% A new axiom: (forall (C_8:(arrow_1196572341e_indi->Prop)) (F_5:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_19:(arrow_1196572341e_indi->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le865407012indi_o C_8) B_19)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(product_unit->Prop)) (F_5:((product_unit->Prop)->(nat->Prop))) (B_19:(product_unit->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1511552390unit_o C_8) B_19)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))) of role axiom named fact_796_xt4
% A new axiom: (forall (C_8:(product_unit->Prop)) (F_5:((product_unit->Prop)->(nat->Prop))) (B_19:(product_unit->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1511552390unit_o C_8) B_19)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_5:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (B_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1463467535_alt_o C_8) B_19)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))) of role axiom named fact_797_xt4
% A new axiom: (forall (C_8:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_5:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (B_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1463467535_alt_o C_8) B_19)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:((produc1572197287le_alt->Prop)->Prop)) (F_5:(((produc1572197287le_alt->Prop)->Prop)->nat)) (B_19:((produc1572197287le_alt->Prop)->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1027220427lt_o_o C_8) B_19)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))) of role axiom named fact_798_xt4
% A new axiom: (forall (C_8:((produc1572197287le_alt->Prop)->Prop)) (F_5:(((produc1572197287le_alt->Prop)->Prop)->nat)) (B_19:((produc1572197287le_alt->Prop)->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1027220427lt_o_o C_8) B_19)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_5:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1805007862lt_o_o C_8) B_19)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))) of role axiom named fact_799_xt4
% A new axiom: (forall (C_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_5:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1805007862lt_o_o C_8) B_19)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le602483040lt_o_o C_8) B_19)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))) of role axiom named fact_800_xt4
% A new axiom: (forall (C_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le602483040lt_o_o C_8) B_19)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(produc1572197287le_alt->Prop)) (F_5:((produc1572197287le_alt->Prop)->nat)) (B_19:(produc1572197287le_alt->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le962286258_alt_o C_8) B_19)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))) of role axiom named fact_801_xt4
% A new axiom: (forall (C_8:(produc1572197287le_alt->Prop)) (F_5:((produc1572197287le_alt->Prop)->nat)) (B_19:(produc1572197287le_alt->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le962286258_alt_o C_8) B_19)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:Prop) (F_5:(Prop->nat)) (B_19:Prop) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_less_eq_o C_8) B_19)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))) of role axiom named fact_802_xt4
% A new axiom: (forall (C_8:Prop) (F_5:(Prop->nat)) (B_19:Prop) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_less_eq_o C_8) B_19)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(arrow_1196572341e_indi->Prop)) (F_5:((arrow_1196572341e_indi->Prop)->nat)) (B_19:(arrow_1196572341e_indi->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le865407012indi_o C_8) B_19)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))) of role axiom named fact_803_xt4
% A new axiom: (forall (C_8:(arrow_1196572341e_indi->Prop)) (F_5:((arrow_1196572341e_indi->Prop)->nat)) (B_19:(arrow_1196572341e_indi->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le865407012indi_o C_8) B_19)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(product_unit->Prop)) (F_5:((product_unit->Prop)->nat)) (B_19:(product_unit->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1511552390unit_o C_8) B_19)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))) of role axiom named fact_804_xt4
% A new axiom: (forall (C_8:(product_unit->Prop)) (F_5:((product_unit->Prop)->nat)) (B_19:(product_unit->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1511552390unit_o C_8) B_19)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21)))))
% FOF formula (forall (C_8:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_5:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (B_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1463467535_alt_o C_8) B_19)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))) of role axiom named fact_805_xt4
% A new axiom: (forall (C_8:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_5:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (B_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1463467535_alt_o C_8) B_19)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21)))))
% FOF formula (forall (C_7:(nat->Prop)) (A_20:(nat->Prop)) (F_4:((nat->Prop)->(nat->Prop))) (B_18:(nat->Prop)), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_less_nat_o B_18) C_7)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7)))))) of role axiom named fact_806_order__le__less__subst1
% A new axiom: (forall (C_7:(nat->Prop)) (A_20:(nat->Prop)) (F_4:((nat->Prop)->(nat->Prop))) (B_18:(nat->Prop)), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_less_nat_o B_18) C_7)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:(product_unit->Prop)) (A_20:(nat->Prop)) (F_4:((product_unit->Prop)->(nat->Prop))) (B_18:(product_unit->Prop)), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_le232288914unit_o B_18) C_7)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7)))))) of role axiom named fact_807_order__le__less__subst1
% A new axiom: (forall (C_7:(product_unit->Prop)) (A_20:(nat->Prop)) (F_4:((product_unit->Prop)->(nat->Prop))) (B_18:(product_unit->Prop)), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_le232288914unit_o B_18) C_7)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:(arrow_1196572341e_indi->Prop)) (A_20:(nat->Prop)) (F_4:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_18:(arrow_1196572341e_indi->Prop)), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_le1991507760indi_o B_18) C_7)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7)))))) of role axiom named fact_808_order__le__less__subst1
% A new axiom: (forall (C_7:(arrow_1196572341e_indi->Prop)) (A_20:(nat->Prop)) (F_4:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_18:(arrow_1196572341e_indi->Prop)), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_le1991507760indi_o B_18) C_7)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:nat) (A_20:(nat->Prop)) (F_4:(nat->(nat->Prop))) (B_18:nat), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7)))))) of role axiom named fact_809_order__le__less__subst1
% A new axiom: (forall (C_7:nat) (A_20:(nat->Prop)) (F_4:(nat->(nat->Prop))) (B_18:nat), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:nat) (A_20:(product_unit->Prop)) (F_4:(nat->(product_unit->Prop))) (B_18:nat), (((ord_le1511552390unit_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le232288914unit_o (F_4 X_1)) (F_4 Y_1))))->((ord_le232288914unit_o A_20) (F_4 C_7)))))) of role axiom named fact_810_order__le__less__subst1
% A new axiom: (forall (C_7:nat) (A_20:(product_unit->Prop)) (F_4:(nat->(product_unit->Prop))) (B_18:nat), (((ord_le1511552390unit_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le232288914unit_o (F_4 X_1)) (F_4 Y_1))))->((ord_le232288914unit_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:nat) (A_20:(arrow_1196572341e_indi->Prop)) (F_4:(nat->(arrow_1196572341e_indi->Prop))) (B_18:nat), (((ord_le865407012indi_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1991507760indi_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1991507760indi_o A_20) (F_4 C_7)))))) of role axiom named fact_811_order__le__less__subst1
% A new axiom: (forall (C_7:nat) (A_20:(arrow_1196572341e_indi->Prop)) (F_4:(nat->(arrow_1196572341e_indi->Prop))) (B_18:nat), (((ord_le865407012indi_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1991507760indi_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1991507760indi_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:nat) (A_20:((produc1572197287le_alt->Prop)->Prop)) (F_4:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_18:nat), (((ord_le1027220427lt_o_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le874404799lt_o_o (F_4 X_1)) (F_4 Y_1))))->((ord_le874404799lt_o_o A_20) (F_4 C_7)))))) of role axiom named fact_812_order__le__less__subst1
% A new axiom: (forall (C_7:nat) (A_20:((produc1572197287le_alt->Prop)->Prop)) (F_4:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_18:nat), (((ord_le1027220427lt_o_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le874404799lt_o_o (F_4 X_1)) (F_4 Y_1))))->((ord_le874404799lt_o_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:nat) (A_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_4:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_18:nat), (((ord_le1805007862lt_o_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1382328578lt_o_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1382328578lt_o_o A_20) (F_4 C_7)))))) of role axiom named fact_813_order__le__less__subst1
% A new axiom: (forall (C_7:nat) (A_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_4:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_18:nat), (((ord_le1805007862lt_o_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1382328578lt_o_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1382328578lt_o_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:nat) (A_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_4:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_18:nat), (((ord_le602483040lt_o_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le914873172lt_o_o (F_4 X_1)) (F_4 Y_1))))->((ord_le914873172lt_o_o A_20) (F_4 C_7)))))) of role axiom named fact_814_order__le__less__subst1
% A new axiom: (forall (C_7:nat) (A_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_4:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_18:nat), (((ord_le602483040lt_o_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le914873172lt_o_o (F_4 X_1)) (F_4 Y_1))))->((ord_le914873172lt_o_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:nat) (A_20:(produc1572197287le_alt->Prop)) (F_4:(nat->(produc1572197287le_alt->Prop))) (B_18:nat), (((ord_le962286258_alt_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1852932542_alt_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1852932542_alt_o A_20) (F_4 C_7)))))) of role axiom named fact_815_order__le__less__subst1
% A new axiom: (forall (C_7:nat) (A_20:(produc1572197287le_alt->Prop)) (F_4:(nat->(produc1572197287le_alt->Prop))) (B_18:nat), (((ord_le962286258_alt_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1852932542_alt_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1852932542_alt_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:nat) (A_20:Prop) (F_4:(nat->Prop)) (B_18:nat), (((ord_less_eq_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_o A_20) (F_4 C_7)))))) of role axiom named fact_816_order__le__less__subst1
% A new axiom: (forall (C_7:nat) (A_20:Prop) (F_4:(nat->Prop)) (B_18:nat), (((ord_less_eq_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:nat) (A_20:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_4:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_18:nat), (((ord_le1463467535_alt_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1339521307_alt_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1339521307_alt_o A_20) (F_4 C_7)))))) of role axiom named fact_817_order__le__less__subst1
% A new axiom: (forall (C_7:nat) (A_20:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_4:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_18:nat), (((ord_le1463467535_alt_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1339521307_alt_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1339521307_alt_o A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:(nat->Prop)) (A_20:nat) (F_4:((nat->Prop)->nat)) (B_18:(nat->Prop)), (((ord_less_eq_nat A_20) (F_4 B_18))->(((ord_less_nat_o B_18) C_7)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat A_20) (F_4 C_7)))))) of role axiom named fact_818_order__le__less__subst1
% A new axiom: (forall (C_7:(nat->Prop)) (A_20:nat) (F_4:((nat->Prop)->nat)) (B_18:(nat->Prop)), (((ord_less_eq_nat A_20) (F_4 B_18))->(((ord_less_nat_o B_18) C_7)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:(product_unit->Prop)) (A_20:nat) (F_4:((product_unit->Prop)->nat)) (B_18:(product_unit->Prop)), (((ord_less_eq_nat A_20) (F_4 B_18))->(((ord_le232288914unit_o B_18) C_7)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat A_20) (F_4 C_7)))))) of role axiom named fact_819_order__le__less__subst1
% A new axiom: (forall (C_7:(product_unit->Prop)) (A_20:nat) (F_4:((product_unit->Prop)->nat)) (B_18:(product_unit->Prop)), (((ord_less_eq_nat A_20) (F_4 B_18))->(((ord_le232288914unit_o B_18) C_7)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat A_20) (F_4 C_7))))))
% FOF formula (forall (C_7:(arrow_1196572341e_indi->Prop)) (A_20:nat) (F_4:((arrow_1196572341e_indi->Prop)->nat)) (B_18:(arrow_1196572341e_indi->Prop)), (((ord_less_eq_nat A_20) (F_4 B_18))->(((ord_le1991507760indi_o B_18) C_7)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat A_20) (F_4 C_7)))))) of role axiom named fact_820_order__le__less__subst1
% A new axiom: (forall (C_7:(arrow_1196572341e_indi->Prop)) (A_20:nat) (F_4:((arrow_1196572341e_indi->Prop)->nat)) (B_18:(arrow_1196572341e_indi->Prop)), (((ord_less_eq_nat A_20) (F_4 B_18))->(((ord_le1991507760indi_o B_18) C_7)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat A_20) (F_4 C_7))))))
% FOF formula (forall (C_6:nat) (A_19:(nat->Prop)) (F_3:(nat->(nat->Prop))) (B_17:nat), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))) of role axiom named fact_821_order__less__le__subst1
% A new axiom: (forall (C_6:nat) (A_19:(nat->Prop)) (F_3:(nat->(nat->Prop))) (B_17:nat), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:nat) (A_19:(product_unit->Prop)) (F_3:(nat->(product_unit->Prop))) (B_17:nat), (((ord_le232288914unit_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1511552390unit_o (F_3 X_1)) (F_3 Y_1))))->((ord_le232288914unit_o A_19) (F_3 C_6)))))) of role axiom named fact_822_order__less__le__subst1
% A new axiom: (forall (C_6:nat) (A_19:(product_unit->Prop)) (F_3:(nat->(product_unit->Prop))) (B_17:nat), (((ord_le232288914unit_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1511552390unit_o (F_3 X_1)) (F_3 Y_1))))->((ord_le232288914unit_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:nat) (A_19:(arrow_1196572341e_indi->Prop)) (F_3:(nat->(arrow_1196572341e_indi->Prop))) (B_17:nat), (((ord_le1991507760indi_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le865407012indi_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1991507760indi_o A_19) (F_3 C_6)))))) of role axiom named fact_823_order__less__le__subst1
% A new axiom: (forall (C_6:nat) (A_19:(arrow_1196572341e_indi->Prop)) (F_3:(nat->(arrow_1196572341e_indi->Prop))) (B_17:nat), (((ord_le1991507760indi_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le865407012indi_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1991507760indi_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:nat) (A_19:((produc1572197287le_alt->Prop)->Prop)) (F_3:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_17:nat), (((ord_le874404799lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1027220427lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le874404799lt_o_o A_19) (F_3 C_6)))))) of role axiom named fact_824_order__less__le__subst1
% A new axiom: (forall (C_6:nat) (A_19:((produc1572197287le_alt->Prop)->Prop)) (F_3:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_17:nat), (((ord_le874404799lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1027220427lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le874404799lt_o_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:nat) (A_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_3:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_17:nat), (((ord_le1382328578lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1805007862lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1382328578lt_o_o A_19) (F_3 C_6)))))) of role axiom named fact_825_order__less__le__subst1
% A new axiom: (forall (C_6:nat) (A_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_3:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_17:nat), (((ord_le1382328578lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1805007862lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1382328578lt_o_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:nat) (A_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_3:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_17:nat), (((ord_le914873172lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le602483040lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le914873172lt_o_o A_19) (F_3 C_6)))))) of role axiom named fact_826_order__less__le__subst1
% A new axiom: (forall (C_6:nat) (A_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_3:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_17:nat), (((ord_le914873172lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le602483040lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le914873172lt_o_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:nat) (A_19:(produc1572197287le_alt->Prop)) (F_3:(nat->(produc1572197287le_alt->Prop))) (B_17:nat), (((ord_le1852932542_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le962286258_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1852932542_alt_o A_19) (F_3 C_6)))))) of role axiom named fact_827_order__less__le__subst1
% A new axiom: (forall (C_6:nat) (A_19:(produc1572197287le_alt->Prop)) (F_3:(nat->(produc1572197287le_alt->Prop))) (B_17:nat), (((ord_le1852932542_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le962286258_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1852932542_alt_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:nat) (A_19:Prop) (F_3:(nat->Prop)) (B_17:nat), (((ord_less_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_o A_19) (F_3 C_6)))))) of role axiom named fact_828_order__less__le__subst1
% A new axiom: (forall (C_6:nat) (A_19:Prop) (F_3:(nat->Prop)) (B_17:nat), (((ord_less_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:nat) (A_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_3:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_17:nat), (((ord_le1339521307_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1463467535_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1339521307_alt_o A_19) (F_3 C_6)))))) of role axiom named fact_829_order__less__le__subst1
% A new axiom: (forall (C_6:nat) (A_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_3:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_17:nat), (((ord_le1339521307_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1463467535_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1339521307_alt_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(nat->Prop)) (A_19:(nat->Prop)) (F_3:((nat->Prop)->(nat->Prop))) (B_17:(nat->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))) of role axiom named fact_830_order__less__le__subst1
% A new axiom: (forall (C_6:(nat->Prop)) (A_19:(nat->Prop)) (F_3:((nat->Prop)->(nat->Prop))) (B_17:(nat->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(nat->Prop)) (A_19:(product_unit->Prop)) (F_3:((nat->Prop)->(product_unit->Prop))) (B_17:(nat->Prop)), (((ord_le232288914unit_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1511552390unit_o (F_3 X_1)) (F_3 Y_1))))->((ord_le232288914unit_o A_19) (F_3 C_6)))))) of role axiom named fact_831_order__less__le__subst1
% A new axiom: (forall (C_6:(nat->Prop)) (A_19:(product_unit->Prop)) (F_3:((nat->Prop)->(product_unit->Prop))) (B_17:(nat->Prop)), (((ord_le232288914unit_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1511552390unit_o (F_3 X_1)) (F_3 Y_1))))->((ord_le232288914unit_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(nat->Prop)) (A_19:(arrow_1196572341e_indi->Prop)) (F_3:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (B_17:(nat->Prop)), (((ord_le1991507760indi_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le865407012indi_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1991507760indi_o A_19) (F_3 C_6)))))) of role axiom named fact_832_order__less__le__subst1
% A new axiom: (forall (C_6:(nat->Prop)) (A_19:(arrow_1196572341e_indi->Prop)) (F_3:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (B_17:(nat->Prop)), (((ord_le1991507760indi_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le865407012indi_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1991507760indi_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(nat->Prop)) (A_19:((produc1572197287le_alt->Prop)->Prop)) (F_3:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (B_17:(nat->Prop)), (((ord_le874404799lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1027220427lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le874404799lt_o_o A_19) (F_3 C_6)))))) of role axiom named fact_833_order__less__le__subst1
% A new axiom: (forall (C_6:(nat->Prop)) (A_19:((produc1572197287le_alt->Prop)->Prop)) (F_3:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (B_17:(nat->Prop)), (((ord_le874404799lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1027220427lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le874404799lt_o_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(nat->Prop)) (A_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_3:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_17:(nat->Prop)), (((ord_le1382328578lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1805007862lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1382328578lt_o_o A_19) (F_3 C_6)))))) of role axiom named fact_834_order__less__le__subst1
% A new axiom: (forall (C_6:(nat->Prop)) (A_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_3:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_17:(nat->Prop)), (((ord_le1382328578lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1805007862lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1382328578lt_o_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(nat->Prop)) (A_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_3:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_17:(nat->Prop)), (((ord_le914873172lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le602483040lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le914873172lt_o_o A_19) (F_3 C_6)))))) of role axiom named fact_835_order__less__le__subst1
% A new axiom: (forall (C_6:(nat->Prop)) (A_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_3:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_17:(nat->Prop)), (((ord_le914873172lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le602483040lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le914873172lt_o_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(nat->Prop)) (A_19:(produc1572197287le_alt->Prop)) (F_3:((nat->Prop)->(produc1572197287le_alt->Prop))) (B_17:(nat->Prop)), (((ord_le1852932542_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le962286258_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1852932542_alt_o A_19) (F_3 C_6)))))) of role axiom named fact_836_order__less__le__subst1
% A new axiom: (forall (C_6:(nat->Prop)) (A_19:(produc1572197287le_alt->Prop)) (F_3:((nat->Prop)->(produc1572197287le_alt->Prop))) (B_17:(nat->Prop)), (((ord_le1852932542_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le962286258_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1852932542_alt_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(nat->Prop)) (A_19:Prop) (F_3:((nat->Prop)->Prop)) (B_17:(nat->Prop)), (((ord_less_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_o A_19) (F_3 C_6)))))) of role axiom named fact_837_order__less__le__subst1
% A new axiom: (forall (C_6:(nat->Prop)) (A_19:Prop) (F_3:((nat->Prop)->Prop)) (B_17:(nat->Prop)), (((ord_less_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(nat->Prop)) (A_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_3:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_17:(nat->Prop)), (((ord_le1339521307_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1463467535_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1339521307_alt_o A_19) (F_3 C_6)))))) of role axiom named fact_838_order__less__le__subst1
% A new axiom: (forall (C_6:(nat->Prop)) (A_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_3:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_17:(nat->Prop)), (((ord_le1339521307_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1463467535_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1339521307_alt_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:((produc1572197287le_alt->Prop)->Prop)) (A_19:(nat->Prop)) (F_3:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (B_17:((produc1572197287le_alt->Prop)->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1027220427lt_o_o B_17) C_6)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))) of role axiom named fact_839_order__less__le__subst1
% A new axiom: (forall (C_6:((produc1572197287le_alt->Prop)->Prop)) (A_19:(nat->Prop)) (F_3:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (B_17:((produc1572197287le_alt->Prop)->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1027220427lt_o_o B_17) C_6)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_19:(nat->Prop)) (F_3:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_17:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1805007862lt_o_o B_17) C_6)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))) of role axiom named fact_840_order__less__le__subst1
% A new axiom: (forall (C_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_19:(nat->Prop)) (F_3:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_17:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1805007862lt_o_o B_17) C_6)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_19:(nat->Prop)) (F_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_17:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le602483040lt_o_o B_17) C_6)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))) of role axiom named fact_841_order__less__le__subst1
% A new axiom: (forall (C_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_19:(nat->Prop)) (F_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_17:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le602483040lt_o_o B_17) C_6)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(produc1572197287le_alt->Prop)) (A_19:(nat->Prop)) (F_3:((produc1572197287le_alt->Prop)->(nat->Prop))) (B_17:(produc1572197287le_alt->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le962286258_alt_o B_17) C_6)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))) of role axiom named fact_842_order__less__le__subst1
% A new axiom: (forall (C_6:(produc1572197287le_alt->Prop)) (A_19:(nat->Prop)) (F_3:((produc1572197287le_alt->Prop)->(nat->Prop))) (B_17:(produc1572197287le_alt->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le962286258_alt_o B_17) C_6)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:Prop) (A_19:(nat->Prop)) (F_3:(Prop->(nat->Prop))) (B_17:Prop), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_less_eq_o B_17) C_6)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))) of role axiom named fact_843_order__less__le__subst1
% A new axiom: (forall (C_6:Prop) (A_19:(nat->Prop)) (F_3:(Prop->(nat->Prop))) (B_17:Prop), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_less_eq_o B_17) C_6)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(arrow_1196572341e_indi->Prop)) (A_19:(nat->Prop)) (F_3:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_17:(arrow_1196572341e_indi->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le865407012indi_o B_17) C_6)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))) of role axiom named fact_844_order__less__le__subst1
% A new axiom: (forall (C_6:(arrow_1196572341e_indi->Prop)) (A_19:(nat->Prop)) (F_3:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_17:(arrow_1196572341e_indi->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le865407012indi_o B_17) C_6)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(product_unit->Prop)) (A_19:(nat->Prop)) (F_3:((product_unit->Prop)->(nat->Prop))) (B_17:(product_unit->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1511552390unit_o B_17) C_6)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))) of role axiom named fact_845_order__less__le__subst1
% A new axiom: (forall (C_6:(product_unit->Prop)) (A_19:(nat->Prop)) (F_3:((product_unit->Prop)->(nat->Prop))) (B_17:(product_unit->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1511552390unit_o B_17) C_6)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_19:(nat->Prop)) (F_3:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (B_17:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1463467535_alt_o B_17) C_6)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))) of role axiom named fact_846_order__less__le__subst1
% A new axiom: (forall (C_6:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_19:(nat->Prop)) (F_3:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (B_17:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1463467535_alt_o B_17) C_6)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:((produc1572197287le_alt->Prop)->Prop)) (A_19:nat) (F_3:(((produc1572197287le_alt->Prop)->Prop)->nat)) (B_17:((produc1572197287le_alt->Prop)->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1027220427lt_o_o B_17) C_6)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))) of role axiom named fact_847_order__less__le__subst1
% A new axiom: (forall (C_6:((produc1572197287le_alt->Prop)->Prop)) (A_19:nat) (F_3:(((produc1572197287le_alt->Prop)->Prop)->nat)) (B_17:((produc1572197287le_alt->Prop)->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1027220427lt_o_o B_17) C_6)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_19:nat) (F_3:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_17:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1805007862lt_o_o B_17) C_6)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))) of role axiom named fact_848_order__less__le__subst1
% A new axiom: (forall (C_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_19:nat) (F_3:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_17:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1805007862lt_o_o B_17) C_6)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_19:nat) (F_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_17:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le602483040lt_o_o B_17) C_6)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))) of role axiom named fact_849_order__less__le__subst1
% A new axiom: (forall (C_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_19:nat) (F_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_17:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le602483040lt_o_o B_17) C_6)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(produc1572197287le_alt->Prop)) (A_19:nat) (F_3:((produc1572197287le_alt->Prop)->nat)) (B_17:(produc1572197287le_alt->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le962286258_alt_o B_17) C_6)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))) of role axiom named fact_850_order__less__le__subst1
% A new axiom: (forall (C_6:(produc1572197287le_alt->Prop)) (A_19:nat) (F_3:((produc1572197287le_alt->Prop)->nat)) (B_17:(produc1572197287le_alt->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le962286258_alt_o B_17) C_6)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:Prop) (A_19:nat) (F_3:(Prop->nat)) (B_17:Prop), (((ord_less_nat A_19) (F_3 B_17))->(((ord_less_eq_o B_17) C_6)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))) of role axiom named fact_851_order__less__le__subst1
% A new axiom: (forall (C_6:Prop) (A_19:nat) (F_3:(Prop->nat)) (B_17:Prop), (((ord_less_nat A_19) (F_3 B_17))->(((ord_less_eq_o B_17) C_6)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(arrow_1196572341e_indi->Prop)) (A_19:nat) (F_3:((arrow_1196572341e_indi->Prop)->nat)) (B_17:(arrow_1196572341e_indi->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le865407012indi_o B_17) C_6)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))) of role axiom named fact_852_order__less__le__subst1
% A new axiom: (forall (C_6:(arrow_1196572341e_indi->Prop)) (A_19:nat) (F_3:((arrow_1196572341e_indi->Prop)->nat)) (B_17:(arrow_1196572341e_indi->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le865407012indi_o B_17) C_6)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(product_unit->Prop)) (A_19:nat) (F_3:((product_unit->Prop)->nat)) (B_17:(product_unit->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1511552390unit_o B_17) C_6)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))) of role axiom named fact_853_order__less__le__subst1
% A new axiom: (forall (C_6:(product_unit->Prop)) (A_19:nat) (F_3:((product_unit->Prop)->nat)) (B_17:(product_unit->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1511552390unit_o B_17) C_6)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6))))))
% FOF formula (forall (C_6:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_19:nat) (F_3:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (B_17:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1463467535_alt_o B_17) C_6)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))) of role axiom named fact_854_order__less__le__subst1
% A new axiom: (forall (C_6:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_19:nat) (F_3:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (B_17:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1463467535_alt_o B_17) C_6)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6))))))
% FOF formula (forall (F_2:(nat->(nat->Prop))) (C_5:(nat->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))) of role axiom named fact_855_order__le__less__subst2
% A new axiom: (forall (F_2:(nat->(nat->Prop))) (C_5:(nat->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(nat->(product_unit->Prop))) (C_5:(product_unit->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le232288914unit_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1511552390unit_o (F_2 X_1)) (F_2 Y_1))))->((ord_le232288914unit_o (F_2 A_18)) C_5))))) of role axiom named fact_856_order__le__less__subst2
% A new axiom: (forall (F_2:(nat->(product_unit->Prop))) (C_5:(product_unit->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le232288914unit_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1511552390unit_o (F_2 X_1)) (F_2 Y_1))))->((ord_le232288914unit_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(nat->(arrow_1196572341e_indi->Prop))) (C_5:(arrow_1196572341e_indi->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1991507760indi_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le865407012indi_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1991507760indi_o (F_2 A_18)) C_5))))) of role axiom named fact_857_order__le__less__subst2
% A new axiom: (forall (F_2:(nat->(arrow_1196572341e_indi->Prop))) (C_5:(arrow_1196572341e_indi->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1991507760indi_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le865407012indi_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1991507760indi_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(nat->((produc1572197287le_alt->Prop)->Prop))) (C_5:((produc1572197287le_alt->Prop)->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le874404799lt_o_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1027220427lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le874404799lt_o_o (F_2 A_18)) C_5))))) of role axiom named fact_858_order__le__less__subst2
% A new axiom: (forall (F_2:(nat->((produc1572197287le_alt->Prop)->Prop))) (C_5:((produc1572197287le_alt->Prop)->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le874404799lt_o_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1027220427lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le874404799lt_o_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (C_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1382328578lt_o_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1805007862lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1382328578lt_o_o (F_2 A_18)) C_5))))) of role axiom named fact_859_order__le__less__subst2
% A new axiom: (forall (F_2:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (C_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1382328578lt_o_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1805007862lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1382328578lt_o_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (C_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le914873172lt_o_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le602483040lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le914873172lt_o_o (F_2 A_18)) C_5))))) of role axiom named fact_860_order__le__less__subst2
% A new axiom: (forall (F_2:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (C_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le914873172lt_o_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le602483040lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le914873172lt_o_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(nat->(produc1572197287le_alt->Prop))) (C_5:(produc1572197287le_alt->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1852932542_alt_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le962286258_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1852932542_alt_o (F_2 A_18)) C_5))))) of role axiom named fact_861_order__le__less__subst2
% A new axiom: (forall (F_2:(nat->(produc1572197287le_alt->Prop))) (C_5:(produc1572197287le_alt->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1852932542_alt_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le962286258_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1852932542_alt_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(nat->Prop)) (C_5:Prop) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_less_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_o (F_2 A_18)) C_5))))) of role axiom named fact_862_order__le__less__subst2
% A new axiom: (forall (F_2:(nat->Prop)) (C_5:Prop) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_less_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (C_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1339521307_alt_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1463467535_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1339521307_alt_o (F_2 A_18)) C_5))))) of role axiom named fact_863_order__le__less__subst2
% A new axiom: (forall (F_2:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (C_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1339521307_alt_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1463467535_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1339521307_alt_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((nat->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))) of role axiom named fact_864_order__le__less__subst2
% A new axiom: (forall (F_2:((nat->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((nat->Prop)->(product_unit->Prop))) (C_5:(product_unit->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le232288914unit_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1511552390unit_o (F_2 X_1)) (F_2 Y_1))))->((ord_le232288914unit_o (F_2 A_18)) C_5))))) of role axiom named fact_865_order__le__less__subst2
% A new axiom: (forall (F_2:((nat->Prop)->(product_unit->Prop))) (C_5:(product_unit->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le232288914unit_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1511552390unit_o (F_2 X_1)) (F_2 Y_1))))->((ord_le232288914unit_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (C_5:(arrow_1196572341e_indi->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1991507760indi_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le865407012indi_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1991507760indi_o (F_2 A_18)) C_5))))) of role axiom named fact_866_order__le__less__subst2
% A new axiom: (forall (F_2:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (C_5:(arrow_1196572341e_indi->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1991507760indi_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le865407012indi_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1991507760indi_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (C_5:((produc1572197287le_alt->Prop)->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le874404799lt_o_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1027220427lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le874404799lt_o_o (F_2 A_18)) C_5))))) of role axiom named fact_867_order__le__less__subst2
% A new axiom: (forall (F_2:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (C_5:((produc1572197287le_alt->Prop)->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le874404799lt_o_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1027220427lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le874404799lt_o_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (C_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1382328578lt_o_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1805007862lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1382328578lt_o_o (F_2 A_18)) C_5))))) of role axiom named fact_868_order__le__less__subst2
% A new axiom: (forall (F_2:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (C_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1382328578lt_o_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1805007862lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1382328578lt_o_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (C_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le914873172lt_o_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le602483040lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le914873172lt_o_o (F_2 A_18)) C_5))))) of role axiom named fact_869_order__le__less__subst2
% A new axiom: (forall (F_2:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (C_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le914873172lt_o_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le602483040lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le914873172lt_o_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((nat->Prop)->(produc1572197287le_alt->Prop))) (C_5:(produc1572197287le_alt->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1852932542_alt_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le962286258_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1852932542_alt_o (F_2 A_18)) C_5))))) of role axiom named fact_870_order__le__less__subst2
% A new axiom: (forall (F_2:((nat->Prop)->(produc1572197287le_alt->Prop))) (C_5:(produc1572197287le_alt->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1852932542_alt_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le962286258_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1852932542_alt_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((nat->Prop)->Prop)) (C_5:Prop) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_less_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_o (F_2 A_18)) C_5))))) of role axiom named fact_871_order__le__less__subst2
% A new axiom: (forall (F_2:((nat->Prop)->Prop)) (C_5:Prop) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_less_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (C_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1339521307_alt_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1463467535_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1339521307_alt_o (F_2 A_18)) C_5))))) of role axiom named fact_872_order__le__less__subst2
% A new axiom: (forall (F_2:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (C_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1339521307_alt_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1463467535_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1339521307_alt_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:((produc1572197287le_alt->Prop)->Prop)) (B_16:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))) of role axiom named fact_873_order__le__less__subst2
% A new axiom: (forall (F_2:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:((produc1572197287le_alt->Prop)->Prop)) (B_16:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_16:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))) of role axiom named fact_874_order__le__less__subst2
% A new axiom: (forall (F_2:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_16:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_16:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))) of role axiom named fact_875_order__le__less__subst2
% A new axiom: (forall (F_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_16:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((produc1572197287le_alt->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(produc1572197287le_alt->Prop)) (B_16:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))) of role axiom named fact_876_order__le__less__subst2
% A new axiom: (forall (F_2:((produc1572197287le_alt->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(produc1572197287le_alt->Prop)) (B_16:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(Prop->(nat->Prop))) (C_5:(nat->Prop)) (A_18:Prop) (B_16:Prop), (((ord_less_eq_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))) of role axiom named fact_877_order__le__less__subst2
% A new axiom: (forall (F_2:(Prop->(nat->Prop))) (C_5:(nat->Prop)) (A_18:Prop) (B_16:Prop), (((ord_less_eq_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(arrow_1196572341e_indi->Prop)) (B_16:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))) of role axiom named fact_878_order__le__less__subst2
% A new axiom: (forall (F_2:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(arrow_1196572341e_indi->Prop)) (B_16:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((product_unit->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(product_unit->Prop)) (B_16:(product_unit->Prop)), (((ord_le1511552390unit_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))) of role axiom named fact_879_order__le__less__subst2
% A new axiom: (forall (F_2:((product_unit->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(product_unit->Prop)) (B_16:(product_unit->Prop)), (((ord_le1511552390unit_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_16:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))) of role axiom named fact_880_order__le__less__subst2
% A new axiom: (forall (F_2:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_16:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(((produc1572197287le_alt->Prop)->Prop)->nat)) (C_5:nat) (A_18:((produc1572197287le_alt->Prop)->Prop)) (B_16:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))) of role axiom named fact_881_order__le__less__subst2
% A new axiom: (forall (F_2:(((produc1572197287le_alt->Prop)->Prop)->nat)) (C_5:nat) (A_18:((produc1572197287le_alt->Prop)->Prop)) (B_16:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (C_5:nat) (A_18:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_16:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))) of role axiom named fact_882_order__le__less__subst2
% A new axiom: (forall (F_2:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (C_5:nat) (A_18:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_16:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (C_5:nat) (A_18:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_16:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))) of role axiom named fact_883_order__le__less__subst2
% A new axiom: (forall (F_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (C_5:nat) (A_18:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_16:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((produc1572197287le_alt->Prop)->nat)) (C_5:nat) (A_18:(produc1572197287le_alt->Prop)) (B_16:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))) of role axiom named fact_884_order__le__less__subst2
% A new axiom: (forall (F_2:((produc1572197287le_alt->Prop)->nat)) (C_5:nat) (A_18:(produc1572197287le_alt->Prop)) (B_16:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:(Prop->nat)) (C_5:nat) (A_18:Prop) (B_16:Prop), (((ord_less_eq_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))) of role axiom named fact_885_order__le__less__subst2
% A new axiom: (forall (F_2:(Prop->nat)) (C_5:nat) (A_18:Prop) (B_16:Prop), (((ord_less_eq_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((arrow_1196572341e_indi->Prop)->nat)) (C_5:nat) (A_18:(arrow_1196572341e_indi->Prop)) (B_16:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))) of role axiom named fact_886_order__le__less__subst2
% A new axiom: (forall (F_2:((arrow_1196572341e_indi->Prop)->nat)) (C_5:nat) (A_18:(arrow_1196572341e_indi->Prop)) (B_16:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((product_unit->Prop)->nat)) (C_5:nat) (A_18:(product_unit->Prop)) (B_16:(product_unit->Prop)), (((ord_le1511552390unit_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))) of role axiom named fact_887_order__le__less__subst2
% A new axiom: (forall (F_2:((product_unit->Prop)->nat)) (C_5:nat) (A_18:(product_unit->Prop)) (B_16:(product_unit->Prop)), (((ord_le1511552390unit_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5)))))
% FOF formula (forall (F_2:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (C_5:nat) (A_18:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_16:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))) of role axiom named fact_888_order__le__less__subst2
% A new axiom: (forall (F_2:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (C_5:nat) (A_18:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_16:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5)))))
% FOF formula (forall (F_1:((nat->Prop)->(nat->Prop))) (C_4:(nat->Prop)) (A_17:(nat->Prop)) (B_15:(nat->Prop)), (((ord_less_nat_o A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4))))) of role axiom named fact_889_order__less__le__subst2
% A new axiom: (forall (F_1:((nat->Prop)->(nat->Prop))) (C_4:(nat->Prop)) (A_17:(nat->Prop)) (B_15:(nat->Prop)), (((ord_less_nat_o A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:((product_unit->Prop)->(nat->Prop))) (C_4:(nat->Prop)) (A_17:(product_unit->Prop)) (B_15:(product_unit->Prop)), (((ord_le232288914unit_o A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4))))) of role axiom named fact_890_order__less__le__subst2
% A new axiom: (forall (F_1:((product_unit->Prop)->(nat->Prop))) (C_4:(nat->Prop)) (A_17:(product_unit->Prop)) (B_15:(product_unit->Prop)), (((ord_le232288914unit_o A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (C_4:(nat->Prop)) (A_17:(arrow_1196572341e_indi->Prop)) (B_15:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4))))) of role axiom named fact_891_order__less__le__subst2
% A new axiom: (forall (F_1:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (C_4:(nat->Prop)) (A_17:(arrow_1196572341e_indi->Prop)) (B_15:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:(nat->(nat->Prop))) (C_4:(nat->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4))))) of role axiom named fact_892_order__less__le__subst2
% A new axiom: (forall (F_1:(nat->(nat->Prop))) (C_4:(nat->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:(nat->(product_unit->Prop))) (C_4:(product_unit->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1511552390unit_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le232288914unit_o (F_1 X_1)) (F_1 Y_1))))->((ord_le232288914unit_o (F_1 A_17)) C_4))))) of role axiom named fact_893_order__less__le__subst2
% A new axiom: (forall (F_1:(nat->(product_unit->Prop))) (C_4:(product_unit->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1511552390unit_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le232288914unit_o (F_1 X_1)) (F_1 Y_1))))->((ord_le232288914unit_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:(nat->(arrow_1196572341e_indi->Prop))) (C_4:(arrow_1196572341e_indi->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le865407012indi_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1991507760indi_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1991507760indi_o (F_1 A_17)) C_4))))) of role axiom named fact_894_order__less__le__subst2
% A new axiom: (forall (F_1:(nat->(arrow_1196572341e_indi->Prop))) (C_4:(arrow_1196572341e_indi->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le865407012indi_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1991507760indi_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1991507760indi_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:(nat->((produc1572197287le_alt->Prop)->Prop))) (C_4:((produc1572197287le_alt->Prop)->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1027220427lt_o_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le874404799lt_o_o (F_1 X_1)) (F_1 Y_1))))->((ord_le874404799lt_o_o (F_1 A_17)) C_4))))) of role axiom named fact_895_order__less__le__subst2
% A new axiom: (forall (F_1:(nat->((produc1572197287le_alt->Prop)->Prop))) (C_4:((produc1572197287le_alt->Prop)->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1027220427lt_o_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le874404799lt_o_o (F_1 X_1)) (F_1 Y_1))))->((ord_le874404799lt_o_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (C_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1805007862lt_o_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1382328578lt_o_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1382328578lt_o_o (F_1 A_17)) C_4))))) of role axiom named fact_896_order__less__le__subst2
% A new axiom: (forall (F_1:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (C_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1805007862lt_o_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1382328578lt_o_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1382328578lt_o_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (C_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le602483040lt_o_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le914873172lt_o_o (F_1 X_1)) (F_1 Y_1))))->((ord_le914873172lt_o_o (F_1 A_17)) C_4))))) of role axiom named fact_897_order__less__le__subst2
% A new axiom: (forall (F_1:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (C_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le602483040lt_o_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le914873172lt_o_o (F_1 X_1)) (F_1 Y_1))))->((ord_le914873172lt_o_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:(nat->(produc1572197287le_alt->Prop))) (C_4:(produc1572197287le_alt->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le962286258_alt_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1852932542_alt_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1852932542_alt_o (F_1 A_17)) C_4))))) of role axiom named fact_898_order__less__le__subst2
% A new axiom: (forall (F_1:(nat->(produc1572197287le_alt->Prop))) (C_4:(produc1572197287le_alt->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le962286258_alt_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1852932542_alt_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1852932542_alt_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:(nat->Prop)) (C_4:Prop) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_less_eq_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_o (F_1 A_17)) C_4))))) of role axiom named fact_899_order__less__le__subst2
% A new axiom: (forall (F_1:(nat->Prop)) (C_4:Prop) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_less_eq_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (C_4:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1463467535_alt_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1339521307_alt_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1339521307_alt_o (F_1 A_17)) C_4))))) of role axiom named fact_900_order__less__le__subst2
% A new axiom: (forall (F_1:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (C_4:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1463467535_alt_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1339521307_alt_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1339521307_alt_o (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:((nat->Prop)->nat)) (C_4:nat) (A_17:(nat->Prop)) (B_15:(nat->Prop)), (((ord_less_nat_o A_17) B_15)->(((ord_less_eq_nat (F_1 B_15)) C_4)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat (F_1 A_17)) C_4))))) of role axiom named fact_901_order__less__le__subst2
% A new axiom: (forall (F_1:((nat->Prop)->nat)) (C_4:nat) (A_17:(nat->Prop)) (B_15:(nat->Prop)), (((ord_less_nat_o A_17) B_15)->(((ord_less_eq_nat (F_1 B_15)) C_4)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:((product_unit->Prop)->nat)) (C_4:nat) (A_17:(product_unit->Prop)) (B_15:(product_unit->Prop)), (((ord_le232288914unit_o A_17) B_15)->(((ord_less_eq_nat (F_1 B_15)) C_4)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat (F_1 A_17)) C_4))))) of role axiom named fact_902_order__less__le__subst2
% A new axiom: (forall (F_1:((product_unit->Prop)->nat)) (C_4:nat) (A_17:(product_unit->Prop)) (B_15:(product_unit->Prop)), (((ord_le232288914unit_o A_17) B_15)->(((ord_less_eq_nat (F_1 B_15)) C_4)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat (F_1 A_17)) C_4)))))
% FOF formula (forall (F_1:((arrow_1196572341e_indi->Prop)->nat)) (C_4:nat) (A_17:(arrow_1196572341e_indi->Prop)) (B_15:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_17) B_15)->(((ord_less_eq_nat (F_1 B_15)) C_4)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat (F_1 A_17)) C_4))))) of role axiom named fact_903_order__less__le__subst2
% A new axiom: (forall (F_1:((arrow_1196572341e_indi->Prop)->nat)) (C_4:nat) (A_17:(arrow_1196572341e_indi->Prop)) (B_15:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_17) B_15)->(((ord_less_eq_nat (F_1 B_15)) C_4)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat (F_1 A_17)) C_4)))))
% FOF formula (forall (M_1:nat) (K:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M_1) K)) N_1)->((((ord_less_eq_nat M_1) N_1)->(((ord_less_eq_nat K) N_1)->False))->False))) of role axiom named fact_904_add__leE
% A new axiom: (forall (M_1:nat) (K:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M_1) K)) N_1)->((((ord_less_eq_nat M_1) N_1)->(((ord_less_eq_nat K) N_1)->False))->False)))
% FOF formula (forall (A_16:((produc1572197287le_alt->Prop)->Prop)) (B_14:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_16) B_14)->(((ord_le1027220427lt_o_o B_14) A_16)->(((eq ((produc1572197287le_alt->Prop)->Prop)) A_16) B_14)))) of role axiom named fact_905_equalityI
% A new axiom: (forall (A_16:((produc1572197287le_alt->Prop)->Prop)) (B_14:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_16) B_14)->(((ord_le1027220427lt_o_o B_14) A_16)->(((eq ((produc1572197287le_alt->Prop)->Prop)) A_16) B_14))))
% FOF formula (forall (A_16:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_16) B_14)->(((ord_le1805007862lt_o_o B_14) A_16)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_16) B_14)))) of role axiom named fact_906_equalityI
% A new axiom: (forall (A_16:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_16) B_14)->(((ord_le1805007862lt_o_o B_14) A_16)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_16) B_14))))
% FOF formula (forall (A_16:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_16) B_14)->(((ord_le602483040lt_o_o B_14) A_16)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_16) B_14)))) of role axiom named fact_907_equalityI
% A new axiom: (forall (A_16:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_16) B_14)->(((ord_le602483040lt_o_o B_14) A_16)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_16) B_14))))
% FOF formula (forall (A_16:(produc1572197287le_alt->Prop)) (B_14:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_16) B_14)->(((ord_le962286258_alt_o B_14) A_16)->(((eq (produc1572197287le_alt->Prop)) A_16) B_14)))) of role axiom named fact_908_equalityI
% A new axiom: (forall (A_16:(produc1572197287le_alt->Prop)) (B_14:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_16) B_14)->(((ord_le962286258_alt_o B_14) A_16)->(((eq (produc1572197287le_alt->Prop)) A_16) B_14))))
% FOF formula (forall (A_16:(arrow_1196572341e_indi->Prop)) (B_14:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_16) B_14)->(((ord_le865407012indi_o B_14) A_16)->(((eq (arrow_1196572341e_indi->Prop)) A_16) B_14)))) of role axiom named fact_909_equalityI
% A new axiom: (forall (A_16:(arrow_1196572341e_indi->Prop)) (B_14:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_16) B_14)->(((ord_le865407012indi_o B_14) A_16)->(((eq (arrow_1196572341e_indi->Prop)) A_16) B_14))))
% FOF formula (forall (A_16:(product_unit->Prop)) (B_14:(product_unit->Prop)), (((ord_le1511552390unit_o A_16) B_14)->(((ord_le1511552390unit_o B_14) A_16)->(((eq (product_unit->Prop)) A_16) B_14)))) of role axiom named fact_910_equalityI
% A new axiom: (forall (A_16:(product_unit->Prop)) (B_14:(product_unit->Prop)), (((ord_le1511552390unit_o A_16) B_14)->(((ord_le1511552390unit_o B_14) A_16)->(((eq (product_unit->Prop)) A_16) B_14))))
% FOF formula (forall (A_16:(nat->Prop)) (B_14:(nat->Prop)), (((ord_less_eq_nat_o A_16) B_14)->(((ord_less_eq_nat_o B_14) A_16)->(((eq (nat->Prop)) A_16) B_14)))) of role axiom named fact_911_equalityI
% A new axiom: (forall (A_16:(nat->Prop)) (B_14:(nat->Prop)), (((ord_less_eq_nat_o A_16) B_14)->(((ord_less_eq_nat_o B_14) A_16)->(((eq (nat->Prop)) A_16) B_14))))
% FOF formula (forall (C_3:arrow_1196572341e_indi) (A_15:(arrow_1196572341e_indi->Prop)) (B_13:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_15) B_13)->(((member1818997282e_indi C_3) A_15)->((member1818997282e_indi C_3) B_13)))) of role axiom named fact_912_subsetD
% A new axiom: (forall (C_3:arrow_1196572341e_indi) (A_15:(arrow_1196572341e_indi->Prop)) (B_13:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_15) B_13)->(((member1818997282e_indi C_3) A_15)->((member1818997282e_indi C_3) B_13))))
% FOF formula (forall (C_3:Prop) (A_15:(Prop->Prop)) (B_13:(Prop->Prop)), (((ord_less_eq_o_o A_15) B_13)->(((member_o C_3) A_15)->((member_o C_3) B_13)))) of role axiom named fact_913_subsetD
% A new axiom: (forall (C_3:Prop) (A_15:(Prop->Prop)) (B_13:(Prop->Prop)), (((ord_less_eq_o_o A_15) B_13)->(((member_o C_3) A_15)->((member_o C_3) B_13))))
% FOF formula (forall (C_3:product_unit) (A_15:(product_unit->Prop)) (B_13:(product_unit->Prop)), (((ord_le1511552390unit_o A_15) B_13)->(((member_Product_unit C_3) A_15)->((member_Product_unit C_3) B_13)))) of role axiom named fact_914_subsetD
% A new axiom: (forall (C_3:product_unit) (A_15:(product_unit->Prop)) (B_13:(product_unit->Prop)), (((ord_le1511552390unit_o A_15) B_13)->(((member_Product_unit C_3) A_15)->((member_Product_unit C_3) B_13))))
% FOF formula (forall (C_3:produc1572197287le_alt) (A_15:(produc1572197287le_alt->Prop)) (B_13:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_15) B_13)->(((member285112084le_alt C_3) A_15)->((member285112084le_alt C_3) B_13)))) of role axiom named fact_915_subsetD
% A new axiom: (forall (C_3:produc1572197287le_alt) (A_15:(produc1572197287le_alt->Prop)) (B_13:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_15) B_13)->(((member285112084le_alt C_3) A_15)->((member285112084le_alt C_3) B_13))))
% FOF formula (forall (C_3:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_15:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_15) B_13)->(((member822980838_alt_o C_3) A_15)->((member822980838_alt_o C_3) B_13)))) of role axiom named fact_916_subsetD
% A new axiom: (forall (C_3:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_15:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_15) B_13)->(((member822980838_alt_o C_3) A_15)->((member822980838_alt_o C_3) B_13))))
% FOF formula (forall (C_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_15:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_13:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_15) B_13)->(((member1425217232_alt_o C_3) A_15)->((member1425217232_alt_o C_3) B_13)))) of role axiom named fact_917_subsetD
% A new axiom: (forall (C_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_15:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_13:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_15) B_13)->(((member1425217232_alt_o C_3) A_15)->((member1425217232_alt_o C_3) B_13))))
% FOF formula (forall (C_3:(produc1572197287le_alt->Prop)) (A_15:((produc1572197287le_alt->Prop)->Prop)) (B_13:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_15) B_13)->(((member1241905979_alt_o C_3) A_15)->((member1241905979_alt_o C_3) B_13)))) of role axiom named fact_918_subsetD
% A new axiom: (forall (C_3:(produc1572197287le_alt->Prop)) (A_15:((produc1572197287le_alt->Prop)->Prop)) (B_13:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_15) B_13)->(((member1241905979_alt_o C_3) A_15)->((member1241905979_alt_o C_3) B_13))))
% FOF formula (forall (C_3:nat) (A_15:(nat->Prop)) (B_13:(nat->Prop)), (((ord_less_eq_nat_o A_15) B_13)->(((member_nat C_3) A_15)->((member_nat C_3) B_13)))) of role axiom named fact_919_subsetD
% A new axiom: (forall (C_3:nat) (A_15:(nat->Prop)) (B_13:(nat->Prop)), (((ord_less_eq_nat_o A_15) B_13)->(((member_nat C_3) A_15)->((member_nat C_3) B_13))))
% FOF formula (forall (A_14:(product_unit->Prop)) (B_12:(product_unit->Prop)), ((iff ((ord_le232288914unit_o A_14) B_12)) ((and ((ord_le1511552390unit_o A_14) B_12)) (not (((eq (product_unit->Prop)) A_14) B_12))))) of role axiom named fact_920_psubset__eq
% A new axiom: (forall (A_14:(product_unit->Prop)) (B_12:(product_unit->Prop)), ((iff ((ord_le232288914unit_o A_14) B_12)) ((and ((ord_le1511552390unit_o A_14) B_12)) (not (((eq (product_unit->Prop)) A_14) B_12)))))
% FOF formula (forall (A_14:(arrow_1196572341e_indi->Prop)) (B_12:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o A_14) B_12)) ((and ((ord_le865407012indi_o A_14) B_12)) (not (((eq (arrow_1196572341e_indi->Prop)) A_14) B_12))))) of role axiom named fact_921_psubset__eq
% A new axiom: (forall (A_14:(arrow_1196572341e_indi->Prop)) (B_12:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o A_14) B_12)) ((and ((ord_le865407012indi_o A_14) B_12)) (not (((eq (arrow_1196572341e_indi->Prop)) A_14) B_12)))))
% FOF formula (forall (A_14:((produc1572197287le_alt->Prop)->Prop)) (B_12:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o A_14) B_12)) ((and ((ord_le1027220427lt_o_o A_14) B_12)) (not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_14) B_12))))) of role axiom named fact_922_psubset__eq
% A new axiom: (forall (A_14:((produc1572197287le_alt->Prop)->Prop)) (B_12:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o A_14) B_12)) ((and ((ord_le1027220427lt_o_o A_14) B_12)) (not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_14) B_12)))))
% FOF formula (forall (A_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_12:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o A_14) B_12)) ((and ((ord_le1805007862lt_o_o A_14) B_12)) (not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_14) B_12))))) of role axiom named fact_923_psubset__eq
% A new axiom: (forall (A_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_12:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o A_14) B_12)) ((and ((ord_le1805007862lt_o_o A_14) B_12)) (not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_14) B_12)))))
% FOF formula (forall (A_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o A_14) B_12)) ((and ((ord_le602483040lt_o_o A_14) B_12)) (not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_14) B_12))))) of role axiom named fact_924_psubset__eq
% A new axiom: (forall (A_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o A_14) B_12)) ((and ((ord_le602483040lt_o_o A_14) B_12)) (not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_14) B_12)))))
% FOF formula (forall (A_14:(produc1572197287le_alt->Prop)) (B_12:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o A_14) B_12)) ((and ((ord_le962286258_alt_o A_14) B_12)) (not (((eq (produc1572197287le_alt->Prop)) A_14) B_12))))) of role axiom named fact_925_psubset__eq
% A new axiom: (forall (A_14:(produc1572197287le_alt->Prop)) (B_12:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o A_14) B_12)) ((and ((ord_le962286258_alt_o A_14) B_12)) (not (((eq (produc1572197287le_alt->Prop)) A_14) B_12)))))
% FOF formula (forall (A_14:(nat->Prop)) (B_12:(nat->Prop)), ((iff ((ord_less_nat_o A_14) B_12)) ((and ((ord_less_eq_nat_o A_14) B_12)) (not (((eq (nat->Prop)) A_14) B_12))))) of role axiom named fact_926_psubset__eq
% A new axiom: (forall (A_14:(nat->Prop)) (B_12:(nat->Prop)), ((iff ((ord_less_nat_o A_14) B_12)) ((and ((ord_less_eq_nat_o A_14) B_12)) (not (((eq (nat->Prop)) A_14) B_12)))))
% FOF formula (forall (A_13:(product_unit->Prop)) (B_11:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o A_13) B_11)) ((or ((ord_le232288914unit_o A_13) B_11)) (((eq (product_unit->Prop)) A_13) B_11)))) of role axiom named fact_927_subset__iff__psubset__eq
% A new axiom: (forall (A_13:(product_unit->Prop)) (B_11:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o A_13) B_11)) ((or ((ord_le232288914unit_o A_13) B_11)) (((eq (product_unit->Prop)) A_13) B_11))))
% FOF formula (forall (A_13:(arrow_1196572341e_indi->Prop)) (B_11:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o A_13) B_11)) ((or ((ord_le1991507760indi_o A_13) B_11)) (((eq (arrow_1196572341e_indi->Prop)) A_13) B_11)))) of role axiom named fact_928_subset__iff__psubset__eq
% A new axiom: (forall (A_13:(arrow_1196572341e_indi->Prop)) (B_11:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o A_13) B_11)) ((or ((ord_le1991507760indi_o A_13) B_11)) (((eq (arrow_1196572341e_indi->Prop)) A_13) B_11))))
% FOF formula (forall (A_13:((produc1572197287le_alt->Prop)->Prop)) (B_11:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o A_13) B_11)) ((or ((ord_le874404799lt_o_o A_13) B_11)) (((eq ((produc1572197287le_alt->Prop)->Prop)) A_13) B_11)))) of role axiom named fact_929_subset__iff__psubset__eq
% A new axiom: (forall (A_13:((produc1572197287le_alt->Prop)->Prop)) (B_11:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o A_13) B_11)) ((or ((ord_le874404799lt_o_o A_13) B_11)) (((eq ((produc1572197287le_alt->Prop)->Prop)) A_13) B_11))))
% FOF formula (forall (A_13:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_11:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o A_13) B_11)) ((or ((ord_le1382328578lt_o_o A_13) B_11)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_13) B_11)))) of role axiom named fact_930_subset__iff__psubset__eq
% A new axiom: (forall (A_13:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_11:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o A_13) B_11)) ((or ((ord_le1382328578lt_o_o A_13) B_11)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_13) B_11))))
% FOF formula (forall (A_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_11:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o A_13) B_11)) ((or ((ord_le914873172lt_o_o A_13) B_11)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_13) B_11)))) of role axiom named fact_931_subset__iff__psubset__eq
% A new axiom: (forall (A_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_11:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o A_13) B_11)) ((or ((ord_le914873172lt_o_o A_13) B_11)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_13) B_11))))
% FOF formula (forall (A_13:(produc1572197287le_alt->Prop)) (B_11:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o A_13) B_11)) ((or ((ord_le1852932542_alt_o A_13) B_11)) (((eq (produc1572197287le_alt->Prop)) A_13) B_11)))) of role axiom named fact_932_subset__iff__psubset__eq
% A new axiom: (forall (A_13:(produc1572197287le_alt->Prop)) (B_11:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o A_13) B_11)) ((or ((ord_le1852932542_alt_o A_13) B_11)) (((eq (produc1572197287le_alt->Prop)) A_13) B_11))))
% FOF formula (forall (A_13:(nat->Prop)) (B_11:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_13) B_11)) ((or ((ord_less_nat_o A_13) B_11)) (((eq (nat->Prop)) A_13) B_11)))) of role axiom named fact_933_subset__iff__psubset__eq
% A new axiom: (forall (A_13:(nat->Prop)) (B_11:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_13) B_11)) ((or ((ord_less_nat_o A_13) B_11)) (((eq (nat->Prop)) A_13) B_11))))
% FOF formula (forall (A_12:(product_unit->Prop)) (B_10:(product_unit->Prop)), (((ord_le232288914unit_o A_12) B_10)->((ord_le1511552390unit_o A_12) B_10))) of role axiom named fact_934_psubset__imp__subset
% A new axiom: (forall (A_12:(product_unit->Prop)) (B_10:(product_unit->Prop)), (((ord_le232288914unit_o A_12) B_10)->((ord_le1511552390unit_o A_12) B_10)))
% FOF formula (forall (A_12:(arrow_1196572341e_indi->Prop)) (B_10:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_12) B_10)->((ord_le865407012indi_o A_12) B_10))) of role axiom named fact_935_psubset__imp__subset
% A new axiom: (forall (A_12:(arrow_1196572341e_indi->Prop)) (B_10:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_12) B_10)->((ord_le865407012indi_o A_12) B_10)))
% FOF formula (forall (A_12:((produc1572197287le_alt->Prop)->Prop)) (B_10:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o A_12) B_10)->((ord_le1027220427lt_o_o A_12) B_10))) of role axiom named fact_936_psubset__imp__subset
% A new axiom: (forall (A_12:((produc1572197287le_alt->Prop)->Prop)) (B_10:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o A_12) B_10)->((ord_le1027220427lt_o_o A_12) B_10)))
% FOF formula (forall (A_12:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o A_12) B_10)->((ord_le1805007862lt_o_o A_12) B_10))) of role axiom named fact_937_psubset__imp__subset
% A new axiom: (forall (A_12:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o A_12) B_10)->((ord_le1805007862lt_o_o A_12) B_10)))
% FOF formula (forall (A_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_10:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o A_12) B_10)->((ord_le602483040lt_o_o A_12) B_10))) of role axiom named fact_938_psubset__imp__subset
% A new axiom: (forall (A_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_10:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o A_12) B_10)->((ord_le602483040lt_o_o A_12) B_10)))
% FOF formula (forall (A_12:(produc1572197287le_alt->Prop)) (B_10:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o A_12) B_10)->((ord_le962286258_alt_o A_12) B_10))) of role axiom named fact_939_psubset__imp__subset
% A new axiom: (forall (A_12:(produc1572197287le_alt->Prop)) (B_10:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o A_12) B_10)->((ord_le962286258_alt_o A_12) B_10)))
% FOF formula (forall (A_12:(nat->Prop)) (B_10:(nat->Prop)), (((ord_less_nat_o A_12) B_10)->((ord_less_eq_nat_o A_12) B_10))) of role axiom named fact_940_psubset__imp__subset
% A new axiom: (forall (A_12:(nat->Prop)) (B_10:(nat->Prop)), (((ord_less_nat_o A_12) B_10)->((ord_less_eq_nat_o A_12) B_10)))
% FOF formula (forall (C_2:(product_unit->Prop)) (A_11:(product_unit->Prop)) (B_9:(product_unit->Prop)), (((ord_le232288914unit_o A_11) B_9)->(((ord_le1511552390unit_o B_9) C_2)->((ord_le232288914unit_o A_11) C_2)))) of role axiom named fact_941_psubset__subset__trans
% A new axiom: (forall (C_2:(product_unit->Prop)) (A_11:(product_unit->Prop)) (B_9:(product_unit->Prop)), (((ord_le232288914unit_o A_11) B_9)->(((ord_le1511552390unit_o B_9) C_2)->((ord_le232288914unit_o A_11) C_2))))
% FOF formula (forall (C_2:(arrow_1196572341e_indi->Prop)) (A_11:(arrow_1196572341e_indi->Prop)) (B_9:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_11) B_9)->(((ord_le865407012indi_o B_9) C_2)->((ord_le1991507760indi_o A_11) C_2)))) of role axiom named fact_942_psubset__subset__trans
% A new axiom: (forall (C_2:(arrow_1196572341e_indi->Prop)) (A_11:(arrow_1196572341e_indi->Prop)) (B_9:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_11) B_9)->(((ord_le865407012indi_o B_9) C_2)->((ord_le1991507760indi_o A_11) C_2))))
% FOF formula (forall (C_2:((produc1572197287le_alt->Prop)->Prop)) (A_11:((produc1572197287le_alt->Prop)->Prop)) (B_9:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o A_11) B_9)->(((ord_le1027220427lt_o_o B_9) C_2)->((ord_le874404799lt_o_o A_11) C_2)))) of role axiom named fact_943_psubset__subset__trans
% A new axiom: (forall (C_2:((produc1572197287le_alt->Prop)->Prop)) (A_11:((produc1572197287le_alt->Prop)->Prop)) (B_9:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o A_11) B_9)->(((ord_le1027220427lt_o_o B_9) C_2)->((ord_le874404799lt_o_o A_11) C_2))))
% FOF formula (forall (C_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_11:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_9:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o A_11) B_9)->(((ord_le1805007862lt_o_o B_9) C_2)->((ord_le1382328578lt_o_o A_11) C_2)))) of role axiom named fact_944_psubset__subset__trans
% A new axiom: (forall (C_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_11:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_9:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o A_11) B_9)->(((ord_le1805007862lt_o_o B_9) C_2)->((ord_le1382328578lt_o_o A_11) C_2))))
% FOF formula (forall (C_2:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_11:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_9:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o A_11) B_9)->(((ord_le602483040lt_o_o B_9) C_2)->((ord_le914873172lt_o_o A_11) C_2)))) of role axiom named fact_945_psubset__subset__trans
% A new axiom: (forall (C_2:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_11:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_9:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o A_11) B_9)->(((ord_le602483040lt_o_o B_9) C_2)->((ord_le914873172lt_o_o A_11) C_2))))
% FOF formula (forall (C_2:(produc1572197287le_alt->Prop)) (A_11:(produc1572197287le_alt->Prop)) (B_9:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o A_11) B_9)->(((ord_le962286258_alt_o B_9) C_2)->((ord_le1852932542_alt_o A_11) C_2)))) of role axiom named fact_946_psubset__subset__trans
% A new axiom: (forall (C_2:(produc1572197287le_alt->Prop)) (A_11:(produc1572197287le_alt->Prop)) (B_9:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o A_11) B_9)->(((ord_le962286258_alt_o B_9) C_2)->((ord_le1852932542_alt_o A_11) C_2))))
% FOF formula (forall (C_2:(nat->Prop)) (A_11:(nat->Prop)) (B_9:(nat->Prop)), (((ord_less_nat_o A_11) B_9)->(((ord_less_eq_nat_o B_9) C_2)->((ord_less_nat_o A_11) C_2)))) of role axiom named fact_947_psubset__subset__trans
% A new axiom: (forall (C_2:(nat->Prop)) (A_11:(nat->Prop)) (B_9:(nat->Prop)), (((ord_less_nat_o A_11) B_9)->(((ord_less_eq_nat_o B_9) C_2)->((ord_less_nat_o A_11) C_2))))
% FOF formula (forall (C_1:((produc1572197287le_alt->Prop)->Prop)) (A_10:((produc1572197287le_alt->Prop)->Prop)) (B_8:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_10) B_8)->(((ord_le874404799lt_o_o B_8) C_1)->((ord_le874404799lt_o_o A_10) C_1)))) of role axiom named fact_948_subset__psubset__trans
% A new axiom: (forall (C_1:((produc1572197287le_alt->Prop)->Prop)) (A_10:((produc1572197287le_alt->Prop)->Prop)) (B_8:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_10) B_8)->(((ord_le874404799lt_o_o B_8) C_1)->((ord_le874404799lt_o_o A_10) C_1))))
% FOF formula (forall (C_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_10) B_8)->(((ord_le1382328578lt_o_o B_8) C_1)->((ord_le1382328578lt_o_o A_10) C_1)))) of role axiom named fact_949_subset__psubset__trans
% A new axiom: (forall (C_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_10) B_8)->(((ord_le1382328578lt_o_o B_8) C_1)->((ord_le1382328578lt_o_o A_10) C_1))))
% FOF formula (forall (C_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_10:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_10) B_8)->(((ord_le914873172lt_o_o B_8) C_1)->((ord_le914873172lt_o_o A_10) C_1)))) of role axiom named fact_950_subset__psubset__trans
% A new axiom: (forall (C_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_10:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_10) B_8)->(((ord_le914873172lt_o_o B_8) C_1)->((ord_le914873172lt_o_o A_10) C_1))))
% FOF formula (forall (C_1:(produc1572197287le_alt->Prop)) (A_10:(produc1572197287le_alt->Prop)) (B_8:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_10) B_8)->(((ord_le1852932542_alt_o B_8) C_1)->((ord_le1852932542_alt_o A_10) C_1)))) of role axiom named fact_951_subset__psubset__trans
% A new axiom: (forall (C_1:(produc1572197287le_alt->Prop)) (A_10:(produc1572197287le_alt->Prop)) (B_8:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_10) B_8)->(((ord_le1852932542_alt_o B_8) C_1)->((ord_le1852932542_alt_o A_10) C_1))))
% FOF formula (forall (C_1:(nat->Prop)) (A_10:(nat->Prop)) (B_8:(nat->Prop)), (((ord_less_eq_nat_o A_10) B_8)->(((ord_less_nat_o B_8) C_1)->((ord_less_nat_o A_10) C_1)))) of role axiom named fact_952_subset__psubset__trans
% A new axiom: (forall (C_1:(nat->Prop)) (A_10:(nat->Prop)) (B_8:(nat->Prop)), (((ord_less_eq_nat_o A_10) B_8)->(((ord_less_nat_o B_8) C_1)->((ord_less_nat_o A_10) C_1))))
% FOF formula (forall (A_9:(nat->Prop)) (B_7:(nat->Prop)), ((((eq (nat->Prop)) A_9) B_7)->((((ord_less_eq_nat_o A_9) B_7)->(((ord_less_eq_nat_o B_7) A_9)->False))->False))) of role axiom named fact_953_equalityE
% A new axiom: (forall (A_9:(nat->Prop)) (B_7:(nat->Prop)), ((((eq (nat->Prop)) A_9) B_7)->((((ord_less_eq_nat_o A_9) B_7)->(((ord_less_eq_nat_o B_7) A_9)->False))->False)))
% FOF formula (forall (C:(nat->Prop)) (A_8:(nat->Prop)) (B_6:(nat->Prop)), (((ord_less_eq_nat_o A_8) B_6)->(((ord_less_eq_nat_o B_6) C)->((ord_less_eq_nat_o A_8) C)))) of role axiom named fact_954_subset__trans
% A new axiom: (forall (C:(nat->Prop)) (A_8:(nat->Prop)) (B_6:(nat->Prop)), (((ord_less_eq_nat_o A_8) B_6)->(((ord_less_eq_nat_o B_6) C)->((ord_less_eq_nat_o A_8) C))))
% FOF formula (forall (X_6:nat) (A_7:(nat->Prop)) (B_5:(nat->Prop)), (((ord_less_eq_nat_o A_7) B_5)->(((member_nat X_6) A_7)->((member_nat X_6) B_5)))) of role axiom named fact_955_set__mp
% A new axiom: (forall (X_6:nat) (A_7:(nat->Prop)) (B_5:(nat->Prop)), (((ord_less_eq_nat_o A_7) B_5)->(((member_nat X_6) A_7)->((member_nat X_6) B_5))))
% FOF formula (forall (X_6:(produc1572197287le_alt->Prop)) (A_7:((produc1572197287le_alt->Prop)->Prop)) (B_5:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_7) B_5)->(((member1241905979_alt_o X_6) A_7)->((member1241905979_alt_o X_6) B_5)))) of role axiom named fact_956_set__mp
% A new axiom: (forall (X_6:(produc1572197287le_alt->Prop)) (A_7:((produc1572197287le_alt->Prop)->Prop)) (B_5:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_7) B_5)->(((member1241905979_alt_o X_6) A_7)->((member1241905979_alt_o X_6) B_5))))
% FOF formula (forall (X_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_7:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_7) B_5)->(((member1425217232_alt_o X_6) A_7)->((member1425217232_alt_o X_6) B_5)))) of role axiom named fact_957_set__mp
% A new axiom: (forall (X_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_7:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_7) B_5)->(((member1425217232_alt_o X_6) A_7)->((member1425217232_alt_o X_6) B_5))))
% FOF formula (forall (X_6:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_7:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_7) B_5)->(((member822980838_alt_o X_6) A_7)->((member822980838_alt_o X_6) B_5)))) of role axiom named fact_958_set__mp
% A new axiom: (forall (X_6:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_7:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_7) B_5)->(((member822980838_alt_o X_6) A_7)->((member822980838_alt_o X_6) B_5))))
% FOF formula (forall (X_6:produc1572197287le_alt) (A_7:(produc1572197287le_alt->Prop)) (B_5:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_7) B_5)->(((member285112084le_alt X_6) A_7)->((member285112084le_alt X_6) B_5)))) of role axiom named fact_959_set__mp
% A new axiom: (forall (X_6:produc1572197287le_alt) (A_7:(produc1572197287le_alt->Prop)) (B_5:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_7) B_5)->(((member285112084le_alt X_6) A_7)->((member285112084le_alt X_6) B_5))))
% FOF formula (forall (B_4:(nat->Prop)) (X_5:nat) (A_6:(nat->Prop)), (((member_nat X_5) A_6)->(((ord_less_eq_nat_o A_6) B_4)->((member_nat X_5) B_4)))) of role axiom named fact_960_set__rev__mp
% A new axiom: (forall (B_4:(nat->Prop)) (X_5:nat) (A_6:(nat->Prop)), (((member_nat X_5) A_6)->(((ord_less_eq_nat_o A_6) B_4)->((member_nat X_5) B_4))))
% FOF formula (forall (B_4:((produc1572197287le_alt->Prop)->Prop)) (X_5:(produc1572197287le_alt->Prop)) (A_6:((produc1572197287le_alt->Prop)->Prop)), (((member1241905979_alt_o X_5) A_6)->(((ord_le1027220427lt_o_o A_6) B_4)->((member1241905979_alt_o X_5) B_4)))) of role axiom named fact_961_set__rev__mp
% A new axiom: (forall (B_4:((produc1572197287le_alt->Prop)->Prop)) (X_5:(produc1572197287le_alt->Prop)) (A_6:((produc1572197287le_alt->Prop)->Prop)), (((member1241905979_alt_o X_5) A_6)->(((ord_le1027220427lt_o_o A_6) B_4)->((member1241905979_alt_o X_5) B_4))))
% FOF formula (forall (B_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member1425217232_alt_o X_5) A_6)->(((ord_le1805007862lt_o_o A_6) B_4)->((member1425217232_alt_o X_5) B_4)))) of role axiom named fact_962_set__rev__mp
% A new axiom: (forall (B_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member1425217232_alt_o X_5) A_6)->(((ord_le1805007862lt_o_o A_6) B_4)->((member1425217232_alt_o X_5) B_4))))
% FOF formula (forall (B_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_5:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member822980838_alt_o X_5) A_6)->(((ord_le602483040lt_o_o A_6) B_4)->((member822980838_alt_o X_5) B_4)))) of role axiom named fact_963_set__rev__mp
% A new axiom: (forall (B_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_5:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member822980838_alt_o X_5) A_6)->(((ord_le602483040lt_o_o A_6) B_4)->((member822980838_alt_o X_5) B_4))))
% FOF formula (forall (B_4:(produc1572197287le_alt->Prop)) (X_5:produc1572197287le_alt) (A_6:(produc1572197287le_alt->Prop)), (((member285112084le_alt X_5) A_6)->(((ord_le962286258_alt_o A_6) B_4)->((member285112084le_alt X_5) B_4)))) of role axiom named fact_964_set__rev__mp
% A new axiom: (forall (B_4:(produc1572197287le_alt->Prop)) (X_5:produc1572197287le_alt) (A_6:(produc1572197287le_alt->Prop)), (((member285112084le_alt X_5) A_6)->(((ord_le962286258_alt_o A_6) B_4)->((member285112084le_alt X_5) B_4))))
% FOF formula (forall (X_4:nat) (P_2:(nat->Prop)) (Q_1:(nat->Prop)), (((ord_less_eq_nat_o P_2) Q_1)->((P_2 X_4)->(Q_1 X_4)))) of role axiom named fact_965_predicate1D
% A new axiom: (forall (X_4:nat) (P_2:(nat->Prop)) (Q_1:(nat->Prop)), (((ord_less_eq_nat_o P_2) Q_1)->((P_2 X_4)->(Q_1 X_4))))
% FOF formula (forall (X_3:nat) (A_5:(nat->Prop)) (B_3:(nat->Prop)), (((ord_less_eq_nat_o A_5) B_3)->(((member_nat X_3) A_5)->((member_nat X_3) B_3)))) of role axiom named fact_966_in__mono
% A new axiom: (forall (X_3:nat) (A_5:(nat->Prop)) (B_3:(nat->Prop)), (((ord_less_eq_nat_o A_5) B_3)->(((member_nat X_3) A_5)->((member_nat X_3) B_3))))
% FOF formula (forall (X_3:(produc1572197287le_alt->Prop)) (A_5:((produc1572197287le_alt->Prop)->Prop)) (B_3:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_5) B_3)->(((member1241905979_alt_o X_3) A_5)->((member1241905979_alt_o X_3) B_3)))) of role axiom named fact_967_in__mono
% A new axiom: (forall (X_3:(produc1572197287le_alt->Prop)) (A_5:((produc1572197287le_alt->Prop)->Prop)) (B_3:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_5) B_3)->(((member1241905979_alt_o X_3) A_5)->((member1241905979_alt_o X_3) B_3))))
% FOF formula (forall (X_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_5) B_3)->(((member1425217232_alt_o X_3) A_5)->((member1425217232_alt_o X_3) B_3)))) of role axiom named fact_968_in__mono
% A new axiom: (forall (X_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_5) B_3)->(((member1425217232_alt_o X_3) A_5)->((member1425217232_alt_o X_3) B_3))))
% FOF formula (forall (X_3:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_5) B_3)->(((member822980838_alt_o X_3) A_5)->((member822980838_alt_o X_3) B_3)))) of role axiom named fact_969_in__mono
% A new axiom: (forall (X_3:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_5) B_3)->(((member822980838_alt_o X_3) A_5)->((member822980838_alt_o X_3) B_3))))
% FOF formula (forall (X_3:produc1572197287le_alt) (A_5:(produc1572197287le_alt->Prop)) (B_3:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_5) B_3)->(((member285112084le_alt X_3) A_5)->((member285112084le_alt X_3) B_3)))) of role axiom named fact_970_in__mono
% A new axiom: (forall (X_3:produc1572197287le_alt) (A_5:(produc1572197287le_alt->Prop)) (B_3:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_5) B_3)->(((member285112084le_alt X_3) A_5)->((member285112084le_alt X_3) B_3))))
% FOF formula (forall (A_4:(nat->Prop)) (B_2:(nat->Prop)), ((((eq (nat->Prop)) A_4) B_2)->((ord_less_eq_nat_o B_2) A_4))) of role axiom named fact_971_equalityD2
% A new axiom: (forall (A_4:(nat->Prop)) (B_2:(nat->Prop)), ((((eq (nat->Prop)) A_4) B_2)->((ord_less_eq_nat_o B_2) A_4)))
% FOF formula (forall (A_3:(nat->Prop)) (B_1:(nat->Prop)), ((((eq (nat->Prop)) A_3) B_1)->((ord_less_eq_nat_o A_3) B_1))) of role axiom named fact_972_equalityD1
% A new axiom: (forall (A_3:(nat->Prop)) (B_1:(nat->Prop)), ((((eq (nat->Prop)) A_3) B_1)->((ord_less_eq_nat_o A_3) B_1)))
% FOF formula (forall (Q:(nat->Prop)) (P_1:(nat->Prop)) (X_2:nat), ((P_1 X_2)->(((ord_less_eq_nat_o P_1) Q)->(Q X_2)))) of role axiom named fact_973_rev__predicate1D
% A new axiom: (forall (Q:(nat->Prop)) (P_1:(nat->Prop)) (X_2:nat), ((P_1 X_2)->(((ord_less_eq_nat_o P_1) Q)->(Q X_2))))
% FOF formula (forall (A_2:(nat->Prop)) (B:(nat->Prop)), ((iff (((eq (nat->Prop)) A_2) B)) ((and ((ord_less_eq_nat_o A_2) B)) ((ord_less_eq_nat_o B) A_2)))) of role axiom named fact_974_set__eq__subset
% A new axiom: (forall (A_2:(nat->Prop)) (B:(nat->Prop)), ((iff (((eq (nat->Prop)) A_2) B)) ((and ((ord_less_eq_nat_o A_2) B)) ((ord_less_eq_nat_o B) A_2))))
% FOF formula (forall (A_1:(nat->Prop)), ((ord_less_eq_nat_o A_1) A_1)) of role axiom named fact_975_subset__refl
% A new axiom: (forall (A_1:(nat->Prop)), ((ord_less_eq_nat_o A_1) A_1))
% FOF formula (forall (R:(nat->Prop)) (S_1:(nat->Prop)), ((iff ((ord_less_eq_nat_o (fun (X_1:nat)=> ((member_nat X_1) R))) (fun (X_1:nat)=> ((member_nat X_1) S_1)))) ((ord_less_eq_nat_o R) S_1))) of role axiom named fact_976_pred__subset__eq
% A new axiom: (forall (R:(nat->Prop)) (S_1:(nat->Prop)), ((iff ((ord_less_eq_nat_o (fun (X_1:nat)=> ((member_nat X_1) R))) (fun (X_1:nat)=> ((member_nat X_1) S_1)))) ((ord_less_eq_nat_o R) S_1)))
% FOF formula (forall (R:((produc1572197287le_alt->Prop)->Prop)) (S_1:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o (fun (X_1:(produc1572197287le_alt->Prop))=> ((member1241905979_alt_o X_1) R))) (fun (X_1:(produc1572197287le_alt->Prop))=> ((member1241905979_alt_o X_1) S_1)))) ((ord_le1027220427lt_o_o R) S_1))) of role axiom named fact_977_pred__subset__eq
% A new axiom: (forall (R:((produc1572197287le_alt->Prop)->Prop)) (S_1:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o (fun (X_1:(produc1572197287le_alt->Prop))=> ((member1241905979_alt_o X_1) R))) (fun (X_1:(produc1572197287le_alt->Prop))=> ((member1241905979_alt_o X_1) S_1)))) ((ord_le1027220427lt_o_o R) S_1)))
% FOF formula (forall (R:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (S_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o (fun (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> ((member1425217232_alt_o X_1) R))) (fun (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> ((member1425217232_alt_o X_1) S_1)))) ((ord_le1805007862lt_o_o R) S_1))) of role axiom named fact_978_pred__subset__eq
% A new axiom: (forall (R:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (S_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o (fun (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> ((member1425217232_alt_o X_1) R))) (fun (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> ((member1425217232_alt_o X_1) S_1)))) ((ord_le1805007862lt_o_o R) S_1)))
% FOF formula (forall (R:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (S_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o (fun (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> ((member822980838_alt_o X_1) R))) (fun (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> ((member822980838_alt_o X_1) S_1)))) ((ord_le602483040lt_o_o R) S_1))) of role axiom named fact_979_pred__subset__eq
% A new axiom: (forall (R:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (S_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o (fun (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> ((member822980838_alt_o X_1) R))) (fun (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> ((member822980838_alt_o X_1) S_1)))) ((ord_le602483040lt_o_o R) S_1)))
% FOF formula (forall (R:(produc1572197287le_alt->Prop)) (S_1:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o (fun (X_1:produc1572197287le_alt)=> ((member285112084le_alt X_1) R))) (fun (X_1:produc1572197287le_alt)=> ((member285112084le_alt X_1) S_1)))) ((ord_le962286258_alt_o R) S_1))) of role axiom named fact_980_pred__subset__eq
% A new axiom: (forall (R:(produc1572197287le_alt->Prop)) (S_1:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o (fun (X_1:produc1572197287le_alt)=> ((member285112084le_alt X_1) R))) (fun (X_1:produc1572197287le_alt)=> ((member285112084le_alt X_1) S_1)))) ((ord_le962286258_alt_o R) S_1)))
% FOF formula (forall (N_1:nat), (((ord_less_nat N_1) N_1)->False)) of role axiom named fact_981_less__not__refl
% A new axiom: (forall (N_1:nat), (((ord_less_nat N_1) N_1)->False))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff (not (((eq nat) M_1) N_1))) ((or ((ord_less_nat M_1) N_1)) ((ord_less_nat N_1) M_1)))) of role axiom named fact_982_nat__neq__iff
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff (not (((eq nat) M_1) N_1))) ((or ((ord_less_nat M_1) N_1)) ((ord_less_nat N_1) M_1))))
% 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_983_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_1:nat), (((ord_less_nat N_1) N_1)->False)) of role axiom named fact_984_less__irrefl__nat
% A new axiom: (forall (N_1:nat), (((ord_less_nat N_1) N_1)->False))
% FOF formula (forall (N_1:nat) (M_1:nat), (((ord_less_nat N_1) M_1)->(not (((eq nat) M_1) N_1)))) of role axiom named fact_985_less__not__refl2
% A new axiom: (forall (N_1:nat) (M_1:nat), (((ord_less_nat N_1) M_1)->(not (((eq nat) M_1) N_1))))
% FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_986_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_1:nat) (N_1:nat), ((((ord_less_nat M_1) N_1)->((P N_1) M_1))->(((((eq nat) M_1) N_1)->((P N_1) M_1))->((((ord_less_nat N_1) M_1)->((P N_1) M_1))->((P N_1) M_1))))) of role axiom named fact_987_nat__less__cases
% A new axiom: (forall (P:(nat->(nat->Prop))) (M_1:nat) (N_1:nat), ((((ord_less_nat M_1) N_1)->((P N_1) M_1))->(((((eq nat) M_1) N_1)->((P N_1) M_1))->((((ord_less_nat N_1) M_1)->((P N_1) M_1))->((P N_1) M_1)))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M_1) N_1)) ((plus_plus_nat N_1) M_1))) of role axiom named fact_988_nat__add__commute
% A new axiom: (forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M_1) N_1)) ((plus_plus_nat N_1) M_1)))
% 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_989_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_1:nat) (N_1:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M_1) N_1)) K)) ((plus_plus_nat M_1) ((plus_plus_nat N_1) K)))) of role axiom named fact_990_nat__add__assoc
% A new axiom: (forall (M_1:nat) (N_1:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M_1) N_1)) K)) ((plus_plus_nat M_1) ((plus_plus_nat N_1) K))))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat K) M_1)) ((plus_plus_nat K) N_1))) (((eq nat) M_1) N_1))) of role axiom named fact_991_nat__add__left__cancel
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat K) M_1)) ((plus_plus_nat K) N_1))) (((eq nat) M_1) N_1)))
% FOF formula (forall (M_1:nat) (K:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M_1) K)) ((plus_plus_nat N_1) K))) (((eq nat) M_1) N_1))) of role axiom named fact_992_nat__add__right__cancel
% A new axiom: (forall (M_1:nat) (K:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M_1) K)) ((plus_plus_nat N_1) K))) (((eq nat) M_1) N_1)))
% FOF formula (forall (N_1:nat), ((ord_less_eq_nat N_1) N_1)) of role axiom named fact_993_le__refl
% A new axiom: (forall (N_1:nat), ((ord_less_eq_nat N_1) N_1))
% FOF formula (forall (M_1:nat) (N_1:nat), ((or ((ord_less_eq_nat M_1) N_1)) ((ord_less_eq_nat N_1) M_1))) of role axiom named fact_994_nat__le__linear
% A new axiom: (forall (M_1:nat) (N_1:nat), ((or ((ord_less_eq_nat M_1) N_1)) ((ord_less_eq_nat N_1) M_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), ((((eq nat) M_1) N_1)->((ord_less_eq_nat M_1) N_1))) of role axiom named fact_995_eq__imp__le
% A new axiom: (forall (M_1:nat) (N_1:nat), ((((eq nat) M_1) N_1)->((ord_less_eq_nat M_1) N_1)))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K)))) of role axiom named fact_996_le__trans
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->(((ord_less_eq_nat N_1) M_1)->(((eq nat) M_1) N_1)))) of role axiom named fact_997_le__antisym
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->(((ord_less_eq_nat N_1) M_1)->(((eq nat) M_1) N_1))))
% FOF formula (forall (K:nat) (N_2:(nat->Prop)), ((inj_on_nat_nat (fun (N:nat)=> ((plus_plus_nat N) K))) N_2)) of role axiom named fact_998_inj__on__add__nat
% A new axiom: (forall (K:nat) (N_2:(nat->Prop)), ((inj_on_nat_nat (fun (N:nat)=> ((plus_plus_nat N) K))) N_2))
% FOF formula (forall (_TPTP_I:nat) (J:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) _TPTP_I)->False)) of role axiom named fact_999_not__add__less1
% A new axiom: (forall (_TPTP_I:nat) (J:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) _TPTP_I)->False))
% FOF formula (forall (J:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J) _TPTP_I)) _TPTP_I)->False)) of role axiom named fact_1000_not__add__less2
% A new axiom: (forall (J:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J) _TPTP_I)) _TPTP_I)->False))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M_1)) ((plus_plus_nat K) N_1))) ((ord_less_nat M_1) N_1))) of role axiom named fact_1001_nat__add__left__cancel__less
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M_1)) ((plus_plus_nat K) N_1))) ((ord_less_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat J) M_1)))) of role axiom named fact_1002_trans__less__add1
% A new axiom: (forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat J) M_1))))
% FOF formula (forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat M_1) J)))) of role axiom named fact_1003_trans__less__add2
% A new axiom: (forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat M_1) J))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))) of role axiom named fact_1004_add__less__mono1
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K))))
% FOF formula (forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))) of role axiom named fact_1005_add__less__mono
% A new axiom: (forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L)))))
% FOF formula (forall (M_1:nat) (N_1:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M_1) L)) ((plus_plus_nat K) N_1))->((ord_less_nat M_1) N_1)))) of role axiom named fact_1006_less__add__eq__less
% A new axiom: (forall (M_1:nat) (N_1:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M_1) L)) ((plus_plus_nat K) N_1))->((ord_less_nat M_1) N_1))))
% FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) K)->((ord_less_nat _TPTP_I) K))) of role axiom named fact_1007_add__lessD1
% A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) K)->((ord_less_nat _TPTP_I) K)))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) N_1)) ((and ((ord_less_eq_nat M_1) N_1)) (not (((eq nat) M_1) N_1))))) of role axiom named fact_1008_nat__less__le
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) N_1)) ((and ((ord_less_eq_nat M_1) N_1)) (not (((eq nat) M_1) N_1)))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_1) N_1)) ((or ((ord_less_nat M_1) N_1)) (((eq nat) M_1) N_1)))) of role axiom named fact_1009_le__eq__less__or__eq
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_1) N_1)) ((or ((ord_less_nat M_1) N_1)) (((eq nat) M_1) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_eq_nat M_1) N_1))) of role axiom named fact_1010_less__imp__le__nat
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_eq_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((not (((eq nat) M_1) N_1))->((ord_less_nat M_1) N_1)))) of role axiom named fact_1011_le__neq__implies__less
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((not (((eq nat) M_1) N_1))->((ord_less_nat M_1) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((or ((ord_less_nat M_1) N_1)) (((eq nat) M_1) N_1))->((ord_less_eq_nat M_1) N_1))) of role axiom named fact_1012_less__or__eq__imp__le
% A new axiom: (forall (M_1:nat) (N_1:nat), (((or ((ord_less_nat M_1) N_1)) (((eq nat) M_1) N_1))->((ord_less_eq_nat M_1) N_1)))
% FOF formula (forall (N_1:nat) (M_1:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat M_1) N_1))) of role axiom named fact_1013_le__add2
% A new axiom: (forall (N_1:nat) (M_1:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat M_1) N_1)))
% FOF formula (forall (N_1:nat) (M_1:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat N_1) M_1))) of role axiom named fact_1014_le__add1
% A new axiom: (forall (N_1:nat) (M_1:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat N_1) M_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_1) N_1)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N_1) ((plus_plus_nat M_1) K_1)))))) of role axiom named fact_1015_le__iff__add
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_1) N_1)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N_1) ((plus_plus_nat M_1) K_1))))))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M_1)) ((plus_plus_nat K) N_1))) ((ord_less_eq_nat M_1) N_1))) of role axiom named fact_1016_nat__add__left__cancel__le
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M_1)) ((plus_plus_nat K) N_1))) ((ord_less_eq_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J) M_1)))) of role axiom named fact_1017_trans__le__add1
% A new axiom: (forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J) M_1))))
% FOF formula (forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M_1) J)))) of role axiom named fact_1018_trans__le__add2
% A new axiom: (forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M_1) J))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))) of role axiom named fact_1019_add__le__mono1
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K))))
% FOF formula (forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))) of role axiom named fact_1020_add__le__mono
% A new axiom: (forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L)))))
% FOF formula (forall (M_1:nat) (K:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M_1) K)) N_1)->((ord_less_eq_nat K) N_1))) of role axiom named fact_1021_add__leD2
% A new axiom: (forall (M_1:nat) (K:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M_1) K)) N_1)->((ord_less_eq_nat K) N_1)))
% FOF formula (forall (M_1:nat) (K:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M_1) K)) N_1)->((ord_less_eq_nat M_1) N_1))) of role axiom named fact_1022_add__leD1
% A new axiom: (forall (M_1:nat) (K:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M_1) K)) N_1)->((ord_less_eq_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (K:nat) (F:(nat->nat)), ((forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (F M)) (F N))))->((ord_less_eq_nat ((plus_plus_nat (F M_1)) K)) (F ((plus_plus_nat M_1) K))))) of role axiom named fact_1023_mono__nat__linear__lb
% A new axiom: (forall (M_1:nat) (K:nat) (F:(nat->nat)), ((forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (F M)) (F N))))->((ord_less_eq_nat ((plus_plus_nat (F M_1)) K)) (F ((plus_plus_nat M_1) K)))))
% FOF formula (forall (_TPTP_I:nat) (J:nat) (F:(nat->nat)), ((forall (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat (F I_1)) (F J_1))))->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat (F _TPTP_I)) (F J))))) of role axiom named fact_1024_less__mono__imp__le__mono
% A new axiom: (forall (_TPTP_I:nat) (J:nat) (F:(nat->nat)), ((forall (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat (F I_1)) (F J_1))))->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat (F _TPTP_I)) (F J)))))
% 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_1025_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_1026_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 (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y))) of role axiom named fact_1027_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 (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_1028_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_1029_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 ((ex (produc1572197287le_alt->Prop)) (fun (L_1:(produc1572197287le_alt->Prop))=> ((member1241905979_alt_o L_1) arrow_1982173296le_Lin))) of role axiom named fact_1030_linear__alt
% A new axiom: ((ex (produc1572197287le_alt->Prop)) (fun (L_1:(produc1572197287le_alt->Prop))=> ((member1241905979_alt_o L_1) arrow_1982173296le_Lin)))
% FOF formula (finite431949602e_indi top_to54564308indi_o) of role axiom named fact_1031_finite__indi
% A new axiom: (finite431949602e_indi top_to54564308indi_o)
% FOF formula (forall (K:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat N) K))))) of role axiom named fact_1032_finite__Collect__le__nat
% A new axiom: (forall (K:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat N) K)))))
% FOF formula (forall (K:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_nat N) K))))) of role axiom named fact_1033_finite__Collect__less__nat
% A new axiom: (forall (K:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_nat N) K)))))
% FOF formula ((finite_finite_nat top_top_nat_o)->False) of role axiom named fact_1034_infinite__UNIV__nat
% A new axiom: ((finite_finite_nat top_top_nat_o)->False)
% FOF formula (((eq nat) (finite1949902593t_unit top_to1984820022unit_o)) one_one_nat) of role axiom named fact_1035_card__UNIV__unit
% A new axiom: (((eq nat) (finite1949902593t_unit top_to1984820022unit_o)) one_one_nat)
% FOF formula (forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_nat I_1) N_1))))) N_1)) of role axiom named fact_1036_card__Collect__less__nat
% A new axiom: (forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_nat I_1) N_1))))) N_1))
% 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_1037_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_1038_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_1039_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:nat), ((ord_less_eq_nat N) (F N)))->(finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat (F N)) U)))))) of role axiom named fact_1040_finite__less__ub
% A new axiom: (forall (U:nat) (F:(nat->nat)), ((forall (N:nat), ((ord_less_eq_nat N) (F N)))->(finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat (F N)) U))))))
% FOF formula (forall (N_1:nat) (N_2:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) N_1)))->(finite_finite_nat N_2))) of role axiom named fact_1041_bounded__nat__set__is__finite
% A new axiom: (forall (N_1:nat) (N_2:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) N_1)))->(finite_finite_nat N_2)))
% FOF formula (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)) of role axiom named fact_1042_less__zeroE
% A new axiom: (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False))
% FOF formula (forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1)) of role axiom named fact_1043_le0
% A new axiom: (forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1))
% FOF formula (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)) of role axiom named fact_1044_not__less0
% A new axiom: (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False))
% FOF formula (forall (N_1:nat), ((iff (not (((eq nat) N_1) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N_1))) of role axiom named fact_1045_neq0__conv
% A new axiom: (forall (N_1:nat), ((iff (not (((eq nat) N_1) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N_1)))
% FOF formula (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)) of role axiom named fact_1046_less__nat__zero__code
% A new axiom: (forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->(not (((eq nat) N_1) zero_zero_nat)))) of role axiom named fact_1047_gr__implies__not0
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->(not (((eq nat) N_1) zero_zero_nat))))
% FOF formula (forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ord_less_nat zero_zero_nat) N_1))) of role axiom named fact_1048_gr0I
% A new axiom: (forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ord_less_nat zero_zero_nat) N_1)))
% FOF formula (forall (N_1:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N_1)) N_1)) of role axiom named fact_1049_plus__nat_Oadd__0
% A new axiom: (forall (N_1:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N_1)) N_1))
% FOF formula (forall (M_1:nat), (((eq nat) ((plus_plus_nat M_1) zero_zero_nat)) M_1)) of role axiom named fact_1050_Nat_Oadd__0__right
% A new axiom: (forall (M_1:nat), (((eq nat) ((plus_plus_nat M_1) zero_zero_nat)) M_1))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M_1) N_1)) zero_zero_nat)) ((and (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat)))) of role axiom named fact_1051_add__is__0
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M_1) N_1)) zero_zero_nat)) ((and (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((((eq nat) ((plus_plus_nat M_1) N_1)) M_1)->(((eq nat) N_1) zero_zero_nat))) of role axiom named fact_1052_add__eq__self__zero
% A new axiom: (forall (M_1:nat) (N_1:nat), ((((eq nat) ((plus_plus_nat M_1) N_1)) M_1)->(((eq nat) N_1) zero_zero_nat)))
% FOF formula (forall (N_1:nat), ((iff ((ord_less_eq_nat N_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat))) of role axiom named fact_1053_le__0__eq
% A new axiom: (forall (N_1:nat), ((iff ((ord_less_eq_nat N_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat)))
% FOF formula (forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1)) of role axiom named fact_1054_less__eq__nat_Osimps_I1_J
% A new axiom: (forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M_1) N_1))) ((or ((ord_less_nat zero_zero_nat) M_1)) ((ord_less_nat zero_zero_nat) N_1)))) of role axiom named fact_1055_add__gr__0
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M_1) N_1))) ((or ((ord_less_nat zero_zero_nat) M_1)) ((ord_less_nat zero_zero_nat) N_1))))
% FOF formula (forall (N_1:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N_1)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N_1)) (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_1056_ex__least__nat__less
% A new axiom: (forall (N_1:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N_1)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N_1)) (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_1:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N_1)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N_1)) (forall (I_1:nat), (((ord_less_nat I_1) K_1)->((P I_1)->False))))) (P K_1))))))) of role axiom named fact_1057_ex__least__nat__le
% A new axiom: (forall (N_1:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N_1)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N_1)) (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:nat), (((ord_less_nat _TPTP_I) J)->((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)))))) of role axiom named fact_1058_less__imp__add__positive
% A new axiom: (forall (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((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))))))
% FOF formula (forall (N_1:nat), ((ord_less_nat N_1) (suc N_1))) of role axiom named fact_1059_lessI
% A new axiom: (forall (N_1:nat), ((ord_less_nat N_1) (suc N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat (suc M_1)) (suc N_1)))) of role axiom named fact_1060_Suc__mono
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat (suc M_1)) (suc N_1))))
% FOF formula (forall (N_1:nat), ((ord_less_nat zero_zero_nat) (suc N_1))) of role axiom named fact_1061_zero__less__Suc
% A new axiom: (forall (N_1:nat), ((ord_less_nat zero_zero_nat) (suc N_1)))
% FOF formula (forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y))) of role axiom named fact_1062_Suc__inject
% A new axiom: (forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y)))
% FOF formula (forall (Nat:nat) (Nat_2:nat), ((iff (((eq nat) (suc Nat)) (suc Nat_2))) (((eq nat) Nat) Nat_2))) of role axiom named fact_1063_nat_Oinject
% A new axiom: (forall (Nat:nat) (Nat_2:nat), ((iff (((eq nat) (suc Nat)) (suc Nat_2))) (((eq nat) Nat) Nat_2)))
% FOF formula (forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1))) of role axiom named fact_1064_Suc__n__not__n
% A new axiom: (forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1)))
% FOF formula (forall (N_1:nat), (not (((eq nat) N_1) (suc N_1)))) of role axiom named fact_1065_n__not__Suc__n
% A new axiom: (forall (N_1:nat), (not (((eq nat) N_1) (suc N_1))))
% FOF formula (forall (M_1:nat), (not (((eq nat) (suc M_1)) zero_zero_nat))) of role axiom named fact_1066_Suc__neq__Zero
% A new axiom: (forall (M_1:nat), (not (((eq nat) (suc M_1)) zero_zero_nat)))
% FOF formula (forall (M_1:nat), (not (((eq nat) zero_zero_nat) (suc M_1)))) of role axiom named fact_1067_Zero__neq__Suc
% A new axiom: (forall (M_1:nat), (not (((eq nat) zero_zero_nat) (suc M_1))))
% FOF formula (forall (Nat_3:nat), (not (((eq nat) (suc Nat_3)) zero_zero_nat))) of role axiom named fact_1068_nat_Osimps_I3_J
% A new axiom: (forall (Nat_3:nat), (not (((eq nat) (suc Nat_3)) zero_zero_nat)))
% FOF formula (forall (M_1:nat), (not (((eq nat) (suc M_1)) zero_zero_nat))) of role axiom named fact_1069_Suc__not__Zero
% A new axiom: (forall (M_1:nat), (not (((eq nat) (suc M_1)) zero_zero_nat)))
% FOF formula (forall (Nat_2:nat), (not (((eq nat) zero_zero_nat) (suc Nat_2)))) of role axiom named fact_1070_nat_Osimps_I2_J
% A new axiom: (forall (Nat_2:nat), (not (((eq nat) zero_zero_nat) (suc Nat_2))))
% FOF formula (forall (M_1:nat), (not (((eq nat) zero_zero_nat) (suc M_1)))) of role axiom named fact_1071_Zero__not__Suc
% A new axiom: (forall (M_1:nat), (not (((eq nat) zero_zero_nat) (suc M_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc M_1)) (suc N_1))->((ord_less_nat M_1) N_1))) of role axiom named fact_1072_Suc__less__SucD
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc M_1)) (suc N_1))->((ord_less_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc M_1)) N_1)->((ord_less_nat M_1) N_1))) of role axiom named fact_1073_Suc__lessD
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc M_1)) N_1)->((ord_less_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) (suc N_1))->((((ord_less_nat M_1) N_1)->False)->(((eq nat) M_1) N_1)))) of role axiom named fact_1074_less__SucE
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) (suc N_1))->((((ord_less_nat M_1) N_1)->False)->(((eq nat) M_1) N_1))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat J) K)->((ord_less_nat (suc _TPTP_I)) K)))) of role axiom named fact_1075_less__trans__Suc
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat J) K)->((ord_less_nat (suc _TPTP_I)) K))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((not (((eq nat) (suc M_1)) N_1))->((ord_less_nat (suc M_1)) N_1)))) of role axiom named fact_1076_Suc__lessI
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((not (((eq nat) (suc M_1)) N_1))->((ord_less_nat (suc M_1)) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat M_1) (suc N_1)))) of role axiom named fact_1077_less__SucI
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat M_1) (suc N_1))))
% FOF formula (forall (N_1:nat) (M_1:nat), ((((ord_less_nat N_1) M_1)->False)->(((ord_less_nat N_1) (suc M_1))->(((eq nat) M_1) N_1)))) of role axiom named fact_1078_less__antisym
% A new axiom: (forall (N_1:nat) (M_1:nat), ((((ord_less_nat N_1) M_1)->False)->(((ord_less_nat N_1) (suc M_1))->(((eq nat) M_1) N_1))))
% FOF formula (forall (N_1:nat) (M_1:nat), ((((ord_less_nat N_1) M_1)->False)->((iff ((ord_less_nat N_1) (suc M_1))) (((eq nat) N_1) M_1)))) of role axiom named fact_1079_not__less__less__Suc__eq
% A new axiom: (forall (N_1:nat) (M_1:nat), ((((ord_less_nat N_1) M_1)->False)->((iff ((ord_less_nat N_1) (suc M_1))) (((eq nat) N_1) M_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat (suc M_1)) (suc N_1))) ((ord_less_nat M_1) N_1))) of role axiom named fact_1080_Suc__less__eq
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat (suc M_1)) (suc N_1))) ((ord_less_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) (suc N_1))) ((or ((ord_less_nat M_1) N_1)) (((eq nat) M_1) N_1)))) of role axiom named fact_1081_less__Suc__eq
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) (suc N_1))) ((or ((ord_less_nat M_1) N_1)) (((eq nat) M_1) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff (((ord_less_nat M_1) N_1)->False)) ((ord_less_nat N_1) (suc M_1)))) of role axiom named fact_1082_not__less__eq
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff (((ord_less_nat M_1) N_1)->False)) ((ord_less_nat N_1) (suc M_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M_1)) N_1)) ((plus_plus_nat M_1) (suc N_1)))) of role axiom named fact_1083_add__Suc__shift
% A new axiom: (forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M_1)) N_1)) ((plus_plus_nat M_1) (suc N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M_1)) N_1)) (suc ((plus_plus_nat M_1) N_1)))) of role axiom named fact_1084_add__Suc
% A new axiom: (forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M_1)) N_1)) (suc ((plus_plus_nat M_1) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M_1) (suc N_1))) (suc ((plus_plus_nat M_1) N_1)))) of role axiom named fact_1085_add__Suc__right
% A new axiom: (forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M_1) (suc N_1))) (suc ((plus_plus_nat M_1) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat (suc M_1)) N_1)->((ord_less_eq_nat M_1) N_1))) of role axiom named fact_1086_Suc__leD
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat (suc M_1)) N_1)->((ord_less_eq_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) (suc N_1))->((((ord_less_eq_nat M_1) N_1)->False)->(((eq nat) M_1) (suc N_1))))) of role axiom named fact_1087_le__SucE
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) (suc N_1))->((((ord_less_eq_nat M_1) N_1)->False)->(((eq nat) M_1) (suc N_1)))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((ord_less_eq_nat M_1) (suc N_1)))) of role axiom named fact_1088_le__SucI
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((ord_less_eq_nat M_1) (suc N_1))))
% FOF formula (forall (N_1:nat) (M_1:nat), ((iff ((ord_less_eq_nat (suc N_1)) (suc M_1))) ((ord_less_eq_nat N_1) M_1))) of role axiom named fact_1089_Suc__le__mono
% A new axiom: (forall (N_1:nat) (M_1:nat), ((iff ((ord_less_eq_nat (suc N_1)) (suc M_1))) ((ord_less_eq_nat N_1) M_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_1) (suc N_1))) ((or ((ord_less_eq_nat M_1) N_1)) (((eq nat) M_1) (suc N_1))))) of role axiom named fact_1090_le__Suc__eq
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_1) (suc N_1))) ((or ((ord_less_eq_nat M_1) N_1)) (((eq nat) M_1) (suc N_1)))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff (((ord_less_eq_nat M_1) N_1)->False)) ((ord_less_eq_nat (suc N_1)) M_1))) of role axiom named fact_1091_not__less__eq__eq
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff (((ord_less_eq_nat M_1) N_1)->False)) ((ord_less_eq_nat (suc N_1)) M_1)))
% FOF formula (forall (N_1:nat), (((ord_less_eq_nat (suc N_1)) N_1)->False)) of role axiom named fact_1092_Suc__n__not__le__n
% A new axiom: (forall (N_1:nat), (((ord_less_eq_nat (suc N_1)) N_1)->False))
% FOF formula (forall (N_2:(nat->Prop)), ((inj_on_nat_nat suc) N_2)) of role axiom named fact_1093_inj__Suc
% A new axiom: (forall (N_2:(nat->Prop)), ((inj_on_nat_nat suc) N_2))
% FOF formula (forall (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) N_1)) ((ex nat) (fun (M:nat)=> (((eq nat) N_1) (suc M)))))) of role axiom named fact_1094_gr0__conv__Suc
% A new axiom: (forall (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) N_1)) ((ex nat) (fun (M:nat)=> (((eq nat) N_1) (suc M))))))
% FOF formula (forall (N_1:nat), ((iff ((ord_less_nat N_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) of role axiom named fact_1095_less__Suc0
% A new axiom: (forall (N_1:nat), ((iff ((ord_less_nat N_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat)))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) (suc N_1))) ((or (((eq nat) M_1) zero_zero_nat)) ((ex nat) (fun (J_1:nat)=> ((and (((eq nat) M_1) (suc J_1))) ((ord_less_nat J_1) N_1))))))) of role axiom named fact_1096_less__Suc__eq__0__disj
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) (suc N_1))) ((or (((eq nat) M_1) zero_zero_nat)) ((ex nat) (fun (J_1:nat)=> ((and (((eq nat) M_1) (suc J_1))) ((ord_less_nat J_1) N_1)))))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M_1) N_1)) (suc zero_zero_nat))) ((or ((and (((eq nat) M_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat)))))) of role axiom named fact_1097_add__is__1
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M_1) N_1)) (suc zero_zero_nat))) ((or ((and (((eq nat) M_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat))))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M_1) N_1))) ((or ((and (((eq nat) M_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat)))))) of role axiom named fact_1098_one__is__add
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M_1) N_1))) ((or ((and (((eq nat) M_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat))))))
% FOF formula (forall (_TPTP_I:nat) (M_1:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat _TPTP_I) M_1)))) of role axiom named fact_1099_less__add__Suc1
% A new axiom: (forall (_TPTP_I:nat) (M_1:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat _TPTP_I) M_1))))
% FOF formula (forall (_TPTP_I:nat) (M_1:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat M_1) _TPTP_I)))) of role axiom named fact_1100_less__add__Suc2
% A new axiom: (forall (_TPTP_I:nat) (M_1:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat M_1) _TPTP_I))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) N_1)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N_1) (suc ((plus_plus_nat M_1) K_1))))))) of role axiom named fact_1101_less__iff__Suc__add
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) N_1)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N_1) (suc ((plus_plus_nat M_1) K_1)))))))
% FOF formula (forall (N_1:nat) (M_1:nat), ((iff ((ord_less_nat N_1) M_1)) ((ord_less_eq_nat (suc N_1)) M_1))) of role axiom named fact_1102_less__eq__Suc__le
% A new axiom: (forall (N_1:nat) (M_1:nat), ((iff ((ord_less_nat N_1) M_1)) ((ord_less_eq_nat (suc N_1)) M_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) (suc N_1))) ((ord_less_eq_nat M_1) N_1))) of role axiom named fact_1103_less__Suc__eq__le
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) (suc N_1))) ((ord_less_eq_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M_1)) N_1)) ((ord_less_nat M_1) N_1))) of role axiom named fact_1104_Suc__le__eq
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M_1)) N_1)) ((ord_less_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((ord_less_nat M_1) (suc N_1)))) of role axiom named fact_1105_le__imp__less__Suc
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((ord_less_nat M_1) (suc N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_eq_nat (suc M_1)) N_1))) of role axiom named fact_1106_Suc__leI
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_eq_nat (suc M_1)) N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((iff ((ord_less_nat N_1) (suc M_1))) (((eq nat) N_1) M_1)))) of role axiom named fact_1107_le__less__Suc__eq
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((iff ((ord_less_nat N_1) (suc M_1))) (((eq nat) N_1) M_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat (suc M_1)) N_1)->((ord_less_nat M_1) N_1))) of role axiom named fact_1108_Suc__le__lessD
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat (suc M_1)) N_1)->((ord_less_nat M_1) N_1)))
% FOF formula (((eq nat) one_one_nat) (suc zero_zero_nat)) of role axiom named fact_1109_One__nat__def
% A new axiom: (((eq nat) one_one_nat) (suc zero_zero_nat))
% 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_1110_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_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_eq_nat I_1) N_1))))) (suc N_1))) of role axiom named fact_1111_card__Collect__le__nat
% A new axiom: (forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_eq_nat I_1) N_1))))) (suc N_1)))
% 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_1112_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_1113_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_1114_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:nat), (((ord_less_eq_nat _TPTP_I) J)->((P J)->((forall (I_1:nat), (((ord_less_nat I_1) J)->((P (suc I_1))->(P I_1))))->(P _TPTP_I))))) of role axiom named fact_1115_inc__induct
% A new axiom: (forall (P:(nat->Prop)) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((P J)->((forall (I_1:nat), (((ord_less_nat I_1) J)->((P (suc I_1))->(P I_1))))->(P _TPTP_I)))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ex nat) (fun (K_1:nat)=> (((eq nat) N_1) (suc ((plus_plus_nat M_1) K_1))))))) of role axiom named fact_1116_less__imp__Suc__add
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ex nat) (fun (K_1:nat)=> (((eq nat) N_1) (suc ((plus_plus_nat M_1) K_1)))))))
% FOF formula (forall (N_1:nat), (((ord_less_nat zero_zero_nat) N_1)->((ex nat) (fun (M:nat)=> (((eq nat) N_1) (suc M)))))) of role axiom named fact_1117_gr0__implies__Suc
% A new axiom: (forall (N_1:nat), (((ord_less_nat zero_zero_nat) N_1)->((ex nat) (fun (M:nat)=> (((eq nat) N_1) (suc M))))))
% FOF formula (forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat N_1) one_one_nat))) of role axiom named fact_1118_Suc__eq__plus1
% A new axiom: (forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat N_1) one_one_nat)))
% FOF formula (forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat one_one_nat) N_1))) of role axiom named fact_1119_Suc__eq__plus1__left
% A new axiom: (forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat one_one_nat) N_1)))
% FOF formula (forall (N_1:nat) (M_2:nat), (((ord_less_eq_nat (suc N_1)) M_2)->((ex nat) (fun (M:nat)=> (((eq nat) M_2) (suc M)))))) of role axiom named fact_1120_Suc__le__D
% A new axiom: (forall (N_1:nat) (M_2:nat), (((ord_less_eq_nat (suc N_1)) M_2)->((ex nat) (fun (M:nat)=> (((eq nat) M_2) (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_1:nat), (((ord_less_nat _TPTP_I) J_1)->(not (((eq nat) K) (suc J_1)))))->False)))) of role axiom named fact_1121_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_1:nat), (((ord_less_nat _TPTP_I) J_1)->(not (((eq nat) K) (suc J_1)))))->False))))
% FOF formula (forall (_TPTP_I:nat) (K:nat), (((ord_less_nat (suc _TPTP_I)) K)->((forall (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->(not (((eq nat) K) (suc J_1)))))->False))) of role axiom named fact_1122_Suc__lessE
% A new axiom: (forall (_TPTP_I:nat) (K:nat), (((ord_less_nat (suc _TPTP_I)) K)->((forall (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->(not (((eq nat) K) (suc J_1)))))->False)))
% FOF formula (forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ex nat) (fun (M:nat)=> (((eq nat) N_1) (suc M)))))) of role axiom named fact_1123_not0__implies__Suc
% A new axiom: (forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ex nat) (fun (M:nat)=> (((eq nat) N_1) (suc M))))))
% FOF formula (forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat_1:nat), (not (((eq nat) Y) (suc Nat_1))))->False))) of role axiom named fact_1124_nat_Oexhaust
% A new axiom: (forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat_1:nat), (not (((eq nat) Y) (suc Nat_1))))->False)))
% FOF formula (forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N:nat), ((P (suc N))->(P N)))->(P zero_zero_nat)))) of role axiom named fact_1125_zero__induct
% A new axiom: (forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N:nat), ((P (suc N))->(P N)))->(P zero_zero_nat))))
% FOF formula (forall (N_1:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N:nat), ((P N)->(P (suc N))))->(P N_1)))) of role axiom named fact_1126_nat__induct
% A new axiom: (forall (N_1:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N:nat), ((P N)->(P (suc N))))->(P N_1))))
% FOF formula (((eq (nat->Prop)) ((image_1011045538di_nat h) top_to54564308indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite2011930979e_indi top_to54564308indi_o))) of role axiom named fact_1127_surjh
% A new axiom: (((eq (nat->Prop)) ((image_1011045538di_nat h) top_to54564308indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite2011930979e_indi top_to54564308indi_o)))
% FOF formula (forall (L:nat) (U:nat), (finite_finite_nat ((ord_at4362885an_nat L) U))) of role axiom named fact_1128_finite__atLeastLessThan
% A new axiom: (forall (L:nat) (U:nat), (finite_finite_nat ((ord_at4362885an_nat L) U)))
% FOF formula ((forall (H:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat H) top_to54564308indi_o)->(not (((eq (nat->Prop)) ((image_1011045538di_nat H) top_to54564308indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite2011930979e_indi top_to54564308indi_o))))))->False) of role axiom named fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12
% A new axiom: ((forall (H:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat H) top_to54564308indi_o)->(not (((eq (nat->Prop)) ((image_1011045538di_nat H) top_to54564308indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite2011930979e_indi top_to54564308indi_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_1130_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 (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat suc) ((ord_at4362885an_nat _TPTP_I) J))) ((ord_at4362885an_nat (suc _TPTP_I)) (suc J)))) of role axiom named fact_1131_image__Suc__atLeastLessThan
% A new axiom: (forall (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat suc) ((ord_at4362885an_nat _TPTP_I) J))) ((ord_at4362885an_nat (suc _TPTP_I)) (suc J))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat (fun (N:nat)=> ((plus_plus_nat N) K))) ((ord_at4362885an_nat _TPTP_I) J))) ((ord_at4362885an_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))) of role axiom named fact_1132_image__add__atLeastLessThan
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat (fun (N:nat)=> ((plus_plus_nat N) K))) ((ord_at4362885an_nat _TPTP_I) J))) ((ord_at4362885an_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K))))
% FOF formula (forall (P:(nat->Prop)) (N_1:nat), ((iff (forall (M:nat), (((ord_less_nat M) N_1)->(P M)))) (forall (X_1:nat), (((member_nat X_1) ((ord_at4362885an_nat zero_zero_nat) N_1))->(P X_1))))) of role axiom named fact_1133_all__nat__less__eq
% A new axiom: (forall (P:(nat->Prop)) (N_1:nat), ((iff (forall (M:nat), (((ord_less_nat M) N_1)->(P M)))) (forall (X_1:nat), (((member_nat X_1) ((ord_at4362885an_nat zero_zero_nat) N_1))->(P X_1)))))
% FOF formula (forall (P:(nat->Prop)) (N_1:nat), ((iff ((ex nat) (fun (M:nat)=> ((and ((ord_less_nat M) N_1)) (P M))))) ((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) ((ord_at4362885an_nat zero_zero_nat) N_1))) (P X_1)))))) of role axiom named fact_1134_ex__nat__less__eq
% A new axiom: (forall (P:(nat->Prop)) (N_1:nat), ((iff ((ex nat) (fun (M:nat)=> ((and ((ord_less_nat M) N_1)) (P M))))) ((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) ((ord_at4362885an_nat zero_zero_nat) N_1))) (P X_1))))))
% FOF formula (((eq (nat->Prop)) (ord_greaterThan_nat zero_zero_nat)) ((image_nat_nat suc) top_top_nat_o)) of role axiom named fact_1135_greaterThan__0
% A new axiom: (((eq (nat->Prop)) (ord_greaterThan_nat zero_zero_nat)) ((image_nat_nat suc) top_top_nat_o))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M_1)) N_1)) (((nat_case_o False) (ord_less_eq_nat M_1)) N_1))) of role axiom named fact_1136_less__eq__nat_Osimps_I2_J
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M_1)) N_1)) (((nat_case_o False) (ord_less_eq_nat M_1)) N_1)))
% FOF formula (forall (L:nat) (U:nat), (finite_finite_nat ((ord_gr375877188st_nat L) U))) of role axiom named fact_1137_finite__greaterThanAtMost
% A new axiom: (forall (L:nat) (U:nat), (finite_finite_nat ((ord_gr375877188st_nat L) U)))
% FOF formula (forall (L:nat) (U:nat), (finite_finite_nat ((ord_gr660468384an_nat L) U))) of role axiom named fact_1138_finite__greaterThanLessThan
% A new axiom: (forall (L:nat) (U:nat), (finite_finite_nat ((ord_gr660468384an_nat L) U)))
% FOF formula (forall (L:nat) (U:nat), (((eq (nat->Prop)) ((ord_at4362885an_nat (suc L)) U)) ((ord_gr660468384an_nat L) U))) of role axiom named fact_1139_atLeastSucLessThan__greaterThanLessThan
% A new axiom: (forall (L:nat) (U:nat), (((eq (nat->Prop)) ((ord_at4362885an_nat (suc L)) U)) ((ord_gr660468384an_nat L) U)))
% FOF formula (forall (M_1:nat), ((ord_less_eq_nat M_1) ((times_times_nat M_1) M_1))) of role axiom named fact_1140_le__square
% A new axiom: (forall (M_1:nat), ((ord_less_eq_nat M_1) ((times_times_nat M_1) M_1)))
% FOF formula (forall (M_1:nat), ((ord_less_eq_nat M_1) ((times_times_nat M_1) ((times_times_nat M_1) M_1)))) of role axiom named fact_1141_le__cube
% A new axiom: (forall (M_1:nat), ((ord_less_eq_nat M_1) ((times_times_nat M_1) ((times_times_nat M_1) M_1))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((times_times_nat _TPTP_I) K)) ((times_times_nat J) K)))) of role axiom named fact_1142_mult__le__mono1
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((times_times_nat _TPTP_I) K)) ((times_times_nat J) K))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((times_times_nat K) _TPTP_I)) ((times_times_nat K) J)))) of role axiom named fact_1143_mult__le__mono2
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((times_times_nat K) _TPTP_I)) ((times_times_nat K) J))))
% FOF formula (forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat _TPTP_I) K)) ((times_times_nat J) L))))) of role axiom named fact_1144_mult__le__mono
% A new axiom: (forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat _TPTP_I) K)) ((times_times_nat J) L)))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) N_1)) one_one_nat)) ((and (((eq nat) M_1) one_one_nat)) (((eq nat) N_1) one_one_nat)))) of role axiom named fact_1145_nat__mult__eq__1__iff
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) N_1)) one_one_nat)) ((and (((eq nat) M_1) one_one_nat)) (((eq nat) N_1) one_one_nat))))
% FOF formula (forall (N_1:nat), (((eq nat) ((times_times_nat N_1) one_one_nat)) N_1)) of role axiom named fact_1146_nat__mult__1__right
% A new axiom: (forall (N_1:nat), (((eq nat) ((times_times_nat N_1) one_one_nat)) N_1))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M_1) N_1))) ((and (((eq nat) M_1) one_one_nat)) (((eq nat) N_1) one_one_nat)))) of role axiom named fact_1147_nat__1__eq__mult__iff
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M_1) N_1))) ((and (((eq nat) M_1) one_one_nat)) (((eq nat) N_1) one_one_nat))))
% FOF formula (forall (N_1:nat), (((eq nat) ((times_times_nat one_one_nat) N_1)) N_1)) of role axiom named fact_1148_nat__mult__1
% A new axiom: (forall (N_1:nat), (((eq nat) ((times_times_nat one_one_nat) N_1)) N_1))
% FOF formula (forall (M_1:nat) (N_1:nat) (K:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M_1) N_1)) K)) ((plus_plus_nat ((times_times_nat M_1) K)) ((times_times_nat N_1) K)))) of role axiom named fact_1149_add__mult__distrib
% A new axiom: (forall (M_1:nat) (N_1:nat) (K:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M_1) N_1)) K)) ((plus_plus_nat ((times_times_nat M_1) K)) ((times_times_nat N_1) K))))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat K) ((plus_plus_nat M_1) N_1))) ((plus_plus_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1)))) of role axiom named fact_1150_add__mult__distrib2
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat K) ((plus_plus_nat M_1) N_1))) ((plus_plus_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat (suc K)) M_1)) ((times_times_nat (suc K)) N_1))) (((eq nat) M_1) N_1))) of role axiom named fact_1151_Suc__mult__cancel1
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat (suc K)) M_1)) ((times_times_nat (suc K)) N_1))) (((eq nat) M_1) N_1)))
% FOF formula (forall (M_1:nat) (K:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) K)) ((times_times_nat N_1) K))) ((or (((eq nat) M_1) N_1)) (((eq nat) K) zero_zero_nat)))) of role axiom named fact_1152_mult__cancel2
% A new axiom: (forall (M_1:nat) (K:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) K)) ((times_times_nat N_1) K))) ((or (((eq nat) M_1) N_1)) (((eq nat) K) zero_zero_nat))))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((or (((eq nat) M_1) N_1)) (((eq nat) K) zero_zero_nat)))) of role axiom named fact_1153_mult__cancel1
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((or (((eq nat) M_1) N_1)) (((eq nat) K) zero_zero_nat))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) N_1)) zero_zero_nat)) ((or (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat)))) of role axiom named fact_1154_mult__is__0
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) N_1)) zero_zero_nat)) ((or (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat))))
% FOF formula (forall (M_1:nat), (((eq nat) ((times_times_nat M_1) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_1155_mult__0__right
% A new axiom: (forall (M_1:nat), (((eq nat) ((times_times_nat M_1) zero_zero_nat)) zero_zero_nat))
% FOF formula (forall (N_1:nat), (((eq nat) ((times_times_nat zero_zero_nat) N_1)) zero_zero_nat)) of role axiom named fact_1156_mult__0
% A new axiom: (forall (N_1:nat), (((eq nat) ((times_times_nat zero_zero_nat) N_1)) zero_zero_nat))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) N_1)) (suc zero_zero_nat))) ((and (((eq nat) M_1) (suc zero_zero_nat))) (((eq nat) N_1) (suc zero_zero_nat))))) of role axiom named fact_1157_mult__eq__1__iff
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) N_1)) (suc zero_zero_nat))) ((and (((eq nat) M_1) (suc zero_zero_nat))) (((eq nat) N_1) (suc zero_zero_nat)))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) _TPTP_I)) ((times_times_nat K) J))))) of role axiom named fact_1158_mult__less__mono2
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) _TPTP_I)) ((times_times_nat K) J)))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat _TPTP_I) K)) ((times_times_nat J) K))))) of role axiom named fact_1159_mult__less__mono1
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat _TPTP_I) K)) ((times_times_nat J) K)))))
% FOF formula (forall (M_1:nat) (K:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat M_1) K)) ((times_times_nat N_1) K))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M_1) N_1)))) of role axiom named fact_1160_mult__less__cancel2
% A new axiom: (forall (M_1:nat) (K:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat M_1) K)) ((times_times_nat N_1) K))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M_1) N_1))))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M_1) N_1)))) of role axiom named fact_1161_mult__less__cancel1
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M_1) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M_1) N_1))) ((and ((ord_less_nat zero_zero_nat) M_1)) ((ord_less_nat zero_zero_nat) N_1)))) of role axiom named fact_1162_nat__0__less__mult__iff
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M_1) N_1))) ((and ((ord_less_nat zero_zero_nat) M_1)) ((ord_less_nat zero_zero_nat) N_1))))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat (suc K)) M_1)) ((times_times_nat (suc K)) N_1))) ((ord_less_nat M_1) N_1))) of role axiom named fact_1163_Suc__mult__less__cancel1
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat (suc K)) M_1)) ((times_times_nat (suc K)) N_1))) ((ord_less_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat M_1) (suc N_1))) ((plus_plus_nat M_1) ((times_times_nat M_1) N_1)))) of role axiom named fact_1164_mult__Suc__right
% A new axiom: (forall (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat M_1) (suc N_1))) ((plus_plus_nat M_1) ((times_times_nat M_1) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat (suc M_1)) N_1)) ((plus_plus_nat N_1) ((times_times_nat M_1) N_1)))) of role axiom named fact_1165_mult__Suc
% A new axiom: (forall (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat (suc M_1)) N_1)) ((plus_plus_nat N_1) ((times_times_nat M_1) N_1))))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat (suc K)) M_1)) ((times_times_nat (suc K)) N_1))) ((ord_less_eq_nat M_1) N_1))) of role axiom named fact_1166_Suc__mult__le__cancel1
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat (suc K)) M_1)) ((times_times_nat (suc K)) N_1))) ((ord_less_eq_nat M_1) N_1)))
% FOF formula (forall (M_1:nat) (N_1:nat), ((((eq nat) M_1) ((times_times_nat M_1) N_1))->((or (((eq nat) N_1) one_one_nat)) (((eq nat) M_1) zero_zero_nat)))) of role axiom named fact_1167_mult__eq__self__implies__10
% A new axiom: (forall (M_1:nat) (N_1:nat), ((((eq nat) M_1) ((times_times_nat M_1) N_1))->((or (((eq nat) N_1) one_one_nat)) (((eq nat) M_1) zero_zero_nat))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc zero_zero_nat)) N_1)->(((ord_less_nat (suc zero_zero_nat)) M_1)->((ord_less_nat N_1) ((times_times_nat M_1) N_1))))) of role axiom named fact_1168_n__less__m__mult__n
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc zero_zero_nat)) N_1)->(((ord_less_nat (suc zero_zero_nat)) M_1)->((ord_less_nat N_1) ((times_times_nat M_1) N_1)))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc zero_zero_nat)) N_1)->(((ord_less_nat (suc zero_zero_nat)) M_1)->((ord_less_nat N_1) ((times_times_nat N_1) M_1))))) of role axiom named fact_1169_n__less__n__mult__m
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc zero_zero_nat)) N_1)->(((ord_less_nat (suc zero_zero_nat)) M_1)->((ord_less_nat N_1) ((times_times_nat N_1) M_1)))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc zero_zero_nat)) N_1)->(((ord_less_nat (suc zero_zero_nat)) M_1)->((ord_less_nat (suc zero_zero_nat)) ((times_times_nat M_1) N_1))))) of role axiom named fact_1170_one__less__mult
% A new axiom: (forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc zero_zero_nat)) N_1)->(((ord_less_nat (suc zero_zero_nat)) M_1)->((ord_less_nat (suc zero_zero_nat)) ((times_times_nat M_1) N_1)))))
% FOF formula (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc zero_zero_nat)) ((times_times_nat M_1) N_1))) ((and ((ord_less_eq_nat (suc zero_zero_nat)) M_1)) ((ord_less_eq_nat (suc zero_zero_nat)) N_1)))) of role axiom named fact_1171_one__le__mult__iff
% A new axiom: (forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc zero_zero_nat)) ((times_times_nat M_1) N_1))) ((and ((ord_less_eq_nat (suc zero_zero_nat)) M_1)) ((ord_less_eq_nat (suc zero_zero_nat)) N_1))))
% FOF formula (forall (M_1:nat) (K:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat M_1) K)) ((times_times_nat N_1) K))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M_1) N_1)))) of role axiom named fact_1172_mult__le__cancel2
% A new axiom: (forall (M_1:nat) (K:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat M_1) K)) ((times_times_nat N_1) K))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M_1) N_1))))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M_1) N_1)))) of role axiom named fact_1173_mult__le__cancel1
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M_1) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat M_1) N_1)) ((times_times_nat N_1) M_1))) of role axiom named fact_1174_nat__mult__commute
% A new axiom: (forall (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat M_1) N_1)) ((times_times_nat N_1) M_1)))
% FOF formula (forall (M_1:nat) (N_1:nat) (K:nat), (((eq nat) ((times_times_nat ((times_times_nat M_1) N_1)) K)) ((times_times_nat M_1) ((times_times_nat N_1) K)))) of role axiom named fact_1175_nat__mult__assoc
% A new axiom: (forall (M_1:nat) (N_1:nat) (K:nat), (((eq nat) ((times_times_nat ((times_times_nat M_1) N_1)) K)) ((times_times_nat M_1) ((times_times_nat N_1) K))))
% FOF formula (forall (M_1:nat) (N_1:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_eq_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((ord_less_eq_nat M_1) N_1)))) of role axiom named fact_1176_nat__mult__le__cancel1
% A new axiom: (forall (M_1:nat) (N_1:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_eq_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((ord_less_eq_nat M_1) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((ord_less_nat M_1) N_1)))) of role axiom named fact_1177_nat__mult__less__cancel1
% A new axiom: (forall (M_1:nat) (N_1:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((ord_less_nat M_1) N_1))))
% FOF formula (forall (M_1:nat) (N_1:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff (((eq nat) ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) (((eq nat) M_1) N_1)))) of role axiom named fact_1178_nat__mult__eq__cancel1
% A new axiom: (forall (M_1:nat) (N_1:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff (((eq nat) ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) (((eq nat) M_1) N_1))))
% FOF formula (forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((or (((eq nat) K) zero_zero_nat)) (((eq nat) M_1) N_1)))) of role axiom named fact_1179_nat__mult__eq__cancel__disj
% A new axiom: (forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((or (((eq nat) K) zero_zero_nat)) (((eq nat) M_1) N_1))))
% FOF formula (forall (_TPTP_I:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat _TPTP_I) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat _TPTP_I) J)) U)) K))) of role axiom named fact_1180_left__add__mult__distrib
% A new axiom: (forall (_TPTP_I:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat _TPTP_I) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat _TPTP_I) J)) U)) K)))
% FOF formula (forall (Nat:nat), (((eq nat) (nat_size (suc Nat))) ((plus_plus_nat (nat_size Nat)) (suc zero_zero_nat)))) of role axiom named fact_1181_nat_Osize_I2_J
% A new axiom: (forall (Nat:nat), (((eq nat) (nat_size (suc Nat))) ((plus_plus_nat (nat_size Nat)) (suc zero_zero_nat))))
% FOF formula (((eq nat) (nat_size zero_zero_nat)) zero_zero_nat) of role axiom named fact_1182_nat_Osize_I1_J
% A new axiom: (((eq nat) (nat_size zero_zero_nat)) zero_zero_nat)
% FOF formula (forall (Nat:nat), (((eq nat) (size_size_nat (suc Nat))) ((plus_plus_nat (size_size_nat Nat)) (suc zero_zero_nat)))) of role axiom named fact_1183_nat_Osize_I4_J
% A new axiom: (forall (Nat:nat), (((eq nat) (size_size_nat (suc Nat))) ((plus_plus_nat (size_size_nat Nat)) (suc zero_zero_nat))))
% FOF formula (forall (N_1:nat), (((eq nat) (size_size_nat N_1)) N_1)) of role axiom named fact_1184_nat__size
% A new axiom: (forall (N_1:nat), (((eq nat) (size_size_nat N_1)) N_1))
% FOF formula (((eq nat) (size_size_nat zero_zero_nat)) zero_zero_nat) of role axiom named fact_1185_nat_Osize_I3_J
% A new axiom: (((eq nat) (size_size_nat zero_zero_nat)) zero_zero_nat)
% FOF formula (forall (F:(nat->nat)), ((forall (I_1:nat), ((ord_less_eq_nat (F (suc I_1))) (F I_1)))->((ex nat) (fun (I_1:nat)=> (forall (K_1:nat), (((eq nat) (F ((plus_plus_nat I_1) K_1))) (F I_1))))))) of role axiom named fact_1186_weak__decr__stable
% A new axiom: (forall (F:(nat->nat)), ((forall (I_1:nat), ((ord_less_eq_nat (F (suc I_1))) (F I_1)))->((ex nat) (fun (I_1:nat)=> (forall (K_1:nat), (((eq nat) (F ((plus_plus_nat I_1) K_1))) (F I_1)))))))
% FOF formula (((eq nat) (bool_size True)) zero_zero_nat) of role axiom named fact_1187_bool_Osize_I1_J
% A new axiom: (((eq nat) (bool_size True)) zero_zero_nat)
% FOF formula (((eq nat) (bool_size False)) zero_zero_nat) of role axiom named fact_1188_bool_Osize_I2_J
% A new axiom: (((eq nat) (bool_size False)) zero_zero_nat)
% FOF formula (forall (L:nat) (U:nat), (finite_finite_nat ((ord_at238088361st_nat L) U))) of role axiom named fact_1189_finite__atLeastAtMost
% A new axiom: (forall (L:nat) (U:nat), (finite_finite_nat ((ord_at238088361st_nat L) U)))
% FOF formula (forall (L:nat) (U:nat), (((eq (nat->Prop)) ((ord_at4362885an_nat L) (suc U))) ((ord_at238088361st_nat L) U))) of role axiom named fact_1190_atLeastLessThanSuc__atLeastAtMost
% A new axiom: (forall (L:nat) (U:nat), (((eq (nat->Prop)) ((ord_at4362885an_nat L) (suc U))) ((ord_at238088361st_nat L) U)))
% FOF formula (forall (P:(nat->Prop)) (N_1:nat), ((iff ((ex nat) (fun (M:nat)=> ((and ((ord_less_eq_nat M) N_1)) (P M))))) ((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) ((ord_at238088361st_nat zero_zero_nat) N_1))) (P X_1)))))) of role axiom named fact_1191_ex__nat__less
% A new axiom: (forall (P:(nat->Prop)) (N_1:nat), ((iff ((ex nat) (fun (M:nat)=> ((and ((ord_less_eq_nat M) N_1)) (P M))))) ((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) ((ord_at238088361st_nat zero_zero_nat) N_1))) (P X_1))))))
% FOF formula (forall (P:(nat->Prop)) (N_1:nat), ((iff (forall (M:nat), (((ord_less_eq_nat M) N_1)->(P M)))) (forall (X_1:nat), (((member_nat X_1) ((ord_at238088361st_nat zero_zero_nat) N_1))->(P X_1))))) of role axiom named fact_1192_all__nat__less
% A new axiom: (forall (P:(nat->Prop)) (N_1:nat), ((iff (forall (M:nat), (((ord_less_eq_nat M) N_1)->(P M)))) (forall (X_1:nat), (((member_nat X_1) ((ord_at238088361st_nat zero_zero_nat) N_1))->(P X_1)))))
% FOF formula (forall (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat suc) ((ord_at238088361st_nat _TPTP_I) J))) ((ord_at238088361st_nat (suc _TPTP_I)) (suc J)))) of role axiom named fact_1193_image__Suc__atLeastAtMost
% A new axiom: (forall (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat suc) ((ord_at238088361st_nat _TPTP_I) J))) ((ord_at238088361st_nat (suc _TPTP_I)) (suc J))))
% FOF formula (forall (L:nat) (U:nat), (((eq (nat->Prop)) ((ord_at238088361st_nat (suc L)) U)) ((ord_gr375877188st_nat L) U))) of role axiom named fact_1194_atLeastSucAtMost__greaterThanAtMost
% A new axiom: (forall (L:nat) (U:nat), (((eq (nat->Prop)) ((ord_at238088361st_nat (suc L)) U)) ((ord_gr375877188st_nat L) U)))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat (fun (N:nat)=> ((plus_plus_nat N) K))) ((ord_at238088361st_nat _TPTP_I) J))) ((ord_at238088361st_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))) of role axiom named fact_1195_image__add__atLeastAtMost
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat (fun (N:nat)=> ((plus_plus_nat N) K))) ((ord_at238088361st_nat _TPTP_I) J))) ((ord_at238088361st_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K))))
% FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((eq (nat->Prop)) ((ord_at4362885an_nat _TPTP_I) ((plus_plus_nat J) K))) ((semila848761471_nat_o ((ord_at4362885an_nat _TPTP_I) J)) ((ord_at4362885an_nat J) ((plus_plus_nat J) K)))))) of role axiom named fact_1196_atLeastLessThan__add__Un
% A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((eq (nat->Prop)) ((ord_at4362885an_nat _TPTP_I) ((plus_plus_nat J) K))) ((semila848761471_nat_o ((ord_at4362885an_nat _TPTP_I) J)) ((ord_at4362885an_nat J) ((plus_plus_nat J) K))))))
% FOF formula (((eq (nat->Prop)) (ord_atLeast_nat zero_zero_nat)) top_top_nat_o) of role axiom named fact_1197_atLeast__0
% A new axiom: (((eq (nat->Prop)) (ord_atLeast_nat zero_zero_nat)) top_top_nat_o)
% FOF formula (forall (K:nat), (((eq (nat->Prop)) (ord_atLeast_nat (suc K))) (ord_greaterThan_nat K))) of role axiom named fact_1198_atLeast__Suc__greaterThan
% A new axiom: (forall (K:nat), (((eq (nat->Prop)) (ord_atLeast_nat (suc K))) (ord_greaterThan_nat K)))
% FOF formula (forall (K:nat) (F:(nat->nat)), ((((eq nat) (F zero_zero_nat)) zero_zero_nat)->(((eq nat) ((big_co387207925at_nat F) ((ord_at238088361st_nat (suc zero_zero_nat)) K))) ((big_co387207925at_nat F) ((ord_at238088361st_nat zero_zero_nat) K))))) of role axiom named fact_1199_setsum__shift__lb__Suc0__0
% A new axiom: (forall (K:nat) (F:(nat->nat)), ((((eq nat) (F zero_zero_nat)) zero_zero_nat)->(((eq nat) ((big_co387207925at_nat F) ((ord_at238088361st_nat (suc zero_zero_nat)) K))) ((big_co387207925at_nat F) ((ord_at238088361st_nat zero_zero_nat) K)))))
% FOF formula (forall (X:(produc1572197287le_alt->Prop)) (Y:(produc1572197287le_alt->Prop)), (((eq (produc1572197287le_alt->Prop)) (((if_Pro278423000_alt_o True) X) Y)) X)) of role axiom named help_If_1_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_
% A new axiom: (forall (X:(produc1572197287le_alt->Prop)) (Y:(produc1572197287le_alt->Prop)), (((eq (produc1572197287le_alt->Prop)) (((if_Pro278423000_alt_o True) X) Y)) X))
% FOF formula (forall (X:(produc1572197287le_alt->Prop)) (Y:(produc1572197287le_alt->Prop)), (((eq (produc1572197287le_alt->Prop)) (((if_Pro278423000_alt_o False) X) Y)) Y)) of role axiom named help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_
% A new axiom: (forall (X:(produc1572197287le_alt->Prop)) (Y:(produc1572197287le_alt->Prop)), (((eq (produc1572197287le_alt->Prop)) (((if_Pro278423000_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____piyeccggrh_
% A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% FOF formula ((member285112084le_alt ((produc897867031le_alt c) d)) (f p)) of role conjecture named conj_0
% Conjecture to prove = ((member285112084le_alt ((produc897867031le_alt c) d)) (f p)):Prop
% Parameter arrow_1196572341e_indi_DUMMY:arrow_1196572341e_indi.
% Parameter product_unit_DUMMY:product_unit.
% Parameter produc1572197287le_alt_DUMMY:produc1572197287le_alt.
% We need to prove ['((member285112084le_alt ((produc897867031le_alt c) d)) (f p))']
% Parameter arrow_1389031998le_alt:Type.
% Parameter arrow_1196572341e_indi:Type.
% Parameter nat:Type.
% Parameter product_unit:Type.
% Parameter produc1572197287le_alt:Type.
% Parameter all:((produc1572197287le_alt->Prop)->Prop).
% Parameter arrow_1955289568le_IIA:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop).
% Parameter arrow_1982173296le_Lin:((produc1572197287le_alt->Prop)->Prop).
% Parameter arrow_1647925946e_Prof:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop).
% Parameter arrow_556571452_above:((produc1572197287le_alt->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->(produc1572197287le_alt->Prop)))).
% Parameter arrow_1865170000_below:((produc1572197287le_alt->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->(produc1572197287le_alt->Prop)))).
% Parameter arrow_968343245ctator:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop)).
% Parameter arrow_1821416136_mkbot:((produc1572197287le_alt->Prop)->(arrow_1389031998le_alt->(produc1572197287le_alt->Prop))).
% Parameter arrow_1970123222_mktop:((produc1572197287le_alt->Prop)->(arrow_1389031998le_alt->(produc1572197287le_alt->Prop))).
% Parameter arrow_1282657667nimity:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop).
% Parameter big_co387207925at_nat:((nat->nat)->((nat->Prop)->nat)).
% Parameter finite2011930979e_indi:((arrow_1196572341e_indi->Prop)->nat).
% Parameter finite_card_nat:((nat->Prop)->nat).
% Parameter finite1949902593t_unit:((product_unit->Prop)->nat).
% Parameter finite431949602e_indi:((arrow_1196572341e_indi->Prop)->Prop).
% Parameter finite_finite_nat:((nat->Prop)->Prop).
% Parameter inj_on1505595958di_nat:((arrow_1196572341e_indi->nat)->((arrow_1196572341e_indi->Prop)->Prop)).
% Parameter inj_on_nat_nat:((nat->nat)->((nat->Prop)->Prop)).
% Parameter pi_Arr1865419731lt_o_o:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->Prop))).
% Parameter pi_Arr470535441e_indi:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->Prop))).
% Parameter pi_Arr2096782767t_unit:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)->Prop))).
% Parameter pi_Arr1196397536_alt_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))).
% Parameter pi_Arr1709554855lt_o_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->Prop))).
% Parameter pi_Arr272777533e_indi:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->Prop))).
% Parameter pi_Arr509685723t_unit:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)->Prop))).
% Parameter pi_Pro386796690lt_o_o:(((produc1572197287le_alt->Prop)->Prop)->(((produc1572197287le_alt->Prop)->(Prop->Prop))->(((produc1572197287le_alt->Prop)->Prop)->Prop))).
% Parameter pi_Pro2039443474e_indi:(((produc1572197287le_alt->Prop)->Prop)->(((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))->(((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)->Prop))).
% Parameter pi_Pro30504752t_unit:(((produc1572197287le_alt->Prop)->Prop)->(((produc1572197287le_alt->Prop)->(product_unit->Prop))->(((produc1572197287le_alt->Prop)->product_unit)->Prop))).
% Parameter pi_o_A1994447367_alt_o:((Prop->Prop)->((Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))->((Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop))).
% Parameter pi_o_A1479825007_alt_o:((Prop->Prop)->((Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))->((Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop))).
% Parameter pi_o_P1417870404_alt_o:((Prop->Prop)->((Prop->((produc1572197287le_alt->Prop)->Prop))->((Prop->(produc1572197287le_alt->Prop))->Prop))).
% Parameter pi_o_nat:((Prop->Prop)->((Prop->(nat->Prop))->((Prop->nat)->Prop))).
% Parameter pi_o_P728361163le_alt:((Prop->Prop)->((Prop->(produc1572197287le_alt->Prop))->((Prop->produc1572197287le_alt)->Prop))).
% Parameter pi_Arr583278353_alt_o:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))->((arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop))).
% Parameter pi_Arr456308197_alt_o:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))->((arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop))).
% Parameter pi_Arr1309696186_alt_o:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))).
% Parameter pi_Arr778514268di_nat:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->(nat->Prop))->((arrow_1196572341e_indi->nat)->Prop))).
% Parameter pi_Arr1762714837le_alt:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((arrow_1196572341e_indi->produc1572197287le_alt)->Prop))).
% Parameter pi_nat_o:((nat->Prop)->((nat->(Prop->Prop))->((nat->Prop)->Prop))).
% Parameter pi_nat986275508e_indi:((nat->Prop)->((nat->(arrow_1196572341e_indi->Prop))->((nat->arrow_1196572341e_indi)->Prop))).
% Parameter pi_nat_Product_unit:((nat->Prop)->((nat->(product_unit->Prop))->((nat->product_unit)->Prop))).
% Parameter pi_Pro443817391_alt_o:((product_unit->Prop)->((product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))->((product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop))).
% Parameter pi_Pro1959068871_alt_o:((product_unit->Prop)->((product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))->((product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop))).
% Parameter pi_Pro29851292_alt_o:((product_unit->Prop)->((product_unit->((produc1572197287le_alt->Prop)->Prop))->((product_unit->(produc1572197287le_alt->Prop))->Prop))).
% Parameter pi_Product_unit_nat:((product_unit->Prop)->((product_unit->(nat->Prop))->((product_unit->nat)->Prop))).
% Parameter pi_Pro772884595le_alt:((product_unit->Prop)->((product_unit->(produc1572197287le_alt->Prop))->((product_unit->produc1572197287le_alt)->Prop))).
% Parameter pi_Pro418549519_alt_o:((produc1572197287le_alt->Prop)->((produc1572197287le_alt->(Prop->Prop))->((produc1572197287le_alt->Prop)->Prop))).
% Parameter pi_Pro1246947541e_indi:((produc1572197287le_alt->Prop)->((produc1572197287le_alt->(arrow_1196572341e_indi->Prop))->((produc1572197287le_alt->arrow_1196572341e_indi)->Prop))).
% Parameter pi_Pro926528371t_unit:((produc1572197287le_alt->Prop)->((produc1572197287le_alt->(product_unit->Prop))->((produc1572197287le_alt->product_unit)->Prop))).
% Parameter one_one_nat:nat.
% Parameter plus_plus_nat:(nat->(nat->nat)).
% Parameter times_times_nat:(nat->(nat->nat)).
% Parameter zero_zero_nat:nat.
% Parameter bool_size:(Prop->nat).
% Parameter hilber1125280539di_nat:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_indi->nat)->(nat->arrow_1196572341e_indi))).
% Parameter hilber195283148at_nat:((nat->Prop)->((nat->nat)->(nat->nat))).
% Parameter if_Pro278423000_alt_o:(Prop->((produc1572197287le_alt->Prop)->((produc1572197287le_alt->Prop)->(produc1572197287le_alt->Prop)))).
% Parameter semila848761471_nat_o:((nat->Prop)->((nat->Prop)->(nat->Prop))).
% Parameter suc:(nat->nat).
% Parameter nat_case_o:(Prop->((nat->Prop)->(nat->Prop))).
% Parameter nat_size:(nat->nat).
% Parameter size_size_nat:(nat->nat).
% Parameter ord_le1382328578lt_o_o:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->Prop)).
% Parameter ord_le914873172lt_o_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->Prop)).
% Parameter ord_le874404799lt_o_o:(((produc1572197287le_alt->Prop)->Prop)->(((produc1572197287le_alt->Prop)->Prop)->Prop)).
% Parameter ord_le1339521307_alt_o:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->Prop)).
% Parameter ord_le1991507760indi_o:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_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_le1852932542_alt_o:((produc1572197287le_alt->Prop)->((produc1572197287le_alt->Prop)->Prop)).
% Parameter ord_less_o:(Prop->(Prop->Prop)).
% Parameter ord_less_nat:(nat->(nat->Prop)).
% Parameter ord_le1805007862lt_o_o:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->Prop)).
% Parameter ord_le602483040lt_o_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->Prop)).
% Parameter ord_le1027220427lt_o_o:(((produc1572197287le_alt->Prop)->Prop)->(((produc1572197287le_alt->Prop)->Prop)->Prop)).
% Parameter ord_less_eq_o_o:((Prop->Prop)->((Prop->Prop)->Prop)).
% Parameter ord_le1463467535_alt_o:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->Prop)).
% Parameter ord_le1423491573_alt_o:((arrow_1389031998le_alt->Prop)->((arrow_1389031998le_alt->Prop)->Prop)).
% Parameter ord_le865407012indi_o:((arrow_1196572341e_indi->Prop)->((arrow_1196572341e_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_le962286258_alt_o:((produc1572197287le_alt->Prop)->((produc1572197287le_alt->Prop)->Prop)).
% Parameter ord_less_eq_o:(Prop->(Prop->Prop)).
% Parameter ord_less_eq_nat:(nat->(nat->Prop)).
% Parameter top_to1492351398lt_o_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop).
% Parameter top_to732317616lt_o_o:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop).
% Parameter top_to1806834203lt_o_o:((produc1572197287le_alt->Prop)->Prop).
% Parameter top_top_o_o:(Prop->Prop).
% Parameter top_to1627321279_alt_o:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)).
% Parameter top_to54564308indi_o:(arrow_1196572341e_indi->Prop).
% Parameter top_top_nat_o:(nat->Prop).
% Parameter top_to1984820022unit_o:(product_unit->Prop).
% Parameter top_to558618722_alt_o:(produc1572197287le_alt->Prop).
% Parameter top_top_o:Prop.
% Parameter produc897867031le_alt:(arrow_1389031998le_alt->(arrow_1389031998le_alt->produc1572197287le_alt)).
% Parameter ord_at238088361st_nat:(nat->(nat->(nat->Prop))).
% Parameter ord_at4362885an_nat:(nat->(nat->(nat->Prop))).
% Parameter ord_atLeast_nat:(nat->(nat->Prop)).
% Parameter ord_gr375877188st_nat:(nat->(nat->(nat->Prop))).
% Parameter ord_gr660468384an_nat:(nat->(nat->(nat->Prop))).
% Parameter ord_greaterThan_nat:(nat->(nat->Prop)).
% Parameter collec670126350_alt_o:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)).
% Parameter collec979749928_alt_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)).
% Parameter collec958969213_alt_o:(((produc1572197287le_alt->Prop)->Prop)->((produc1572197287le_alt->Prop)->Prop)).
% Parameter collec1936859488e_indi:((arrow_1196572341e_indi->Prop)->(arrow_1196572341e_indi->Prop)).
% Parameter collect_nat:((nat->Prop)->(nat->Prop)).
% Parameter collect_Product_unit:((product_unit->Prop)->(product_unit->Prop)).
% Parameter collec940901970le_alt:((produc1572197287le_alt->Prop)->(produc1572197287le_alt->Prop)).
% Parameter image_1011045538di_nat:((arrow_1196572341e_indi->nat)->((arrow_1196572341e_indi->Prop)->(nat->Prop))).
% Parameter image_nat_nat:((nat->nat)->((nat->Prop)->(nat->Prop))).
% Parameter member1346253567lt_o_o:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->Prop)->Prop)).
% Parameter member1539010427e_indi:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->(((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->Prop)->Prop)).
% Parameter member1043380889t_unit:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)->(((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)->Prop)->Prop)).
% Parameter member1425217232_alt_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->Prop)).
% Parameter member1696373143lt_o_o:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->Prop)->Prop)).
% Parameter member1186582243e_indi:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)->Prop)->Prop)).
% Parameter member1537523201t_unit:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)->((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)->Prop)->Prop)).
% Parameter member1925470338lt_o_o:(((produc1572197287le_alt->Prop)->Prop)->((((produc1572197287le_alt->Prop)->Prop)->Prop)->Prop)).
% Parameter member1830244024e_indi:(((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)->((((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)->Prop)->Prop)).
% Parameter member1092867670t_unit:(((produc1572197287le_alt->Prop)->product_unit)->((((produc1572197287le_alt->Prop)->product_unit)->Prop)->Prop)).
% Parameter member161783341_alt_o:((Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->(((Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop)->Prop)).
% Parameter member984757343_alt_o:((Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->(((Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop)->Prop)).
% Parameter member1495989556_alt_o:((Prop->(produc1572197287le_alt->Prop))->(((Prop->(produc1572197287le_alt->Prop))->Prop)->Prop)).
% Parameter member_o_nat:((Prop->nat)->(((Prop->nat)->Prop)->Prop)).
% Parameter member1158049649le_alt:((Prop->produc1572197287le_alt)->(((Prop->produc1572197287le_alt)->Prop)->Prop)).
% Parameter member1521294075_alt_o:((arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->(((arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop)->Prop)).
% Parameter member2071265553_alt_o:((arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->(((arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop)->Prop)).
% Parameter member822980838_alt_o:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->Prop)).
% Parameter member1842285448di_nat:((arrow_1196572341e_indi->nat)->(((arrow_1196572341e_indi->nat)->Prop)->Prop)).
% Parameter member232085823le_alt:((arrow_1196572341e_indi->produc1572197287le_alt)->(((arrow_1196572341e_indi->produc1572197287le_alt)->Prop)->Prop)).
% Parameter member_nat_o:((nat->Prop)->(((nat->Prop)->Prop)->Prop)).
% Parameter member1113138010e_indi:((nat->arrow_1196572341e_indi)->(((nat->arrow_1196572341e_indi)->Prop)->Prop)).
% Parameter member616671224t_unit:((nat->product_unit)->(((nat->product_unit)->Prop)->Prop)).
% Parameter member1888392857_alt_o:((product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->(((product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))->Prop)->Prop)).
% Parameter member2021528307_alt_o:((product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->(((product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))->Prop)->Prop)).
% Parameter member1295651272_alt_o:((product_unit->(produc1572197287le_alt->Prop))->(((product_unit->(produc1572197287le_alt->Prop))->Prop)->Prop)).
% Parameter member1827227242it_nat:((product_unit->nat)->(((product_unit->nat)->Prop)->Prop)).
% Parameter member1161214429le_alt:((product_unit->produc1572197287le_alt)->(((product_unit->produc1572197287le_alt)->Prop)->Prop)).
% Parameter member1241905979_alt_o:((produc1572197287le_alt->Prop)->(((produc1572197287le_alt->Prop)->Prop)->Prop)).
% Parameter member1074431551e_indi:((produc1572197287le_alt->arrow_1196572341e_indi)->(((produc1572197287le_alt->arrow_1196572341e_indi)->Prop)->Prop)).
% Parameter member44534621t_unit:((produc1572197287le_alt->product_unit)->(((produc1572197287le_alt->product_unit)->Prop)->Prop)).
% Parameter member_o:(Prop->((Prop->Prop)->Prop)).
% Parameter member1818997282e_indi:(arrow_1196572341e_indi->((arrow_1196572341e_indi->Prop)->Prop)).
% Parameter member_nat:(nat->((nat->Prop)->Prop)).
% Parameter member_Product_unit:(product_unit->((product_unit->Prop)->Prop)).
% Parameter member285112084le_alt:(produc1572197287le_alt->((produc1572197287le_alt->Prop)->Prop)).
% Parameter f:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)).
% Parameter lab:(produc1572197287le_alt->Prop).
% Parameter lba:(produc1572197287le_alt->Prop).
% Parameter p:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)).
% Parameter a:arrow_1389031998le_alt.
% Parameter b:arrow_1389031998le_alt.
% Parameter c:arrow_1389031998le_alt.
% Parameter d:arrow_1389031998le_alt.
% Parameter e:arrow_1389031998le_alt.
% Parameter h:(arrow_1196572341e_indi->nat).
% Parameter n:nat.
% Axiom fact_0_assms_I3_J:(arrow_1955289568le_IIA f).
% Axiom fact_1_u:(arrow_1282657667nimity f).
% Axiom fact_2__096c_A_126_061_Ad_096:(not (((eq arrow_1389031998le_alt) c) d)).
% Axiom fact_3__096P_A_058_AProf_096:((member822980838_alt_o p) arrow_1647925946e_Prof).
% Axiom fact_4_in__mkbot:(forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (Z:arrow_1389031998le_alt), ((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) ((arrow_1821416136_mkbot L_2) Z))) ((and ((and (not (((eq arrow_1389031998le_alt) Y) Z))) ((((eq arrow_1389031998le_alt) X) Z)->(not (((eq arrow_1389031998le_alt) X) Y))))) ((not (((eq arrow_1389031998le_alt) X) Z))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2))))).
% Axiom fact_5_in__mktop:(forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (Z:arrow_1389031998le_alt), ((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) ((arrow_1970123222_mktop L_2) Z))) ((and ((and (not (((eq arrow_1389031998le_alt) X) Z))) ((((eq arrow_1389031998le_alt) Y) Z)->(not (((eq arrow_1389031998le_alt) X) Y))))) ((not (((eq arrow_1389031998le_alt) Y) Z))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2))))).
% Axiom fact_6__C2_C:(forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_91:arrow_1389031998le_alt) (B_72:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) A_91) B_72))->((not (((eq arrow_1389031998le_alt) A_90) B_72))->((not (((eq arrow_1389031998le_alt) B_71) A_91))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (f P_8))))))))))).
% Axiom fact_7__C1_C:(forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_91:arrow_1389031998le_alt) (B_72:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) A_91) B_72))->((not (((eq arrow_1389031998le_alt) A_90) B_72))->((not (((eq arrow_1389031998le_alt) B_71) A_91))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (P_8 I_1))))->(((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))->((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (f P_8))))))))))).
% Axiom fact_8__C4_C:(forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (C_42:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) B_71) C_42))->((not (((eq arrow_1389031998le_alt) A_90) C_42))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt B_71) C_42)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt B_71) C_42)) (f P_8)))))))))).
% Axiom fact_9_pairwise__neutrality:(forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_91:arrow_1389031998le_alt) (B_72:arrow_1389031998le_alt) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->((not (((eq arrow_1389031998le_alt) A_91) B_72))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt A_91) B_72)) (f P_8))))))))).
% Axiom fact_10__C3_C:(forall (P_8:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (P_7:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_90:arrow_1389031998le_alt) (B_71:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_90) B_71))->(((member822980838_alt_o P_7) arrow_1647925946e_Prof)->(((member822980838_alt_o P_8) arrow_1647925946e_Prof)->((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (P_7 I_1))) ((member285112084le_alt ((produc897867031le_alt B_71) A_90)) (P_8 I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_90) B_71)) (f P_7))) ((member285112084le_alt ((produc897867031le_alt B_71) A_90)) (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_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt c) d)) (p I_1))) ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) d)) ((arrow_1970123222_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) d)) (((arrow_556571452_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member285112084le_alt ((produc897867031le_alt c) d)) ((arrow_1821416136_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:((member285112084le_alt ((produc897867031le_alt c) d)) (p (((hilber1125280539di_nat top_to54564308indi_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:((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))).
% Axiom fact_14_PW:((iff ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))) ((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))).
% Axiom fact_15_split__paired__All:(forall (P_6:(produc1572197287le_alt->Prop)), ((iff (all P_6)) (forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), (P_6 ((produc897867031le_alt A_76) B_60))))).
% Axiom fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai:((member822980838_alt_o (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))) arrow_1647925946e_Prof).
% Axiom fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto:((member285112084le_alt ((produc897867031le_alt c) e)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_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:((member285112084le_alt ((produc897867031le_alt e) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))).
% Axiom fact_19_n_I1_J:((ord_less_nat n) (finite2011930979e_indi top_to54564308indi_o)).
% Axiom fact_20_injh:((inj_on1505595958di_nat h) top_to54564308indi_o).
% Axiom fact_21_Pair__inject:(forall (A_89:arrow_1389031998le_alt) (B_70:arrow_1389031998le_alt) (A_88:arrow_1389031998le_alt) (B_69:arrow_1389031998le_alt), ((((eq produc1572197287le_alt) ((produc897867031le_alt A_89) B_70)) ((produc897867031le_alt A_88) B_69))->(((((eq arrow_1389031998le_alt) A_89) A_88)->(not (((eq arrow_1389031998le_alt) B_70) B_69)))->False))).
% Axiom fact_22_Pair__eq:(forall (A_87:arrow_1389031998le_alt) (B_68:arrow_1389031998le_alt) (A_86:arrow_1389031998le_alt) (B_67:arrow_1389031998le_alt), ((iff (((eq produc1572197287le_alt) ((produc897867031le_alt A_87) B_68)) ((produc897867031le_alt A_86) B_67))) ((and (((eq arrow_1389031998le_alt) A_87) A_86)) (((eq arrow_1389031998le_alt) B_68) B_67)))).
% Axiom fact_23_IIA__def:(forall (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((iff (arrow_1955289568le_IIA F_31)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(forall (Xa:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o Xa) arrow_1647925946e_Prof)->(forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), ((forall (I_1:arrow_1196572341e_indi), ((iff ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (X_1 I_1))) ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (Xa I_1))))->((iff ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 X_1))) ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 Xa))))))))))).
% Axiom fact_24_unanimity__def:(forall (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((iff (arrow_1282657667nimity F_31)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), ((forall (I_1:arrow_1196572341e_indi), ((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (X_1 I_1)))->((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 X_1)))))))).
% Axiom fact_25_top1I:(forall (X_69:(produc1572197287le_alt->Prop)), (top_to1806834203lt_o_o X_69)).
% Axiom fact_26_top1I:(forall (X_69:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (top_to732317616lt_o_o X_69)).
% Axiom fact_27_top1I:(forall (X_69:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (top_to1492351398lt_o_o X_69)).
% Axiom fact_28_top1I:(forall (X_69:produc1572197287le_alt), (top_to558618722_alt_o X_69)).
% Axiom fact_29_top1I:(forall (X_69:arrow_1196572341e_indi), (top_to54564308indi_o X_69)).
% Axiom fact_30_top1I:(forall (X_69:nat), (top_top_nat_o X_69)).
% Axiom fact_31_top1I:(forall (X_69:product_unit), (top_to1984820022unit_o X_69)).
% Axiom fact_32_UNIV__I:(forall (X_68:Prop), ((member_o X_68) top_top_o_o)).
% Axiom fact_33_UNIV__I:(forall (X_68:arrow_1196572341e_indi), ((member1818997282e_indi X_68) top_to54564308indi_o)).
% Axiom fact_34_UNIV__I:(forall (X_68:product_unit), ((member_Product_unit X_68) top_to1984820022unit_o)).
% Axiom fact_35_UNIV__I:(forall (X_68:produc1572197287le_alt), ((member285112084le_alt X_68) top_to558618722_alt_o)).
% Axiom fact_36_UNIV__I:(forall (X_68:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((member822980838_alt_o X_68) top_to732317616lt_o_o)).
% Axiom fact_37_UNIV__I:(forall (X_68:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((member1425217232_alt_o X_68) top_to1492351398lt_o_o)).
% Axiom fact_38_UNIV__I:(forall (X_68:(produc1572197287le_alt->Prop)), ((member1241905979_alt_o X_68) top_to1806834203lt_o_o)).
% Axiom fact_39_UNIV__I:(forall (X_68:nat), ((member_nat X_68) top_top_nat_o)).
% Axiom fact_40_iso__tuple__UNIV__I:(forall (X_67:Prop), ((member_o X_67) top_top_o_o)).
% Axiom fact_41_iso__tuple__UNIV__I:(forall (X_67:arrow_1196572341e_indi), ((member1818997282e_indi X_67) top_to54564308indi_o)).
% Axiom fact_42_iso__tuple__UNIV__I:(forall (X_67:product_unit), ((member_Product_unit X_67) top_to1984820022unit_o)).
% Axiom fact_43_iso__tuple__UNIV__I:(forall (X_67:produc1572197287le_alt), ((member285112084le_alt X_67) top_to558618722_alt_o)).
% Axiom fact_44_iso__tuple__UNIV__I:(forall (X_67:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((member822980838_alt_o X_67) top_to732317616lt_o_o)).
% Axiom fact_45_iso__tuple__UNIV__I:(forall (X_67:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((member1425217232_alt_o X_67) top_to1492351398lt_o_o)).
% Axiom fact_46_iso__tuple__UNIV__I:(forall (X_67:(produc1572197287le_alt->Prop)), ((member1241905979_alt_o X_67) top_to1806834203lt_o_o)).
% Axiom fact_47_iso__tuple__UNIV__I:(forall (X_67:nat), ((member_nat X_67) top_top_nat_o)).
% Axiom fact_48_top__apply:(forall (X_66:(produc1572197287le_alt->Prop)), ((iff (top_to1806834203lt_o_o X_66)) top_top_o)).
% Axiom fact_49_top__apply:(forall (X_66:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((iff (top_to732317616lt_o_o X_66)) top_top_o)).
% Axiom fact_50_top__apply:(forall (X_66:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((iff (top_to1492351398lt_o_o X_66)) top_top_o)).
% Axiom fact_51_top__apply:(forall (X_66:produc1572197287le_alt), ((iff (top_to558618722_alt_o X_66)) top_top_o)).
% Axiom fact_52_top__apply:(forall (X_66:arrow_1196572341e_indi), ((iff (top_to54564308indi_o X_66)) top_top_o)).
% Axiom fact_53_top__apply:(forall (X_66:nat), ((iff (top_top_nat_o X_66)) top_top_o)).
% Axiom fact_54_top__apply:(forall (X_66:product_unit), ((iff (top_to1984820022unit_o X_66)) top_top_o)).
% Axiom fact_55_not__top__less:(forall (A_85:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o top_to1806834203lt_o_o) A_85)->False)).
% Axiom fact_56_not__top__less:(forall (A_85:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o top_to732317616lt_o_o) A_85)->False)).
% Axiom fact_57_not__top__less:(forall (A_85:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o top_to1492351398lt_o_o) A_85)->False)).
% Axiom fact_58_not__top__less:(forall (A_85:Prop), (((ord_less_o top_top_o) A_85)->False)).
% Axiom fact_59_not__top__less:(forall (A_85:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o top_to558618722_alt_o) A_85)->False)).
% Axiom fact_60_not__top__less:(forall (A_85:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o top_to54564308indi_o) A_85)->False)).
% Axiom fact_61_not__top__less:(forall (A_85:(nat->Prop)), (((ord_less_nat_o top_top_nat_o) A_85)->False)).
% Axiom fact_62_not__top__less:(forall (A_85:(product_unit->Prop)), (((ord_le232288914unit_o top_to1984820022unit_o) A_85)->False)).
% Axiom fact_63_less__top:(forall (A_84:((produc1572197287le_alt->Prop)->Prop)), ((iff (not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_84) top_to1806834203lt_o_o))) ((ord_le874404799lt_o_o A_84) top_to1806834203lt_o_o))).
% Axiom fact_64_less__top:(forall (A_84:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff (not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_84) top_to732317616lt_o_o))) ((ord_le914873172lt_o_o A_84) top_to732317616lt_o_o))).
% Axiom fact_65_less__top:(forall (A_84:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff (not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_84) top_to1492351398lt_o_o))) ((ord_le1382328578lt_o_o A_84) top_to1492351398lt_o_o))).
% Axiom fact_66_less__top:(forall (A_84:Prop), ((iff (((iff A_84) top_top_o)->False)) ((ord_less_o A_84) top_top_o))).
% Axiom fact_67_less__top:(forall (A_84:(produc1572197287le_alt->Prop)), ((iff (not (((eq (produc1572197287le_alt->Prop)) A_84) top_to558618722_alt_o))) ((ord_le1852932542_alt_o A_84) top_to558618722_alt_o))).
% Axiom fact_68_less__top:(forall (A_84:(arrow_1196572341e_indi->Prop)), ((iff (not (((eq (arrow_1196572341e_indi->Prop)) A_84) top_to54564308indi_o))) ((ord_le1991507760indi_o A_84) top_to54564308indi_o))).
% Axiom fact_69_less__top:(forall (A_84:(nat->Prop)), ((iff (not (((eq (nat->Prop)) A_84) top_top_nat_o))) ((ord_less_nat_o A_84) top_top_nat_o))).
% Axiom fact_70_less__top:(forall (A_84:(product_unit->Prop)), ((iff (not (((eq (product_unit->Prop)) A_84) top_to1984820022unit_o))) ((ord_le232288914unit_o A_84) top_to1984820022unit_o))).
% Axiom fact_71_assms_I1_J:((member1425217232_alt_o f) ((pi_Arr1196397536_alt_o arrow_1647925946e_Prof) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> arrow_1982173296le_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 ((member285112084le_alt ((produc897867031le_alt e) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) lab) lba))))).
% Axiom fact_73_dictator__def:(forall (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (_TPTP_I:arrow_1196572341e_indi), ((iff ((arrow_968343245ctator F_31) _TPTP_I)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(((eq (produc1572197287le_alt->Prop)) (F_31 X_1)) (X_1 _TPTP_I)))))).
% Axiom fact_74__096Lab_A_058_ALin_096:((member1241905979_alt_o lab) arrow_1982173296le_Lin).
% Axiom fact_75__096Lba_A_058_ALin_096:((member1241905979_alt_o lba) arrow_1982173296le_Lin).
% Axiom fact_76__096a_A_126_061_Ab_096:(not (((eq arrow_1389031998le_alt) a) b)).
% Axiom fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096:((member285112084le_alt ((produc897867031le_alt a) b)) lab).
% Axiom fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096:((member285112084le_alt ((produc897867031le_alt b) a)) lba).
% Axiom fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096:(((member285112084le_alt ((produc897867031le_alt a) b)) lba)->False).
% Axiom fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096:(((member285112084le_alt ((produc897867031le_alt b) a)) lab)->False).
% Axiom fact_81_PiProf:(forall (N_1:nat), ((member822980838_alt_o (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) N_1)) lab) lba))) arrow_1647925946e_Prof)).
% Axiom fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_:((forall (Lab:(produc1572197287le_alt->Prop)), (((member285112084le_alt ((produc897867031le_alt a) b)) Lab)->(((member1241905979_alt_o Lab) arrow_1982173296le_Lin)->False)))->False).
% Axiom fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_:((forall (Lba:(produc1572197287le_alt->Prop)), (((member285112084le_alt ((produc897867031le_alt b) a)) Lba)->(((member1241905979_alt_o Lba) arrow_1982173296le_Lin)->False)))->False).
% Axiom fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk:(forall (I_1:arrow_1196572341e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt e) d)) ((arrow_1970123222_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt e) d)) (((arrow_556571452_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member285112084le_alt ((produc897867031le_alt e) d)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt b) a)) lab))) ((((ord_less_nat (h I_1)) n)->False)->((member285112084le_alt ((produc897867031le_alt b) a)) lba))))).
% Axiom fact_85_n_I2_J:(forall (M:nat), (((ord_less_eq_nat M) n)->((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) M)) lab) lba)))))).
% Axiom fact_86_notin__Lin__iff:(forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((not (((eq arrow_1389031998le_alt) X) Y))->((iff (((member285112084le_alt ((produc897867031le_alt X) Y)) L_2)->False)) ((member285112084le_alt ((produc897867031le_alt Y) X)) L_2))))).
% Axiom fact_87_Lin__irrefl:(forall (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->(((member285112084le_alt ((produc897867031le_alt A_73) B_58)) L_2)->(((member285112084le_alt ((produc897867031le_alt B_58) A_73)) L_2)->False)))).
% Axiom fact_88_mktop__Lin:(forall (X:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o ((arrow_1970123222_mktop L_2) X)) arrow_1982173296le_Lin))).
% Axiom fact_89_mkbot__Lin:(forall (X:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o ((arrow_1821416136_mkbot L_2) X)) arrow_1982173296le_Lin))).
% Axiom fact_90_above__Lin:(forall (L_2:(produc1572197287le_alt->Prop)) (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) X) Y))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o (((arrow_556571452_above L_2) X) Y)) arrow_1982173296le_Lin)))).
% Axiom fact_91_const__Lin__Prof:(forall (L_2:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member822980838_alt_o (fun (P_5:arrow_1196572341e_indi)=> L_2)) arrow_1647925946e_Prof))).
% Axiom fact_92_linorder__cases:(forall (X_65:nat) (Y_49:nat), ((((ord_less_nat X_65) Y_49)->False)->((not (((eq nat) X_65) Y_49))->((ord_less_nat Y_49) X_65)))).
% Axiom fact_93_order__less__asym:(forall (X_64:(nat->Prop)) (Y_48:(nat->Prop)), (((ord_less_nat_o X_64) Y_48)->(((ord_less_nat_o Y_48) X_64)->False))).
% Axiom fact_94_order__less__asym:(forall (X_64:(product_unit->Prop)) (Y_48:(product_unit->Prop)), (((ord_le232288914unit_o X_64) Y_48)->(((ord_le232288914unit_o Y_48) X_64)->False))).
% Axiom fact_95_order__less__asym:(forall (X_64:(arrow_1196572341e_indi->Prop)) (Y_48:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_64) Y_48)->(((ord_le1991507760indi_o Y_48) X_64)->False))).
% Axiom fact_96_order__less__asym:(forall (X_64:nat) (Y_48:nat), (((ord_less_nat X_64) Y_48)->(((ord_less_nat Y_48) X_64)->False))).
% Axiom fact_97_xt1_I10_J:(forall (Z_8:(nat->Prop)) (Y_47:(nat->Prop)) (X_63:(nat->Prop)), (((ord_less_nat_o Y_47) X_63)->(((ord_less_nat_o Z_8) Y_47)->((ord_less_nat_o Z_8) X_63)))).
% Axiom fact_98_xt1_I10_J:(forall (Z_8:(product_unit->Prop)) (Y_47:(product_unit->Prop)) (X_63:(product_unit->Prop)), (((ord_le232288914unit_o Y_47) X_63)->(((ord_le232288914unit_o Z_8) Y_47)->((ord_le232288914unit_o Z_8) X_63)))).
% Axiom fact_99_xt1_I10_J:(forall (Z_8:(arrow_1196572341e_indi->Prop)) (Y_47:(arrow_1196572341e_indi->Prop)) (X_63:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_47) X_63)->(((ord_le1991507760indi_o Z_8) Y_47)->((ord_le1991507760indi_o Z_8) X_63)))).
% Axiom fact_100_xt1_I10_J:(forall (Z_8:nat) (Y_47:nat) (X_63:nat), (((ord_less_nat Y_47) X_63)->(((ord_less_nat Z_8) Y_47)->((ord_less_nat Z_8) X_63)))).
% Axiom fact_101_order__less__trans:(forall (Z_7:(nat->Prop)) (X_62:(nat->Prop)) (Y_46:(nat->Prop)), (((ord_less_nat_o X_62) Y_46)->(((ord_less_nat_o Y_46) Z_7)->((ord_less_nat_o X_62) Z_7)))).
% Axiom fact_102_order__less__trans:(forall (Z_7:(product_unit->Prop)) (X_62:(product_unit->Prop)) (Y_46:(product_unit->Prop)), (((ord_le232288914unit_o X_62) Y_46)->(((ord_le232288914unit_o Y_46) Z_7)->((ord_le232288914unit_o X_62) Z_7)))).
% Axiom fact_103_order__less__trans:(forall (Z_7:(arrow_1196572341e_indi->Prop)) (X_62:(arrow_1196572341e_indi->Prop)) (Y_46:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_62) Y_46)->(((ord_le1991507760indi_o Y_46) Z_7)->((ord_le1991507760indi_o X_62) Z_7)))).
% Axiom fact_104_order__less__trans:(forall (Z_7:nat) (X_62:nat) (Y_46:nat), (((ord_less_nat X_62) Y_46)->(((ord_less_nat Y_46) Z_7)->((ord_less_nat X_62) Z_7)))).
% Axiom fact_105_xt1_I2_J:(forall (C_41:(nat->Prop)) (B_66:(nat->Prop)) (A_83:(nat->Prop)), (((ord_less_nat_o B_66) A_83)->((((eq (nat->Prop)) B_66) C_41)->((ord_less_nat_o C_41) A_83)))).
% Axiom fact_106_xt1_I2_J:(forall (C_41:(product_unit->Prop)) (B_66:(product_unit->Prop)) (A_83:(product_unit->Prop)), (((ord_le232288914unit_o B_66) A_83)->((((eq (product_unit->Prop)) B_66) C_41)->((ord_le232288914unit_o C_41) A_83)))).
% Axiom fact_107_xt1_I2_J:(forall (C_41:(arrow_1196572341e_indi->Prop)) (B_66:(arrow_1196572341e_indi->Prop)) (A_83:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_66) A_83)->((((eq (arrow_1196572341e_indi->Prop)) B_66) C_41)->((ord_le1991507760indi_o C_41) A_83)))).
% Axiom fact_108_xt1_I2_J:(forall (C_41:nat) (B_66:nat) (A_83:nat), (((ord_less_nat B_66) A_83)->((((eq nat) B_66) C_41)->((ord_less_nat C_41) A_83)))).
% Axiom fact_109_ord__less__eq__trans:(forall (C_40:(nat->Prop)) (A_82:(nat->Prop)) (B_65:(nat->Prop)), (((ord_less_nat_o A_82) B_65)->((((eq (nat->Prop)) B_65) C_40)->((ord_less_nat_o A_82) C_40)))).
% Axiom fact_110_ord__less__eq__trans:(forall (C_40:(product_unit->Prop)) (A_82:(product_unit->Prop)) (B_65:(product_unit->Prop)), (((ord_le232288914unit_o A_82) B_65)->((((eq (product_unit->Prop)) B_65) C_40)->((ord_le232288914unit_o A_82) C_40)))).
% Axiom fact_111_ord__less__eq__trans:(forall (C_40:(arrow_1196572341e_indi->Prop)) (A_82:(arrow_1196572341e_indi->Prop)) (B_65:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_82) B_65)->((((eq (arrow_1196572341e_indi->Prop)) B_65) C_40)->((ord_le1991507760indi_o A_82) C_40)))).
% Axiom fact_112_ord__less__eq__trans:(forall (C_40:nat) (A_82:nat) (B_65:nat), (((ord_less_nat A_82) B_65)->((((eq nat) B_65) C_40)->((ord_less_nat A_82) C_40)))).
% Axiom fact_113_xt1_I1_J:(forall (C_39:(nat->Prop)) (A_81:(nat->Prop)) (B_64:(nat->Prop)), ((((eq (nat->Prop)) A_81) B_64)->(((ord_less_nat_o C_39) B_64)->((ord_less_nat_o C_39) A_81)))).
% Axiom fact_114_xt1_I1_J:(forall (C_39:(product_unit->Prop)) (A_81:(product_unit->Prop)) (B_64:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_81) B_64)->(((ord_le232288914unit_o C_39) B_64)->((ord_le232288914unit_o C_39) A_81)))).
% Axiom fact_115_xt1_I1_J:(forall (C_39:(arrow_1196572341e_indi->Prop)) (A_81:(arrow_1196572341e_indi->Prop)) (B_64:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_81) B_64)->(((ord_le1991507760indi_o C_39) B_64)->((ord_le1991507760indi_o C_39) A_81)))).
% Axiom fact_116_xt1_I1_J:(forall (C_39:nat) (A_81:nat) (B_64:nat), ((((eq nat) A_81) B_64)->(((ord_less_nat C_39) B_64)->((ord_less_nat C_39) A_81)))).
% Axiom fact_117_ord__eq__less__trans:(forall (C_38:(nat->Prop)) (A_80:(nat->Prop)) (B_63:(nat->Prop)), ((((eq (nat->Prop)) A_80) B_63)->(((ord_less_nat_o B_63) C_38)->((ord_less_nat_o A_80) C_38)))).
% Axiom fact_118_ord__eq__less__trans:(forall (C_38:(product_unit->Prop)) (A_80:(product_unit->Prop)) (B_63:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_80) B_63)->(((ord_le232288914unit_o B_63) C_38)->((ord_le232288914unit_o A_80) C_38)))).
% Axiom fact_119_ord__eq__less__trans:(forall (C_38:(arrow_1196572341e_indi->Prop)) (A_80:(arrow_1196572341e_indi->Prop)) (B_63:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_80) B_63)->(((ord_le1991507760indi_o B_63) C_38)->((ord_le1991507760indi_o A_80) C_38)))).
% Axiom fact_120_ord__eq__less__trans:(forall (C_38:nat) (A_80:nat) (B_63:nat), ((((eq nat) A_80) B_63)->(((ord_less_nat B_63) C_38)->((ord_less_nat A_80) C_38)))).
% Axiom fact_121_xt1_I9_J:(forall (B_62:(nat->Prop)) (A_79:(nat->Prop)), (((ord_less_nat_o B_62) A_79)->(((ord_less_nat_o A_79) B_62)->False))).
% Axiom fact_122_xt1_I9_J:(forall (B_62:(product_unit->Prop)) (A_79:(product_unit->Prop)), (((ord_le232288914unit_o B_62) A_79)->(((ord_le232288914unit_o A_79) B_62)->False))).
% Axiom fact_123_xt1_I9_J:(forall (B_62:(arrow_1196572341e_indi->Prop)) (A_79:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_62) A_79)->(((ord_le1991507760indi_o A_79) B_62)->False))).
% Axiom fact_124_xt1_I9_J:(forall (B_62:nat) (A_79:nat), (((ord_less_nat B_62) A_79)->(((ord_less_nat A_79) B_62)->False))).
% Axiom fact_125_order__less__asym_H:(forall (A_78:(nat->Prop)) (B_61:(nat->Prop)), (((ord_less_nat_o A_78) B_61)->(((ord_less_nat_o B_61) A_78)->False))).
% Axiom fact_126_order__less__asym_H:(forall (A_78:(product_unit->Prop)) (B_61:(product_unit->Prop)), (((ord_le232288914unit_o A_78) B_61)->(((ord_le232288914unit_o B_61) A_78)->False))).
% Axiom fact_127_order__less__asym_H:(forall (A_78:(arrow_1196572341e_indi->Prop)) (B_61:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_78) B_61)->(((ord_le1991507760indi_o B_61) A_78)->False))).
% Axiom fact_128_order__less__asym_H:(forall (A_78:nat) (B_61:nat), (((ord_less_nat A_78) B_61)->(((ord_less_nat B_61) A_78)->False))).
% Axiom fact_129_order__less__imp__triv:(forall (P_4:Prop) (X_61:(nat->Prop)) (Y_45:(nat->Prop)), (((ord_less_nat_o X_61) Y_45)->(((ord_less_nat_o Y_45) X_61)->P_4))).
% Axiom fact_130_order__less__imp__triv:(forall (P_4:Prop) (X_61:(product_unit->Prop)) (Y_45:(product_unit->Prop)), (((ord_le232288914unit_o X_61) Y_45)->(((ord_le232288914unit_o Y_45) X_61)->P_4))).
% Axiom fact_131_order__less__imp__triv:(forall (P_4:Prop) (X_61:(arrow_1196572341e_indi->Prop)) (Y_45:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_61) Y_45)->(((ord_le1991507760indi_o Y_45) X_61)->P_4))).
% Axiom fact_132_order__less__imp__triv:(forall (P_4:Prop) (X_61:nat) (Y_45:nat), (((ord_less_nat X_61) Y_45)->(((ord_less_nat Y_45) X_61)->P_4))).
% Axiom fact_133_order__less__imp__not__eq2:(forall (X_60:(nat->Prop)) (Y_44:(nat->Prop)), (((ord_less_nat_o X_60) Y_44)->(not (((eq (nat->Prop)) Y_44) X_60)))).
% Axiom fact_134_order__less__imp__not__eq2:(forall (X_60:(product_unit->Prop)) (Y_44:(product_unit->Prop)), (((ord_le232288914unit_o X_60) Y_44)->(not (((eq (product_unit->Prop)) Y_44) X_60)))).
% Axiom fact_135_order__less__imp__not__eq2:(forall (X_60:(arrow_1196572341e_indi->Prop)) (Y_44:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_60) Y_44)->(not (((eq (arrow_1196572341e_indi->Prop)) Y_44) X_60)))).
% Axiom fact_136_order__less__imp__not__eq2:(forall (X_60:nat) (Y_44:nat), (((ord_less_nat X_60) Y_44)->(not (((eq nat) Y_44) X_60)))).
% Axiom fact_137_order__less__imp__not__eq:(forall (X_59:(nat->Prop)) (Y_43:(nat->Prop)), (((ord_less_nat_o X_59) Y_43)->(not (((eq (nat->Prop)) X_59) Y_43)))).
% Axiom fact_138_order__less__imp__not__eq:(forall (X_59:(product_unit->Prop)) (Y_43:(product_unit->Prop)), (((ord_le232288914unit_o X_59) Y_43)->(not (((eq (product_unit->Prop)) X_59) Y_43)))).
% Axiom fact_139_order__less__imp__not__eq:(forall (X_59:(arrow_1196572341e_indi->Prop)) (Y_43:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_59) Y_43)->(not (((eq (arrow_1196572341e_indi->Prop)) X_59) Y_43)))).
% Axiom fact_140_order__less__imp__not__eq:(forall (X_59:nat) (Y_43:nat), (((ord_less_nat X_59) Y_43)->(not (((eq nat) X_59) Y_43)))).
% Axiom fact_141_order__less__imp__not__less:(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_142_order__less__imp__not__less:(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_143_order__less__imp__not__less:(forall (X_58:(arrow_1196572341e_indi->Prop)) (Y_42:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_58) Y_42)->(((ord_le1991507760indi_o Y_42) X_58)->False))).
% Axiom fact_144_order__less__imp__not__less:(forall (X_58:nat) (Y_42:nat), (((ord_less_nat X_58) Y_42)->(((ord_less_nat Y_42) X_58)->False))).
% Axiom fact_145_order__less__not__sym:(forall (X_57:(nat->Prop)) (Y_41:(nat->Prop)), (((ord_less_nat_o X_57) Y_41)->(((ord_less_nat_o Y_41) X_57)->False))).
% Axiom fact_146_order__less__not__sym:(forall (X_57:(product_unit->Prop)) (Y_41:(product_unit->Prop)), (((ord_le232288914unit_o X_57) Y_41)->(((ord_le232288914unit_o Y_41) X_57)->False))).
% Axiom fact_147_order__less__not__sym:(forall (X_57:(arrow_1196572341e_indi->Prop)) (Y_41:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_57) Y_41)->(((ord_le1991507760indi_o Y_41) X_57)->False))).
% Axiom fact_148_order__less__not__sym:(forall (X_57:nat) (Y_41:nat), (((ord_less_nat X_57) Y_41)->(((ord_less_nat Y_41) X_57)->False))).
% Axiom fact_149_less__imp__neq:(forall (X_56:(nat->Prop)) (Y_40:(nat->Prop)), (((ord_less_nat_o X_56) Y_40)->(not (((eq (nat->Prop)) X_56) Y_40)))).
% Axiom fact_150_less__imp__neq:(forall (X_56:(product_unit->Prop)) (Y_40:(product_unit->Prop)), (((ord_le232288914unit_o X_56) Y_40)->(not (((eq (product_unit->Prop)) X_56) Y_40)))).
% Axiom fact_151_less__imp__neq:(forall (X_56:(arrow_1196572341e_indi->Prop)) (Y_40:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_56) Y_40)->(not (((eq (arrow_1196572341e_indi->Prop)) X_56) Y_40)))).
% Axiom fact_152_less__imp__neq:(forall (X_56:nat) (Y_40:nat), (((ord_less_nat X_56) Y_40)->(not (((eq nat) X_56) Y_40)))).
% Axiom fact_153_linorder__neqE:(forall (X_55:nat) (Y_39:nat), ((not (((eq nat) X_55) Y_39))->((((ord_less_nat X_55) Y_39)->False)->((ord_less_nat Y_39) X_55)))).
% Axiom fact_154_linorder__antisym__conv3:(forall (Y_38:nat) (X_54:nat), ((((ord_less_nat Y_38) X_54)->False)->((iff (((ord_less_nat X_54) Y_38)->False)) (((eq nat) X_54) Y_38)))).
% Axiom fact_155_linorder__less__linear:(forall (X_53:nat) (Y_37:nat), ((or ((or ((ord_less_nat X_53) Y_37)) (((eq nat) X_53) Y_37))) ((ord_less_nat Y_37) X_53))).
% Axiom fact_156_not__less__iff__gr__or__eq:(forall (X_52:nat) (Y_36:nat), ((iff (((ord_less_nat X_52) Y_36)->False)) ((or ((ord_less_nat Y_36) X_52)) (((eq nat) X_52) Y_36)))).
% Axiom fact_157_linorder__neq__iff:(forall (X_51:nat) (Y_35:nat), ((iff (not (((eq nat) X_51) Y_35))) ((or ((ord_less_nat X_51) Y_35)) ((ord_less_nat Y_35) X_51)))).
% Axiom fact_158_order__less__irrefl:(forall (X_50:(nat->Prop)), (((ord_less_nat_o X_50) X_50)->False)).
% Axiom fact_159_order__less__irrefl:(forall (X_50:(product_unit->Prop)), (((ord_le232288914unit_o X_50) X_50)->False)).
% Axiom fact_160_order__less__irrefl:(forall (X_50:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_50) X_50)->False)).
% Axiom fact_161_order__less__irrefl:(forall (X_50:nat), (((ord_less_nat X_50) X_50)->False)).
% Axiom fact_162_mem__def:(forall (X_49:arrow_1196572341e_indi) (A_77:(arrow_1196572341e_indi->Prop)), ((iff ((member1818997282e_indi X_49) A_77)) (A_77 X_49))).
% Axiom fact_163_mem__def:(forall (X_49:Prop) (A_77:(Prop->Prop)), ((iff ((member_o X_49) A_77)) (A_77 X_49))).
% Axiom fact_164_mem__def:(forall (X_49:product_unit) (A_77:(product_unit->Prop)), ((iff ((member_Product_unit X_49) A_77)) (A_77 X_49))).
% Axiom fact_165_mem__def:(forall (X_49:produc1572197287le_alt) (A_77:(produc1572197287le_alt->Prop)), ((iff ((member285112084le_alt X_49) A_77)) (A_77 X_49))).
% Axiom fact_166_mem__def:(forall (X_49:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_77:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((member822980838_alt_o X_49) A_77)) (A_77 X_49))).
% Axiom fact_167_mem__def:(forall (X_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_77:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((member1425217232_alt_o X_49) A_77)) (A_77 X_49))).
% Axiom fact_168_mem__def:(forall (X_49:(produc1572197287le_alt->Prop)) (A_77:((produc1572197287le_alt->Prop)->Prop)), ((iff ((member1241905979_alt_o X_49) A_77)) (A_77 X_49))).
% Axiom fact_169_mem__def:(forall (X_49:nat) (A_77:(nat->Prop)), ((iff ((member_nat X_49) A_77)) (A_77 X_49))).
% Axiom fact_170_Collect__def:(forall (P_3:(product_unit->Prop)), (((eq (product_unit->Prop)) (collect_Product_unit P_3)) P_3)).
% Axiom fact_171_Collect__def:(forall (P_3:(arrow_1196572341e_indi->Prop)), (((eq (arrow_1196572341e_indi->Prop)) (collec1936859488e_indi P_3)) P_3)).
% Axiom fact_172_Collect__def:(forall (P_3:(nat->Prop)), (((eq (nat->Prop)) (collect_nat P_3)) P_3)).
% Axiom fact_173_UNIV__def:(((eq ((produc1572197287le_alt->Prop)->Prop)) top_to1806834203lt_o_o) (collec958969213_alt_o (fun (X_1:(produc1572197287le_alt->Prop))=> True))).
% Axiom fact_174_UNIV__def:(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) top_to732317616lt_o_o) (collec979749928_alt_o (fun (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> True))).
% Axiom fact_175_UNIV__def:(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) top_to1492351398lt_o_o) (collec670126350_alt_o (fun (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> True))).
% Axiom fact_176_UNIV__def:(((eq (produc1572197287le_alt->Prop)) top_to558618722_alt_o) (collec940901970le_alt (fun (X_1:produc1572197287le_alt)=> True))).
% Axiom fact_177_UNIV__def:(((eq (arrow_1196572341e_indi->Prop)) top_to54564308indi_o) (collec1936859488e_indi (fun (X_1:arrow_1196572341e_indi)=> True))).
% Axiom fact_178_UNIV__def:(((eq (product_unit->Prop)) top_to1984820022unit_o) (collect_Product_unit (fun (X_1:product_unit)=> True))).
% Axiom fact_179_UNIV__def:(((eq (nat->Prop)) top_top_nat_o) (collect_nat (fun (X_1:nat)=> True))).
% Axiom fact_180_in__above:(forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_73) B_58))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) (((arrow_556571452_above L_2) A_73) B_58))) ((and ((and (not (((eq arrow_1389031998le_alt) X) Y))) ((((eq arrow_1389031998le_alt) X) B_58)->((member285112084le_alt ((produc897867031le_alt A_73) Y)) L_2)))) ((not (((eq arrow_1389031998le_alt) X) B_58))->((and ((((eq arrow_1389031998le_alt) Y) B_58)->((or (((eq arrow_1389031998le_alt) X) A_73)) ((member285112084le_alt ((produc897867031le_alt X) A_73)) L_2)))) ((not (((eq arrow_1389031998le_alt) Y) B_58))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2))))))))).
% Axiom fact_181_pred__equals__eq2:(forall (S_3:(produc1572197287le_alt->Prop)) (R_2:(produc1572197287le_alt->Prop)), ((iff (forall (X_1:arrow_1389031998le_alt) (Xa:arrow_1389031998le_alt), ((iff ((member285112084le_alt ((produc897867031le_alt X_1) Xa)) R_2)) ((member285112084le_alt ((produc897867031le_alt X_1) Xa)) S_3)))) (((eq (produc1572197287le_alt->Prop)) R_2) S_3))).
% Axiom fact_182_dictatorI:(forall (_TPTP_I:arrow_1196572341e_indi) (F_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o F_31) ((pi_Arr1196397536_alt_o arrow_1647925946e_Prof) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> arrow_1982173296le_Lin)))->((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) arrow_1647925946e_Prof)->(forall (A_76:arrow_1389031998le_alt) (B_60:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_76) B_60))->(((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (X_1 _TPTP_I))->((member285112084le_alt ((produc897867031le_alt A_76) B_60)) (F_31 X_1)))))))->((arrow_968343245ctator F_31) _TPTP_I)))).
% Axiom fact_183_n_I3_J:((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba)))).
% Axiom fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am:((iff ((member285112084le_alt ((produc897867031le_alt c) e)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))) lab) lba))))).
% Axiom fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am:(forall (I_1:arrow_1196572341e_indi), ((iff ((and (((ord_less_nat (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) e)) ((arrow_1970123222_mktop (p I_1)) e)))) ((((ord_less_nat (h I_1)) n)->False)->((and ((((eq nat) (h I_1)) n)->((member285112084le_alt ((produc897867031le_alt c) e)) (((arrow_556571452_above (p I_1)) c) e)))) ((not (((eq nat) (h I_1)) n))->((member285112084le_alt ((produc897867031le_alt c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))) ((and (((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->((member285112084le_alt ((produc897867031le_alt a) b)) lab))) ((((ord_less_nat (h I_1)) ((plus_plus_nat n) one_one_nat))->False)->((member285112084le_alt ((produc897867031le_alt a) b)) lba))))).
% Axiom fact_186_inv__f__eq:(forall (X_48:arrow_1196572341e_indi) (Y_34:nat) (F_30:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_30) top_to54564308indi_o)->((((eq nat) (F_30 X_48)) Y_34)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat top_to54564308indi_o) F_30) Y_34)) X_48)))).
% Axiom fact_187_inv__f__eq:(forall (X_48:nat) (Y_34:nat) (F_30:(nat->nat)), (((inj_on_nat_nat F_30) top_top_nat_o)->((((eq nat) (F_30 X_48)) Y_34)->(((eq nat) (((hilber195283148at_nat top_top_nat_o) F_30) Y_34)) X_48)))).
% Axiom fact_188_inv__f__f:(forall (X_47:arrow_1196572341e_indi) (F_29:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_29) top_to54564308indi_o)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat top_to54564308indi_o) F_29) (F_29 X_47))) X_47))).
% Axiom fact_189_inv__f__f:(forall (X_47: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_47))) X_47))).
% Axiom fact_190_PiE:(forall (X_46:produc1572197287le_alt) (F_28:(produc1572197287le_alt->Prop)) (A_75:(produc1572197287le_alt->Prop)) (B_59:(produc1572197287le_alt->(Prop->Prop))), (((member1241905979_alt_o F_28) ((pi_Pro418549519_alt_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member285112084le_alt X_46) A_75)->False)))).
% Axiom fact_191_PiE:(forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->produc1572197287le_alt)) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member232085823le_alt F_28) ((pi_Arr1762714837le_alt A_75) B_59))->((((member285112084le_alt (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False)))).
% Axiom fact_192_PiE:(forall (X_46:Prop) (F_28:(Prop->produc1572197287le_alt)) (A_75:(Prop->Prop)) (B_59:(Prop->(produc1572197287le_alt->Prop))), (((member1158049649le_alt F_28) ((pi_o_P728361163le_alt A_75) B_59))->((((member285112084le_alt (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False)))).
% Axiom fact_193_PiE:(forall (X_46:product_unit) (F_28:(product_unit->produc1572197287le_alt)) (A_75:(product_unit->Prop)) (B_59:(product_unit->(produc1572197287le_alt->Prop))), (((member1161214429le_alt F_28) ((pi_Pro772884595le_alt A_75) B_59))->((((member285112084le_alt (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False)))).
% Axiom fact_194_PiE:(forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2071265553_alt_o F_28) ((pi_Arr456308197_alt_o A_75) B_59))->((((member822980838_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False)))).
% Axiom fact_195_PiE:(forall (X_46:Prop) (F_28:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_75:(Prop->Prop)) (B_59:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member984757343_alt_o F_28) ((pi_o_A1479825007_alt_o A_75) B_59))->((((member822980838_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False)))).
% Axiom fact_196_PiE:(forall (X_46:product_unit) (F_28:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_75:(product_unit->Prop)) (B_59:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2021528307_alt_o F_28) ((pi_Pro1959068871_alt_o A_75) B_59))->((((member822980838_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False)))).
% Axiom fact_197_PiE:(forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1521294075_alt_o F_28) ((pi_Arr583278353_alt_o A_75) B_59))->((((member1425217232_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False)))).
% Axiom fact_198_PiE:(forall (X_46:Prop) (F_28:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_75:(Prop->Prop)) (B_59:(Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member161783341_alt_o F_28) ((pi_o_A1994447367_alt_o A_75) B_59))->((((member1425217232_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False)))).
% Axiom fact_199_PiE:(forall (X_46:product_unit) (F_28:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_75:(product_unit->Prop)) (B_59:(product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1888392857_alt_o F_28) ((pi_Pro443817391_alt_o A_75) B_59))->((((member1425217232_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False)))).
% Axiom fact_200_PiE:(forall (X_46:Prop) (F_28:(Prop->(produc1572197287le_alt->Prop))) (A_75:(Prop->Prop)) (B_59:(Prop->((produc1572197287le_alt->Prop)->Prop))), (((member1495989556_alt_o F_28) ((pi_o_P1417870404_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False)))).
% Axiom fact_201_PiE:(forall (X_46:product_unit) (F_28:(product_unit->(produc1572197287le_alt->Prop))) (A_75:(product_unit->Prop)) (B_59:(product_unit->((produc1572197287le_alt->Prop)->Prop))), (((member1295651272_alt_o F_28) ((pi_Pro29851292_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False)))).
% Axiom fact_202_PiE:(forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->nat)) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->(nat->Prop))), (((member1842285448di_nat F_28) ((pi_Arr778514268di_nat A_75) B_59))->((((member_nat (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False)))).
% Axiom fact_203_PiE:(forall (X_46:Prop) (F_28:(Prop->nat)) (A_75:(Prop->Prop)) (B_59:(Prop->(nat->Prop))), (((member_o_nat F_28) ((pi_o_nat A_75) B_59))->((((member_nat (F_28 X_46)) (B_59 X_46))->False)->(((member_o X_46) A_75)->False)))).
% Axiom fact_204_PiE:(forall (X_46:product_unit) (F_28:(product_unit->nat)) (A_75:(product_unit->Prop)) (B_59:(product_unit->(nat->Prop))), (((member1827227242it_nat F_28) ((pi_Product_unit_nat A_75) B_59))->((((member_nat (F_28 X_46)) (B_59 X_46))->False)->(((member_Product_unit X_46) A_75)->False)))).
% Axiom fact_205_PiE:(forall (X_46:produc1572197287le_alt) (F_28:(produc1572197287le_alt->arrow_1196572341e_indi)) (A_75:(produc1572197287le_alt->Prop)) (B_59:(produc1572197287le_alt->(arrow_1196572341e_indi->Prop))), (((member1074431551e_indi F_28) ((pi_Pro1246947541e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member285112084le_alt X_46) A_75)->False)))).
% Axiom fact_206_PiE:(forall (X_46:produc1572197287le_alt) (F_28:(produc1572197287le_alt->product_unit)) (A_75:(produc1572197287le_alt->Prop)) (B_59:(produc1572197287le_alt->(product_unit->Prop))), (((member44534621t_unit F_28) ((pi_Pro926528371t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member285112084le_alt X_46) A_75)->False)))).
% Axiom fact_207_PiE:(forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1186582243e_indi F_28) ((pi_Arr272777533e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False)))).
% Axiom fact_208_PiE:(forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1696373143lt_o_o F_28) ((pi_Arr1709554855lt_o_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False)))).
% Axiom fact_209_PiE:(forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1537523201t_unit F_28) ((pi_Arr509685723t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False)))).
% Axiom fact_210_PiE:(forall (X_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_75:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_59:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1539010427e_indi F_28) ((pi_Arr470535441e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member1425217232_alt_o X_46) A_75)->False)))).
% Axiom fact_211_PiE:(forall (X_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_75:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_59:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1346253567lt_o_o F_28) ((pi_Arr1865419731lt_o_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member1425217232_alt_o X_46) A_75)->False)))).
% Axiom fact_212_PiE:(forall (X_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (A_75:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_59:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1043380889t_unit F_28) ((pi_Arr2096782767t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member1425217232_alt_o X_46) A_75)->False)))).
% Axiom fact_213_PiE:(forall (X_46:(produc1572197287le_alt->Prop)) (F_28:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (A_75:((produc1572197287le_alt->Prop)->Prop)) (B_59:((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))), (((member1830244024e_indi F_28) ((pi_Pro2039443474e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member1241905979_alt_o X_46) A_75)->False)))).
% Axiom fact_214_PiE:(forall (X_46:(produc1572197287le_alt->Prop)) (F_28:((produc1572197287le_alt->Prop)->Prop)) (A_75:((produc1572197287le_alt->Prop)->Prop)) (B_59:((produc1572197287le_alt->Prop)->(Prop->Prop))), (((member1925470338lt_o_o F_28) ((pi_Pro386796690lt_o_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member1241905979_alt_o X_46) A_75)->False)))).
% Axiom fact_215_PiE:(forall (X_46:(produc1572197287le_alt->Prop)) (F_28:((produc1572197287le_alt->Prop)->product_unit)) (A_75:((produc1572197287le_alt->Prop)->Prop)) (B_59:((produc1572197287le_alt->Prop)->(product_unit->Prop))), (((member1092867670t_unit F_28) ((pi_Pro30504752t_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member1241905979_alt_o X_46) A_75)->False)))).
% Axiom fact_216_PiE:(forall (X_46:nat) (F_28:(nat->arrow_1196572341e_indi)) (A_75:(nat->Prop)) (B_59:(nat->(arrow_1196572341e_indi->Prop))), (((member1113138010e_indi F_28) ((pi_nat986275508e_indi A_75) B_59))->((((member1818997282e_indi (F_28 X_46)) (B_59 X_46))->False)->(((member_nat X_46) A_75)->False)))).
% Axiom fact_217_PiE:(forall (X_46:nat) (F_28:(nat->Prop)) (A_75:(nat->Prop)) (B_59:(nat->(Prop->Prop))), (((member_nat_o F_28) ((pi_nat_o A_75) B_59))->((((member_o (F_28 X_46)) (B_59 X_46))->False)->(((member_nat X_46) A_75)->False)))).
% Axiom fact_218_PiE:(forall (X_46:nat) (F_28:(nat->product_unit)) (A_75:(nat->Prop)) (B_59:(nat->(product_unit->Prop))), (((member616671224t_unit F_28) ((pi_nat_Product_unit A_75) B_59))->((((member_Product_unit (F_28 X_46)) (B_59 X_46))->False)->(((member_nat X_46) A_75)->False)))).
% Axiom fact_219_PiE:(forall (X_46:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_75:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_59:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))), (((member1425217232_alt_o F_28) ((pi_Arr1196397536_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member822980838_alt_o X_46) A_75)->False)))).
% Axiom fact_220_PiE:(forall (X_46:arrow_1196572341e_indi) (F_28:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_75:(arrow_1196572341e_indi->Prop)) (B_59:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))), (((member822980838_alt_o F_28) ((pi_Arr1309696186_alt_o A_75) B_59))->((((member1241905979_alt_o (F_28 X_46)) (B_59 X_46))->False)->(((member1818997282e_indi X_46) A_75)->False)))).
% Axiom fact_221_complete__Lin:(forall (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_73) B_58))->((ex (produc1572197287le_alt->Prop)) (fun (X_1:(produc1572197287le_alt->Prop))=> ((and ((member1241905979_alt_o X_1) arrow_1982173296le_Lin)) ((member285112084le_alt ((produc897867031le_alt A_73) B_58)) X_1)))))).
% Axiom fact_222_Pi__UNIV:(forall (A_74:(produc1572197287le_alt->Prop)), (((eq ((produc1572197287le_alt->Prop)->Prop)) ((pi_Pro418549519_alt_o A_74) (fun (Uu:produc1572197287le_alt)=> top_top_o_o))) top_to1806834203lt_o_o)).
% Axiom fact_223_Pi__UNIV:(forall (A_74:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) ((pi_Arr1196397536_alt_o A_74) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> top_to1806834203lt_o_o))) top_to1492351398lt_o_o)).
% Axiom fact_224_Pi__UNIV:(forall (A_74:(arrow_1196572341e_indi->Prop)), (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) ((pi_Arr1309696186_alt_o A_74) (fun (Uu:arrow_1196572341e_indi)=> top_to1806834203lt_o_o))) top_to732317616lt_o_o)).
% Axiom fact_225_in__below:(forall (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt) (L_2:(produc1572197287le_alt->Prop)) (A_73:arrow_1389031998le_alt) (B_58:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) A_73) B_58))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((iff ((member285112084le_alt ((produc897867031le_alt X) Y)) (((arrow_1865170000_below L_2) A_73) B_58))) ((and ((and (not (((eq arrow_1389031998le_alt) X) Y))) ((((eq arrow_1389031998le_alt) Y) A_73)->((member285112084le_alt ((produc897867031le_alt X) B_58)) L_2)))) ((not (((eq arrow_1389031998le_alt) Y) A_73))->((and ((((eq arrow_1389031998le_alt) X) A_73)->((or (((eq arrow_1389031998le_alt) Y) B_58)) ((member285112084le_alt ((produc897867031le_alt B_58) Y)) L_2)))) ((not (((eq arrow_1389031998le_alt) X) A_73))->((member285112084le_alt ((produc897867031le_alt X) Y)) L_2))))))))).
% Axiom fact_226_order__refl:(forall (X_45:((produc1572197287le_alt->Prop)->Prop)), ((ord_le1027220427lt_o_o X_45) X_45)).
% Axiom fact_227_order__refl:(forall (X_45:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((ord_le1805007862lt_o_o X_45) X_45)).
% Axiom fact_228_order__refl:(forall (X_45:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((ord_le602483040lt_o_o X_45) X_45)).
% Axiom fact_229_order__refl:(forall (X_45:(produc1572197287le_alt->Prop)), ((ord_le962286258_alt_o X_45) X_45)).
% Axiom fact_230_order__refl:(forall (X_45:Prop), ((ord_less_eq_o X_45) X_45)).
% Axiom fact_231_order__refl:(forall (X_45:(arrow_1196572341e_indi->Prop)), ((ord_le865407012indi_o X_45) X_45)).
% Axiom fact_232_order__refl:(forall (X_45:(product_unit->Prop)), ((ord_le1511552390unit_o X_45) X_45)).
% Axiom fact_233_order__refl:(forall (X_45:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((ord_le1463467535_alt_o X_45) X_45)).
% Axiom fact_234_order__refl:(forall (X_45:nat), ((ord_less_eq_nat X_45) X_45)).
% Axiom fact_235_order__refl:(forall (X_45:(nat->Prop)), ((ord_less_eq_nat_o X_45) X_45)).
% Axiom fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I:((ex nat) (fun (N:nat)=> ((and ((and ((ord_less_nat N) (finite2011930979e_indi top_to54564308indi_o))) (forall (M:nat), (((ord_less_eq_nat M) N)->((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) M)) lab) lba)))))))) ((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N) one_one_nat))) lab) lba))))))).
% Axiom fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_:((forall (N:nat), (((ord_less_nat N) (finite2011930979e_indi top_to54564308indi_o))->((forall (M:nat), (((ord_less_eq_nat M) N)->((member285112084le_alt ((produc897867031le_alt b) a)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) M)) lab) lba))))))->(((member285112084le_alt ((produc897867031le_alt a) b)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) ((plus_plus_nat N) one_one_nat))) lab) lba))))->False))))->False).
% Axiom fact_238_linorder__le__cases:(forall (X_44:nat) (Y_33:nat), ((((ord_less_eq_nat X_44) Y_33)->False)->((ord_less_eq_nat Y_33) X_44))).
% Axiom fact_239_le__funE:(forall (X_43:(produc1572197287le_alt->Prop)) (F_27:((produc1572197287le_alt->Prop)->Prop)) (G_5:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))).
% Axiom fact_240_le__funE:(forall (X_43:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_27:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))).
% Axiom fact_241_le__funE:(forall (X_43:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_27:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))).
% Axiom fact_242_le__funE:(forall (X_43:produc1572197287le_alt) (F_27:(produc1572197287le_alt->Prop)) (G_5:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))).
% Axiom fact_243_le__funE:(forall (X_43:arrow_1196572341e_indi) (F_27:(arrow_1196572341e_indi->Prop)) (G_5:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))).
% Axiom fact_244_le__funE:(forall (X_43:product_unit) (F_27:(product_unit->Prop)) (G_5:(product_unit->Prop)), (((ord_le1511552390unit_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))).
% Axiom fact_245_le__funE:(forall (X_43:arrow_1389031998le_alt) (F_27:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o F_27) G_5)->((ord_le1423491573_alt_o (F_27 X_43)) (G_5 X_43)))).
% Axiom fact_246_le__funE:(forall (X_43:nat) (F_27:(nat->Prop)) (G_5:(nat->Prop)), (((ord_less_eq_nat_o F_27) G_5)->((ord_less_eq_o (F_27 X_43)) (G_5 X_43)))).
% Axiom fact_247_xt1_I6_J:(forall (Z_6:((produc1572197287le_alt->Prop)->Prop)) (Y_32:((produc1572197287le_alt->Prop)->Prop)) (X_42:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_32) X_42)->(((ord_le1027220427lt_o_o Z_6) Y_32)->((ord_le1027220427lt_o_o Z_6) X_42)))).
% Axiom fact_248_xt1_I6_J:(forall (Z_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_32:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_42:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_32) X_42)->(((ord_le1805007862lt_o_o Z_6) Y_32)->((ord_le1805007862lt_o_o Z_6) X_42)))).
% Axiom fact_249_xt1_I6_J:(forall (Z_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_32:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_42:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_32) X_42)->(((ord_le602483040lt_o_o Z_6) Y_32)->((ord_le602483040lt_o_o Z_6) X_42)))).
% Axiom fact_250_xt1_I6_J:(forall (Z_6:(produc1572197287le_alt->Prop)) (Y_32:(produc1572197287le_alt->Prop)) (X_42:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_32) X_42)->(((ord_le962286258_alt_o Z_6) Y_32)->((ord_le962286258_alt_o Z_6) X_42)))).
% Axiom fact_251_xt1_I6_J:(forall (Z_6:Prop) (Y_32:Prop) (X_42:Prop), (((ord_less_eq_o Y_32) X_42)->(((ord_less_eq_o Z_6) Y_32)->((ord_less_eq_o Z_6) X_42)))).
% Axiom fact_252_xt1_I6_J:(forall (Z_6:(arrow_1196572341e_indi->Prop)) (Y_32:(arrow_1196572341e_indi->Prop)) (X_42:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_32) X_42)->(((ord_le865407012indi_o Z_6) Y_32)->((ord_le865407012indi_o Z_6) X_42)))).
% Axiom fact_253_xt1_I6_J:(forall (Z_6:(product_unit->Prop)) (Y_32:(product_unit->Prop)) (X_42:(product_unit->Prop)), (((ord_le1511552390unit_o Y_32) X_42)->(((ord_le1511552390unit_o Z_6) Y_32)->((ord_le1511552390unit_o Z_6) X_42)))).
% Axiom fact_254_xt1_I6_J:(forall (Z_6:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_32:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_42:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_32) X_42)->(((ord_le1463467535_alt_o Z_6) Y_32)->((ord_le1463467535_alt_o Z_6) X_42)))).
% Axiom fact_255_xt1_I6_J:(forall (Z_6:nat) (Y_32:nat) (X_42:nat), (((ord_less_eq_nat Y_32) X_42)->(((ord_less_eq_nat Z_6) Y_32)->((ord_less_eq_nat Z_6) X_42)))).
% Axiom fact_256_xt1_I6_J:(forall (Z_6:(nat->Prop)) (Y_32:(nat->Prop)) (X_42:(nat->Prop)), (((ord_less_eq_nat_o Y_32) X_42)->(((ord_less_eq_nat_o Z_6) Y_32)->((ord_less_eq_nat_o Z_6) X_42)))).
% Axiom fact_257_xt1_I5_J:(forall (Y_31:((produc1572197287le_alt->Prop)->Prop)) (X_41:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_31) X_41)->(((ord_le1027220427lt_o_o X_41) Y_31)->(((eq ((produc1572197287le_alt->Prop)->Prop)) X_41) Y_31)))).
% Axiom fact_258_xt1_I5_J:(forall (Y_31:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_41:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_31) X_41)->(((ord_le1805007862lt_o_o X_41) Y_31)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_41) Y_31)))).
% Axiom fact_259_xt1_I5_J:(forall (Y_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_41:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_31) X_41)->(((ord_le602483040lt_o_o X_41) Y_31)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_41) Y_31)))).
% Axiom fact_260_xt1_I5_J:(forall (Y_31:(produc1572197287le_alt->Prop)) (X_41:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_31) X_41)->(((ord_le962286258_alt_o X_41) Y_31)->(((eq (produc1572197287le_alt->Prop)) X_41) Y_31)))).
% Axiom fact_261_xt1_I5_J:(forall (Y_31:Prop) (X_41:Prop), (((ord_less_eq_o Y_31) X_41)->(((ord_less_eq_o X_41) Y_31)->((iff X_41) Y_31)))).
% Axiom fact_262_xt1_I5_J:(forall (Y_31:(arrow_1196572341e_indi->Prop)) (X_41:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_31) X_41)->(((ord_le865407012indi_o X_41) Y_31)->(((eq (arrow_1196572341e_indi->Prop)) X_41) Y_31)))).
% Axiom fact_263_xt1_I5_J:(forall (Y_31:(product_unit->Prop)) (X_41:(product_unit->Prop)), (((ord_le1511552390unit_o Y_31) X_41)->(((ord_le1511552390unit_o X_41) Y_31)->(((eq (product_unit->Prop)) X_41) Y_31)))).
% Axiom fact_264_xt1_I5_J:(forall (Y_31:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_41:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_31) X_41)->(((ord_le1463467535_alt_o X_41) Y_31)->(((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_41) Y_31)))).
% Axiom fact_265_xt1_I5_J:(forall (Y_31:nat) (X_41:nat), (((ord_less_eq_nat Y_31) X_41)->(((ord_less_eq_nat X_41) Y_31)->(((eq nat) X_41) Y_31)))).
% Axiom fact_266_xt1_I5_J:(forall (Y_31:(nat->Prop)) (X_41:(nat->Prop)), (((ord_less_eq_nat_o Y_31) X_41)->(((ord_less_eq_nat_o X_41) Y_31)->(((eq (nat->Prop)) X_41) Y_31)))).
% Axiom fact_267_order__trans:(forall (Z_5:((produc1572197287le_alt->Prop)->Prop)) (X_40:((produc1572197287le_alt->Prop)->Prop)) (Y_30:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_40) Y_30)->(((ord_le1027220427lt_o_o Y_30) Z_5)->((ord_le1027220427lt_o_o X_40) Z_5)))).
% Axiom fact_268_order__trans:(forall (Z_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_40:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_40) Y_30)->(((ord_le1805007862lt_o_o Y_30) Z_5)->((ord_le1805007862lt_o_o X_40) Z_5)))).
% Axiom fact_269_order__trans:(forall (Z_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_40:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_40) Y_30)->(((ord_le602483040lt_o_o Y_30) Z_5)->((ord_le602483040lt_o_o X_40) Z_5)))).
% Axiom fact_270_order__trans:(forall (Z_5:(produc1572197287le_alt->Prop)) (X_40:(produc1572197287le_alt->Prop)) (Y_30:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_40) Y_30)->(((ord_le962286258_alt_o Y_30) Z_5)->((ord_le962286258_alt_o X_40) Z_5)))).
% Axiom fact_271_order__trans:(forall (Z_5:Prop) (X_40:Prop) (Y_30:Prop), (((ord_less_eq_o X_40) Y_30)->(((ord_less_eq_o Y_30) Z_5)->((ord_less_eq_o X_40) Z_5)))).
% Axiom fact_272_order__trans:(forall (Z_5:(arrow_1196572341e_indi->Prop)) (X_40:(arrow_1196572341e_indi->Prop)) (Y_30:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_40) Y_30)->(((ord_le865407012indi_o Y_30) Z_5)->((ord_le865407012indi_o X_40) Z_5)))).
% Axiom fact_273_order__trans:(forall (Z_5:(product_unit->Prop)) (X_40:(product_unit->Prop)) (Y_30:(product_unit->Prop)), (((ord_le1511552390unit_o X_40) Y_30)->(((ord_le1511552390unit_o Y_30) Z_5)->((ord_le1511552390unit_o X_40) Z_5)))).
% Axiom fact_274_order__trans:(forall (Z_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_40:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_40) Y_30)->(((ord_le1463467535_alt_o Y_30) Z_5)->((ord_le1463467535_alt_o X_40) Z_5)))).
% Axiom fact_275_order__trans:(forall (Z_5:nat) (X_40:nat) (Y_30:nat), (((ord_less_eq_nat X_40) Y_30)->(((ord_less_eq_nat Y_30) Z_5)->((ord_less_eq_nat X_40) Z_5)))).
% Axiom fact_276_order__trans:(forall (Z_5:(nat->Prop)) (X_40:(nat->Prop)) (Y_30:(nat->Prop)), (((ord_less_eq_nat_o X_40) Y_30)->(((ord_less_eq_nat_o Y_30) Z_5)->((ord_less_eq_nat_o X_40) Z_5)))).
% Axiom fact_277_order__antisym:(forall (X_39:((produc1572197287le_alt->Prop)->Prop)) (Y_29:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_39) Y_29)->(((ord_le1027220427lt_o_o Y_29) X_39)->(((eq ((produc1572197287le_alt->Prop)->Prop)) X_39) Y_29)))).
% Axiom fact_278_order__antisym:(forall (X_39:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_29:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_39) Y_29)->(((ord_le1805007862lt_o_o Y_29) X_39)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_39) Y_29)))).
% Axiom fact_279_order__antisym:(forall (X_39:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_29:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_39) Y_29)->(((ord_le602483040lt_o_o Y_29) X_39)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_39) Y_29)))).
% Axiom fact_280_order__antisym:(forall (X_39:(produc1572197287le_alt->Prop)) (Y_29:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_39) Y_29)->(((ord_le962286258_alt_o Y_29) X_39)->(((eq (produc1572197287le_alt->Prop)) X_39) Y_29)))).
% Axiom fact_281_order__antisym:(forall (X_39:Prop) (Y_29:Prop), (((ord_less_eq_o X_39) Y_29)->(((ord_less_eq_o Y_29) X_39)->((iff X_39) Y_29)))).
% Axiom fact_282_order__antisym:(forall (X_39:(arrow_1196572341e_indi->Prop)) (Y_29:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_39) Y_29)->(((ord_le865407012indi_o Y_29) X_39)->(((eq (arrow_1196572341e_indi->Prop)) X_39) Y_29)))).
% Axiom fact_283_order__antisym:(forall (X_39:(product_unit->Prop)) (Y_29:(product_unit->Prop)), (((ord_le1511552390unit_o X_39) Y_29)->(((ord_le1511552390unit_o Y_29) X_39)->(((eq (product_unit->Prop)) X_39) Y_29)))).
% Axiom fact_284_order__antisym:(forall (X_39:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_29:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_39) Y_29)->(((ord_le1463467535_alt_o Y_29) X_39)->(((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_39) Y_29)))).
% Axiom fact_285_order__antisym:(forall (X_39:nat) (Y_29:nat), (((ord_less_eq_nat X_39) Y_29)->(((ord_less_eq_nat Y_29) X_39)->(((eq nat) X_39) Y_29)))).
% Axiom fact_286_order__antisym:(forall (X_39:(nat->Prop)) (Y_29:(nat->Prop)), (((ord_less_eq_nat_o X_39) Y_29)->(((ord_less_eq_nat_o Y_29) X_39)->(((eq (nat->Prop)) X_39) Y_29)))).
% Axiom fact_287_xt1_I4_J:(forall (C_37:((produc1572197287le_alt->Prop)->Prop)) (B_57:((produc1572197287le_alt->Prop)->Prop)) (A_72:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_57) A_72)->((((eq ((produc1572197287le_alt->Prop)->Prop)) B_57) C_37)->((ord_le1027220427lt_o_o C_37) A_72)))).
% Axiom fact_288_xt1_I4_J:(forall (C_37:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_72:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_57) A_72)->((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) B_57) C_37)->((ord_le1805007862lt_o_o C_37) A_72)))).
% Axiom fact_289_xt1_I4_J:(forall (C_37:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_72:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_57) A_72)->((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) B_57) C_37)->((ord_le602483040lt_o_o C_37) A_72)))).
% Axiom fact_290_xt1_I4_J:(forall (C_37:(produc1572197287le_alt->Prop)) (B_57:(produc1572197287le_alt->Prop)) (A_72:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_57) A_72)->((((eq (produc1572197287le_alt->Prop)) B_57) C_37)->((ord_le962286258_alt_o C_37) A_72)))).
% Axiom fact_291_xt1_I4_J:(forall (C_37:Prop) (B_57:Prop) (A_72:Prop), (((ord_less_eq_o B_57) A_72)->(((iff B_57) C_37)->((ord_less_eq_o C_37) A_72)))).
% Axiom fact_292_xt1_I4_J:(forall (C_37:(arrow_1196572341e_indi->Prop)) (B_57:(arrow_1196572341e_indi->Prop)) (A_72:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_57) A_72)->((((eq (arrow_1196572341e_indi->Prop)) B_57) C_37)->((ord_le865407012indi_o C_37) A_72)))).
% Axiom fact_293_xt1_I4_J:(forall (C_37:(product_unit->Prop)) (B_57:(product_unit->Prop)) (A_72:(product_unit->Prop)), (((ord_le1511552390unit_o B_57) A_72)->((((eq (product_unit->Prop)) B_57) C_37)->((ord_le1511552390unit_o C_37) A_72)))).
% Axiom fact_294_xt1_I4_J:(forall (C_37:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_57:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_72:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_57) A_72)->((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) B_57) C_37)->((ord_le1463467535_alt_o C_37) A_72)))).
% Axiom fact_295_xt1_I4_J:(forall (C_37:nat) (B_57:nat) (A_72:nat), (((ord_less_eq_nat B_57) A_72)->((((eq nat) B_57) C_37)->((ord_less_eq_nat C_37) A_72)))).
% Axiom fact_296_xt1_I4_J:(forall (C_37:(nat->Prop)) (B_57:(nat->Prop)) (A_72:(nat->Prop)), (((ord_less_eq_nat_o B_57) A_72)->((((eq (nat->Prop)) B_57) C_37)->((ord_less_eq_nat_o C_37) A_72)))).
% Axiom fact_297_ord__le__eq__trans:(forall (C_36:((produc1572197287le_alt->Prop)->Prop)) (A_71:((produc1572197287le_alt->Prop)->Prop)) (B_56:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_71) B_56)->((((eq ((produc1572197287le_alt->Prop)->Prop)) B_56) C_36)->((ord_le1027220427lt_o_o A_71) C_36)))).
% Axiom fact_298_ord__le__eq__trans:(forall (C_36:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_71:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_56:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_71) B_56)->((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) B_56) C_36)->((ord_le1805007862lt_o_o A_71) C_36)))).
% Axiom fact_299_ord__le__eq__trans:(forall (C_36:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_71:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_56:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_71) B_56)->((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) B_56) C_36)->((ord_le602483040lt_o_o A_71) C_36)))).
% Axiom fact_300_ord__le__eq__trans:(forall (C_36:(produc1572197287le_alt->Prop)) (A_71:(produc1572197287le_alt->Prop)) (B_56:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_71) B_56)->((((eq (produc1572197287le_alt->Prop)) B_56) C_36)->((ord_le962286258_alt_o A_71) C_36)))).
% Axiom fact_301_ord__le__eq__trans:(forall (C_36:Prop) (A_71:Prop) (B_56:Prop), (((ord_less_eq_o A_71) B_56)->(((iff B_56) C_36)->((ord_less_eq_o A_71) C_36)))).
% Axiom fact_302_ord__le__eq__trans:(forall (C_36:(arrow_1196572341e_indi->Prop)) (A_71:(arrow_1196572341e_indi->Prop)) (B_56:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_71) B_56)->((((eq (arrow_1196572341e_indi->Prop)) B_56) C_36)->((ord_le865407012indi_o A_71) C_36)))).
% Axiom fact_303_ord__le__eq__trans:(forall (C_36:(product_unit->Prop)) (A_71:(product_unit->Prop)) (B_56:(product_unit->Prop)), (((ord_le1511552390unit_o A_71) B_56)->((((eq (product_unit->Prop)) B_56) C_36)->((ord_le1511552390unit_o A_71) C_36)))).
% Axiom fact_304_ord__le__eq__trans:(forall (C_36:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_71:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_56:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_71) B_56)->((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) B_56) C_36)->((ord_le1463467535_alt_o A_71) C_36)))).
% Axiom fact_305_ord__le__eq__trans:(forall (C_36:nat) (A_71:nat) (B_56:nat), (((ord_less_eq_nat A_71) B_56)->((((eq nat) B_56) C_36)->((ord_less_eq_nat A_71) C_36)))).
% Axiom fact_306_ord__le__eq__trans:(forall (C_36:(nat->Prop)) (A_71:(nat->Prop)) (B_56:(nat->Prop)), (((ord_less_eq_nat_o A_71) B_56)->((((eq (nat->Prop)) B_56) C_36)->((ord_less_eq_nat_o A_71) C_36)))).
% Axiom fact_307_xt1_I3_J:(forall (C_35:((produc1572197287le_alt->Prop)->Prop)) (A_70:((produc1572197287le_alt->Prop)->Prop)) (B_55:((produc1572197287le_alt->Prop)->Prop)), ((((eq ((produc1572197287le_alt->Prop)->Prop)) A_70) B_55)->(((ord_le1027220427lt_o_o C_35) B_55)->((ord_le1027220427lt_o_o C_35) A_70)))).
% Axiom fact_308_xt1_I3_J:(forall (C_35:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_70:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_70) B_55)->(((ord_le1805007862lt_o_o C_35) B_55)->((ord_le1805007862lt_o_o C_35) A_70)))).
% Axiom fact_309_xt1_I3_J:(forall (C_35:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_70:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_70) B_55)->(((ord_le602483040lt_o_o C_35) B_55)->((ord_le602483040lt_o_o C_35) A_70)))).
% Axiom fact_310_xt1_I3_J:(forall (C_35:(produc1572197287le_alt->Prop)) (A_70:(produc1572197287le_alt->Prop)) (B_55:(produc1572197287le_alt->Prop)), ((((eq (produc1572197287le_alt->Prop)) A_70) B_55)->(((ord_le962286258_alt_o C_35) B_55)->((ord_le962286258_alt_o C_35) A_70)))).
% Axiom fact_311_xt1_I3_J:(forall (C_35:Prop) (B_55:Prop) (A_70:Prop), (((iff A_70) B_55)->(((ord_less_eq_o C_35) B_55)->((ord_less_eq_o C_35) A_70)))).
% Axiom fact_312_xt1_I3_J:(forall (C_35:(arrow_1196572341e_indi->Prop)) (A_70:(arrow_1196572341e_indi->Prop)) (B_55:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_70) B_55)->(((ord_le865407012indi_o C_35) B_55)->((ord_le865407012indi_o C_35) A_70)))).
% Axiom fact_313_xt1_I3_J:(forall (C_35:(product_unit->Prop)) (A_70:(product_unit->Prop)) (B_55:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_70) B_55)->(((ord_le1511552390unit_o C_35) B_55)->((ord_le1511552390unit_o C_35) A_70)))).
% Axiom fact_314_xt1_I3_J:(forall (C_35:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_70:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_55:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_70) B_55)->(((ord_le1463467535_alt_o C_35) B_55)->((ord_le1463467535_alt_o C_35) A_70)))).
% Axiom fact_315_xt1_I3_J:(forall (C_35:nat) (A_70:nat) (B_55:nat), ((((eq nat) A_70) B_55)->(((ord_less_eq_nat C_35) B_55)->((ord_less_eq_nat C_35) A_70)))).
% Axiom fact_316_xt1_I3_J:(forall (C_35:(nat->Prop)) (A_70:(nat->Prop)) (B_55:(nat->Prop)), ((((eq (nat->Prop)) A_70) B_55)->(((ord_less_eq_nat_o C_35) B_55)->((ord_less_eq_nat_o C_35) A_70)))).
% Axiom fact_317_ord__eq__le__trans:(forall (C_34:((produc1572197287le_alt->Prop)->Prop)) (A_69:((produc1572197287le_alt->Prop)->Prop)) (B_54:((produc1572197287le_alt->Prop)->Prop)), ((((eq ((produc1572197287le_alt->Prop)->Prop)) A_69) B_54)->(((ord_le1027220427lt_o_o B_54) C_34)->((ord_le1027220427lt_o_o A_69) C_34)))).
% Axiom fact_318_ord__eq__le__trans:(forall (C_34:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_69:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_54:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_69) B_54)->(((ord_le1805007862lt_o_o B_54) C_34)->((ord_le1805007862lt_o_o A_69) C_34)))).
% Axiom fact_319_ord__eq__le__trans:(forall (C_34:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_69:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_54:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_69) B_54)->(((ord_le602483040lt_o_o B_54) C_34)->((ord_le602483040lt_o_o A_69) C_34)))).
% Axiom fact_320_ord__eq__le__trans:(forall (C_34:(produc1572197287le_alt->Prop)) (A_69:(produc1572197287le_alt->Prop)) (B_54:(produc1572197287le_alt->Prop)), ((((eq (produc1572197287le_alt->Prop)) A_69) B_54)->(((ord_le962286258_alt_o B_54) C_34)->((ord_le962286258_alt_o A_69) C_34)))).
% Axiom fact_321_ord__eq__le__trans:(forall (C_34:Prop) (B_54:Prop) (A_69:Prop), (((iff A_69) B_54)->(((ord_less_eq_o B_54) C_34)->((ord_less_eq_o A_69) C_34)))).
% Axiom fact_322_ord__eq__le__trans:(forall (C_34:(arrow_1196572341e_indi->Prop)) (A_69:(arrow_1196572341e_indi->Prop)) (B_54:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) A_69) B_54)->(((ord_le865407012indi_o B_54) C_34)->((ord_le865407012indi_o A_69) C_34)))).
% Axiom fact_323_ord__eq__le__trans:(forall (C_34:(product_unit->Prop)) (A_69:(product_unit->Prop)) (B_54:(product_unit->Prop)), ((((eq (product_unit->Prop)) A_69) B_54)->(((ord_le1511552390unit_o B_54) C_34)->((ord_le1511552390unit_o A_69) C_34)))).
% Axiom fact_324_ord__eq__le__trans:(forall (C_34:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_69:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_54:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_69) B_54)->(((ord_le1463467535_alt_o B_54) C_34)->((ord_le1463467535_alt_o A_69) C_34)))).
% Axiom fact_325_ord__eq__le__trans:(forall (C_34:nat) (A_69:nat) (B_54:nat), ((((eq nat) A_69) B_54)->(((ord_less_eq_nat B_54) C_34)->((ord_less_eq_nat A_69) C_34)))).
% Axiom fact_326_ord__eq__le__trans:(forall (C_34:(nat->Prop)) (A_69:(nat->Prop)) (B_54:(nat->Prop)), ((((eq (nat->Prop)) A_69) B_54)->(((ord_less_eq_nat_o B_54) C_34)->((ord_less_eq_nat_o A_69) C_34)))).
% Axiom fact_327_order__antisym__conv:(forall (Y_28:((produc1572197287le_alt->Prop)->Prop)) (X_38:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_28) X_38)->((iff ((ord_le1027220427lt_o_o X_38) Y_28)) (((eq ((produc1572197287le_alt->Prop)->Prop)) X_38) Y_28)))).
% Axiom fact_328_order__antisym__conv:(forall (Y_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_38:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_28) X_38)->((iff ((ord_le1805007862lt_o_o X_38) Y_28)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_38) Y_28)))).
% Axiom fact_329_order__antisym__conv:(forall (Y_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_38:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_28) X_38)->((iff ((ord_le602483040lt_o_o X_38) Y_28)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_38) Y_28)))).
% Axiom fact_330_order__antisym__conv:(forall (Y_28:(produc1572197287le_alt->Prop)) (X_38:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_28) X_38)->((iff ((ord_le962286258_alt_o X_38) Y_28)) (((eq (produc1572197287le_alt->Prop)) X_38) Y_28)))).
% Axiom fact_331_order__antisym__conv:(forall (Y_28:Prop) (X_38:Prop), (((ord_less_eq_o Y_28) X_38)->((iff ((ord_less_eq_o X_38) Y_28)) ((iff X_38) Y_28)))).
% Axiom fact_332_order__antisym__conv:(forall (Y_28:(arrow_1196572341e_indi->Prop)) (X_38:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_28) X_38)->((iff ((ord_le865407012indi_o X_38) Y_28)) (((eq (arrow_1196572341e_indi->Prop)) X_38) Y_28)))).
% Axiom fact_333_order__antisym__conv:(forall (Y_28:(product_unit->Prop)) (X_38:(product_unit->Prop)), (((ord_le1511552390unit_o Y_28) X_38)->((iff ((ord_le1511552390unit_o X_38) Y_28)) (((eq (product_unit->Prop)) X_38) Y_28)))).
% Axiom fact_334_order__antisym__conv:(forall (Y_28:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_38:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_28) X_38)->((iff ((ord_le1463467535_alt_o X_38) Y_28)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_38) Y_28)))).
% Axiom fact_335_order__antisym__conv:(forall (Y_28:nat) (X_38:nat), (((ord_less_eq_nat Y_28) X_38)->((iff ((ord_less_eq_nat X_38) Y_28)) (((eq nat) X_38) Y_28)))).
% Axiom fact_336_order__antisym__conv:(forall (Y_28:(nat->Prop)) (X_38:(nat->Prop)), (((ord_less_eq_nat_o Y_28) X_38)->((iff ((ord_less_eq_nat_o X_38) Y_28)) (((eq (nat->Prop)) X_38) Y_28)))).
% Axiom fact_337_le__funD:(forall (X_37:(produc1572197287le_alt->Prop)) (F_26:((produc1572197287le_alt->Prop)->Prop)) (G_4:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))).
% Axiom fact_338_le__funD:(forall (X_37:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_26:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))).
% Axiom fact_339_le__funD:(forall (X_37:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_26:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))).
% Axiom fact_340_le__funD:(forall (X_37:produc1572197287le_alt) (F_26:(produc1572197287le_alt->Prop)) (G_4:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))).
% Axiom fact_341_le__funD:(forall (X_37:arrow_1196572341e_indi) (F_26:(arrow_1196572341e_indi->Prop)) (G_4:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))).
% Axiom fact_342_le__funD:(forall (X_37:product_unit) (F_26:(product_unit->Prop)) (G_4:(product_unit->Prop)), (((ord_le1511552390unit_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))).
% Axiom fact_343_le__funD:(forall (X_37:arrow_1389031998le_alt) (F_26:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_4:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o F_26) G_4)->((ord_le1423491573_alt_o (F_26 X_37)) (G_4 X_37)))).
% Axiom fact_344_le__funD:(forall (X_37:nat) (F_26:(nat->Prop)) (G_4:(nat->Prop)), (((ord_less_eq_nat_o F_26) G_4)->((ord_less_eq_o (F_26 X_37)) (G_4 X_37)))).
% Axiom fact_345_order__eq__refl:(forall (X_36:((produc1572197287le_alt->Prop)->Prop)) (Y_27:((produc1572197287le_alt->Prop)->Prop)), ((((eq ((produc1572197287le_alt->Prop)->Prop)) X_36) Y_27)->((ord_le1027220427lt_o_o X_36) Y_27))).
% Axiom fact_346_order__eq__refl:(forall (X_36:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_27:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_36) Y_27)->((ord_le1805007862lt_o_o X_36) Y_27))).
% Axiom fact_347_order__eq__refl:(forall (X_36:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_27:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_36) Y_27)->((ord_le602483040lt_o_o X_36) Y_27))).
% Axiom fact_348_order__eq__refl:(forall (X_36:(produc1572197287le_alt->Prop)) (Y_27:(produc1572197287le_alt->Prop)), ((((eq (produc1572197287le_alt->Prop)) X_36) Y_27)->((ord_le962286258_alt_o X_36) Y_27))).
% Axiom fact_349_order__eq__refl:(forall (Y_27:Prop) (X_36:Prop), (((iff X_36) Y_27)->((ord_less_eq_o X_36) Y_27))).
% Axiom fact_350_order__eq__refl:(forall (X_36:(arrow_1196572341e_indi->Prop)) (Y_27:(arrow_1196572341e_indi->Prop)), ((((eq (arrow_1196572341e_indi->Prop)) X_36) Y_27)->((ord_le865407012indi_o X_36) Y_27))).
% Axiom fact_351_order__eq__refl:(forall (X_36:(product_unit->Prop)) (Y_27:(product_unit->Prop)), ((((eq (product_unit->Prop)) X_36) Y_27)->((ord_le1511552390unit_o X_36) Y_27))).
% Axiom fact_352_order__eq__refl:(forall (X_36:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_27:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_36) Y_27)->((ord_le1463467535_alt_o X_36) Y_27))).
% Axiom fact_353_order__eq__refl:(forall (X_36:nat) (Y_27:nat), ((((eq nat) X_36) Y_27)->((ord_less_eq_nat X_36) Y_27))).
% Axiom fact_354_order__eq__refl:(forall (X_36:(nat->Prop)) (Y_27:(nat->Prop)), ((((eq (nat->Prop)) X_36) Y_27)->((ord_less_eq_nat_o X_36) Y_27))).
% Axiom fact_355_order__eq__iff:(forall (X_35:((produc1572197287le_alt->Prop)->Prop)) (Y_26:((produc1572197287le_alt->Prop)->Prop)), ((iff (((eq ((produc1572197287le_alt->Prop)->Prop)) X_35) Y_26)) ((and ((ord_le1027220427lt_o_o X_35) Y_26)) ((ord_le1027220427lt_o_o Y_26) X_35)))).
% Axiom fact_356_order__eq__iff:(forall (X_35:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_26:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_35) Y_26)) ((and ((ord_le1805007862lt_o_o X_35) Y_26)) ((ord_le1805007862lt_o_o Y_26) X_35)))).
% Axiom fact_357_order__eq__iff:(forall (X_35:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_26:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_35) Y_26)) ((and ((ord_le602483040lt_o_o X_35) Y_26)) ((ord_le602483040lt_o_o Y_26) X_35)))).
% Axiom fact_358_order__eq__iff:(forall (X_35:(produc1572197287le_alt->Prop)) (Y_26:(produc1572197287le_alt->Prop)), ((iff (((eq (produc1572197287le_alt->Prop)) X_35) Y_26)) ((and ((ord_le962286258_alt_o X_35) Y_26)) ((ord_le962286258_alt_o Y_26) X_35)))).
% Axiom fact_359_order__eq__iff:(forall (Y_26:Prop) (X_35:Prop), ((iff ((iff X_35) Y_26)) ((and ((ord_less_eq_o X_35) Y_26)) ((ord_less_eq_o Y_26) X_35)))).
% Axiom fact_360_order__eq__iff:(forall (X_35:(arrow_1196572341e_indi->Prop)) (Y_26:(arrow_1196572341e_indi->Prop)), ((iff (((eq (arrow_1196572341e_indi->Prop)) X_35) Y_26)) ((and ((ord_le865407012indi_o X_35) Y_26)) ((ord_le865407012indi_o Y_26) X_35)))).
% Axiom fact_361_order__eq__iff:(forall (X_35:(product_unit->Prop)) (Y_26:(product_unit->Prop)), ((iff (((eq (product_unit->Prop)) X_35) Y_26)) ((and ((ord_le1511552390unit_o X_35) Y_26)) ((ord_le1511552390unit_o Y_26) X_35)))).
% Axiom fact_362_order__eq__iff:(forall (X_35:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_26:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_35) Y_26)) ((and ((ord_le1463467535_alt_o X_35) Y_26)) ((ord_le1463467535_alt_o Y_26) X_35)))).
% Axiom fact_363_order__eq__iff:(forall (X_35:nat) (Y_26:nat), ((iff (((eq nat) X_35) Y_26)) ((and ((ord_less_eq_nat X_35) Y_26)) ((ord_less_eq_nat Y_26) X_35)))).
% Axiom fact_364_order__eq__iff:(forall (X_35:(nat->Prop)) (Y_26:(nat->Prop)), ((iff (((eq (nat->Prop)) X_35) Y_26)) ((and ((ord_less_eq_nat_o X_35) Y_26)) ((ord_less_eq_nat_o Y_26) X_35)))).
% Axiom fact_365_linorder__linear:(forall (X_34:nat) (Y_25:nat), ((or ((ord_less_eq_nat X_34) Y_25)) ((ord_less_eq_nat Y_25) X_34))).
% Axiom fact_366_le__fun__def:(forall (F_25:((produc1572197287le_alt->Prop)->Prop)) (G_3:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o F_25) G_3)) (forall (X_1:(produc1572197287le_alt->Prop)), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))).
% Axiom fact_367_le__fun__def:(forall (F_25:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o F_25) G_3)) (forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))).
% Axiom fact_368_le__fun__def:(forall (F_25:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o F_25) G_3)) (forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))).
% Axiom fact_369_le__fun__def:(forall (F_25:(produc1572197287le_alt->Prop)) (G_3:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o F_25) G_3)) (forall (X_1:produc1572197287le_alt), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))).
% Axiom fact_370_le__fun__def:(forall (F_25:(arrow_1196572341e_indi->Prop)) (G_3:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o F_25) G_3)) (forall (X_1:arrow_1196572341e_indi), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))).
% Axiom fact_371_le__fun__def:(forall (F_25:(product_unit->Prop)) (G_3:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o F_25) G_3)) (forall (X_1:product_unit), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))).
% Axiom fact_372_le__fun__def:(forall (F_25:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_3:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1463467535_alt_o F_25) G_3)) (forall (X_1:arrow_1389031998le_alt), ((ord_le1423491573_alt_o (F_25 X_1)) (G_3 X_1))))).
% Axiom fact_373_le__fun__def:(forall (F_25:(nat->Prop)) (G_3:(nat->Prop)), ((iff ((ord_less_eq_nat_o F_25) G_3)) (forall (X_1:nat), ((ord_less_eq_o (F_25 X_1)) (G_3 X_1))))).
% Axiom fact_374_linorder__not__less:(forall (X_33:nat) (Y_24:nat), ((iff (((ord_less_nat X_33) Y_24)->False)) ((ord_less_eq_nat Y_24) X_33))).
% Axiom fact_375_linorder__not__le:(forall (X_32:nat) (Y_23:nat), ((iff (((ord_less_eq_nat X_32) Y_23)->False)) ((ord_less_nat Y_23) X_32))).
% Axiom fact_376_linorder__le__less__linear:(forall (X_31:nat) (Y_22:nat), ((or ((ord_less_eq_nat X_31) Y_22)) ((ord_less_nat Y_22) X_31))).
% Axiom fact_377_order__less__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)) (not (((eq (product_unit->Prop)) X_30) Y_21))))).
% Axiom fact_378_order__less__le:(forall (X_30:(arrow_1196572341e_indi->Prop)) (Y_21:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o X_30) Y_21)) ((and ((ord_le865407012indi_o X_30) Y_21)) (not (((eq (arrow_1196572341e_indi->Prop)) X_30) Y_21))))).
% Axiom fact_379_order__less__le:(forall (X_30:((produc1572197287le_alt->Prop)->Prop)) (Y_21:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o X_30) Y_21)) ((and ((ord_le1027220427lt_o_o X_30) Y_21)) (not (((eq ((produc1572197287le_alt->Prop)->Prop)) X_30) Y_21))))).
% Axiom fact_380_order__less__le:(forall (X_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o X_30) Y_21)) ((and ((ord_le1805007862lt_o_o X_30) Y_21)) (not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_30) Y_21))))).
% Axiom fact_381_order__less__le:(forall (X_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o X_30) Y_21)) ((and ((ord_le602483040lt_o_o X_30) Y_21)) (not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_30) Y_21))))).
% Axiom fact_382_order__less__le:(forall (X_30:(produc1572197287le_alt->Prop)) (Y_21:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o X_30) Y_21)) ((and ((ord_le962286258_alt_o X_30) Y_21)) (not (((eq (produc1572197287le_alt->Prop)) X_30) Y_21))))).
% Axiom fact_383_order__less__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)) (((iff X_30) Y_21)->False)))).
% Axiom fact_384_order__less__le:(forall (X_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1339521307_alt_o X_30) Y_21)) ((and ((ord_le1463467535_alt_o X_30) Y_21)) (not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_30) Y_21))))).
% Axiom fact_385_order__less__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)) (not (((eq (nat->Prop)) X_30) Y_21))))).
% Axiom fact_386_order__less__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)) (not (((eq nat) X_30) Y_21))))).
% Axiom fact_387_less__le__not__le:(forall (X_29:(product_unit->Prop)) (Y_20:(product_unit->Prop)), ((iff ((ord_le232288914unit_o X_29) Y_20)) ((and ((ord_le1511552390unit_o X_29) Y_20)) (((ord_le1511552390unit_o Y_20) X_29)->False)))).
% Axiom fact_388_less__le__not__le:(forall (X_29:(arrow_1196572341e_indi->Prop)) (Y_20:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o X_29) Y_20)) ((and ((ord_le865407012indi_o X_29) Y_20)) (((ord_le865407012indi_o Y_20) X_29)->False)))).
% Axiom fact_389_less__le__not__le:(forall (X_29:((produc1572197287le_alt->Prop)->Prop)) (Y_20:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o X_29) Y_20)) ((and ((ord_le1027220427lt_o_o X_29) Y_20)) (((ord_le1027220427lt_o_o Y_20) X_29)->False)))).
% Axiom fact_390_less__le__not__le:(forall (X_29:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o X_29) Y_20)) ((and ((ord_le1805007862lt_o_o X_29) Y_20)) (((ord_le1805007862lt_o_o Y_20) X_29)->False)))).
% Axiom fact_391_less__le__not__le:(forall (X_29:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o X_29) Y_20)) ((and ((ord_le602483040lt_o_o X_29) Y_20)) (((ord_le602483040lt_o_o Y_20) X_29)->False)))).
% Axiom fact_392_less__le__not__le:(forall (X_29:(produc1572197287le_alt->Prop)) (Y_20:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o X_29) Y_20)) ((and ((ord_le962286258_alt_o X_29) Y_20)) (((ord_le962286258_alt_o Y_20) X_29)->False)))).
% Axiom fact_393_less__le__not__le:(forall (X_29:Prop) (Y_20:Prop), ((iff ((ord_less_o X_29) Y_20)) ((and ((ord_less_eq_o X_29) Y_20)) (((ord_less_eq_o Y_20) X_29)->False)))).
% Axiom fact_394_less__le__not__le:(forall (X_29:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_20:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1339521307_alt_o X_29) Y_20)) ((and ((ord_le1463467535_alt_o X_29) Y_20)) (((ord_le1463467535_alt_o Y_20) X_29)->False)))).
% Axiom fact_395_less__le__not__le:(forall (X_29:(nat->Prop)) (Y_20:(nat->Prop)), ((iff ((ord_less_nat_o X_29) Y_20)) ((and ((ord_less_eq_nat_o X_29) Y_20)) (((ord_less_eq_nat_o Y_20) X_29)->False)))).
% Axiom fact_396_less__le__not__le:(forall (X_29:nat) (Y_20:nat), ((iff ((ord_less_nat X_29) Y_20)) ((and ((ord_less_eq_nat X_29) Y_20)) (((ord_less_eq_nat Y_20) X_29)->False)))).
% Axiom fact_397_order__le__less:(forall (X_28:(product_unit->Prop)) (Y_19:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o X_28) Y_19)) ((or ((ord_le232288914unit_o X_28) Y_19)) (((eq (product_unit->Prop)) X_28) Y_19)))).
% Axiom fact_398_order__le__less:(forall (X_28:(arrow_1196572341e_indi->Prop)) (Y_19:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o X_28) Y_19)) ((or ((ord_le1991507760indi_o X_28) Y_19)) (((eq (arrow_1196572341e_indi->Prop)) X_28) Y_19)))).
% Axiom fact_399_order__le__less:(forall (X_28:((produc1572197287le_alt->Prop)->Prop)) (Y_19:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o X_28) Y_19)) ((or ((ord_le874404799lt_o_o X_28) Y_19)) (((eq ((produc1572197287le_alt->Prop)->Prop)) X_28) Y_19)))).
% Axiom fact_400_order__le__less:(forall (X_28:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o X_28) Y_19)) ((or ((ord_le1382328578lt_o_o X_28) Y_19)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_28) Y_19)))).
% Axiom fact_401_order__le__less:(forall (X_28:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o X_28) Y_19)) ((or ((ord_le914873172lt_o_o X_28) Y_19)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_28) Y_19)))).
% Axiom fact_402_order__le__less:(forall (X_28:(produc1572197287le_alt->Prop)) (Y_19:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o X_28) Y_19)) ((or ((ord_le1852932542_alt_o X_28) Y_19)) (((eq (produc1572197287le_alt->Prop)) X_28) Y_19)))).
% Axiom fact_403_order__le__less:(forall (X_28:Prop) (Y_19:Prop), ((iff ((ord_less_eq_o X_28) Y_19)) ((or ((ord_less_o X_28) Y_19)) ((iff X_28) Y_19)))).
% Axiom fact_404_order__le__less:(forall (X_28:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1463467535_alt_o X_28) Y_19)) ((or ((ord_le1339521307_alt_o X_28) Y_19)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_28) Y_19)))).
% Axiom fact_405_order__le__less:(forall (X_28:(nat->Prop)) (Y_19:(nat->Prop)), ((iff ((ord_less_eq_nat_o X_28) Y_19)) ((or ((ord_less_nat_o X_28) Y_19)) (((eq (nat->Prop)) X_28) Y_19)))).
% Axiom fact_406_order__le__less:(forall (X_28:nat) (Y_19:nat), ((iff ((ord_less_eq_nat X_28) Y_19)) ((or ((ord_less_nat X_28) Y_19)) (((eq nat) X_28) Y_19)))).
% Axiom fact_407_leI:(forall (X_27:nat) (Y_18:nat), ((((ord_less_nat X_27) Y_18)->False)->((ord_less_eq_nat Y_18) X_27))).
% Axiom fact_408_not__leE:(forall (Y_17:nat) (X_26:nat), ((((ord_less_eq_nat Y_17) X_26)->False)->((ord_less_nat X_26) Y_17))).
% Axiom fact_409_linorder__antisym__conv1:(forall (X_25:nat) (Y_16:nat), ((((ord_less_nat X_25) Y_16)->False)->((iff ((ord_less_eq_nat X_25) Y_16)) (((eq nat) X_25) Y_16)))).
% Axiom fact_410_order__neq__le__trans:(forall (A_68:(product_unit->Prop)) (B_53:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_68) B_53))->(((ord_le1511552390unit_o A_68) B_53)->((ord_le232288914unit_o A_68) B_53)))).
% Axiom fact_411_order__neq__le__trans:(forall (A_68:(arrow_1196572341e_indi->Prop)) (B_53:(arrow_1196572341e_indi->Prop)), ((not (((eq (arrow_1196572341e_indi->Prop)) A_68) B_53))->(((ord_le865407012indi_o A_68) B_53)->((ord_le1991507760indi_o A_68) B_53)))).
% Axiom fact_412_order__neq__le__trans:(forall (A_68:((produc1572197287le_alt->Prop)->Prop)) (B_53:((produc1572197287le_alt->Prop)->Prop)), ((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_68) B_53))->(((ord_le1027220427lt_o_o A_68) B_53)->((ord_le874404799lt_o_o A_68) B_53)))).
% Axiom fact_413_order__neq__le__trans:(forall (A_68:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_53:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_68) B_53))->(((ord_le1805007862lt_o_o A_68) B_53)->((ord_le1382328578lt_o_o A_68) B_53)))).
% Axiom fact_414_order__neq__le__trans:(forall (A_68:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_53:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_68) B_53))->(((ord_le602483040lt_o_o A_68) B_53)->((ord_le914873172lt_o_o A_68) B_53)))).
% Axiom fact_415_order__neq__le__trans:(forall (A_68:(produc1572197287le_alt->Prop)) (B_53:(produc1572197287le_alt->Prop)), ((not (((eq (produc1572197287le_alt->Prop)) A_68) B_53))->(((ord_le962286258_alt_o A_68) B_53)->((ord_le1852932542_alt_o A_68) B_53)))).
% Axiom fact_416_order__neq__le__trans:(forall (B_53:Prop) (A_68:Prop), ((((iff A_68) B_53)->False)->(((ord_less_eq_o A_68) B_53)->((ord_less_o A_68) B_53)))).
% Axiom fact_417_order__neq__le__trans:(forall (A_68:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_53:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_68) B_53))->(((ord_le1463467535_alt_o A_68) B_53)->((ord_le1339521307_alt_o A_68) B_53)))).
% Axiom fact_418_order__neq__le__trans:(forall (A_68:(nat->Prop)) (B_53:(nat->Prop)), ((not (((eq (nat->Prop)) A_68) B_53))->(((ord_less_eq_nat_o A_68) B_53)->((ord_less_nat_o A_68) B_53)))).
% Axiom fact_419_order__neq__le__trans:(forall (A_68:nat) (B_53:nat), ((not (((eq nat) A_68) B_53))->(((ord_less_eq_nat A_68) B_53)->((ord_less_nat A_68) B_53)))).
% Axiom fact_420_xt1_I12_J:(forall (A_67:(product_unit->Prop)) (B_52:(product_unit->Prop)), ((not (((eq (product_unit->Prop)) A_67) B_52))->(((ord_le1511552390unit_o B_52) A_67)->((ord_le232288914unit_o B_52) A_67)))).
% Axiom fact_421_xt1_I12_J:(forall (A_67:(arrow_1196572341e_indi->Prop)) (B_52:(arrow_1196572341e_indi->Prop)), ((not (((eq (arrow_1196572341e_indi->Prop)) A_67) B_52))->(((ord_le865407012indi_o B_52) A_67)->((ord_le1991507760indi_o B_52) A_67)))).
% Axiom fact_422_xt1_I12_J:(forall (A_67:((produc1572197287le_alt->Prop)->Prop)) (B_52:((produc1572197287le_alt->Prop)->Prop)), ((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_67) B_52))->(((ord_le1027220427lt_o_o B_52) A_67)->((ord_le874404799lt_o_o B_52) A_67)))).
% Axiom fact_423_xt1_I12_J:(forall (A_67:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_67) B_52))->(((ord_le1805007862lt_o_o B_52) A_67)->((ord_le1382328578lt_o_o B_52) A_67)))).
% Axiom fact_424_xt1_I12_J:(forall (A_67:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_67) B_52))->(((ord_le602483040lt_o_o B_52) A_67)->((ord_le914873172lt_o_o B_52) A_67)))).
% Axiom fact_425_xt1_I12_J:(forall (A_67:(produc1572197287le_alt->Prop)) (B_52:(produc1572197287le_alt->Prop)), ((not (((eq (produc1572197287le_alt->Prop)) A_67) B_52))->(((ord_le962286258_alt_o B_52) A_67)->((ord_le1852932542_alt_o B_52) A_67)))).
% Axiom fact_426_xt1_I12_J:(forall (B_52:Prop) (A_67:Prop), ((((iff A_67) B_52)->False)->(((ord_less_eq_o B_52) A_67)->((ord_less_o B_52) A_67)))).
% Axiom fact_427_xt1_I12_J:(forall (A_67:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_52:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_67) B_52))->(((ord_le1463467535_alt_o B_52) A_67)->((ord_le1339521307_alt_o B_52) A_67)))).
% Axiom fact_428_xt1_I12_J:(forall (A_67:(nat->Prop)) (B_52:(nat->Prop)), ((not (((eq (nat->Prop)) A_67) B_52))->(((ord_less_eq_nat_o B_52) A_67)->((ord_less_nat_o B_52) A_67)))).
% Axiom fact_429_xt1_I12_J:(forall (A_67:nat) (B_52:nat), ((not (((eq nat) A_67) B_52))->(((ord_less_eq_nat B_52) A_67)->((ord_less_nat B_52) A_67)))).
% Axiom fact_430_leD:(forall (Y_15:nat) (X_24:nat), (((ord_less_eq_nat Y_15) X_24)->(((ord_less_nat X_24) Y_15)->False))).
% Axiom fact_431_order__less__imp__le:(forall (X_23:(product_unit->Prop)) (Y_14:(product_unit->Prop)), (((ord_le232288914unit_o X_23) Y_14)->((ord_le1511552390unit_o X_23) Y_14))).
% Axiom fact_432_order__less__imp__le:(forall (X_23:(arrow_1196572341e_indi->Prop)) (Y_14:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_23) Y_14)->((ord_le865407012indi_o X_23) Y_14))).
% Axiom fact_433_order__less__imp__le:(forall (X_23:((produc1572197287le_alt->Prop)->Prop)) (Y_14:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o X_23) Y_14)->((ord_le1027220427lt_o_o X_23) Y_14))).
% Axiom fact_434_order__less__imp__le:(forall (X_23:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o X_23) Y_14)->((ord_le1805007862lt_o_o X_23) Y_14))).
% Axiom fact_435_order__less__imp__le:(forall (X_23:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o X_23) Y_14)->((ord_le602483040lt_o_o X_23) Y_14))).
% Axiom fact_436_order__less__imp__le:(forall (X_23:(produc1572197287le_alt->Prop)) (Y_14:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o X_23) Y_14)->((ord_le962286258_alt_o X_23) Y_14))).
% Axiom fact_437_order__less__imp__le:(forall (X_23:Prop) (Y_14:Prop), (((ord_less_o X_23) Y_14)->((ord_less_eq_o X_23) Y_14))).
% Axiom fact_438_order__less__imp__le:(forall (X_23:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_14:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o X_23) Y_14)->((ord_le1463467535_alt_o X_23) Y_14))).
% Axiom fact_439_order__less__imp__le:(forall (X_23:(nat->Prop)) (Y_14:(nat->Prop)), (((ord_less_nat_o X_23) Y_14)->((ord_less_eq_nat_o X_23) Y_14))).
% Axiom fact_440_order__less__imp__le:(forall (X_23:nat) (Y_14:nat), (((ord_less_nat X_23) Y_14)->((ord_less_eq_nat X_23) Y_14))).
% Axiom fact_441_linorder__antisym__conv2:(forall (X_22:nat) (Y_13:nat), (((ord_less_eq_nat X_22) Y_13)->((iff (((ord_less_nat X_22) Y_13)->False)) (((eq nat) X_22) Y_13)))).
% Axiom fact_442_order__le__imp__less__or__eq:(forall (X_21:(product_unit->Prop)) (Y_12:(product_unit->Prop)), (((ord_le1511552390unit_o X_21) Y_12)->((or ((ord_le232288914unit_o X_21) Y_12)) (((eq (product_unit->Prop)) X_21) Y_12)))).
% Axiom fact_443_order__le__imp__less__or__eq:(forall (X_21:(arrow_1196572341e_indi->Prop)) (Y_12:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_21) Y_12)->((or ((ord_le1991507760indi_o X_21) Y_12)) (((eq (arrow_1196572341e_indi->Prop)) X_21) Y_12)))).
% Axiom fact_444_order__le__imp__less__or__eq:(forall (X_21:((produc1572197287le_alt->Prop)->Prop)) (Y_12:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_21) Y_12)->((or ((ord_le874404799lt_o_o X_21) Y_12)) (((eq ((produc1572197287le_alt->Prop)->Prop)) X_21) Y_12)))).
% Axiom fact_445_order__le__imp__less__or__eq:(forall (X_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_12:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_21) Y_12)->((or ((ord_le1382328578lt_o_o X_21) Y_12)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) X_21) Y_12)))).
% Axiom fact_446_order__le__imp__less__or__eq:(forall (X_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_21) Y_12)->((or ((ord_le914873172lt_o_o X_21) Y_12)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) X_21) Y_12)))).
% Axiom fact_447_order__le__imp__less__or__eq:(forall (X_21:(produc1572197287le_alt->Prop)) (Y_12:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_21) Y_12)->((or ((ord_le1852932542_alt_o X_21) Y_12)) (((eq (produc1572197287le_alt->Prop)) X_21) Y_12)))).
% Axiom fact_448_order__le__imp__less__or__eq:(forall (X_21:Prop) (Y_12:Prop), (((ord_less_eq_o X_21) Y_12)->((or ((ord_less_o X_21) Y_12)) ((iff X_21) Y_12)))).
% Axiom fact_449_order__le__imp__less__or__eq:(forall (X_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_12:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_21) Y_12)->((or ((ord_le1339521307_alt_o X_21) Y_12)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) X_21) Y_12)))).
% Axiom fact_450_order__le__imp__less__or__eq:(forall (X_21:(nat->Prop)) (Y_12:(nat->Prop)), (((ord_less_eq_nat_o X_21) Y_12)->((or ((ord_less_nat_o X_21) Y_12)) (((eq (nat->Prop)) X_21) Y_12)))).
% Axiom fact_451_order__le__imp__less__or__eq:(forall (X_21:nat) (Y_12:nat), (((ord_less_eq_nat X_21) Y_12)->((or ((ord_less_nat X_21) Y_12)) (((eq nat) X_21) Y_12)))).
% Axiom fact_452_order__le__neq__trans:(forall (A_66:(product_unit->Prop)) (B_51:(product_unit->Prop)), (((ord_le1511552390unit_o A_66) B_51)->((not (((eq (product_unit->Prop)) A_66) B_51))->((ord_le232288914unit_o A_66) B_51)))).
% Axiom fact_453_order__le__neq__trans:(forall (A_66:(arrow_1196572341e_indi->Prop)) (B_51:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_66) B_51)->((not (((eq (arrow_1196572341e_indi->Prop)) A_66) B_51))->((ord_le1991507760indi_o A_66) B_51)))).
% Axiom fact_454_order__le__neq__trans:(forall (A_66:((produc1572197287le_alt->Prop)->Prop)) (B_51:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_66) B_51)->((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_66) B_51))->((ord_le874404799lt_o_o A_66) B_51)))).
% Axiom fact_455_order__le__neq__trans:(forall (A_66:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_51:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_66) B_51)->((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_66) B_51))->((ord_le1382328578lt_o_o A_66) B_51)))).
% Axiom fact_456_order__le__neq__trans:(forall (A_66:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_51:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_66) B_51)->((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_66) B_51))->((ord_le914873172lt_o_o A_66) B_51)))).
% Axiom fact_457_order__le__neq__trans:(forall (A_66:(produc1572197287le_alt->Prop)) (B_51:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_66) B_51)->((not (((eq (produc1572197287le_alt->Prop)) A_66) B_51))->((ord_le1852932542_alt_o A_66) B_51)))).
% Axiom fact_458_order__le__neq__trans:(forall (A_66:Prop) (B_51:Prop), (((ord_less_eq_o A_66) B_51)->((((iff A_66) B_51)->False)->((ord_less_o A_66) B_51)))).
% Axiom fact_459_order__le__neq__trans:(forall (A_66:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_51:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_66) B_51)->((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_66) B_51))->((ord_le1339521307_alt_o A_66) B_51)))).
% Axiom fact_460_order__le__neq__trans:(forall (A_66:(nat->Prop)) (B_51:(nat->Prop)), (((ord_less_eq_nat_o A_66) B_51)->((not (((eq (nat->Prop)) A_66) B_51))->((ord_less_nat_o A_66) B_51)))).
% Axiom fact_461_order__le__neq__trans:(forall (A_66:nat) (B_51:nat), (((ord_less_eq_nat A_66) B_51)->((not (((eq nat) A_66) B_51))->((ord_less_nat A_66) B_51)))).
% Axiom fact_462_xt1_I11_J:(forall (B_50:(product_unit->Prop)) (A_65:(product_unit->Prop)), (((ord_le1511552390unit_o B_50) A_65)->((not (((eq (product_unit->Prop)) A_65) B_50))->((ord_le232288914unit_o B_50) A_65)))).
% Axiom fact_463_xt1_I11_J:(forall (B_50:(arrow_1196572341e_indi->Prop)) (A_65:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_50) A_65)->((not (((eq (arrow_1196572341e_indi->Prop)) A_65) B_50))->((ord_le1991507760indi_o B_50) A_65)))).
% Axiom fact_464_xt1_I11_J:(forall (B_50:((produc1572197287le_alt->Prop)->Prop)) (A_65:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_50) A_65)->((not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_65) B_50))->((ord_le874404799lt_o_o B_50) A_65)))).
% Axiom fact_465_xt1_I11_J:(forall (B_50:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_65:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_50) A_65)->((not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_65) B_50))->((ord_le1382328578lt_o_o B_50) A_65)))).
% Axiom fact_466_xt1_I11_J:(forall (B_50:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_65:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_50) A_65)->((not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_65) B_50))->((ord_le914873172lt_o_o B_50) A_65)))).
% Axiom fact_467_xt1_I11_J:(forall (B_50:(produc1572197287le_alt->Prop)) (A_65:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_50) A_65)->((not (((eq (produc1572197287le_alt->Prop)) A_65) B_50))->((ord_le1852932542_alt_o B_50) A_65)))).
% Axiom fact_468_xt1_I11_J:(forall (B_50:Prop) (A_65:Prop), (((ord_less_eq_o B_50) A_65)->((((iff A_65) B_50)->False)->((ord_less_o B_50) A_65)))).
% Axiom fact_469_xt1_I11_J:(forall (B_50:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_65:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_50) A_65)->((not (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_65) B_50))->((ord_le1339521307_alt_o B_50) A_65)))).
% Axiom fact_470_xt1_I11_J:(forall (B_50:(nat->Prop)) (A_65:(nat->Prop)), (((ord_less_eq_nat_o B_50) A_65)->((not (((eq (nat->Prop)) A_65) B_50))->((ord_less_nat_o B_50) A_65)))).
% Axiom fact_471_xt1_I11_J:(forall (B_50:nat) (A_65:nat), (((ord_less_eq_nat B_50) A_65)->((not (((eq nat) A_65) B_50))->((ord_less_nat B_50) A_65)))).
% Axiom fact_472_order__less__le__trans:(forall (Z_4:(product_unit->Prop)) (X_20:(product_unit->Prop)) (Y_11:(product_unit->Prop)), (((ord_le232288914unit_o X_20) Y_11)->(((ord_le1511552390unit_o Y_11) Z_4)->((ord_le232288914unit_o X_20) Z_4)))).
% Axiom fact_473_order__less__le__trans:(forall (Z_4:(arrow_1196572341e_indi->Prop)) (X_20:(arrow_1196572341e_indi->Prop)) (Y_11:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_20) Y_11)->(((ord_le865407012indi_o Y_11) Z_4)->((ord_le1991507760indi_o X_20) Z_4)))).
% Axiom fact_474_order__less__le__trans:(forall (Z_4:((produc1572197287le_alt->Prop)->Prop)) (X_20:((produc1572197287le_alt->Prop)->Prop)) (Y_11:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o X_20) Y_11)->(((ord_le1027220427lt_o_o Y_11) Z_4)->((ord_le874404799lt_o_o X_20) Z_4)))).
% Axiom fact_475_order__less__le__trans:(forall (Z_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_11:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o X_20) Y_11)->(((ord_le1805007862lt_o_o Y_11) Z_4)->((ord_le1382328578lt_o_o X_20) Z_4)))).
% Axiom fact_476_order__less__le__trans:(forall (Z_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_11:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o X_20) Y_11)->(((ord_le602483040lt_o_o Y_11) Z_4)->((ord_le914873172lt_o_o X_20) Z_4)))).
% Axiom fact_477_order__less__le__trans:(forall (Z_4:(produc1572197287le_alt->Prop)) (X_20:(produc1572197287le_alt->Prop)) (Y_11:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o X_20) Y_11)->(((ord_le962286258_alt_o Y_11) Z_4)->((ord_le1852932542_alt_o X_20) Z_4)))).
% Axiom fact_478_order__less__le__trans:(forall (Z_4:Prop) (X_20:Prop) (Y_11:Prop), (((ord_less_o X_20) Y_11)->(((ord_less_eq_o Y_11) Z_4)->((ord_less_o X_20) Z_4)))).
% Axiom fact_479_order__less__le__trans:(forall (Z_4:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_20:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_11:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o X_20) Y_11)->(((ord_le1463467535_alt_o Y_11) Z_4)->((ord_le1339521307_alt_o X_20) Z_4)))).
% Axiom fact_480_order__less__le__trans:(forall (Z_4:(nat->Prop)) (X_20:(nat->Prop)) (Y_11:(nat->Prop)), (((ord_less_nat_o X_20) Y_11)->(((ord_less_eq_nat_o Y_11) Z_4)->((ord_less_nat_o X_20) Z_4)))).
% Axiom fact_481_order__less__le__trans:(forall (Z_4:nat) (X_20:nat) (Y_11:nat), (((ord_less_nat X_20) Y_11)->(((ord_less_eq_nat Y_11) Z_4)->((ord_less_nat X_20) Z_4)))).
% Axiom fact_482_xt1_I7_J:(forall (Z_3:(product_unit->Prop)) (Y_10:(product_unit->Prop)) (X_19:(product_unit->Prop)), (((ord_le232288914unit_o Y_10) X_19)->(((ord_le1511552390unit_o Z_3) Y_10)->((ord_le232288914unit_o Z_3) X_19)))).
% Axiom fact_483_xt1_I7_J:(forall (Z_3:(arrow_1196572341e_indi->Prop)) (Y_10:(arrow_1196572341e_indi->Prop)) (X_19:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_10) X_19)->(((ord_le865407012indi_o Z_3) Y_10)->((ord_le1991507760indi_o Z_3) X_19)))).
% Axiom fact_484_xt1_I7_J:(forall (Z_3:((produc1572197287le_alt->Prop)->Prop)) (Y_10:((produc1572197287le_alt->Prop)->Prop)) (X_19:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o Y_10) X_19)->(((ord_le1027220427lt_o_o Z_3) Y_10)->((ord_le874404799lt_o_o Z_3) X_19)))).
% Axiom fact_485_xt1_I7_J:(forall (Z_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o Y_10) X_19)->(((ord_le1805007862lt_o_o Z_3) Y_10)->((ord_le1382328578lt_o_o Z_3) X_19)))).
% Axiom fact_486_xt1_I7_J:(forall (Z_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_10:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o Y_10) X_19)->(((ord_le602483040lt_o_o Z_3) Y_10)->((ord_le914873172lt_o_o Z_3) X_19)))).
% Axiom fact_487_xt1_I7_J:(forall (Z_3:(produc1572197287le_alt->Prop)) (Y_10:(produc1572197287le_alt->Prop)) (X_19:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o Y_10) X_19)->(((ord_le962286258_alt_o Z_3) Y_10)->((ord_le1852932542_alt_o Z_3) X_19)))).
% Axiom fact_488_xt1_I7_J:(forall (Z_3:Prop) (Y_10:Prop) (X_19:Prop), (((ord_less_o Y_10) X_19)->(((ord_less_eq_o Z_3) Y_10)->((ord_less_o Z_3) X_19)))).
% Axiom fact_489_xt1_I7_J:(forall (Z_3:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_10:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o Y_10) X_19)->(((ord_le1463467535_alt_o Z_3) Y_10)->((ord_le1339521307_alt_o Z_3) X_19)))).
% Axiom fact_490_xt1_I7_J:(forall (Z_3:(nat->Prop)) (Y_10:(nat->Prop)) (X_19:(nat->Prop)), (((ord_less_nat_o Y_10) X_19)->(((ord_less_eq_nat_o Z_3) Y_10)->((ord_less_nat_o Z_3) X_19)))).
% Axiom fact_491_xt1_I7_J:(forall (Z_3:nat) (Y_10:nat) (X_19:nat), (((ord_less_nat Y_10) X_19)->(((ord_less_eq_nat Z_3) Y_10)->((ord_less_nat Z_3) X_19)))).
% Axiom fact_492_order__le__less__trans:(forall (Z_2:(product_unit->Prop)) (X_18:(product_unit->Prop)) (Y_9:(product_unit->Prop)), (((ord_le1511552390unit_o X_18) Y_9)->(((ord_le232288914unit_o Y_9) Z_2)->((ord_le232288914unit_o X_18) Z_2)))).
% Axiom fact_493_order__le__less__trans:(forall (Z_2:(arrow_1196572341e_indi->Prop)) (X_18:(arrow_1196572341e_indi->Prop)) (Y_9:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_18) Y_9)->(((ord_le1991507760indi_o Y_9) Z_2)->((ord_le1991507760indi_o X_18) Z_2)))).
% Axiom fact_494_order__le__less__trans:(forall (Z_2:((produc1572197287le_alt->Prop)->Prop)) (X_18:((produc1572197287le_alt->Prop)->Prop)) (Y_9:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_18) Y_9)->(((ord_le874404799lt_o_o Y_9) Z_2)->((ord_le874404799lt_o_o X_18) Z_2)))).
% Axiom fact_495_order__le__less__trans:(forall (Z_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_18:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_9:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_18) Y_9)->(((ord_le1382328578lt_o_o Y_9) Z_2)->((ord_le1382328578lt_o_o X_18) Z_2)))).
% Axiom fact_496_order__le__less__trans:(forall (Z_2:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_18:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_9:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_18) Y_9)->(((ord_le914873172lt_o_o Y_9) Z_2)->((ord_le914873172lt_o_o X_18) Z_2)))).
% Axiom fact_497_order__le__less__trans:(forall (Z_2:(produc1572197287le_alt->Prop)) (X_18:(produc1572197287le_alt->Prop)) (Y_9:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_18) Y_9)->(((ord_le1852932542_alt_o Y_9) Z_2)->((ord_le1852932542_alt_o X_18) Z_2)))).
% Axiom fact_498_order__le__less__trans:(forall (Z_2:Prop) (X_18:Prop) (Y_9:Prop), (((ord_less_eq_o X_18) Y_9)->(((ord_less_o Y_9) Z_2)->((ord_less_o X_18) Z_2)))).
% Axiom fact_499_order__le__less__trans:(forall (Z_2:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_18:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_9:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_18) Y_9)->(((ord_le1339521307_alt_o Y_9) Z_2)->((ord_le1339521307_alt_o X_18) Z_2)))).
% Axiom fact_500_order__le__less__trans:(forall (Z_2:(nat->Prop)) (X_18:(nat->Prop)) (Y_9:(nat->Prop)), (((ord_less_eq_nat_o X_18) Y_9)->(((ord_less_nat_o Y_9) Z_2)->((ord_less_nat_o X_18) Z_2)))).
% Axiom fact_501_order__le__less__trans:(forall (Z_2:nat) (X_18:nat) (Y_9:nat), (((ord_less_eq_nat X_18) Y_9)->(((ord_less_nat Y_9) Z_2)->((ord_less_nat X_18) Z_2)))).
% Axiom fact_502_xt1_I8_J:(forall (Z_1:(product_unit->Prop)) (Y_8:(product_unit->Prop)) (X_17:(product_unit->Prop)), (((ord_le1511552390unit_o Y_8) X_17)->(((ord_le232288914unit_o Z_1) Y_8)->((ord_le232288914unit_o Z_1) X_17)))).
% Axiom fact_503_xt1_I8_J:(forall (Z_1:(arrow_1196572341e_indi->Prop)) (Y_8:(arrow_1196572341e_indi->Prop)) (X_17:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_8) X_17)->(((ord_le1991507760indi_o Z_1) Y_8)->((ord_le1991507760indi_o Z_1) X_17)))).
% Axiom fact_504_xt1_I8_J:(forall (Z_1:((produc1572197287le_alt->Prop)->Prop)) (Y_8:((produc1572197287le_alt->Prop)->Prop)) (X_17:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_8) X_17)->(((ord_le874404799lt_o_o Z_1) Y_8)->((ord_le874404799lt_o_o Z_1) X_17)))).
% Axiom fact_505_xt1_I8_J:(forall (Z_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_17:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_8) X_17)->(((ord_le1382328578lt_o_o Z_1) Y_8)->((ord_le1382328578lt_o_o Z_1) X_17)))).
% Axiom fact_506_xt1_I8_J:(forall (Z_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_17:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_8) X_17)->(((ord_le914873172lt_o_o Z_1) Y_8)->((ord_le914873172lt_o_o Z_1) X_17)))).
% Axiom fact_507_xt1_I8_J:(forall (Z_1:(produc1572197287le_alt->Prop)) (Y_8:(produc1572197287le_alt->Prop)) (X_17:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_8) X_17)->(((ord_le1852932542_alt_o Z_1) Y_8)->((ord_le1852932542_alt_o Z_1) X_17)))).
% Axiom fact_508_xt1_I8_J:(forall (Z_1:Prop) (Y_8:Prop) (X_17:Prop), (((ord_less_eq_o Y_8) X_17)->(((ord_less_o Z_1) Y_8)->((ord_less_o Z_1) X_17)))).
% Axiom fact_509_xt1_I8_J:(forall (Z_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_8:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (X_17:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_8) X_17)->(((ord_le1339521307_alt_o Z_1) Y_8)->((ord_le1339521307_alt_o Z_1) X_17)))).
% Axiom fact_510_xt1_I8_J:(forall (Z_1:(nat->Prop)) (Y_8:(nat->Prop)) (X_17:(nat->Prop)), (((ord_less_eq_nat_o Y_8) X_17)->(((ord_less_nat_o Z_1) Y_8)->((ord_less_nat_o Z_1) X_17)))).
% Axiom fact_511_xt1_I8_J:(forall (Z_1:nat) (Y_8:nat) (X_17:nat), (((ord_less_eq_nat Y_8) X_17)->(((ord_less_nat Z_1) Y_8)->((ord_less_nat Z_1) X_17)))).
% Axiom fact_512_top__greatest:(forall (A_64:((produc1572197287le_alt->Prop)->Prop)), ((ord_le1027220427lt_o_o A_64) top_to1806834203lt_o_o)).
% Axiom fact_513_top__greatest:(forall (A_64:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((ord_le602483040lt_o_o A_64) top_to732317616lt_o_o)).
% Axiom fact_514_top__greatest:(forall (A_64:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((ord_le1805007862lt_o_o A_64) top_to1492351398lt_o_o)).
% Axiom fact_515_top__greatest:(forall (A_64:Prop), ((ord_less_eq_o A_64) top_top_o)).
% Axiom fact_516_top__greatest:(forall (A_64:(produc1572197287le_alt->Prop)), ((ord_le962286258_alt_o A_64) top_to558618722_alt_o)).
% Axiom fact_517_top__greatest:(forall (A_64:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((ord_le1463467535_alt_o A_64) top_to1627321279_alt_o)).
% Axiom fact_518_top__greatest:(forall (A_64:(arrow_1196572341e_indi->Prop)), ((ord_le865407012indi_o A_64) top_to54564308indi_o)).
% Axiom fact_519_top__greatest:(forall (A_64:(nat->Prop)), ((ord_less_eq_nat_o A_64) top_top_nat_o)).
% Axiom fact_520_top__greatest:(forall (A_64:(product_unit->Prop)), ((ord_le1511552390unit_o A_64) top_to1984820022unit_o)).
% Axiom fact_521_top__unique:(forall (A_63:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o top_to1806834203lt_o_o) A_63)) (((eq ((produc1572197287le_alt->Prop)->Prop)) A_63) top_to1806834203lt_o_o))).
% Axiom fact_522_top__unique:(forall (A_63:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o top_to732317616lt_o_o) A_63)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_63) top_to732317616lt_o_o))).
% Axiom fact_523_top__unique:(forall (A_63:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o top_to1492351398lt_o_o) A_63)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_63) top_to1492351398lt_o_o))).
% Axiom fact_524_top__unique:(forall (A_63:Prop), ((iff ((ord_less_eq_o top_top_o) A_63)) ((iff A_63) top_top_o))).
% Axiom fact_525_top__unique:(forall (A_63:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o top_to558618722_alt_o) A_63)) (((eq (produc1572197287le_alt->Prop)) A_63) top_to558618722_alt_o))).
% Axiom fact_526_top__unique:(forall (A_63:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1463467535_alt_o top_to1627321279_alt_o) A_63)) (((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_63) top_to1627321279_alt_o))).
% Axiom fact_527_top__unique:(forall (A_63:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o top_to54564308indi_o) A_63)) (((eq (arrow_1196572341e_indi->Prop)) A_63) top_to54564308indi_o))).
% Axiom fact_528_top__unique:(forall (A_63:(nat->Prop)), ((iff ((ord_less_eq_nat_o top_top_nat_o) A_63)) (((eq (nat->Prop)) A_63) top_top_nat_o))).
% Axiom fact_529_top__unique:(forall (A_63:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o top_to1984820022unit_o) A_63)) (((eq (product_unit->Prop)) A_63) top_to1984820022unit_o))).
% Axiom fact_530_top__le:(forall (A_62:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o top_to1806834203lt_o_o) A_62)->(((eq ((produc1572197287le_alt->Prop)->Prop)) A_62) top_to1806834203lt_o_o))).
% Axiom fact_531_top__le:(forall (A_62:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o top_to732317616lt_o_o) A_62)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_62) top_to732317616lt_o_o))).
% Axiom fact_532_top__le:(forall (A_62:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o top_to1492351398lt_o_o) A_62)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_62) top_to1492351398lt_o_o))).
% Axiom fact_533_top__le:(forall (A_62:Prop), (((ord_less_eq_o top_top_o) A_62)->((iff A_62) top_top_o))).
% Axiom fact_534_top__le:(forall (A_62:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o top_to558618722_alt_o) A_62)->(((eq (produc1572197287le_alt->Prop)) A_62) top_to558618722_alt_o))).
% Axiom fact_535_top__le:(forall (A_62:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o top_to1627321279_alt_o) A_62)->(((eq (arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) A_62) top_to1627321279_alt_o))).
% Axiom fact_536_top__le:(forall (A_62:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o top_to54564308indi_o) A_62)->(((eq (arrow_1196572341e_indi->Prop)) A_62) top_to54564308indi_o))).
% Axiom fact_537_top__le:(forall (A_62:(nat->Prop)), (((ord_less_eq_nat_o top_top_nat_o) A_62)->(((eq (nat->Prop)) A_62) top_top_nat_o))).
% Axiom fact_538_top__le:(forall (A_62:(product_unit->Prop)), (((ord_le1511552390unit_o top_to1984820022unit_o) A_62)->(((eq (product_unit->Prop)) A_62) top_to1984820022unit_o))).
% Axiom fact_539_inj__on__def:(forall (F_24:(arrow_1196572341e_indi->nat)) (A_61:(arrow_1196572341e_indi->Prop)), ((iff ((inj_on1505595958di_nat F_24) A_61)) (forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_61)->(forall (Xa:arrow_1196572341e_indi), (((member1818997282e_indi Xa) A_61)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq arrow_1196572341e_indi) X_1) Xa)))))))).
% Axiom fact_540_inj__on__def:(forall (F_24:(nat->nat)) (A_61:(nat->Prop)), ((iff ((inj_on_nat_nat F_24) A_61)) (forall (X_1:nat), (((member_nat X_1) A_61)->(forall (Xa:nat), (((member_nat Xa) A_61)->((((eq nat) (F_24 X_1)) (F_24 Xa))->(((eq nat) X_1) Xa)))))))).
% Axiom fact_541_inj__on__contraD:(forall (X_16:arrow_1196572341e_indi) (Y_7:arrow_1196572341e_indi) (F_23:(arrow_1196572341e_indi->nat)) (A_60:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_23) A_60)->((not (((eq arrow_1196572341e_indi) X_16) Y_7))->(((member1818997282e_indi X_16) A_60)->(((member1818997282e_indi Y_7) A_60)->(not (((eq nat) (F_23 X_16)) (F_23 Y_7)))))))).
% Axiom fact_542_inj__on__contraD:(forall (X_16:nat) (Y_7:nat) (F_23:(nat->nat)) (A_60:(nat->Prop)), (((inj_on_nat_nat F_23) A_60)->((not (((eq nat) X_16) Y_7))->(((member_nat X_16) A_60)->(((member_nat Y_7) A_60)->(not (((eq nat) (F_23 X_16)) (F_23 Y_7)))))))).
% Axiom fact_543_inj__on__iff:(forall (Y_6:arrow_1196572341e_indi) (X_15:arrow_1196572341e_indi) (F_22:(arrow_1196572341e_indi->nat)) (A_59:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_22) A_59)->(((member1818997282e_indi X_15) A_59)->(((member1818997282e_indi Y_6) A_59)->((iff (((eq nat) (F_22 X_15)) (F_22 Y_6))) (((eq arrow_1196572341e_indi) X_15) Y_6)))))).
% Axiom fact_544_inj__on__iff:(forall (Y_6:nat) (X_15:nat) (F_22:(nat->nat)) (A_59:(nat->Prop)), (((inj_on_nat_nat F_22) A_59)->(((member_nat X_15) A_59)->(((member_nat Y_6) A_59)->((iff (((eq nat) (F_22 X_15)) (F_22 Y_6))) (((eq nat) X_15) Y_6)))))).
% Axiom fact_545_inj__onD:(forall (X_14:arrow_1196572341e_indi) (Y_5:arrow_1196572341e_indi) (F_21:(arrow_1196572341e_indi->nat)) (A_58:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_21) A_58)->((((eq nat) (F_21 X_14)) (F_21 Y_5))->(((member1818997282e_indi X_14) A_58)->(((member1818997282e_indi Y_5) A_58)->(((eq arrow_1196572341e_indi) X_14) Y_5)))))).
% Axiom fact_546_inj__onD:(forall (X_14:nat) (Y_5:nat) (F_21:(nat->nat)) (A_58:(nat->Prop)), (((inj_on_nat_nat F_21) A_58)->((((eq nat) (F_21 X_14)) (F_21 Y_5))->(((member_nat X_14) A_58)->(((member_nat Y_5) A_58)->(((eq nat) X_14) Y_5)))))).
% Axiom fact_547_Pi__mem:(forall (X_13:produc1572197287le_alt) (F_20:(produc1572197287le_alt->Prop)) (A_57:(produc1572197287le_alt->Prop)) (B_49:(produc1572197287le_alt->(Prop->Prop))), (((member1241905979_alt_o F_20) ((pi_Pro418549519_alt_o A_57) B_49))->(((member285112084le_alt X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_548_Pi__mem:(forall (X_13:produc1572197287le_alt) (F_20:(produc1572197287le_alt->arrow_1196572341e_indi)) (A_57:(produc1572197287le_alt->Prop)) (B_49:(produc1572197287le_alt->(arrow_1196572341e_indi->Prop))), (((member1074431551e_indi F_20) ((pi_Pro1246947541e_indi A_57) B_49))->(((member285112084le_alt X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_549_Pi__mem:(forall (X_13:produc1572197287le_alt) (F_20:(produc1572197287le_alt->product_unit)) (A_57:(produc1572197287le_alt->Prop)) (B_49:(produc1572197287le_alt->(product_unit->Prop))), (((member44534621t_unit F_20) ((pi_Pro926528371t_unit A_57) B_49))->(((member285112084le_alt X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_550_Pi__mem:(forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1186582243e_indi F_20) ((pi_Arr272777533e_indi A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_551_Pi__mem:(forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1696373143lt_o_o F_20) ((pi_Arr1709554855lt_o_o A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_552_Pi__mem:(forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1537523201t_unit F_20) ((pi_Arr509685723t_unit A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_553_Pi__mem:(forall (X_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_49:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))), (((member1539010427e_indi F_20) ((pi_Arr470535441e_indi A_57) B_49))->(((member1425217232_alt_o X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_554_Pi__mem:(forall (X_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_49:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))), (((member1346253567lt_o_o F_20) ((pi_Arr1865419731lt_o_o A_57) B_49))->(((member1425217232_alt_o X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_555_Pi__mem:(forall (X_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (A_57:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_49:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))), (((member1043380889t_unit F_20) ((pi_Arr2096782767t_unit A_57) B_49))->(((member1425217232_alt_o X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_556_Pi__mem:(forall (X_13:(produc1572197287le_alt->Prop)) (F_20:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (A_57:((produc1572197287le_alt->Prop)->Prop)) (B_49:((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))), (((member1830244024e_indi F_20) ((pi_Pro2039443474e_indi A_57) B_49))->(((member1241905979_alt_o X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_557_Pi__mem:(forall (X_13:(produc1572197287le_alt->Prop)) (F_20:((produc1572197287le_alt->Prop)->Prop)) (A_57:((produc1572197287le_alt->Prop)->Prop)) (B_49:((produc1572197287le_alt->Prop)->(Prop->Prop))), (((member1925470338lt_o_o F_20) ((pi_Pro386796690lt_o_o A_57) B_49))->(((member1241905979_alt_o X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_558_Pi__mem:(forall (X_13:(produc1572197287le_alt->Prop)) (F_20:((produc1572197287le_alt->Prop)->product_unit)) (A_57:((produc1572197287le_alt->Prop)->Prop)) (B_49:((produc1572197287le_alt->Prop)->(product_unit->Prop))), (((member1092867670t_unit F_20) ((pi_Pro30504752t_unit A_57) B_49))->(((member1241905979_alt_o X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_559_Pi__mem:(forall (X_13:nat) (F_20:(nat->arrow_1196572341e_indi)) (A_57:(nat->Prop)) (B_49:(nat->(arrow_1196572341e_indi->Prop))), (((member1113138010e_indi F_20) ((pi_nat986275508e_indi A_57) B_49))->(((member_nat X_13) A_57)->((member1818997282e_indi (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_560_Pi__mem:(forall (X_13:nat) (F_20:(nat->Prop)) (A_57:(nat->Prop)) (B_49:(nat->(Prop->Prop))), (((member_nat_o F_20) ((pi_nat_o A_57) B_49))->(((member_nat X_13) A_57)->((member_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_561_Pi__mem:(forall (X_13:nat) (F_20:(nat->product_unit)) (A_57:(nat->Prop)) (B_49:(nat->(product_unit->Prop))), (((member616671224t_unit F_20) ((pi_nat_Product_unit A_57) B_49))->(((member_nat X_13) A_57)->((member_Product_unit (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_562_Pi__mem:(forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->produc1572197287le_alt)) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member232085823le_alt F_20) ((pi_Arr1762714837le_alt A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member285112084le_alt (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_563_Pi__mem:(forall (X_13:Prop) (F_20:(Prop->produc1572197287le_alt)) (A_57:(Prop->Prop)) (B_49:(Prop->(produc1572197287le_alt->Prop))), (((member1158049649le_alt F_20) ((pi_o_P728361163le_alt A_57) B_49))->(((member_o X_13) A_57)->((member285112084le_alt (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_564_Pi__mem:(forall (X_13:product_unit) (F_20:(product_unit->produc1572197287le_alt)) (A_57:(product_unit->Prop)) (B_49:(product_unit->(produc1572197287le_alt->Prop))), (((member1161214429le_alt F_20) ((pi_Pro772884595le_alt A_57) B_49))->(((member_Product_unit X_13) A_57)->((member285112084le_alt (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_565_Pi__mem:(forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2071265553_alt_o F_20) ((pi_Arr456308197_alt_o A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member822980838_alt_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_566_Pi__mem:(forall (X_13:Prop) (F_20:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_57:(Prop->Prop)) (B_49:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member984757343_alt_o F_20) ((pi_o_A1479825007_alt_o A_57) B_49))->(((member_o X_13) A_57)->((member822980838_alt_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_567_Pi__mem:(forall (X_13:product_unit) (F_20:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_57:(product_unit->Prop)) (B_49:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))), (((member2021528307_alt_o F_20) ((pi_Pro1959068871_alt_o A_57) B_49))->(((member_Product_unit X_13) A_57)->((member822980838_alt_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_568_Pi__mem:(forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1521294075_alt_o F_20) ((pi_Arr583278353_alt_o A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member1425217232_alt_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_569_Pi__mem:(forall (X_13:Prop) (F_20:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_57:(Prop->Prop)) (B_49:(Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member161783341_alt_o F_20) ((pi_o_A1994447367_alt_o A_57) B_49))->(((member_o X_13) A_57)->((member1425217232_alt_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_570_Pi__mem:(forall (X_13:product_unit) (F_20:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_57:(product_unit->Prop)) (B_49:(product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))), (((member1888392857_alt_o F_20) ((pi_Pro443817391_alt_o A_57) B_49))->(((member_Product_unit X_13) A_57)->((member1425217232_alt_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_571_Pi__mem:(forall (X_13:Prop) (F_20:(Prop->(produc1572197287le_alt->Prop))) (A_57:(Prop->Prop)) (B_49:(Prop->((produc1572197287le_alt->Prop)->Prop))), (((member1495989556_alt_o F_20) ((pi_o_P1417870404_alt_o A_57) B_49))->(((member_o X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_572_Pi__mem:(forall (X_13:product_unit) (F_20:(product_unit->(produc1572197287le_alt->Prop))) (A_57:(product_unit->Prop)) (B_49:(product_unit->((produc1572197287le_alt->Prop)->Prop))), (((member1295651272_alt_o F_20) ((pi_Pro29851292_alt_o A_57) B_49))->(((member_Product_unit X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_573_Pi__mem:(forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->nat)) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->(nat->Prop))), (((member1842285448di_nat F_20) ((pi_Arr778514268di_nat A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member_nat (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_574_Pi__mem:(forall (X_13:Prop) (F_20:(Prop->nat)) (A_57:(Prop->Prop)) (B_49:(Prop->(nat->Prop))), (((member_o_nat F_20) ((pi_o_nat A_57) B_49))->(((member_o X_13) A_57)->((member_nat (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_575_Pi__mem:(forall (X_13:product_unit) (F_20:(product_unit->nat)) (A_57:(product_unit->Prop)) (B_49:(product_unit->(nat->Prop))), (((member1827227242it_nat F_20) ((pi_Product_unit_nat A_57) B_49))->(((member_Product_unit X_13) A_57)->((member_nat (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_576_Pi__mem:(forall (X_13:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_57:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_49:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))), (((member1425217232_alt_o F_20) ((pi_Arr1196397536_alt_o A_57) B_49))->(((member822980838_alt_o X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_577_Pi__mem:(forall (X_13:arrow_1196572341e_indi) (F_20:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_57:(arrow_1196572341e_indi->Prop)) (B_49:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))), (((member822980838_alt_o F_20) ((pi_Arr1309696186_alt_o A_57) B_49))->(((member1818997282e_indi X_13) A_57)->((member1241905979_alt_o (F_20 X_13)) (B_49 X_13))))).
% Axiom fact_578_below__Lin:(forall (L_2:(produc1572197287le_alt->Prop)) (X:arrow_1389031998le_alt) (Y:arrow_1389031998le_alt), ((not (((eq arrow_1389031998le_alt) X) Y))->(((member1241905979_alt_o L_2) arrow_1982173296le_Lin)->((member1241905979_alt_o (((arrow_1865170000_below L_2) X) Y)) arrow_1982173296le_Lin)))).
% Axiom fact_579_Prof__def:(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) arrow_1647925946e_Prof) ((pi_Arr1309696186_alt_o top_to54564308indi_o) (fun (Uu:arrow_1196572341e_indi)=> arrow_1982173296le_Lin))).
% Axiom fact_580_inj__on__id2:(forall (A_56:(nat->Prop)), ((inj_on_nat_nat (fun (X_1:nat)=> X_1)) A_56)).
% Axiom fact_581_funcset__mem:(forall (X_12:produc1572197287le_alt) (F_19:(produc1572197287le_alt->Prop)) (A_55:(produc1572197287le_alt->Prop)) (B_48:(Prop->Prop)), (((member1241905979_alt_o F_19) ((pi_Pro418549519_alt_o A_55) (fun (Uu:produc1572197287le_alt)=> B_48)))->(((member285112084le_alt X_12) A_55)->((member_o (F_19 X_12)) B_48)))).
% Axiom fact_582_funcset__mem:(forall (X_12:produc1572197287le_alt) (F_19:(produc1572197287le_alt->arrow_1196572341e_indi)) (A_55:(produc1572197287le_alt->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1074431551e_indi F_19) ((pi_Pro1246947541e_indi A_55) (fun (Uu:produc1572197287le_alt)=> B_48)))->(((member285112084le_alt X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48)))).
% Axiom fact_583_funcset__mem:(forall (X_12:produc1572197287le_alt) (F_19:(produc1572197287le_alt->product_unit)) (A_55:(produc1572197287le_alt->Prop)) (B_48:(product_unit->Prop)), (((member44534621t_unit F_19) ((pi_Pro926528371t_unit A_55) (fun (Uu:produc1572197287le_alt)=> B_48)))->(((member285112084le_alt X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48)))).
% Axiom fact_584_funcset__mem:(forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1186582243e_indi F_19) ((pi_Arr272777533e_indi A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48)))).
% Axiom fact_585_funcset__mem:(forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:(Prop->Prop)), (((member1696373143lt_o_o F_19) ((pi_Arr1709554855lt_o_o A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member_o (F_19 X_12)) B_48)))).
% Axiom fact_586_funcset__mem:(forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:(product_unit->Prop)), (((member1537523201t_unit F_19) ((pi_Arr509685723t_unit A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48)))).
% Axiom fact_587_funcset__mem:(forall (X_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (A_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1539010427e_indi F_19) ((pi_Arr470535441e_indi A_55) (fun (Uu:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> B_48)))->(((member1425217232_alt_o X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48)))).
% Axiom fact_588_funcset__mem:(forall (X_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_48:(Prop->Prop)), (((member1346253567lt_o_o F_19) ((pi_Arr1865419731lt_o_o A_55) (fun (Uu:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> B_48)))->(((member1425217232_alt_o X_12) A_55)->((member_o (F_19 X_12)) B_48)))).
% Axiom fact_589_funcset__mem:(forall (X_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (F_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (A_55:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_48:(product_unit->Prop)), (((member1043380889t_unit F_19) ((pi_Arr2096782767t_unit A_55) (fun (Uu:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> B_48)))->(((member1425217232_alt_o X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48)))).
% Axiom fact_590_funcset__mem:(forall (X_12:(produc1572197287le_alt->Prop)) (F_19:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (A_55:((produc1572197287le_alt->Prop)->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1830244024e_indi F_19) ((pi_Pro2039443474e_indi A_55) (fun (Uu:(produc1572197287le_alt->Prop))=> B_48)))->(((member1241905979_alt_o X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48)))).
% Axiom fact_591_funcset__mem:(forall (X_12:(produc1572197287le_alt->Prop)) (F_19:((produc1572197287le_alt->Prop)->Prop)) (A_55:((produc1572197287le_alt->Prop)->Prop)) (B_48:(Prop->Prop)), (((member1925470338lt_o_o F_19) ((pi_Pro386796690lt_o_o A_55) (fun (Uu:(produc1572197287le_alt->Prop))=> B_48)))->(((member1241905979_alt_o X_12) A_55)->((member_o (F_19 X_12)) B_48)))).
% Axiom fact_592_funcset__mem:(forall (X_12:(produc1572197287le_alt->Prop)) (F_19:((produc1572197287le_alt->Prop)->product_unit)) (A_55:((produc1572197287le_alt->Prop)->Prop)) (B_48:(product_unit->Prop)), (((member1092867670t_unit F_19) ((pi_Pro30504752t_unit A_55) (fun (Uu:(produc1572197287le_alt->Prop))=> B_48)))->(((member1241905979_alt_o X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48)))).
% Axiom fact_593_funcset__mem:(forall (X_12:nat) (F_19:(nat->arrow_1196572341e_indi)) (A_55:(nat->Prop)) (B_48:(arrow_1196572341e_indi->Prop)), (((member1113138010e_indi F_19) ((pi_nat986275508e_indi A_55) (fun (Uu:nat)=> B_48)))->(((member_nat X_12) A_55)->((member1818997282e_indi (F_19 X_12)) B_48)))).
% Axiom fact_594_funcset__mem:(forall (X_12:nat) (F_19:(nat->Prop)) (A_55:(nat->Prop)) (B_48:(Prop->Prop)), (((member_nat_o F_19) ((pi_nat_o A_55) (fun (Uu:nat)=> B_48)))->(((member_nat X_12) A_55)->((member_o (F_19 X_12)) B_48)))).
% Axiom fact_595_funcset__mem:(forall (X_12:nat) (F_19:(nat->product_unit)) (A_55:(nat->Prop)) (B_48:(product_unit->Prop)), (((member616671224t_unit F_19) ((pi_nat_Product_unit A_55) (fun (Uu:nat)=> B_48)))->(((member_nat X_12) A_55)->((member_Product_unit (F_19 X_12)) B_48)))).
% Axiom fact_596_funcset__mem:(forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->produc1572197287le_alt)) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:(produc1572197287le_alt->Prop)), (((member232085823le_alt F_19) ((pi_Arr1762714837le_alt A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member285112084le_alt (F_19 X_12)) B_48)))).
% Axiom fact_597_funcset__mem:(forall (X_12:Prop) (F_19:(Prop->produc1572197287le_alt)) (A_55:(Prop->Prop)) (B_48:(produc1572197287le_alt->Prop)), (((member1158049649le_alt F_19) ((pi_o_P728361163le_alt A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member285112084le_alt (F_19 X_12)) B_48)))).
% Axiom fact_598_funcset__mem:(forall (X_12:product_unit) (F_19:(product_unit->produc1572197287le_alt)) (A_55:(product_unit->Prop)) (B_48:(produc1572197287le_alt->Prop)), (((member1161214429le_alt F_19) ((pi_Pro772884595le_alt A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member285112084le_alt (F_19 X_12)) B_48)))).
% Axiom fact_599_funcset__mem:(forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member2071265553_alt_o F_19) ((pi_Arr456308197_alt_o A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member822980838_alt_o (F_19 X_12)) B_48)))).
% Axiom fact_600_funcset__mem:(forall (X_12:Prop) (F_19:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_55:(Prop->Prop)) (B_48:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member984757343_alt_o F_19) ((pi_o_A1479825007_alt_o A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member822980838_alt_o (F_19 X_12)) B_48)))).
% Axiom fact_601_funcset__mem:(forall (X_12:product_unit) (F_19:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (A_55:(product_unit->Prop)) (B_48:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member2021528307_alt_o F_19) ((pi_Pro1959068871_alt_o A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member822980838_alt_o (F_19 X_12)) B_48)))).
% Axiom fact_602_funcset__mem:(forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member1521294075_alt_o F_19) ((pi_Arr583278353_alt_o A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member1425217232_alt_o (F_19 X_12)) B_48)))).
% Axiom fact_603_funcset__mem:(forall (X_12:Prop) (F_19:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_55:(Prop->Prop)) (B_48:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member161783341_alt_o F_19) ((pi_o_A1994447367_alt_o A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member1425217232_alt_o (F_19 X_12)) B_48)))).
% Axiom fact_604_funcset__mem:(forall (X_12:product_unit) (F_19:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (A_55:(product_unit->Prop)) (B_48:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member1888392857_alt_o F_19) ((pi_Pro443817391_alt_o A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member1425217232_alt_o (F_19 X_12)) B_48)))).
% Axiom fact_605_funcset__mem:(forall (X_12:Prop) (F_19:(Prop->(produc1572197287le_alt->Prop))) (A_55:(Prop->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member1495989556_alt_o F_19) ((pi_o_P1417870404_alt_o A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48)))).
% Axiom fact_606_funcset__mem:(forall (X_12:product_unit) (F_19:(product_unit->(produc1572197287le_alt->Prop))) (A_55:(product_unit->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member1295651272_alt_o F_19) ((pi_Pro29851292_alt_o A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48)))).
% Axiom fact_607_funcset__mem:(forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->nat)) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:(nat->Prop)), (((member1842285448di_nat F_19) ((pi_Arr778514268di_nat A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member_nat (F_19 X_12)) B_48)))).
% Axiom fact_608_funcset__mem:(forall (X_12:Prop) (F_19:(Prop->nat)) (A_55:(Prop->Prop)) (B_48:(nat->Prop)), (((member_o_nat F_19) ((pi_o_nat A_55) (fun (Uu:Prop)=> B_48)))->(((member_o X_12) A_55)->((member_nat (F_19 X_12)) B_48)))).
% Axiom fact_609_funcset__mem:(forall (X_12:product_unit) (F_19:(product_unit->nat)) (A_55:(product_unit->Prop)) (B_48:(nat->Prop)), (((member1827227242it_nat F_19) ((pi_Product_unit_nat A_55) (fun (Uu:product_unit)=> B_48)))->(((member_Product_unit X_12) A_55)->((member_nat (F_19 X_12)) B_48)))).
% Axiom fact_610_funcset__mem:(forall (X_12:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (F_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_55:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member1425217232_alt_o F_19) ((pi_Arr1196397536_alt_o A_55) (fun (Uu:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> B_48)))->(((member822980838_alt_o X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48)))).
% Axiom fact_611_funcset__mem:(forall (X_12:arrow_1196572341e_indi) (F_19:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_55:(arrow_1196572341e_indi->Prop)) (B_48:((produc1572197287le_alt->Prop)->Prop)), (((member822980838_alt_o F_19) ((pi_Arr1309696186_alt_o A_55) (fun (Uu:arrow_1196572341e_indi)=> B_48)))->(((member1818997282e_indi X_12) A_55)->((member1241905979_alt_o (F_19 X_12)) B_48)))).
% Axiom fact_612_inj__eq:(forall (X_11:arrow_1196572341e_indi) (Y_4:arrow_1196572341e_indi) (F_18:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_18) top_to54564308indi_o)->((iff (((eq nat) (F_18 X_11)) (F_18 Y_4))) (((eq arrow_1196572341e_indi) X_11) Y_4)))).
% Axiom fact_613_inj__eq:(forall (X_11:nat) (Y_4:nat) (F_18:(nat->nat)), (((inj_on_nat_nat F_18) top_top_nat_o)->((iff (((eq nat) (F_18 X_11)) (F_18 Y_4))) (((eq nat) X_11) Y_4)))).
% Axiom fact_614_injD:(forall (X_10:arrow_1196572341e_indi) (Y_3:arrow_1196572341e_indi) (F_17:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_17) top_to54564308indi_o)->((((eq nat) (F_17 X_10)) (F_17 Y_3))->(((eq arrow_1196572341e_indi) X_10) Y_3)))).
% Axiom fact_615_injD:(forall (X_10:nat) (Y_3:nat) (F_17:(nat->nat)), (((inj_on_nat_nat F_17) top_top_nat_o)->((((eq nat) (F_17 X_10)) (F_17 Y_3))->(((eq nat) X_10) Y_3)))).
% Axiom fact_616_inv__into__f__f:(forall (X_9:arrow_1196572341e_indi) (F_16:(arrow_1196572341e_indi->nat)) (A_54:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_16) A_54)->(((member1818997282e_indi X_9) A_54)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat A_54) F_16) (F_16 X_9))) X_9)))).
% Axiom fact_617_inv__into__f__f:(forall (X_9:nat) (F_16:(nat->nat)) (A_54:(nat->Prop)), (((inj_on_nat_nat F_16) A_54)->(((member_nat X_9) A_54)->(((eq nat) (((hilber195283148at_nat A_54) F_16) (F_16 X_9))) X_9)))).
% Axiom fact_618_inv__into__f__eq:(forall (Y_2:nat) (X_8:arrow_1196572341e_indi) (F_15:(arrow_1196572341e_indi->nat)) (A_53:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_15) A_53)->(((member1818997282e_indi X_8) A_53)->((((eq nat) (F_15 X_8)) Y_2)->(((eq arrow_1196572341e_indi) (((hilber1125280539di_nat A_53) F_15) Y_2)) X_8))))).
% Axiom fact_619_inv__into__f__eq:(forall (Y_2:nat) (X_8:nat) (F_15:(nat->nat)) (A_53:(nat->Prop)), (((inj_on_nat_nat F_15) A_53)->(((member_nat X_8) A_53)->((((eq nat) (F_15 X_8)) Y_2)->(((eq nat) (((hilber195283148at_nat A_53) F_15) Y_2)) X_8))))).
% Axiom fact_620_Pi__I:(forall (F_14:(produc1572197287le_alt->arrow_1196572341e_indi)) (B_47:(produc1572197287le_alt->(arrow_1196572341e_indi->Prop))) (A_52:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), (((member285112084le_alt X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1074431551e_indi F_14) ((pi_Pro1246947541e_indi A_52) B_47)))).
% Axiom fact_621_Pi__I:(forall (F_14:(produc1572197287le_alt->product_unit)) (B_47:(produc1572197287le_alt->(product_unit->Prop))) (A_52:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), (((member285112084le_alt X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member44534621t_unit F_14) ((pi_Pro926528371t_unit A_52) B_47)))).
% Axiom fact_622_Pi__I:(forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1186582243e_indi F_14) ((pi_Arr272777533e_indi A_52) B_47)))).
% Axiom fact_623_Pi__I:(forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(Prop->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1696373143lt_o_o F_14) ((pi_Arr1709554855lt_o_o A_52) B_47)))).
% Axiom fact_624_Pi__I:(forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->product_unit)) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(product_unit->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member1537523201t_unit F_14) ((pi_Arr509685723t_unit A_52) B_47)))).
% Axiom fact_625_Pi__I:(forall (F_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->arrow_1196572341e_indi)) (B_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(arrow_1196572341e_indi->Prop))) (A_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1539010427e_indi F_14) ((pi_Arr470535441e_indi A_52) B_47)))).
% Axiom fact_626_Pi__I:(forall (F_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(Prop->Prop))) (A_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1346253567lt_o_o F_14) ((pi_Arr1865419731lt_o_o A_52) B_47)))).
% Axiom fact_627_Pi__I:(forall (F_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->product_unit)) (B_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->(product_unit->Prop))) (A_52:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), (((member1425217232_alt_o X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member1043380889t_unit F_14) ((pi_Arr2096782767t_unit A_52) B_47)))).
% Axiom fact_628_Pi__I:(forall (F_14:((produc1572197287le_alt->Prop)->arrow_1196572341e_indi)) (B_47:((produc1572197287le_alt->Prop)->(arrow_1196572341e_indi->Prop))) (A_52:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1830244024e_indi F_14) ((pi_Pro2039443474e_indi A_52) B_47)))).
% Axiom fact_629_Pi__I:(forall (F_14:((produc1572197287le_alt->Prop)->Prop)) (B_47:((produc1572197287le_alt->Prop)->(Prop->Prop))) (A_52:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1925470338lt_o_o F_14) ((pi_Pro386796690lt_o_o A_52) B_47)))).
% Axiom fact_630_Pi__I:(forall (F_14:((produc1572197287le_alt->Prop)->product_unit)) (B_47:((produc1572197287le_alt->Prop)->(product_unit->Prop))) (A_52:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), (((member1241905979_alt_o X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member1092867670t_unit F_14) ((pi_Pro30504752t_unit A_52) B_47)))).
% Axiom fact_631_Pi__I:(forall (F_14:(nat->arrow_1196572341e_indi)) (B_47:(nat->(arrow_1196572341e_indi->Prop))) (A_52:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_52)->((member1818997282e_indi (F_14 X_1)) (B_47 X_1))))->((member1113138010e_indi F_14) ((pi_nat986275508e_indi A_52) B_47)))).
% Axiom fact_632_Pi__I:(forall (F_14:(nat->Prop)) (B_47:(nat->(Prop->Prop))) (A_52:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member_nat_o F_14) ((pi_nat_o A_52) B_47)))).
% Axiom fact_633_Pi__I:(forall (F_14:(nat->product_unit)) (B_47:(nat->(product_unit->Prop))) (A_52:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) A_52)->((member_Product_unit (F_14 X_1)) (B_47 X_1))))->((member616671224t_unit F_14) ((pi_nat_Product_unit A_52) B_47)))).
% Axiom fact_634_Pi__I:(forall (F_14:(arrow_1196572341e_indi->produc1572197287le_alt)) (B_47:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member285112084le_alt (F_14 X_1)) (B_47 X_1))))->((member232085823le_alt F_14) ((pi_Arr1762714837le_alt A_52) B_47)))).
% Axiom fact_635_Pi__I:(forall (F_14:(Prop->produc1572197287le_alt)) (B_47:(Prop->(produc1572197287le_alt->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member285112084le_alt (F_14 X_1)) (B_47 X_1))))->((member1158049649le_alt F_14) ((pi_o_P728361163le_alt A_52) B_47)))).
% Axiom fact_636_Pi__I:(forall (F_14:(product_unit->produc1572197287le_alt)) (B_47:(product_unit->(produc1572197287le_alt->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member285112084le_alt (F_14 X_1)) (B_47 X_1))))->((member1161214429le_alt F_14) ((pi_Pro772884595le_alt A_52) B_47)))).
% Axiom fact_637_Pi__I:(forall (F_14:(arrow_1196572341e_indi->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (B_47:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member822980838_alt_o (F_14 X_1)) (B_47 X_1))))->((member2071265553_alt_o F_14) ((pi_Arr456308197_alt_o A_52) B_47)))).
% Axiom fact_638_Pi__I:(forall (F_14:(Prop->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (B_47:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member822980838_alt_o (F_14 X_1)) (B_47 X_1))))->((member984757343_alt_o F_14) ((pi_o_A1479825007_alt_o A_52) B_47)))).
% Axiom fact_639_Pi__I:(forall (F_14:(product_unit->(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))) (B_47:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member822980838_alt_o (F_14 X_1)) (B_47 X_1))))->((member2021528307_alt_o F_14) ((pi_Pro1959068871_alt_o A_52) B_47)))).
% Axiom fact_640_Pi__I:(forall (F_14:(arrow_1196572341e_indi->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (B_47:(arrow_1196572341e_indi->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member1425217232_alt_o (F_14 X_1)) (B_47 X_1))))->((member1521294075_alt_o F_14) ((pi_Arr583278353_alt_o A_52) B_47)))).
% Axiom fact_641_Pi__I:(forall (F_14:(Prop->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (B_47:(Prop->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member1425217232_alt_o (F_14 X_1)) (B_47 X_1))))->((member161783341_alt_o F_14) ((pi_o_A1994447367_alt_o A_52) B_47)))).
% Axiom fact_642_Pi__I:(forall (F_14:(product_unit->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))) (B_47:(product_unit->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member1425217232_alt_o (F_14 X_1)) (B_47 X_1))))->((member1888392857_alt_o F_14) ((pi_Pro443817391_alt_o A_52) B_47)))).
% Axiom fact_643_Pi__I:(forall (F_14:(Prop->(produc1572197287le_alt->Prop))) (B_47:(Prop->((produc1572197287le_alt->Prop)->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member1495989556_alt_o F_14) ((pi_o_P1417870404_alt_o A_52) B_47)))).
% Axiom fact_644_Pi__I:(forall (F_14:(product_unit->(produc1572197287le_alt->Prop))) (B_47:(product_unit->((produc1572197287le_alt->Prop)->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member1295651272_alt_o F_14) ((pi_Pro29851292_alt_o A_52) B_47)))).
% Axiom fact_645_Pi__I:(forall (F_14:(arrow_1196572341e_indi->nat)) (B_47:(arrow_1196572341e_indi->(nat->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member_nat (F_14 X_1)) (B_47 X_1))))->((member1842285448di_nat F_14) ((pi_Arr778514268di_nat A_52) B_47)))).
% Axiom fact_646_Pi__I:(forall (F_14:(Prop->nat)) (B_47:(Prop->(nat->Prop))) (A_52:(Prop->Prop)), ((forall (X_1:Prop), (((member_o X_1) A_52)->((member_nat (F_14 X_1)) (B_47 X_1))))->((member_o_nat F_14) ((pi_o_nat A_52) B_47)))).
% Axiom fact_647_Pi__I:(forall (F_14:(product_unit->nat)) (B_47:(product_unit->(nat->Prop))) (A_52:(product_unit->Prop)), ((forall (X_1:product_unit), (((member_Product_unit X_1) A_52)->((member_nat (F_14 X_1)) (B_47 X_1))))->((member1827227242it_nat F_14) ((pi_Product_unit_nat A_52) B_47)))).
% Axiom fact_648_Pi__I:(forall (F_14:(produc1572197287le_alt->Prop)) (B_47:(produc1572197287le_alt->(Prop->Prop))) (A_52:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), (((member285112084le_alt X_1) A_52)->((member_o (F_14 X_1)) (B_47 X_1))))->((member1241905979_alt_o F_14) ((pi_Pro418549519_alt_o A_52) B_47)))).
% Axiom fact_649_Pi__I:(forall (F_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (B_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))) (A_52:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), (((member822980838_alt_o X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member1425217232_alt_o F_14) ((pi_Arr1196397536_alt_o A_52) B_47)))).
% Axiom fact_650_Pi__I:(forall (F_14:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (B_47:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))) (A_52:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), (((member1818997282e_indi X_1) A_52)->((member1241905979_alt_o (F_14 X_1)) (B_47 X_1))))->((member822980838_alt_o F_14) ((pi_Arr1309696186_alt_o A_52) B_47)))).
% Axiom fact_651_inj__imp__inv__eq:(forall (G_2:(nat->arrow_1196572341e_indi)) (F_13:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat F_13) top_to54564308indi_o)->((forall (X_1:nat), (((eq nat) (F_13 (G_2 X_1))) X_1))->(((eq (nat->arrow_1196572341e_indi)) ((hilber1125280539di_nat top_to54564308indi_o) F_13)) G_2)))).
% Axiom fact_652_inj__imp__inv__eq:(forall (G_2:(nat->nat)) (F_13:(nat->nat)), (((inj_on_nat_nat F_13) top_top_nat_o)->((forall (X_1:nat), (((eq nat) (F_13 (G_2 X_1))) X_1))->(((eq (nat->nat)) ((hilber195283148at_nat top_top_nat_o) F_13)) G_2)))).
% Axiom fact_653_less__add__one:(forall (A_51:nat), ((ord_less_nat A_51) ((plus_plus_nat A_51) one_one_nat))).
% Axiom fact_654_add__less__le__mono:(forall (C_33:nat) (D_3:nat) (A_50:nat) (B_46:nat), (((ord_less_nat A_50) B_46)->(((ord_less_eq_nat C_33) D_3)->((ord_less_nat ((plus_plus_nat A_50) C_33)) ((plus_plus_nat B_46) D_3))))).
% Axiom fact_655_add__le__less__mono:(forall (C_32:nat) (D_2:nat) (A_49:nat) (B_45:nat), (((ord_less_eq_nat A_49) B_45)->(((ord_less_nat C_32) D_2)->((ord_less_nat ((plus_plus_nat A_49) C_32)) ((plus_plus_nat B_45) D_2))))).
% Axiom fact_656_injI:(forall (F_12:(arrow_1196572341e_indi->nat)), ((forall (X_1:arrow_1196572341e_indi) (Y_1:arrow_1196572341e_indi), ((((eq nat) (F_12 X_1)) (F_12 Y_1))->(((eq arrow_1196572341e_indi) X_1) Y_1)))->((inj_on1505595958di_nat F_12) top_to54564308indi_o))).
% Axiom fact_657_injI:(forall (F_12:(nat->nat)), ((forall (X_1:nat) (Y_1:nat), ((((eq nat) (F_12 X_1)) (F_12 Y_1))->(((eq nat) X_1) Y_1)))->((inj_on_nat_nat F_12) top_top_nat_o))).
% Axiom fact_658_xt5:(forall (C_31:(nat->Prop)) (F_11:((nat->Prop)->(nat->Prop))) (B_44:(nat->Prop)) (A_48:(nat->Prop)), (((ord_less_nat_o B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48)))))).
% Axiom fact_659_xt5:(forall (C_31:(nat->Prop)) (F_11:((product_unit->Prop)->(nat->Prop))) (B_44:(product_unit->Prop)) (A_48:(product_unit->Prop)), (((ord_le232288914unit_o B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48)))))).
% Axiom fact_660_xt5:(forall (C_31:(nat->Prop)) (F_11:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_44:(arrow_1196572341e_indi->Prop)) (A_48:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48)))))).
% Axiom fact_661_xt5:(forall (C_31:(nat->Prop)) (F_11:(nat->(nat->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_less_eq_nat_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_nat_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat_o C_31) (F_11 A_48)))))).
% Axiom fact_662_xt5:(forall (C_31:(product_unit->Prop)) (F_11:(nat->(product_unit->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1511552390unit_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le232288914unit_o (F_11 Y_1)) (F_11 X_1))))->((ord_le232288914unit_o C_31) (F_11 A_48)))))).
% Axiom fact_663_xt5:(forall (C_31:(arrow_1196572341e_indi->Prop)) (F_11:(nat->(arrow_1196572341e_indi->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le865407012indi_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1991507760indi_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1991507760indi_o C_31) (F_11 A_48)))))).
% Axiom fact_664_xt5:(forall (C_31:((produc1572197287le_alt->Prop)->Prop)) (F_11:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1027220427lt_o_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le874404799lt_o_o (F_11 Y_1)) (F_11 X_1))))->((ord_le874404799lt_o_o C_31) (F_11 A_48)))))).
% Axiom fact_665_xt5:(forall (C_31:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_11:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1805007862lt_o_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1382328578lt_o_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1382328578lt_o_o C_31) (F_11 A_48)))))).
% Axiom fact_666_xt5:(forall (C_31:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_11:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le602483040lt_o_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le914873172lt_o_o (F_11 Y_1)) (F_11 X_1))))->((ord_le914873172lt_o_o C_31) (F_11 A_48)))))).
% Axiom fact_667_xt5:(forall (C_31:(produc1572197287le_alt->Prop)) (F_11:(nat->(produc1572197287le_alt->Prop))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le962286258_alt_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1852932542_alt_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1852932542_alt_o C_31) (F_11 A_48)))))).
% Axiom fact_668_xt5:(forall (C_31:Prop) (F_11:(nat->Prop)) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_less_eq_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_o (F_11 Y_1)) (F_11 X_1))))->((ord_less_o C_31) (F_11 A_48)))))).
% Axiom fact_669_xt5:(forall (C_31:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_11:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_44:nat) (A_48:nat), (((ord_less_nat B_44) A_48)->(((ord_le1463467535_alt_o C_31) (F_11 B_44))->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1339521307_alt_o (F_11 Y_1)) (F_11 X_1))))->((ord_le1339521307_alt_o C_31) (F_11 A_48)))))).
% Axiom fact_670_xt5:(forall (C_31:nat) (F_11:((nat->Prop)->nat)) (B_44:(nat->Prop)) (A_48:(nat->Prop)), (((ord_less_nat_o B_44) A_48)->(((ord_less_eq_nat C_31) (F_11 B_44))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat C_31) (F_11 A_48)))))).
% Axiom fact_671_xt5:(forall (C_31:nat) (F_11:((product_unit->Prop)->nat)) (B_44:(product_unit->Prop)) (A_48:(product_unit->Prop)), (((ord_le232288914unit_o B_44) A_48)->(((ord_less_eq_nat C_31) (F_11 B_44))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat C_31) (F_11 A_48)))))).
% Axiom fact_672_xt5:(forall (C_31:nat) (F_11:((arrow_1196572341e_indi->Prop)->nat)) (B_44:(arrow_1196572341e_indi->Prop)) (A_48:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o B_44) A_48)->(((ord_less_eq_nat C_31) (F_11 B_44))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat (F_11 Y_1)) (F_11 X_1))))->((ord_less_nat C_31) (F_11 A_48)))))).
% Axiom fact_673_xt7:(forall (C_30:(nat->Prop)) (F_10:(nat->(nat->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))).
% Axiom fact_674_xt7:(forall (C_30:(product_unit->Prop)) (F_10:(nat->(product_unit->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le232288914unit_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1511552390unit_o (F_10 Y_1)) (F_10 X_1))))->((ord_le232288914unit_o C_30) (F_10 A_47)))))).
% Axiom fact_675_xt7:(forall (C_30:(arrow_1196572341e_indi->Prop)) (F_10:(nat->(arrow_1196572341e_indi->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1991507760indi_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le865407012indi_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1991507760indi_o C_30) (F_10 A_47)))))).
% Axiom fact_676_xt7:(forall (C_30:((produc1572197287le_alt->Prop)->Prop)) (F_10:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le874404799lt_o_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1027220427lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le874404799lt_o_o C_30) (F_10 A_47)))))).
% Axiom fact_677_xt7:(forall (C_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_10:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1382328578lt_o_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1805007862lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1382328578lt_o_o C_30) (F_10 A_47)))))).
% Axiom fact_678_xt7:(forall (C_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_10:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le914873172lt_o_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le602483040lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le914873172lt_o_o C_30) (F_10 A_47)))))).
% Axiom fact_679_xt7:(forall (C_30:(produc1572197287le_alt->Prop)) (F_10:(nat->(produc1572197287le_alt->Prop))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1852932542_alt_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le962286258_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1852932542_alt_o C_30) (F_10 A_47)))))).
% Axiom fact_680_xt7:(forall (C_30:Prop) (F_10:(nat->Prop)) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_less_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_o C_30) (F_10 A_47)))))).
% Axiom fact_681_xt7:(forall (C_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_10:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_43:nat) (A_47:nat), (((ord_less_eq_nat B_43) A_47)->(((ord_le1339521307_alt_o C_30) (F_10 B_43))->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1463467535_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1339521307_alt_o C_30) (F_10 A_47)))))).
% Axiom fact_682_xt7:(forall (C_30:(nat->Prop)) (F_10:((nat->Prop)->(nat->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))).
% Axiom fact_683_xt7:(forall (C_30:(product_unit->Prop)) (F_10:((nat->Prop)->(product_unit->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le232288914unit_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1511552390unit_o (F_10 Y_1)) (F_10 X_1))))->((ord_le232288914unit_o C_30) (F_10 A_47)))))).
% Axiom fact_684_xt7:(forall (C_30:(arrow_1196572341e_indi->Prop)) (F_10:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1991507760indi_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le865407012indi_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1991507760indi_o C_30) (F_10 A_47)))))).
% Axiom fact_685_xt7:(forall (C_30:((produc1572197287le_alt->Prop)->Prop)) (F_10:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le874404799lt_o_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1027220427lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le874404799lt_o_o C_30) (F_10 A_47)))))).
% Axiom fact_686_xt7:(forall (C_30:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_10:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1382328578lt_o_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1805007862lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1382328578lt_o_o C_30) (F_10 A_47)))))).
% Axiom fact_687_xt7:(forall (C_30:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_10:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le914873172lt_o_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le602483040lt_o_o (F_10 Y_1)) (F_10 X_1))))->((ord_le914873172lt_o_o C_30) (F_10 A_47)))))).
% Axiom fact_688_xt7:(forall (C_30:(produc1572197287le_alt->Prop)) (F_10:((nat->Prop)->(produc1572197287le_alt->Prop))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1852932542_alt_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le962286258_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1852932542_alt_o C_30) (F_10 A_47)))))).
% Axiom fact_689_xt7:(forall (C_30:Prop) (F_10:((nat->Prop)->Prop)) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_less_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_o C_30) (F_10 A_47)))))).
% Axiom fact_690_xt7:(forall (C_30:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_10:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_43:(nat->Prop)) (A_47:(nat->Prop)), (((ord_less_eq_nat_o B_43) A_47)->(((ord_le1339521307_alt_o C_30) (F_10 B_43))->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1463467535_alt_o (F_10 Y_1)) (F_10 X_1))))->((ord_le1339521307_alt_o C_30) (F_10 A_47)))))).
% Axiom fact_691_xt7:(forall (C_30:(nat->Prop)) (F_10:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (B_43:((produc1572197287le_alt->Prop)->Prop)) (A_47:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))).
% Axiom fact_692_xt7:(forall (C_30:(nat->Prop)) (F_10:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_43:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))).
% Axiom fact_693_xt7:(forall (C_30:(nat->Prop)) (F_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_43:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))).
% Axiom fact_694_xt7:(forall (C_30:(nat->Prop)) (F_10:((produc1572197287le_alt->Prop)->(nat->Prop))) (B_43:(produc1572197287le_alt->Prop)) (A_47:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))).
% Axiom fact_695_xt7:(forall (C_30:(nat->Prop)) (F_10:(Prop->(nat->Prop))) (B_43:Prop) (A_47:Prop), (((ord_less_eq_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))).
% Axiom fact_696_xt7:(forall (C_30:(nat->Prop)) (F_10:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_43:(arrow_1196572341e_indi->Prop)) (A_47:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))).
% Axiom fact_697_xt7:(forall (C_30:(nat->Prop)) (F_10:((product_unit->Prop)->(nat->Prop))) (B_43:(product_unit->Prop)) (A_47:(product_unit->Prop)), (((ord_le1511552390unit_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))).
% Axiom fact_698_xt7:(forall (C_30:(nat->Prop)) (F_10:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (B_43:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_47:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_43) A_47)->(((ord_less_nat_o C_30) (F_10 B_43))->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat_o C_30) (F_10 A_47)))))).
% Axiom fact_699_xt7:(forall (C_30:nat) (F_10:(((produc1572197287le_alt->Prop)->Prop)->nat)) (B_43:((produc1572197287le_alt->Prop)->Prop)) (A_47:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))).
% Axiom fact_700_xt7:(forall (C_30:nat) (F_10:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_43:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_47:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))).
% Axiom fact_701_xt7:(forall (C_30:nat) (F_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_43:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_47:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))).
% Axiom fact_702_xt7:(forall (C_30:nat) (F_10:((produc1572197287le_alt->Prop)->nat)) (B_43:(produc1572197287le_alt->Prop)) (A_47:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))).
% Axiom fact_703_xt7:(forall (C_30:nat) (F_10:(Prop->nat)) (B_43:Prop) (A_47:Prop), (((ord_less_eq_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))).
% Axiom fact_704_xt7:(forall (C_30:nat) (F_10:((arrow_1196572341e_indi->Prop)->nat)) (B_43:(arrow_1196572341e_indi->Prop)) (A_47:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))).
% Axiom fact_705_xt7:(forall (C_30:nat) (F_10:((product_unit->Prop)->nat)) (B_43:(product_unit->Prop)) (A_47:(product_unit->Prop)), (((ord_le1511552390unit_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))).
% Axiom fact_706_xt7:(forall (C_30:nat) (F_10:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (B_43:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_47:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o B_43) A_47)->(((ord_less_nat C_30) (F_10 B_43))->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat (F_10 Y_1)) (F_10 X_1))))->((ord_less_nat C_30) (F_10 A_47)))))).
% Axiom fact_707_less__fun__def:(forall (F_9:(product_unit->Prop)) (G_1:(product_unit->Prop)), ((iff ((ord_le232288914unit_o F_9) G_1)) ((and ((ord_le1511552390unit_o F_9) G_1)) (((ord_le1511552390unit_o G_1) F_9)->False)))).
% Axiom fact_708_less__fun__def:(forall (F_9:(arrow_1196572341e_indi->Prop)) (G_1:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o F_9) G_1)) ((and ((ord_le865407012indi_o F_9) G_1)) (((ord_le865407012indi_o G_1) F_9)->False)))).
% Axiom fact_709_less__fun__def:(forall (F_9:((produc1572197287le_alt->Prop)->Prop)) (G_1:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o F_9) G_1)) ((and ((ord_le1027220427lt_o_o F_9) G_1)) (((ord_le1027220427lt_o_o G_1) F_9)->False)))).
% Axiom fact_710_less__fun__def:(forall (F_9:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o F_9) G_1)) ((and ((ord_le1805007862lt_o_o F_9) G_1)) (((ord_le1805007862lt_o_o G_1) F_9)->False)))).
% Axiom fact_711_less__fun__def:(forall (F_9:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o F_9) G_1)) ((and ((ord_le602483040lt_o_o F_9) G_1)) (((ord_le602483040lt_o_o G_1) F_9)->False)))).
% Axiom fact_712_less__fun__def:(forall (F_9:(produc1572197287le_alt->Prop)) (G_1:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o F_9) G_1)) ((and ((ord_le962286258_alt_o F_9) G_1)) (((ord_le962286258_alt_o G_1) F_9)->False)))).
% Axiom fact_713_less__fun__def:(forall (F_9:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((iff ((ord_le1339521307_alt_o F_9) G_1)) ((and ((ord_le1463467535_alt_o F_9) G_1)) (((ord_le1463467535_alt_o G_1) F_9)->False)))).
% Axiom fact_714_less__fun__def:(forall (F_9:(nat->Prop)) (G_1:(nat->Prop)), ((iff ((ord_less_nat_o F_9) G_1)) ((and ((ord_less_eq_nat_o F_9) G_1)) (((ord_less_eq_nat_o G_1) F_9)->False)))).
% Axiom fact_715_Pi__anti__mono:(forall (B_42:(produc1572197287le_alt->(Prop->Prop))) (A_46:(produc1572197287le_alt->Prop)) (A_45:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_46) A_45)->((ord_le1027220427lt_o_o ((pi_Pro418549519_alt_o A_45) B_42)) ((pi_Pro418549519_alt_o A_46) B_42)))).
% Axiom fact_716_Pi__anti__mono:(forall (B_42:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->((produc1572197287le_alt->Prop)->Prop))) (A_46:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_45:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_46) A_45)->((ord_le1805007862lt_o_o ((pi_Arr1196397536_alt_o A_45) B_42)) ((pi_Arr1196397536_alt_o A_46) B_42)))).
% Axiom fact_717_Pi__anti__mono:(forall (B_42:(arrow_1196572341e_indi->((produc1572197287le_alt->Prop)->Prop))) (A_46:(arrow_1196572341e_indi->Prop)) (A_45:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_46) A_45)->((ord_le602483040lt_o_o ((pi_Arr1309696186_alt_o A_45) B_42)) ((pi_Arr1309696186_alt_o A_46) B_42)))).
% Axiom fact_718_pred__subset__eq2:(forall (R_1:(produc1572197287le_alt->Prop)) (S_2:(produc1572197287le_alt->Prop)), ((iff ((ord_le1463467535_alt_o (fun (X_1:arrow_1389031998le_alt) (Y_1:arrow_1389031998le_alt)=> ((member285112084le_alt ((produc897867031le_alt X_1) Y_1)) R_1))) (fun (X_1:arrow_1389031998le_alt) (Y_1:arrow_1389031998le_alt)=> ((member285112084le_alt ((produc897867031le_alt X_1) Y_1)) S_2)))) ((ord_le962286258_alt_o R_1) S_2))).
% Axiom fact_719_subset__UNIV:(forall (A_44:((produc1572197287le_alt->Prop)->Prop)), ((ord_le1027220427lt_o_o A_44) top_to1806834203lt_o_o)).
% Axiom fact_720_subset__UNIV:(forall (A_44:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((ord_le602483040lt_o_o A_44) top_to732317616lt_o_o)).
% Axiom fact_721_subset__UNIV:(forall (A_44:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((ord_le1805007862lt_o_o A_44) top_to1492351398lt_o_o)).
% Axiom fact_722_subset__UNIV:(forall (A_44:(produc1572197287le_alt->Prop)), ((ord_le962286258_alt_o A_44) top_to558618722_alt_o)).
% Axiom fact_723_subset__UNIV:(forall (A_44:(arrow_1196572341e_indi->Prop)), ((ord_le865407012indi_o A_44) top_to54564308indi_o)).
% Axiom fact_724_subset__UNIV:(forall (A_44:(nat->Prop)), ((ord_less_eq_nat_o A_44) top_top_nat_o)).
% Axiom fact_725_subset__UNIV:(forall (A_44:(product_unit->Prop)), ((ord_le1511552390unit_o A_44) top_to1984820022unit_o)).
% Axiom fact_726_subset__inj__on:(forall (A_43:(arrow_1196572341e_indi->Prop)) (F_8:(arrow_1196572341e_indi->nat)) (B_41:(arrow_1196572341e_indi->Prop)), (((inj_on1505595958di_nat F_8) B_41)->(((ord_le865407012indi_o A_43) B_41)->((inj_on1505595958di_nat F_8) A_43)))).
% Axiom fact_727_subset__inj__on:(forall (A_43:(nat->Prop)) (F_8:(nat->nat)) (B_41:(nat->Prop)), (((inj_on_nat_nat F_8) B_41)->(((ord_less_eq_nat_o A_43) B_41)->((inj_on_nat_nat F_8) A_43)))).
% Axiom fact_728_add__right__imp__eq:(forall (B_40:nat) (A_42:nat) (C_29:nat), ((((eq nat) ((plus_plus_nat B_40) A_42)) ((plus_plus_nat C_29) A_42))->(((eq nat) B_40) C_29))).
% Axiom fact_729_add__imp__eq:(forall (A_41:nat) (B_39:nat) (C_28:nat), ((((eq nat) ((plus_plus_nat A_41) B_39)) ((plus_plus_nat A_41) C_28))->(((eq nat) B_39) C_28))).
% Axiom fact_730_add__left__imp__eq:(forall (A_40:nat) (B_38:nat) (C_27:nat), ((((eq nat) ((plus_plus_nat A_40) B_38)) ((plus_plus_nat A_40) C_27))->(((eq nat) B_38) C_27))).
% Axiom fact_731_add__right__cancel:(forall (B_37:nat) (A_39:nat) (C_26:nat), ((iff (((eq nat) ((plus_plus_nat B_37) A_39)) ((plus_plus_nat C_26) A_39))) (((eq nat) B_37) C_26))).
% Axiom fact_732_add__left__cancel:(forall (A_38:nat) (B_36:nat) (C_25:nat), ((iff (((eq nat) ((plus_plus_nat A_38) B_36)) ((plus_plus_nat A_38) C_25))) (((eq nat) B_36) C_25))).
% Axiom fact_733_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_37:nat) (B_35:nat) (C_24:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_37) B_35)) C_24)) ((plus_plus_nat A_37) ((plus_plus_nat B_35) C_24)))).
% Axiom fact_734_one__reorient:(forall (X_7:nat), ((iff (((eq nat) one_one_nat) X_7)) (((eq nat) X_7) one_one_nat))).
% Axiom fact_735_add__le__imp__le__left:(forall (C_23:nat) (A_36:nat) (B_34:nat), (((ord_less_eq_nat ((plus_plus_nat C_23) A_36)) ((plus_plus_nat C_23) B_34))->((ord_less_eq_nat A_36) B_34))).
% Axiom fact_736_add__le__imp__le__right:(forall (A_35:nat) (C_22:nat) (B_33:nat), (((ord_less_eq_nat ((plus_plus_nat A_35) C_22)) ((plus_plus_nat B_33) C_22))->((ord_less_eq_nat A_35) B_33))).
% Axiom fact_737_add__mono:(forall (C_21:nat) (D_1:nat) (A_34:nat) (B_32:nat), (((ord_less_eq_nat A_34) B_32)->(((ord_less_eq_nat C_21) D_1)->((ord_less_eq_nat ((plus_plus_nat A_34) C_21)) ((plus_plus_nat B_32) D_1))))).
% Axiom fact_738_add__left__mono:(forall (C_20:nat) (A_33:nat) (B_31:nat), (((ord_less_eq_nat A_33) B_31)->((ord_less_eq_nat ((plus_plus_nat C_20) A_33)) ((plus_plus_nat C_20) B_31)))).
% Axiom fact_739_add__right__mono:(forall (C_19:nat) (A_32:nat) (B_30:nat), (((ord_less_eq_nat A_32) B_30)->((ord_less_eq_nat ((plus_plus_nat A_32) C_19)) ((plus_plus_nat B_30) C_19)))).
% Axiom fact_740_add__le__cancel__left:(forall (C_18:nat) (A_31:nat) (B_29:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_18) A_31)) ((plus_plus_nat C_18) B_29))) ((ord_less_eq_nat A_31) B_29))).
% Axiom fact_741_add__le__cancel__right:(forall (A_30:nat) (C_17:nat) (B_28:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_30) C_17)) ((plus_plus_nat B_28) C_17))) ((ord_less_eq_nat A_30) B_28))).
% Axiom fact_742_add__less__imp__less__left:(forall (C_16:nat) (A_29:nat) (B_27:nat), (((ord_less_nat ((plus_plus_nat C_16) A_29)) ((plus_plus_nat C_16) B_27))->((ord_less_nat A_29) B_27))).
% Axiom fact_743_add__less__imp__less__right:(forall (A_28:nat) (C_15:nat) (B_26:nat), (((ord_less_nat ((plus_plus_nat A_28) C_15)) ((plus_plus_nat B_26) C_15))->((ord_less_nat A_28) B_26))).
% Axiom fact_744_add__strict__mono:(forall (C_14:nat) (D:nat) (A_27:nat) (B_25:nat), (((ord_less_nat A_27) B_25)->(((ord_less_nat C_14) D)->((ord_less_nat ((plus_plus_nat A_27) C_14)) ((plus_plus_nat B_25) D))))).
% Axiom fact_745_add__strict__left__mono:(forall (C_13:nat) (A_26:nat) (B_24:nat), (((ord_less_nat A_26) B_24)->((ord_less_nat ((plus_plus_nat C_13) A_26)) ((plus_plus_nat C_13) B_24)))).
% Axiom fact_746_add__strict__right__mono:(forall (C_12:nat) (A_25:nat) (B_23:nat), (((ord_less_nat A_25) B_23)->((ord_less_nat ((plus_plus_nat A_25) C_12)) ((plus_plus_nat B_23) C_12)))).
% Axiom fact_747_add__less__cancel__left:(forall (C_11:nat) (A_24:nat) (B_22:nat), ((iff ((ord_less_nat ((plus_plus_nat C_11) A_24)) ((plus_plus_nat C_11) B_22))) ((ord_less_nat A_24) B_22))).
% Axiom fact_748_add__less__cancel__right:(forall (A_23:nat) (C_10:nat) (B_21:nat), ((iff ((ord_less_nat ((plus_plus_nat A_23) C_10)) ((plus_plus_nat B_21) C_10))) ((ord_less_nat A_23) B_21))).
% Axiom fact_749_le__funI:(forall (F_7:((produc1572197287le_alt->Prop)->Prop)) (G:((produc1572197287le_alt->Prop)->Prop)), ((forall (X_1:(produc1572197287le_alt->Prop)), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le1027220427lt_o_o F_7) G))).
% Axiom fact_750_le__funI:(forall (F_7:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (G:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le1805007862lt_o_o F_7) G))).
% Axiom fact_751_le__funI:(forall (F_7:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (G:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((forall (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le602483040lt_o_o F_7) G))).
% Axiom fact_752_le__funI:(forall (F_7:(produc1572197287le_alt->Prop)) (G:(produc1572197287le_alt->Prop)), ((forall (X_1:produc1572197287le_alt), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le962286258_alt_o F_7) G))).
% Axiom fact_753_le__funI:(forall (F_7:(arrow_1196572341e_indi->Prop)) (G:(arrow_1196572341e_indi->Prop)), ((forall (X_1:arrow_1196572341e_indi), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le865407012indi_o F_7) G))).
% Axiom fact_754_le__funI:(forall (F_7:(product_unit->Prop)) (G:(product_unit->Prop)), ((forall (X_1:product_unit), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_le1511552390unit_o F_7) G))).
% Axiom fact_755_le__funI:(forall (F_7:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (G:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), ((forall (X_1:arrow_1389031998le_alt), ((ord_le1423491573_alt_o (F_7 X_1)) (G X_1)))->((ord_le1463467535_alt_o F_7) G))).
% Axiom fact_756_le__funI:(forall (F_7:(nat->Prop)) (G:(nat->Prop)), ((forall (X_1:nat), ((ord_less_eq_o (F_7 X_1)) (G X_1)))->((ord_less_eq_nat_o F_7) G))).
% Axiom fact_757_xt6:(forall (C_9:(nat->Prop)) (F_6:((nat->Prop)->(nat->Prop))) (B_20:(nat->Prop)) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_less_nat_o C_9) B_20)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22))))).
% Axiom fact_758_xt6:(forall (C_9:(product_unit->Prop)) (F_6:((product_unit->Prop)->(nat->Prop))) (B_20:(product_unit->Prop)) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_le232288914unit_o C_9) B_20)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22))))).
% Axiom fact_759_xt6:(forall (C_9:(arrow_1196572341e_indi->Prop)) (F_6:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_20:(arrow_1196572341e_indi->Prop)) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_le1991507760indi_o C_9) B_20)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22))))).
% Axiom fact_760_xt6:(forall (C_9:nat) (F_6:(nat->(nat->Prop))) (B_20:nat) (A_22:(nat->Prop)), (((ord_less_eq_nat_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_nat_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat_o (F_6 C_9)) A_22))))).
% Axiom fact_761_xt6:(forall (C_9:nat) (F_6:(nat->(product_unit->Prop))) (B_20:nat) (A_22:(product_unit->Prop)), (((ord_le1511552390unit_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le232288914unit_o (F_6 Y_1)) (F_6 X_1))))->((ord_le232288914unit_o (F_6 C_9)) A_22))))).
% Axiom fact_762_xt6:(forall (C_9:nat) (F_6:(nat->(arrow_1196572341e_indi->Prop))) (B_20:nat) (A_22:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1991507760indi_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1991507760indi_o (F_6 C_9)) A_22))))).
% Axiom fact_763_xt6:(forall (C_9:nat) (F_6:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_20:nat) (A_22:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le874404799lt_o_o (F_6 Y_1)) (F_6 X_1))))->((ord_le874404799lt_o_o (F_6 C_9)) A_22))))).
% Axiom fact_764_xt6:(forall (C_9:nat) (F_6:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_20:nat) (A_22:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1382328578lt_o_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1382328578lt_o_o (F_6 C_9)) A_22))))).
% Axiom fact_765_xt6:(forall (C_9:nat) (F_6:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_20:nat) (A_22:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le914873172lt_o_o (F_6 Y_1)) (F_6 X_1))))->((ord_le914873172lt_o_o (F_6 C_9)) A_22))))).
% Axiom fact_766_xt6:(forall (C_9:nat) (F_6:(nat->(produc1572197287le_alt->Prop))) (B_20:nat) (A_22:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1852932542_alt_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1852932542_alt_o (F_6 C_9)) A_22))))).
% Axiom fact_767_xt6:(forall (C_9:nat) (F_6:(nat->Prop)) (B_20:nat) (A_22:Prop), (((ord_less_eq_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_less_o (F_6 Y_1)) (F_6 X_1))))->((ord_less_o (F_6 C_9)) A_22))))).
% Axiom fact_768_xt6:(forall (C_9:nat) (F_6:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_20:nat) (A_22:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o (F_6 B_20)) A_22)->(((ord_less_nat C_9) B_20)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat Y_1) X_1)->((ord_le1339521307_alt_o (F_6 Y_1)) (F_6 X_1))))->((ord_le1339521307_alt_o (F_6 C_9)) A_22))))).
% Axiom fact_769_xt6:(forall (C_9:(nat->Prop)) (F_6:((nat->Prop)->nat)) (B_20:(nat->Prop)) (A_22:nat), (((ord_less_eq_nat (F_6 B_20)) A_22)->(((ord_less_nat_o C_9) B_20)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o Y_1) X_1)->((ord_less_nat (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat (F_6 C_9)) A_22))))).
% Axiom fact_770_xt6:(forall (C_9:(product_unit->Prop)) (F_6:((product_unit->Prop)->nat)) (B_20:(product_unit->Prop)) (A_22:nat), (((ord_less_eq_nat (F_6 B_20)) A_22)->(((ord_le232288914unit_o C_9) B_20)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o Y_1) X_1)->((ord_less_nat (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat (F_6 C_9)) A_22))))).
% Axiom fact_771_xt6:(forall (C_9:(arrow_1196572341e_indi->Prop)) (F_6:((arrow_1196572341e_indi->Prop)->nat)) (B_20:(arrow_1196572341e_indi->Prop)) (A_22:nat), (((ord_less_eq_nat (F_6 B_20)) A_22)->(((ord_le1991507760indi_o C_9) B_20)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o Y_1) X_1)->((ord_less_nat (F_6 Y_1)) (F_6 X_1))))->((ord_less_nat (F_6 C_9)) A_22))))).
% Axiom fact_772_xt4:(forall (C_8:nat) (F_5:(nat->(nat->Prop))) (B_19:nat) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))).
% Axiom fact_773_xt4:(forall (C_8:nat) (F_5:(nat->(product_unit->Prop))) (B_19:nat) (A_21:(product_unit->Prop)), (((ord_le232288914unit_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1511552390unit_o (F_5 Y_1)) (F_5 X_1))))->((ord_le232288914unit_o (F_5 C_8)) A_21))))).
% Axiom fact_774_xt4:(forall (C_8:nat) (F_5:(nat->(arrow_1196572341e_indi->Prop))) (B_19:nat) (A_21:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le865407012indi_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1991507760indi_o (F_5 C_8)) A_21))))).
% Axiom fact_775_xt4:(forall (C_8:nat) (F_5:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_19:nat) (A_21:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1027220427lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le874404799lt_o_o (F_5 C_8)) A_21))))).
% Axiom fact_776_xt4:(forall (C_8:nat) (F_5:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_19:nat) (A_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1805007862lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1382328578lt_o_o (F_5 C_8)) A_21))))).
% Axiom fact_777_xt4:(forall (C_8:nat) (F_5:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_19:nat) (A_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le602483040lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le914873172lt_o_o (F_5 C_8)) A_21))))).
% Axiom fact_778_xt4:(forall (C_8:nat) (F_5:(nat->(produc1572197287le_alt->Prop))) (B_19:nat) (A_21:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le962286258_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1852932542_alt_o (F_5 C_8)) A_21))))).
% Axiom fact_779_xt4:(forall (C_8:nat) (F_5:(nat->Prop)) (B_19:nat) (A_21:Prop), (((ord_less_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_less_eq_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_o (F_5 C_8)) A_21))))).
% Axiom fact_780_xt4:(forall (C_8:nat) (F_5:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_19:nat) (A_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat C_8) B_19)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat Y_1) X_1)->((ord_le1463467535_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1339521307_alt_o (F_5 C_8)) A_21))))).
% Axiom fact_781_xt4:(forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(nat->Prop))) (B_19:(nat->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))).
% Axiom fact_782_xt4:(forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(product_unit->Prop))) (B_19:(nat->Prop)) (A_21:(product_unit->Prop)), (((ord_le232288914unit_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1511552390unit_o (F_5 Y_1)) (F_5 X_1))))->((ord_le232288914unit_o (F_5 C_8)) A_21))))).
% Axiom fact_783_xt4:(forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (B_19:(nat->Prop)) (A_21:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le865407012indi_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1991507760indi_o (F_5 C_8)) A_21))))).
% Axiom fact_784_xt4:(forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (B_19:(nat->Prop)) (A_21:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1027220427lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le874404799lt_o_o (F_5 C_8)) A_21))))).
% Axiom fact_785_xt4:(forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_19:(nat->Prop)) (A_21:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1805007862lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1382328578lt_o_o (F_5 C_8)) A_21))))).
% Axiom fact_786_xt4:(forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_19:(nat->Prop)) (A_21:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le602483040lt_o_o (F_5 Y_1)) (F_5 X_1))))->((ord_le914873172lt_o_o (F_5 C_8)) A_21))))).
% Axiom fact_787_xt4:(forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(produc1572197287le_alt->Prop))) (B_19:(nat->Prop)) (A_21:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le962286258_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1852932542_alt_o (F_5 C_8)) A_21))))).
% Axiom fact_788_xt4:(forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->Prop)) (B_19:(nat->Prop)) (A_21:Prop), (((ord_less_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_less_eq_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_o (F_5 C_8)) A_21))))).
% Axiom fact_789_xt4:(forall (C_8:(nat->Prop)) (F_5:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_19:(nat->Prop)) (A_21:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1339521307_alt_o (F_5 B_19)) A_21)->(((ord_less_eq_nat_o C_8) B_19)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o Y_1) X_1)->((ord_le1463467535_alt_o (F_5 Y_1)) (F_5 X_1))))->((ord_le1339521307_alt_o (F_5 C_8)) A_21))))).
% Axiom fact_790_xt4:(forall (C_8:((produc1572197287le_alt->Prop)->Prop)) (F_5:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (B_19:((produc1572197287le_alt->Prop)->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1027220427lt_o_o C_8) B_19)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))).
% Axiom fact_791_xt4:(forall (C_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_5:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1805007862lt_o_o C_8) B_19)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))).
% Axiom fact_792_xt4:(forall (C_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le602483040lt_o_o C_8) B_19)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))).
% Axiom fact_793_xt4:(forall (C_8:(produc1572197287le_alt->Prop)) (F_5:((produc1572197287le_alt->Prop)->(nat->Prop))) (B_19:(produc1572197287le_alt->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le962286258_alt_o C_8) B_19)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))).
% Axiom fact_794_xt4:(forall (C_8:Prop) (F_5:(Prop->(nat->Prop))) (B_19:Prop) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_less_eq_o C_8) B_19)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))).
% Axiom fact_795_xt4:(forall (C_8:(arrow_1196572341e_indi->Prop)) (F_5:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_19:(arrow_1196572341e_indi->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le865407012indi_o C_8) B_19)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))).
% Axiom fact_796_xt4:(forall (C_8:(product_unit->Prop)) (F_5:((product_unit->Prop)->(nat->Prop))) (B_19:(product_unit->Prop)) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1511552390unit_o C_8) B_19)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))).
% Axiom fact_797_xt4:(forall (C_8:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_5:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (B_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_21:(nat->Prop)), (((ord_less_nat_o (F_5 B_19)) A_21)->(((ord_le1463467535_alt_o C_8) B_19)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat_o (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat_o (F_5 C_8)) A_21))))).
% Axiom fact_798_xt4:(forall (C_8:((produc1572197287le_alt->Prop)->Prop)) (F_5:(((produc1572197287le_alt->Prop)->Prop)->nat)) (B_19:((produc1572197287le_alt->Prop)->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1027220427lt_o_o C_8) B_19)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))).
% Axiom fact_799_xt4:(forall (C_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_5:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1805007862lt_o_o C_8) B_19)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))).
% Axiom fact_800_xt4:(forall (C_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le602483040lt_o_o C_8) B_19)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))).
% Axiom fact_801_xt4:(forall (C_8:(produc1572197287le_alt->Prop)) (F_5:((produc1572197287le_alt->Prop)->nat)) (B_19:(produc1572197287le_alt->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le962286258_alt_o C_8) B_19)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))).
% Axiom fact_802_xt4:(forall (C_8:Prop) (F_5:(Prop->nat)) (B_19:Prop) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_less_eq_o C_8) B_19)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))).
% Axiom fact_803_xt4:(forall (C_8:(arrow_1196572341e_indi->Prop)) (F_5:((arrow_1196572341e_indi->Prop)->nat)) (B_19:(arrow_1196572341e_indi->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le865407012indi_o C_8) B_19)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))).
% Axiom fact_804_xt4:(forall (C_8:(product_unit->Prop)) (F_5:((product_unit->Prop)->nat)) (B_19:(product_unit->Prop)) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1511552390unit_o C_8) B_19)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))).
% Axiom fact_805_xt4:(forall (C_8:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_5:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (B_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_21:nat), (((ord_less_nat (F_5 B_19)) A_21)->(((ord_le1463467535_alt_o C_8) B_19)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o Y_1) X_1)->((ord_less_eq_nat (F_5 Y_1)) (F_5 X_1))))->((ord_less_nat (F_5 C_8)) A_21))))).
% Axiom fact_806_order__le__less__subst1:(forall (C_7:(nat->Prop)) (A_20:(nat->Prop)) (F_4:((nat->Prop)->(nat->Prop))) (B_18:(nat->Prop)), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_less_nat_o B_18) C_7)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7)))))).
% Axiom fact_807_order__le__less__subst1:(forall (C_7:(product_unit->Prop)) (A_20:(nat->Prop)) (F_4:((product_unit->Prop)->(nat->Prop))) (B_18:(product_unit->Prop)), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_le232288914unit_o B_18) C_7)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7)))))).
% Axiom fact_808_order__le__less__subst1:(forall (C_7:(arrow_1196572341e_indi->Prop)) (A_20:(nat->Prop)) (F_4:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_18:(arrow_1196572341e_indi->Prop)), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_le1991507760indi_o B_18) C_7)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7)))))).
% Axiom fact_809_order__le__less__subst1:(forall (C_7:nat) (A_20:(nat->Prop)) (F_4:(nat->(nat->Prop))) (B_18:nat), (((ord_less_eq_nat_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_nat_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat_o A_20) (F_4 C_7)))))).
% Axiom fact_810_order__le__less__subst1:(forall (C_7:nat) (A_20:(product_unit->Prop)) (F_4:(nat->(product_unit->Prop))) (B_18:nat), (((ord_le1511552390unit_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le232288914unit_o (F_4 X_1)) (F_4 Y_1))))->((ord_le232288914unit_o A_20) (F_4 C_7)))))).
% Axiom fact_811_order__le__less__subst1:(forall (C_7:nat) (A_20:(arrow_1196572341e_indi->Prop)) (F_4:(nat->(arrow_1196572341e_indi->Prop))) (B_18:nat), (((ord_le865407012indi_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1991507760indi_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1991507760indi_o A_20) (F_4 C_7)))))).
% Axiom fact_812_order__le__less__subst1:(forall (C_7:nat) (A_20:((produc1572197287le_alt->Prop)->Prop)) (F_4:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_18:nat), (((ord_le1027220427lt_o_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le874404799lt_o_o (F_4 X_1)) (F_4 Y_1))))->((ord_le874404799lt_o_o A_20) (F_4 C_7)))))).
% Axiom fact_813_order__le__less__subst1:(forall (C_7:nat) (A_20:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_4:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_18:nat), (((ord_le1805007862lt_o_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1382328578lt_o_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1382328578lt_o_o A_20) (F_4 C_7)))))).
% Axiom fact_814_order__le__less__subst1:(forall (C_7:nat) (A_20:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_4:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_18:nat), (((ord_le602483040lt_o_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le914873172lt_o_o (F_4 X_1)) (F_4 Y_1))))->((ord_le914873172lt_o_o A_20) (F_4 C_7)))))).
% Axiom fact_815_order__le__less__subst1:(forall (C_7:nat) (A_20:(produc1572197287le_alt->Prop)) (F_4:(nat->(produc1572197287le_alt->Prop))) (B_18:nat), (((ord_le962286258_alt_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1852932542_alt_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1852932542_alt_o A_20) (F_4 C_7)))))).
% Axiom fact_816_order__le__less__subst1:(forall (C_7:nat) (A_20:Prop) (F_4:(nat->Prop)) (B_18:nat), (((ord_less_eq_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_o (F_4 X_1)) (F_4 Y_1))))->((ord_less_o A_20) (F_4 C_7)))))).
% Axiom fact_817_order__le__less__subst1:(forall (C_7:nat) (A_20:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_4:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_18:nat), (((ord_le1463467535_alt_o A_20) (F_4 B_18))->(((ord_less_nat B_18) C_7)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1339521307_alt_o (F_4 X_1)) (F_4 Y_1))))->((ord_le1339521307_alt_o A_20) (F_4 C_7)))))).
% Axiom fact_818_order__le__less__subst1:(forall (C_7:(nat->Prop)) (A_20:nat) (F_4:((nat->Prop)->nat)) (B_18:(nat->Prop)), (((ord_less_eq_nat A_20) (F_4 B_18))->(((ord_less_nat_o B_18) C_7)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat A_20) (F_4 C_7)))))).
% Axiom fact_819_order__le__less__subst1:(forall (C_7:(product_unit->Prop)) (A_20:nat) (F_4:((product_unit->Prop)->nat)) (B_18:(product_unit->Prop)), (((ord_less_eq_nat A_20) (F_4 B_18))->(((ord_le232288914unit_o B_18) C_7)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat A_20) (F_4 C_7)))))).
% Axiom fact_820_order__le__less__subst1:(forall (C_7:(arrow_1196572341e_indi->Prop)) (A_20:nat) (F_4:((arrow_1196572341e_indi->Prop)->nat)) (B_18:(arrow_1196572341e_indi->Prop)), (((ord_less_eq_nat A_20) (F_4 B_18))->(((ord_le1991507760indi_o B_18) C_7)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat (F_4 X_1)) (F_4 Y_1))))->((ord_less_nat A_20) (F_4 C_7)))))).
% Axiom fact_821_order__less__le__subst1:(forall (C_6:nat) (A_19:(nat->Prop)) (F_3:(nat->(nat->Prop))) (B_17:nat), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))).
% Axiom fact_822_order__less__le__subst1:(forall (C_6:nat) (A_19:(product_unit->Prop)) (F_3:(nat->(product_unit->Prop))) (B_17:nat), (((ord_le232288914unit_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1511552390unit_o (F_3 X_1)) (F_3 Y_1))))->((ord_le232288914unit_o A_19) (F_3 C_6)))))).
% Axiom fact_823_order__less__le__subst1:(forall (C_6:nat) (A_19:(arrow_1196572341e_indi->Prop)) (F_3:(nat->(arrow_1196572341e_indi->Prop))) (B_17:nat), (((ord_le1991507760indi_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le865407012indi_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1991507760indi_o A_19) (F_3 C_6)))))).
% Axiom fact_824_order__less__le__subst1:(forall (C_6:nat) (A_19:((produc1572197287le_alt->Prop)->Prop)) (F_3:(nat->((produc1572197287le_alt->Prop)->Prop))) (B_17:nat), (((ord_le874404799lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1027220427lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le874404799lt_o_o A_19) (F_3 C_6)))))).
% Axiom fact_825_order__less__le__subst1:(forall (C_6:nat) (A_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_3:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_17:nat), (((ord_le1382328578lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1805007862lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1382328578lt_o_o A_19) (F_3 C_6)))))).
% Axiom fact_826_order__less__le__subst1:(forall (C_6:nat) (A_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_3:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_17:nat), (((ord_le914873172lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le602483040lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le914873172lt_o_o A_19) (F_3 C_6)))))).
% Axiom fact_827_order__less__le__subst1:(forall (C_6:nat) (A_19:(produc1572197287le_alt->Prop)) (F_3:(nat->(produc1572197287le_alt->Prop))) (B_17:nat), (((ord_le1852932542_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le962286258_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1852932542_alt_o A_19) (F_3 C_6)))))).
% Axiom fact_828_order__less__le__subst1:(forall (C_6:nat) (A_19:Prop) (F_3:(nat->Prop)) (B_17:nat), (((ord_less_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_o A_19) (F_3 C_6)))))).
% Axiom fact_829_order__less__le__subst1:(forall (C_6:nat) (A_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_3:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_17:nat), (((ord_le1339521307_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat B_17) C_6)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1463467535_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1339521307_alt_o A_19) (F_3 C_6)))))).
% Axiom fact_830_order__less__le__subst1:(forall (C_6:(nat->Prop)) (A_19:(nat->Prop)) (F_3:((nat->Prop)->(nat->Prop))) (B_17:(nat->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))).
% Axiom fact_831_order__less__le__subst1:(forall (C_6:(nat->Prop)) (A_19:(product_unit->Prop)) (F_3:((nat->Prop)->(product_unit->Prop))) (B_17:(nat->Prop)), (((ord_le232288914unit_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1511552390unit_o (F_3 X_1)) (F_3 Y_1))))->((ord_le232288914unit_o A_19) (F_3 C_6)))))).
% Axiom fact_832_order__less__le__subst1:(forall (C_6:(nat->Prop)) (A_19:(arrow_1196572341e_indi->Prop)) (F_3:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (B_17:(nat->Prop)), (((ord_le1991507760indi_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le865407012indi_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1991507760indi_o A_19) (F_3 C_6)))))).
% Axiom fact_833_order__less__le__subst1:(forall (C_6:(nat->Prop)) (A_19:((produc1572197287le_alt->Prop)->Prop)) (F_3:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (B_17:(nat->Prop)), (((ord_le874404799lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1027220427lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le874404799lt_o_o A_19) (F_3 C_6)))))).
% Axiom fact_834_order__less__le__subst1:(forall (C_6:(nat->Prop)) (A_19:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (F_3:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (B_17:(nat->Prop)), (((ord_le1382328578lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1805007862lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1382328578lt_o_o A_19) (F_3 C_6)))))).
% Axiom fact_835_order__less__le__subst1:(forall (C_6:(nat->Prop)) (A_19:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (F_3:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (B_17:(nat->Prop)), (((ord_le914873172lt_o_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le602483040lt_o_o (F_3 X_1)) (F_3 Y_1))))->((ord_le914873172lt_o_o A_19) (F_3 C_6)))))).
% Axiom fact_836_order__less__le__subst1:(forall (C_6:(nat->Prop)) (A_19:(produc1572197287le_alt->Prop)) (F_3:((nat->Prop)->(produc1572197287le_alt->Prop))) (B_17:(nat->Prop)), (((ord_le1852932542_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le962286258_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1852932542_alt_o A_19) (F_3 C_6)))))).
% Axiom fact_837_order__less__le__subst1:(forall (C_6:(nat->Prop)) (A_19:Prop) (F_3:((nat->Prop)->Prop)) (B_17:(nat->Prop)), (((ord_less_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_o A_19) (F_3 C_6)))))).
% Axiom fact_838_order__less__le__subst1:(forall (C_6:(nat->Prop)) (A_19:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (F_3:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (B_17:(nat->Prop)), (((ord_le1339521307_alt_o A_19) (F_3 B_17))->(((ord_less_eq_nat_o B_17) C_6)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1463467535_alt_o (F_3 X_1)) (F_3 Y_1))))->((ord_le1339521307_alt_o A_19) (F_3 C_6)))))).
% Axiom fact_839_order__less__le__subst1:(forall (C_6:((produc1572197287le_alt->Prop)->Prop)) (A_19:(nat->Prop)) (F_3:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (B_17:((produc1572197287le_alt->Prop)->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1027220427lt_o_o B_17) C_6)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))).
% Axiom fact_840_order__less__le__subst1:(forall (C_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_19:(nat->Prop)) (F_3:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_17:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1805007862lt_o_o B_17) C_6)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))).
% Axiom fact_841_order__less__le__subst1:(forall (C_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_19:(nat->Prop)) (F_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (B_17:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le602483040lt_o_o B_17) C_6)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))).
% Axiom fact_842_order__less__le__subst1:(forall (C_6:(produc1572197287le_alt->Prop)) (A_19:(nat->Prop)) (F_3:((produc1572197287le_alt->Prop)->(nat->Prop))) (B_17:(produc1572197287le_alt->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le962286258_alt_o B_17) C_6)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))).
% Axiom fact_843_order__less__le__subst1:(forall (C_6:Prop) (A_19:(nat->Prop)) (F_3:(Prop->(nat->Prop))) (B_17:Prop), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_less_eq_o B_17) C_6)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))).
% Axiom fact_844_order__less__le__subst1:(forall (C_6:(arrow_1196572341e_indi->Prop)) (A_19:(nat->Prop)) (F_3:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (B_17:(arrow_1196572341e_indi->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le865407012indi_o B_17) C_6)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))).
% Axiom fact_845_order__less__le__subst1:(forall (C_6:(product_unit->Prop)) (A_19:(nat->Prop)) (F_3:((product_unit->Prop)->(nat->Prop))) (B_17:(product_unit->Prop)), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1511552390unit_o B_17) C_6)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))).
% Axiom fact_846_order__less__le__subst1:(forall (C_6:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_19:(nat->Prop)) (F_3:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (B_17:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_less_nat_o A_19) (F_3 B_17))->(((ord_le1463467535_alt_o B_17) C_6)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat_o A_19) (F_3 C_6)))))).
% Axiom fact_847_order__less__le__subst1:(forall (C_6:((produc1572197287le_alt->Prop)->Prop)) (A_19:nat) (F_3:(((produc1572197287le_alt->Prop)->Prop)->nat)) (B_17:((produc1572197287le_alt->Prop)->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1027220427lt_o_o B_17) C_6)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))).
% Axiom fact_848_order__less__le__subst1:(forall (C_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_19:nat) (F_3:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_17:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1805007862lt_o_o B_17) C_6)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))).
% Axiom fact_849_order__less__le__subst1:(forall (C_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_19:nat) (F_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (B_17:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le602483040lt_o_o B_17) C_6)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))).
% Axiom fact_850_order__less__le__subst1:(forall (C_6:(produc1572197287le_alt->Prop)) (A_19:nat) (F_3:((produc1572197287le_alt->Prop)->nat)) (B_17:(produc1572197287le_alt->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le962286258_alt_o B_17) C_6)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))).
% Axiom fact_851_order__less__le__subst1:(forall (C_6:Prop) (A_19:nat) (F_3:(Prop->nat)) (B_17:Prop), (((ord_less_nat A_19) (F_3 B_17))->(((ord_less_eq_o B_17) C_6)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))).
% Axiom fact_852_order__less__le__subst1:(forall (C_6:(arrow_1196572341e_indi->Prop)) (A_19:nat) (F_3:((arrow_1196572341e_indi->Prop)->nat)) (B_17:(arrow_1196572341e_indi->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le865407012indi_o B_17) C_6)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))).
% Axiom fact_853_order__less__le__subst1:(forall (C_6:(product_unit->Prop)) (A_19:nat) (F_3:((product_unit->Prop)->nat)) (B_17:(product_unit->Prop)), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1511552390unit_o B_17) C_6)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))).
% Axiom fact_854_order__less__le__subst1:(forall (C_6:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_19:nat) (F_3:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (B_17:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_less_nat A_19) (F_3 B_17))->(((ord_le1463467535_alt_o B_17) C_6)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat (F_3 X_1)) (F_3 Y_1))))->((ord_less_nat A_19) (F_3 C_6)))))).
% Axiom fact_855_order__le__less__subst2:(forall (F_2:(nat->(nat->Prop))) (C_5:(nat->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))).
% Axiom fact_856_order__le__less__subst2:(forall (F_2:(nat->(product_unit->Prop))) (C_5:(product_unit->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le232288914unit_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1511552390unit_o (F_2 X_1)) (F_2 Y_1))))->((ord_le232288914unit_o (F_2 A_18)) C_5))))).
% Axiom fact_857_order__le__less__subst2:(forall (F_2:(nat->(arrow_1196572341e_indi->Prop))) (C_5:(arrow_1196572341e_indi->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1991507760indi_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le865407012indi_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1991507760indi_o (F_2 A_18)) C_5))))).
% Axiom fact_858_order__le__less__subst2:(forall (F_2:(nat->((produc1572197287le_alt->Prop)->Prop))) (C_5:((produc1572197287le_alt->Prop)->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le874404799lt_o_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1027220427lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le874404799lt_o_o (F_2 A_18)) C_5))))).
% Axiom fact_859_order__le__less__subst2:(forall (F_2:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (C_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1382328578lt_o_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1805007862lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1382328578lt_o_o (F_2 A_18)) C_5))))).
% Axiom fact_860_order__le__less__subst2:(forall (F_2:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (C_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le914873172lt_o_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le602483040lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le914873172lt_o_o (F_2 A_18)) C_5))))).
% Axiom fact_861_order__le__less__subst2:(forall (F_2:(nat->(produc1572197287le_alt->Prop))) (C_5:(produc1572197287le_alt->Prop)) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1852932542_alt_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le962286258_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1852932542_alt_o (F_2 A_18)) C_5))))).
% Axiom fact_862_order__le__less__subst2:(forall (F_2:(nat->Prop)) (C_5:Prop) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_less_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_less_eq_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_o (F_2 A_18)) C_5))))).
% Axiom fact_863_order__le__less__subst2:(forall (F_2:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (C_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_18:nat) (B_16:nat), (((ord_less_eq_nat A_18) B_16)->(((ord_le1339521307_alt_o (F_2 B_16)) C_5)->((forall (X_1:nat) (Y_1:nat), (((ord_less_eq_nat X_1) Y_1)->((ord_le1463467535_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1339521307_alt_o (F_2 A_18)) C_5))))).
% Axiom fact_864_order__le__less__subst2:(forall (F_2:((nat->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))).
% Axiom fact_865_order__le__less__subst2:(forall (F_2:((nat->Prop)->(product_unit->Prop))) (C_5:(product_unit->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le232288914unit_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1511552390unit_o (F_2 X_1)) (F_2 Y_1))))->((ord_le232288914unit_o (F_2 A_18)) C_5))))).
% Axiom fact_866_order__le__less__subst2:(forall (F_2:((nat->Prop)->(arrow_1196572341e_indi->Prop))) (C_5:(arrow_1196572341e_indi->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1991507760indi_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le865407012indi_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1991507760indi_o (F_2 A_18)) C_5))))).
% Axiom fact_867_order__le__less__subst2:(forall (F_2:((nat->Prop)->((produc1572197287le_alt->Prop)->Prop))) (C_5:((produc1572197287le_alt->Prop)->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le874404799lt_o_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1027220427lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le874404799lt_o_o (F_2 A_18)) C_5))))).
% Axiom fact_868_order__le__less__subst2:(forall (F_2:((nat->Prop)->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (C_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1382328578lt_o_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1805007862lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1382328578lt_o_o (F_2 A_18)) C_5))))).
% Axiom fact_869_order__le__less__subst2:(forall (F_2:((nat->Prop)->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (C_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le914873172lt_o_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le602483040lt_o_o (F_2 X_1)) (F_2 Y_1))))->((ord_le914873172lt_o_o (F_2 A_18)) C_5))))).
% Axiom fact_870_order__le__less__subst2:(forall (F_2:((nat->Prop)->(produc1572197287le_alt->Prop))) (C_5:(produc1572197287le_alt->Prop)) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1852932542_alt_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le962286258_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1852932542_alt_o (F_2 A_18)) C_5))))).
% Axiom fact_871_order__le__less__subst2:(forall (F_2:((nat->Prop)->Prop)) (C_5:Prop) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_less_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_less_eq_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_o (F_2 A_18)) C_5))))).
% Axiom fact_872_order__le__less__subst2:(forall (F_2:((nat->Prop)->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (C_5:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_18:(nat->Prop)) (B_16:(nat->Prop)), (((ord_less_eq_nat_o A_18) B_16)->(((ord_le1339521307_alt_o (F_2 B_16)) C_5)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_eq_nat_o X_1) Y_1)->((ord_le1463467535_alt_o (F_2 X_1)) (F_2 Y_1))))->((ord_le1339521307_alt_o (F_2 A_18)) C_5))))).
% Axiom fact_873_order__le__less__subst2:(forall (F_2:(((produc1572197287le_alt->Prop)->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:((produc1572197287le_alt->Prop)->Prop)) (B_16:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))).
% Axiom fact_874_order__le__less__subst2:(forall (F_2:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_16:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))).
% Axiom fact_875_order__le__less__subst2:(forall (F_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_16:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))).
% Axiom fact_876_order__le__less__subst2:(forall (F_2:((produc1572197287le_alt->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(produc1572197287le_alt->Prop)) (B_16:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))).
% Axiom fact_877_order__le__less__subst2:(forall (F_2:(Prop->(nat->Prop))) (C_5:(nat->Prop)) (A_18:Prop) (B_16:Prop), (((ord_less_eq_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))).
% Axiom fact_878_order__le__less__subst2:(forall (F_2:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(arrow_1196572341e_indi->Prop)) (B_16:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))).
% Axiom fact_879_order__le__less__subst2:(forall (F_2:((product_unit->Prop)->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(product_unit->Prop)) (B_16:(product_unit->Prop)), (((ord_le1511552390unit_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))).
% Axiom fact_880_order__le__less__subst2:(forall (F_2:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->(nat->Prop))) (C_5:(nat->Prop)) (A_18:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_16:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_18) B_16)->(((ord_less_nat_o (F_2 B_16)) C_5)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat_o (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat_o (F_2 A_18)) C_5))))).
% Axiom fact_881_order__le__less__subst2:(forall (F_2:(((produc1572197287le_alt->Prop)->Prop)->nat)) (C_5:nat) (A_18:((produc1572197287le_alt->Prop)->Prop)) (B_16:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:((produc1572197287le_alt->Prop)->Prop)) (Y_1:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))).
% Axiom fact_882_order__le__less__subst2:(forall (F_2:((((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)->nat)) (C_5:nat) (A_18:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_16:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (Y_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))).
% Axiom fact_883_order__le__less__subst2:(forall (F_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)->nat)) (C_5:nat) (A_18:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_16:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (Y_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))).
% Axiom fact_884_order__le__less__subst2:(forall (F_2:((produc1572197287le_alt->Prop)->nat)) (C_5:nat) (A_18:(produc1572197287le_alt->Prop)) (B_16:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(produc1572197287le_alt->Prop)) (Y_1:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))).
% Axiom fact_885_order__le__less__subst2:(forall (F_2:(Prop->nat)) (C_5:nat) (A_18:Prop) (B_16:Prop), (((ord_less_eq_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:Prop) (Y_1:Prop), (((ord_less_eq_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))).
% Axiom fact_886_order__le__less__subst2:(forall (F_2:((arrow_1196572341e_indi->Prop)->nat)) (C_5:nat) (A_18:(arrow_1196572341e_indi->Prop)) (B_16:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))).
% Axiom fact_887_order__le__less__subst2:(forall (F_2:((product_unit->Prop)->nat)) (C_5:nat) (A_18:(product_unit->Prop)) (B_16:(product_unit->Prop)), (((ord_le1511552390unit_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le1511552390unit_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))).
% Axiom fact_888_order__le__less__subst2:(forall (F_2:((arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))->nat)) (C_5:nat) (A_18:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (B_16:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o A_18) B_16)->(((ord_less_nat (F_2 B_16)) C_5)->((forall (X_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (Y_1:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))), (((ord_le1463467535_alt_o X_1) Y_1)->((ord_less_eq_nat (F_2 X_1)) (F_2 Y_1))))->((ord_less_nat (F_2 A_18)) C_5))))).
% Axiom fact_889_order__less__le__subst2:(forall (F_1:((nat->Prop)->(nat->Prop))) (C_4:(nat->Prop)) (A_17:(nat->Prop)) (B_15:(nat->Prop)), (((ord_less_nat_o A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4))))).
% Axiom fact_890_order__less__le__subst2:(forall (F_1:((product_unit->Prop)->(nat->Prop))) (C_4:(nat->Prop)) (A_17:(product_unit->Prop)) (B_15:(product_unit->Prop)), (((ord_le232288914unit_o A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4))))).
% Axiom fact_891_order__less__le__subst2:(forall (F_1:((arrow_1196572341e_indi->Prop)->(nat->Prop))) (C_4:(nat->Prop)) (A_17:(arrow_1196572341e_indi->Prop)) (B_15:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4))))).
% Axiom fact_892_order__less__le__subst2:(forall (F_1:(nat->(nat->Prop))) (C_4:(nat->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_less_eq_nat_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_nat_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat_o (F_1 A_17)) C_4))))).
% Axiom fact_893_order__less__le__subst2:(forall (F_1:(nat->(product_unit->Prop))) (C_4:(product_unit->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1511552390unit_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le232288914unit_o (F_1 X_1)) (F_1 Y_1))))->((ord_le232288914unit_o (F_1 A_17)) C_4))))).
% Axiom fact_894_order__less__le__subst2:(forall (F_1:(nat->(arrow_1196572341e_indi->Prop))) (C_4:(arrow_1196572341e_indi->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le865407012indi_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1991507760indi_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1991507760indi_o (F_1 A_17)) C_4))))).
% Axiom fact_895_order__less__le__subst2:(forall (F_1:(nat->((produc1572197287le_alt->Prop)->Prop))) (C_4:((produc1572197287le_alt->Prop)->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1027220427lt_o_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le874404799lt_o_o (F_1 X_1)) (F_1 Y_1))))->((ord_le874404799lt_o_o (F_1 A_17)) C_4))))).
% Axiom fact_896_order__less__le__subst2:(forall (F_1:(nat->(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop))) (C_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1805007862lt_o_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1382328578lt_o_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1382328578lt_o_o (F_1 A_17)) C_4))))).
% Axiom fact_897_order__less__le__subst2:(forall (F_1:(nat->((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop))) (C_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le602483040lt_o_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le914873172lt_o_o (F_1 X_1)) (F_1 Y_1))))->((ord_le914873172lt_o_o (F_1 A_17)) C_4))))).
% Axiom fact_898_order__less__le__subst2:(forall (F_1:(nat->(produc1572197287le_alt->Prop))) (C_4:(produc1572197287le_alt->Prop)) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le962286258_alt_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1852932542_alt_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1852932542_alt_o (F_1 A_17)) C_4))))).
% Axiom fact_899_order__less__le__subst2:(forall (F_1:(nat->Prop)) (C_4:Prop) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_less_eq_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_less_o (F_1 X_1)) (F_1 Y_1))))->((ord_less_o (F_1 A_17)) C_4))))).
% Axiom fact_900_order__less__le__subst2:(forall (F_1:(nat->(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop)))) (C_4:(arrow_1389031998le_alt->(arrow_1389031998le_alt->Prop))) (A_17:nat) (B_15:nat), (((ord_less_nat A_17) B_15)->(((ord_le1463467535_alt_o (F_1 B_15)) C_4)->((forall (X_1:nat) (Y_1:nat), (((ord_less_nat X_1) Y_1)->((ord_le1339521307_alt_o (F_1 X_1)) (F_1 Y_1))))->((ord_le1339521307_alt_o (F_1 A_17)) C_4))))).
% Axiom fact_901_order__less__le__subst2:(forall (F_1:((nat->Prop)->nat)) (C_4:nat) (A_17:(nat->Prop)) (B_15:(nat->Prop)), (((ord_less_nat_o A_17) B_15)->(((ord_less_eq_nat (F_1 B_15)) C_4)->((forall (X_1:(nat->Prop)) (Y_1:(nat->Prop)), (((ord_less_nat_o X_1) Y_1)->((ord_less_nat (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat (F_1 A_17)) C_4))))).
% Axiom fact_902_order__less__le__subst2:(forall (F_1:((product_unit->Prop)->nat)) (C_4:nat) (A_17:(product_unit->Prop)) (B_15:(product_unit->Prop)), (((ord_le232288914unit_o A_17) B_15)->(((ord_less_eq_nat (F_1 B_15)) C_4)->((forall (X_1:(product_unit->Prop)) (Y_1:(product_unit->Prop)), (((ord_le232288914unit_o X_1) Y_1)->((ord_less_nat (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat (F_1 A_17)) C_4))))).
% Axiom fact_903_order__less__le__subst2:(forall (F_1:((arrow_1196572341e_indi->Prop)->nat)) (C_4:nat) (A_17:(arrow_1196572341e_indi->Prop)) (B_15:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_17) B_15)->(((ord_less_eq_nat (F_1 B_15)) C_4)->((forall (X_1:(arrow_1196572341e_indi->Prop)) (Y_1:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o X_1) Y_1)->((ord_less_nat (F_1 X_1)) (F_1 Y_1))))->((ord_less_nat (F_1 A_17)) C_4))))).
% Axiom fact_904_add__leE:(forall (M_1:nat) (K:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M_1) K)) N_1)->((((ord_less_eq_nat M_1) N_1)->(((ord_less_eq_nat K) N_1)->False))->False))).
% Axiom fact_905_equalityI:(forall (A_16:((produc1572197287le_alt->Prop)->Prop)) (B_14:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_16) B_14)->(((ord_le1027220427lt_o_o B_14) A_16)->(((eq ((produc1572197287le_alt->Prop)->Prop)) A_16) B_14)))).
% Axiom fact_906_equalityI:(forall (A_16:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_16) B_14)->(((ord_le1805007862lt_o_o B_14) A_16)->(((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_16) B_14)))).
% Axiom fact_907_equalityI:(forall (A_16:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_16) B_14)->(((ord_le602483040lt_o_o B_14) A_16)->(((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_16) B_14)))).
% Axiom fact_908_equalityI:(forall (A_16:(produc1572197287le_alt->Prop)) (B_14:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_16) B_14)->(((ord_le962286258_alt_o B_14) A_16)->(((eq (produc1572197287le_alt->Prop)) A_16) B_14)))).
% Axiom fact_909_equalityI:(forall (A_16:(arrow_1196572341e_indi->Prop)) (B_14:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_16) B_14)->(((ord_le865407012indi_o B_14) A_16)->(((eq (arrow_1196572341e_indi->Prop)) A_16) B_14)))).
% Axiom fact_910_equalityI:(forall (A_16:(product_unit->Prop)) (B_14:(product_unit->Prop)), (((ord_le1511552390unit_o A_16) B_14)->(((ord_le1511552390unit_o B_14) A_16)->(((eq (product_unit->Prop)) A_16) B_14)))).
% Axiom fact_911_equalityI:(forall (A_16:(nat->Prop)) (B_14:(nat->Prop)), (((ord_less_eq_nat_o A_16) B_14)->(((ord_less_eq_nat_o B_14) A_16)->(((eq (nat->Prop)) A_16) B_14)))).
% Axiom fact_912_subsetD:(forall (C_3:arrow_1196572341e_indi) (A_15:(arrow_1196572341e_indi->Prop)) (B_13:(arrow_1196572341e_indi->Prop)), (((ord_le865407012indi_o A_15) B_13)->(((member1818997282e_indi C_3) A_15)->((member1818997282e_indi C_3) B_13)))).
% Axiom fact_913_subsetD:(forall (C_3:Prop) (A_15:(Prop->Prop)) (B_13:(Prop->Prop)), (((ord_less_eq_o_o A_15) B_13)->(((member_o C_3) A_15)->((member_o C_3) B_13)))).
% Axiom fact_914_subsetD:(forall (C_3:product_unit) (A_15:(product_unit->Prop)) (B_13:(product_unit->Prop)), (((ord_le1511552390unit_o A_15) B_13)->(((member_Product_unit C_3) A_15)->((member_Product_unit C_3) B_13)))).
% Axiom fact_915_subsetD:(forall (C_3:produc1572197287le_alt) (A_15:(produc1572197287le_alt->Prop)) (B_13:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_15) B_13)->(((member285112084le_alt C_3) A_15)->((member285112084le_alt C_3) B_13)))).
% Axiom fact_916_subsetD:(forall (C_3:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_15:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_15) B_13)->(((member822980838_alt_o C_3) A_15)->((member822980838_alt_o C_3) B_13)))).
% Axiom fact_917_subsetD:(forall (C_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_15:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_13:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_15) B_13)->(((member1425217232_alt_o C_3) A_15)->((member1425217232_alt_o C_3) B_13)))).
% Axiom fact_918_subsetD:(forall (C_3:(produc1572197287le_alt->Prop)) (A_15:((produc1572197287le_alt->Prop)->Prop)) (B_13:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_15) B_13)->(((member1241905979_alt_o C_3) A_15)->((member1241905979_alt_o C_3) B_13)))).
% Axiom fact_919_subsetD:(forall (C_3:nat) (A_15:(nat->Prop)) (B_13:(nat->Prop)), (((ord_less_eq_nat_o A_15) B_13)->(((member_nat C_3) A_15)->((member_nat C_3) B_13)))).
% Axiom fact_920_psubset__eq:(forall (A_14:(product_unit->Prop)) (B_12:(product_unit->Prop)), ((iff ((ord_le232288914unit_o A_14) B_12)) ((and ((ord_le1511552390unit_o A_14) B_12)) (not (((eq (product_unit->Prop)) A_14) B_12))))).
% Axiom fact_921_psubset__eq:(forall (A_14:(arrow_1196572341e_indi->Prop)) (B_12:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le1991507760indi_o A_14) B_12)) ((and ((ord_le865407012indi_o A_14) B_12)) (not (((eq (arrow_1196572341e_indi->Prop)) A_14) B_12))))).
% Axiom fact_922_psubset__eq:(forall (A_14:((produc1572197287le_alt->Prop)->Prop)) (B_12:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le874404799lt_o_o A_14) B_12)) ((and ((ord_le1027220427lt_o_o A_14) B_12)) (not (((eq ((produc1572197287le_alt->Prop)->Prop)) A_14) B_12))))).
% Axiom fact_923_psubset__eq:(forall (A_14:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_12:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1382328578lt_o_o A_14) B_12)) ((and ((ord_le1805007862lt_o_o A_14) B_12)) (not (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_14) B_12))))).
% Axiom fact_924_psubset__eq:(forall (A_14:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le914873172lt_o_o A_14) B_12)) ((and ((ord_le602483040lt_o_o A_14) B_12)) (not (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_14) B_12))))).
% Axiom fact_925_psubset__eq:(forall (A_14:(produc1572197287le_alt->Prop)) (B_12:(produc1572197287le_alt->Prop)), ((iff ((ord_le1852932542_alt_o A_14) B_12)) ((and ((ord_le962286258_alt_o A_14) B_12)) (not (((eq (produc1572197287le_alt->Prop)) A_14) B_12))))).
% Axiom fact_926_psubset__eq:(forall (A_14:(nat->Prop)) (B_12:(nat->Prop)), ((iff ((ord_less_nat_o A_14) B_12)) ((and ((ord_less_eq_nat_o A_14) B_12)) (not (((eq (nat->Prop)) A_14) B_12))))).
% Axiom fact_927_subset__iff__psubset__eq:(forall (A_13:(product_unit->Prop)) (B_11:(product_unit->Prop)), ((iff ((ord_le1511552390unit_o A_13) B_11)) ((or ((ord_le232288914unit_o A_13) B_11)) (((eq (product_unit->Prop)) A_13) B_11)))).
% Axiom fact_928_subset__iff__psubset__eq:(forall (A_13:(arrow_1196572341e_indi->Prop)) (B_11:(arrow_1196572341e_indi->Prop)), ((iff ((ord_le865407012indi_o A_13) B_11)) ((or ((ord_le1991507760indi_o A_13) B_11)) (((eq (arrow_1196572341e_indi->Prop)) A_13) B_11)))).
% Axiom fact_929_subset__iff__psubset__eq:(forall (A_13:((produc1572197287le_alt->Prop)->Prop)) (B_11:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o A_13) B_11)) ((or ((ord_le874404799lt_o_o A_13) B_11)) (((eq ((produc1572197287le_alt->Prop)->Prop)) A_13) B_11)))).
% Axiom fact_930_subset__iff__psubset__eq:(forall (A_13:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_11:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o A_13) B_11)) ((or ((ord_le1382328578lt_o_o A_13) B_11)) (((eq (((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) A_13) B_11)))).
% Axiom fact_931_subset__iff__psubset__eq:(forall (A_13:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_11:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o A_13) B_11)) ((or ((ord_le914873172lt_o_o A_13) B_11)) (((eq ((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) A_13) B_11)))).
% Axiom fact_932_subset__iff__psubset__eq:(forall (A_13:(produc1572197287le_alt->Prop)) (B_11:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o A_13) B_11)) ((or ((ord_le1852932542_alt_o A_13) B_11)) (((eq (produc1572197287le_alt->Prop)) A_13) B_11)))).
% Axiom fact_933_subset__iff__psubset__eq:(forall (A_13:(nat->Prop)) (B_11:(nat->Prop)), ((iff ((ord_less_eq_nat_o A_13) B_11)) ((or ((ord_less_nat_o A_13) B_11)) (((eq (nat->Prop)) A_13) B_11)))).
% Axiom fact_934_psubset__imp__subset:(forall (A_12:(product_unit->Prop)) (B_10:(product_unit->Prop)), (((ord_le232288914unit_o A_12) B_10)->((ord_le1511552390unit_o A_12) B_10))).
% Axiom fact_935_psubset__imp__subset:(forall (A_12:(arrow_1196572341e_indi->Prop)) (B_10:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_12) B_10)->((ord_le865407012indi_o A_12) B_10))).
% Axiom fact_936_psubset__imp__subset:(forall (A_12:((produc1572197287le_alt->Prop)->Prop)) (B_10:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o A_12) B_10)->((ord_le1027220427lt_o_o A_12) B_10))).
% Axiom fact_937_psubset__imp__subset:(forall (A_12:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o A_12) B_10)->((ord_le1805007862lt_o_o A_12) B_10))).
% Axiom fact_938_psubset__imp__subset:(forall (A_12:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_10:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o A_12) B_10)->((ord_le602483040lt_o_o A_12) B_10))).
% Axiom fact_939_psubset__imp__subset:(forall (A_12:(produc1572197287le_alt->Prop)) (B_10:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o A_12) B_10)->((ord_le962286258_alt_o A_12) B_10))).
% Axiom fact_940_psubset__imp__subset:(forall (A_12:(nat->Prop)) (B_10:(nat->Prop)), (((ord_less_nat_o A_12) B_10)->((ord_less_eq_nat_o A_12) B_10))).
% Axiom fact_941_psubset__subset__trans:(forall (C_2:(product_unit->Prop)) (A_11:(product_unit->Prop)) (B_9:(product_unit->Prop)), (((ord_le232288914unit_o A_11) B_9)->(((ord_le1511552390unit_o B_9) C_2)->((ord_le232288914unit_o A_11) C_2)))).
% Axiom fact_942_psubset__subset__trans:(forall (C_2:(arrow_1196572341e_indi->Prop)) (A_11:(arrow_1196572341e_indi->Prop)) (B_9:(arrow_1196572341e_indi->Prop)), (((ord_le1991507760indi_o A_11) B_9)->(((ord_le865407012indi_o B_9) C_2)->((ord_le1991507760indi_o A_11) C_2)))).
% Axiom fact_943_psubset__subset__trans:(forall (C_2:((produc1572197287le_alt->Prop)->Prop)) (A_11:((produc1572197287le_alt->Prop)->Prop)) (B_9:((produc1572197287le_alt->Prop)->Prop)), (((ord_le874404799lt_o_o A_11) B_9)->(((ord_le1027220427lt_o_o B_9) C_2)->((ord_le874404799lt_o_o A_11) C_2)))).
% Axiom fact_944_psubset__subset__trans:(forall (C_2:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_11:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_9:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1382328578lt_o_o A_11) B_9)->(((ord_le1805007862lt_o_o B_9) C_2)->((ord_le1382328578lt_o_o A_11) C_2)))).
% Axiom fact_945_psubset__subset__trans:(forall (C_2:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_11:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_9:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le914873172lt_o_o A_11) B_9)->(((ord_le602483040lt_o_o B_9) C_2)->((ord_le914873172lt_o_o A_11) C_2)))).
% Axiom fact_946_psubset__subset__trans:(forall (C_2:(produc1572197287le_alt->Prop)) (A_11:(produc1572197287le_alt->Prop)) (B_9:(produc1572197287le_alt->Prop)), (((ord_le1852932542_alt_o A_11) B_9)->(((ord_le962286258_alt_o B_9) C_2)->((ord_le1852932542_alt_o A_11) C_2)))).
% Axiom fact_947_psubset__subset__trans:(forall (C_2:(nat->Prop)) (A_11:(nat->Prop)) (B_9:(nat->Prop)), (((ord_less_nat_o A_11) B_9)->(((ord_less_eq_nat_o B_9) C_2)->((ord_less_nat_o A_11) C_2)))).
% Axiom fact_948_subset__psubset__trans:(forall (C_1:((produc1572197287le_alt->Prop)->Prop)) (A_10:((produc1572197287le_alt->Prop)->Prop)) (B_8:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_10) B_8)->(((ord_le874404799lt_o_o B_8) C_1)->((ord_le874404799lt_o_o A_10) C_1)))).
% Axiom fact_949_subset__psubset__trans:(forall (C_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (A_10:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_8:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_10) B_8)->(((ord_le1382328578lt_o_o B_8) C_1)->((ord_le1382328578lt_o_o A_10) C_1)))).
% Axiom fact_950_subset__psubset__trans:(forall (C_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (A_10:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_8:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_10) B_8)->(((ord_le914873172lt_o_o B_8) C_1)->((ord_le914873172lt_o_o A_10) C_1)))).
% Axiom fact_951_subset__psubset__trans:(forall (C_1:(produc1572197287le_alt->Prop)) (A_10:(produc1572197287le_alt->Prop)) (B_8:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_10) B_8)->(((ord_le1852932542_alt_o B_8) C_1)->((ord_le1852932542_alt_o A_10) C_1)))).
% Axiom fact_952_subset__psubset__trans:(forall (C_1:(nat->Prop)) (A_10:(nat->Prop)) (B_8:(nat->Prop)), (((ord_less_eq_nat_o A_10) B_8)->(((ord_less_nat_o B_8) C_1)->((ord_less_nat_o A_10) C_1)))).
% Axiom fact_953_equalityE:(forall (A_9:(nat->Prop)) (B_7:(nat->Prop)), ((((eq (nat->Prop)) A_9) B_7)->((((ord_less_eq_nat_o A_9) B_7)->(((ord_less_eq_nat_o B_7) A_9)->False))->False))).
% Axiom fact_954_subset__trans:(forall (C:(nat->Prop)) (A_8:(nat->Prop)) (B_6:(nat->Prop)), (((ord_less_eq_nat_o A_8) B_6)->(((ord_less_eq_nat_o B_6) C)->((ord_less_eq_nat_o A_8) C)))).
% Axiom fact_955_set__mp:(forall (X_6:nat) (A_7:(nat->Prop)) (B_5:(nat->Prop)), (((ord_less_eq_nat_o A_7) B_5)->(((member_nat X_6) A_7)->((member_nat X_6) B_5)))).
% Axiom fact_956_set__mp:(forall (X_6:(produc1572197287le_alt->Prop)) (A_7:((produc1572197287le_alt->Prop)->Prop)) (B_5:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_7) B_5)->(((member1241905979_alt_o X_6) A_7)->((member1241905979_alt_o X_6) B_5)))).
% Axiom fact_957_set__mp:(forall (X_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_7:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_7) B_5)->(((member1425217232_alt_o X_6) A_7)->((member1425217232_alt_o X_6) B_5)))).
% Axiom fact_958_set__mp:(forall (X_6:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_7:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_7) B_5)->(((member822980838_alt_o X_6) A_7)->((member822980838_alt_o X_6) B_5)))).
% Axiom fact_959_set__mp:(forall (X_6:produc1572197287le_alt) (A_7:(produc1572197287le_alt->Prop)) (B_5:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_7) B_5)->(((member285112084le_alt X_6) A_7)->((member285112084le_alt X_6) B_5)))).
% Axiom fact_960_set__rev__mp:(forall (B_4:(nat->Prop)) (X_5:nat) (A_6:(nat->Prop)), (((member_nat X_5) A_6)->(((ord_less_eq_nat_o A_6) B_4)->((member_nat X_5) B_4)))).
% Axiom fact_961_set__rev__mp:(forall (B_4:((produc1572197287le_alt->Prop)->Prop)) (X_5:(produc1572197287le_alt->Prop)) (A_6:((produc1572197287le_alt->Prop)->Prop)), (((member1241905979_alt_o X_5) A_6)->(((ord_le1027220427lt_o_o A_6) B_4)->((member1241905979_alt_o X_5) B_4)))).
% Axiom fact_962_set__rev__mp:(forall (B_4:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (X_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_6:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((member1425217232_alt_o X_5) A_6)->(((ord_le1805007862lt_o_o A_6) B_4)->((member1425217232_alt_o X_5) B_4)))).
% Axiom fact_963_set__rev__mp:(forall (B_4:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (X_5:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_6:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((member822980838_alt_o X_5) A_6)->(((ord_le602483040lt_o_o A_6) B_4)->((member822980838_alt_o X_5) B_4)))).
% Axiom fact_964_set__rev__mp:(forall (B_4:(produc1572197287le_alt->Prop)) (X_5:produc1572197287le_alt) (A_6:(produc1572197287le_alt->Prop)), (((member285112084le_alt X_5) A_6)->(((ord_le962286258_alt_o A_6) B_4)->((member285112084le_alt X_5) B_4)))).
% Axiom fact_965_predicate1D:(forall (X_4:nat) (P_2:(nat->Prop)) (Q_1:(nat->Prop)), (((ord_less_eq_nat_o P_2) Q_1)->((P_2 X_4)->(Q_1 X_4)))).
% Axiom fact_966_in__mono:(forall (X_3:nat) (A_5:(nat->Prop)) (B_3:(nat->Prop)), (((ord_less_eq_nat_o A_5) B_3)->(((member_nat X_3) A_5)->((member_nat X_3) B_3)))).
% Axiom fact_967_in__mono:(forall (X_3:(produc1572197287le_alt->Prop)) (A_5:((produc1572197287le_alt->Prop)->Prop)) (B_3:((produc1572197287le_alt->Prop)->Prop)), (((ord_le1027220427lt_o_o A_5) B_3)->(((member1241905979_alt_o X_3) A_5)->((member1241905979_alt_o X_3) B_3)))).
% Axiom fact_968_in__mono:(forall (X_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))) (A_5:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (B_3:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), (((ord_le1805007862lt_o_o A_5) B_3)->(((member1425217232_alt_o X_3) A_5)->((member1425217232_alt_o X_3) B_3)))).
% Axiom fact_969_in__mono:(forall (X_3:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop))) (A_5:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (B_3:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), (((ord_le602483040lt_o_o A_5) B_3)->(((member822980838_alt_o X_3) A_5)->((member822980838_alt_o X_3) B_3)))).
% Axiom fact_970_in__mono:(forall (X_3:produc1572197287le_alt) (A_5:(produc1572197287le_alt->Prop)) (B_3:(produc1572197287le_alt->Prop)), (((ord_le962286258_alt_o A_5) B_3)->(((member285112084le_alt X_3) A_5)->((member285112084le_alt X_3) B_3)))).
% Axiom fact_971_equalityD2:(forall (A_4:(nat->Prop)) (B_2:(nat->Prop)), ((((eq (nat->Prop)) A_4) B_2)->((ord_less_eq_nat_o B_2) A_4))).
% Axiom fact_972_equalityD1:(forall (A_3:(nat->Prop)) (B_1:(nat->Prop)), ((((eq (nat->Prop)) A_3) B_1)->((ord_less_eq_nat_o A_3) B_1))).
% Axiom fact_973_rev__predicate1D:(forall (Q:(nat->Prop)) (P_1:(nat->Prop)) (X_2:nat), ((P_1 X_2)->(((ord_less_eq_nat_o P_1) Q)->(Q X_2)))).
% Axiom fact_974_set__eq__subset:(forall (A_2:(nat->Prop)) (B:(nat->Prop)), ((iff (((eq (nat->Prop)) A_2) B)) ((and ((ord_less_eq_nat_o A_2) B)) ((ord_less_eq_nat_o B) A_2)))).
% Axiom fact_975_subset__refl:(forall (A_1:(nat->Prop)), ((ord_less_eq_nat_o A_1) A_1)).
% Axiom fact_976_pred__subset__eq:(forall (R:(nat->Prop)) (S_1:(nat->Prop)), ((iff ((ord_less_eq_nat_o (fun (X_1:nat)=> ((member_nat X_1) R))) (fun (X_1:nat)=> ((member_nat X_1) S_1)))) ((ord_less_eq_nat_o R) S_1))).
% Axiom fact_977_pred__subset__eq:(forall (R:((produc1572197287le_alt->Prop)->Prop)) (S_1:((produc1572197287le_alt->Prop)->Prop)), ((iff ((ord_le1027220427lt_o_o (fun (X_1:(produc1572197287le_alt->Prop))=> ((member1241905979_alt_o X_1) R))) (fun (X_1:(produc1572197287le_alt->Prop))=> ((member1241905979_alt_o X_1) S_1)))) ((ord_le1027220427lt_o_o R) S_1))).
% Axiom fact_978_pred__subset__eq:(forall (R:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)) (S_1:(((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le1805007862lt_o_o (fun (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> ((member1425217232_alt_o X_1) R))) (fun (X_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->(produc1572197287le_alt->Prop)))=> ((member1425217232_alt_o X_1) S_1)))) ((ord_le1805007862lt_o_o R) S_1))).
% Axiom fact_979_pred__subset__eq:(forall (R:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)) (S_1:((arrow_1196572341e_indi->(produc1572197287le_alt->Prop))->Prop)), ((iff ((ord_le602483040lt_o_o (fun (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> ((member822980838_alt_o X_1) R))) (fun (X_1:(arrow_1196572341e_indi->(produc1572197287le_alt->Prop)))=> ((member822980838_alt_o X_1) S_1)))) ((ord_le602483040lt_o_o R) S_1))).
% Axiom fact_980_pred__subset__eq:(forall (R:(produc1572197287le_alt->Prop)) (S_1:(produc1572197287le_alt->Prop)), ((iff ((ord_le962286258_alt_o (fun (X_1:produc1572197287le_alt)=> ((member285112084le_alt X_1) R))) (fun (X_1:produc1572197287le_alt)=> ((member285112084le_alt X_1) S_1)))) ((ord_le962286258_alt_o R) S_1))).
% Axiom fact_981_less__not__refl:(forall (N_1:nat), (((ord_less_nat N_1) N_1)->False)).
% Axiom fact_982_nat__neq__iff:(forall (M_1:nat) (N_1:nat), ((iff (not (((eq nat) M_1) N_1))) ((or ((ord_less_nat M_1) N_1)) ((ord_less_nat N_1) M_1)))).
% Axiom fact_983_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_984_less__irrefl__nat:(forall (N_1:nat), (((ord_less_nat N_1) N_1)->False)).
% Axiom fact_985_less__not__refl2:(forall (N_1:nat) (M_1:nat), (((ord_less_nat N_1) M_1)->(not (((eq nat) M_1) N_1)))).
% Axiom fact_986_less__not__refl3:(forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))).
% Axiom fact_987_nat__less__cases:(forall (P:(nat->(nat->Prop))) (M_1:nat) (N_1:nat), ((((ord_less_nat M_1) N_1)->((P N_1) M_1))->(((((eq nat) M_1) N_1)->((P N_1) M_1))->((((ord_less_nat N_1) M_1)->((P N_1) M_1))->((P N_1) M_1))))).
% Axiom fact_988_nat__add__commute:(forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M_1) N_1)) ((plus_plus_nat N_1) M_1))).
% Axiom fact_989_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_990_nat__add__assoc:(forall (M_1:nat) (N_1:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M_1) N_1)) K)) ((plus_plus_nat M_1) ((plus_plus_nat N_1) K)))).
% Axiom fact_991_nat__add__left__cancel:(forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat K) M_1)) ((plus_plus_nat K) N_1))) (((eq nat) M_1) N_1))).
% Axiom fact_992_nat__add__right__cancel:(forall (M_1:nat) (K:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M_1) K)) ((plus_plus_nat N_1) K))) (((eq nat) M_1) N_1))).
% Axiom fact_993_le__refl:(forall (N_1:nat), ((ord_less_eq_nat N_1) N_1)).
% Axiom fact_994_nat__le__linear:(forall (M_1:nat) (N_1:nat), ((or ((ord_less_eq_nat M_1) N_1)) ((ord_less_eq_nat N_1) M_1))).
% Axiom fact_995_eq__imp__le:(forall (M_1:nat) (N_1:nat), ((((eq nat) M_1) N_1)->((ord_less_eq_nat M_1) N_1))).
% Axiom fact_996_le__trans:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K)))).
% Axiom fact_997_le__antisym:(forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->(((ord_less_eq_nat N_1) M_1)->(((eq nat) M_1) N_1)))).
% Axiom fact_998_inj__on__add__nat:(forall (K:nat) (N_2:(nat->Prop)), ((inj_on_nat_nat (fun (N:nat)=> ((plus_plus_nat N) K))) N_2)).
% Axiom fact_999_not__add__less1:(forall (_TPTP_I:nat) (J:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) _TPTP_I)->False)).
% Axiom fact_1000_not__add__less2:(forall (J:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J) _TPTP_I)) _TPTP_I)->False)).
% Axiom fact_1001_nat__add__left__cancel__less:(forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M_1)) ((plus_plus_nat K) N_1))) ((ord_less_nat M_1) N_1))).
% Axiom fact_1002_trans__less__add1:(forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat J) M_1)))).
% Axiom fact_1003_trans__less__add2:(forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat M_1) J)))).
% Axiom fact_1004_add__less__mono1:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))).
% Axiom fact_1005_add__less__mono:(forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))).
% Axiom fact_1006_less__add__eq__less:(forall (M_1:nat) (N_1:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M_1) L)) ((plus_plus_nat K) N_1))->((ord_less_nat M_1) N_1)))).
% Axiom fact_1007_add__lessD1:(forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) K)->((ord_less_nat _TPTP_I) K))).
% Axiom fact_1008_nat__less__le:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) N_1)) ((and ((ord_less_eq_nat M_1) N_1)) (not (((eq nat) M_1) N_1))))).
% Axiom fact_1009_le__eq__less__or__eq:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_1) N_1)) ((or ((ord_less_nat M_1) N_1)) (((eq nat) M_1) N_1)))).
% Axiom fact_1010_less__imp__le__nat:(forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_eq_nat M_1) N_1))).
% Axiom fact_1011_le__neq__implies__less:(forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((not (((eq nat) M_1) N_1))->((ord_less_nat M_1) N_1)))).
% Axiom fact_1012_less__or__eq__imp__le:(forall (M_1:nat) (N_1:nat), (((or ((ord_less_nat M_1) N_1)) (((eq nat) M_1) N_1))->((ord_less_eq_nat M_1) N_1))).
% Axiom fact_1013_le__add2:(forall (N_1:nat) (M_1:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat M_1) N_1))).
% Axiom fact_1014_le__add1:(forall (N_1:nat) (M_1:nat), ((ord_less_eq_nat N_1) ((plus_plus_nat N_1) M_1))).
% Axiom fact_1015_le__iff__add:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_1) N_1)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N_1) ((plus_plus_nat M_1) K_1)))))).
% Axiom fact_1016_nat__add__left__cancel__le:(forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M_1)) ((plus_plus_nat K) N_1))) ((ord_less_eq_nat M_1) N_1))).
% Axiom fact_1017_trans__le__add1:(forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J) M_1)))).
% Axiom fact_1018_trans__le__add2:(forall (M_1:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M_1) J)))).
% Axiom fact_1019_add__le__mono1:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))).
% Axiom fact_1020_add__le__mono:(forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))).
% Axiom fact_1021_add__leD2:(forall (M_1:nat) (K:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M_1) K)) N_1)->((ord_less_eq_nat K) N_1))).
% Axiom fact_1022_add__leD1:(forall (M_1:nat) (K:nat) (N_1:nat), (((ord_less_eq_nat ((plus_plus_nat M_1) K)) N_1)->((ord_less_eq_nat M_1) N_1))).
% Axiom fact_1023_mono__nat__linear__lb:(forall (M_1:nat) (K:nat) (F:(nat->nat)), ((forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (F M)) (F N))))->((ord_less_eq_nat ((plus_plus_nat (F M_1)) K)) (F ((plus_plus_nat M_1) K))))).
% Axiom fact_1024_less__mono__imp__le__mono:(forall (_TPTP_I:nat) (J:nat) (F:(nat->nat)), ((forall (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat (F I_1)) (F J_1))))->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat (F _TPTP_I)) (F J))))).
% Axiom fact_1025_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_1026_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_1027_termination__basic__simps_I5_J:(forall (X:nat) (Y:nat), (((ord_less_nat X) Y)->((ord_less_eq_nat X) Y))).
% Axiom fact_1028_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_1029_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_1030_linear__alt:((ex (produc1572197287le_alt->Prop)) (fun (L_1:(produc1572197287le_alt->Prop))=> ((member1241905979_alt_o L_1) arrow_1982173296le_Lin))).
% Axiom fact_1031_finite__indi:(finite431949602e_indi top_to54564308indi_o).
% Axiom fact_1032_finite__Collect__le__nat:(forall (K:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat N) K))))).
% Axiom fact_1033_finite__Collect__less__nat:(forall (K:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_nat N) K))))).
% Axiom fact_1034_infinite__UNIV__nat:((finite_finite_nat top_top_nat_o)->False).
% Axiom fact_1035_card__UNIV__unit:(((eq nat) (finite1949902593t_unit top_to1984820022unit_o)) one_one_nat).
% Axiom fact_1036_card__Collect__less__nat:(forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_nat I_1) N_1))))) N_1)).
% Axiom fact_1037_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_1038_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_1039_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_1040_finite__less__ub:(forall (U:nat) (F:(nat->nat)), ((forall (N:nat), ((ord_less_eq_nat N) (F N)))->(finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat (F N)) U)))))).
% Axiom fact_1041_bounded__nat__set__is__finite:(forall (N_1:nat) (N_2:(nat->Prop)), ((forall (X_1:nat), (((member_nat X_1) N_2)->((ord_less_nat X_1) N_1)))->(finite_finite_nat N_2))).
% Axiom fact_1042_less__zeroE:(forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)).
% Axiom fact_1043_le0:(forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1)).
% Axiom fact_1044_not__less0:(forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)).
% Axiom fact_1045_neq0__conv:(forall (N_1:nat), ((iff (not (((eq nat) N_1) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N_1))).
% Axiom fact_1046_less__nat__zero__code:(forall (N_1:nat), (((ord_less_nat N_1) zero_zero_nat)->False)).
% Axiom fact_1047_gr__implies__not0:(forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->(not (((eq nat) N_1) zero_zero_nat)))).
% Axiom fact_1048_gr0I:(forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ord_less_nat zero_zero_nat) N_1))).
% Axiom fact_1049_plus__nat_Oadd__0:(forall (N_1:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N_1)) N_1)).
% Axiom fact_1050_Nat_Oadd__0__right:(forall (M_1:nat), (((eq nat) ((plus_plus_nat M_1) zero_zero_nat)) M_1)).
% Axiom fact_1051_add__is__0:(forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M_1) N_1)) zero_zero_nat)) ((and (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat)))).
% Axiom fact_1052_add__eq__self__zero:(forall (M_1:nat) (N_1:nat), ((((eq nat) ((plus_plus_nat M_1) N_1)) M_1)->(((eq nat) N_1) zero_zero_nat))).
% Axiom fact_1053_le__0__eq:(forall (N_1:nat), ((iff ((ord_less_eq_nat N_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat))).
% Axiom fact_1054_less__eq__nat_Osimps_I1_J:(forall (N_1:nat), ((ord_less_eq_nat zero_zero_nat) N_1)).
% Axiom fact_1055_add__gr__0:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M_1) N_1))) ((or ((ord_less_nat zero_zero_nat) M_1)) ((ord_less_nat zero_zero_nat) N_1)))).
% Axiom fact_1056_ex__least__nat__less:(forall (N_1:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N_1)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N_1)) (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_1057_ex__least__nat__le:(forall (N_1:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N_1)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N_1)) (forall (I_1:nat), (((ord_less_nat I_1) K_1)->((P I_1)->False))))) (P K_1))))))).
% Axiom fact_1058_less__imp__add__positive:(forall (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((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)))))).
% Axiom fact_1059_lessI:(forall (N_1:nat), ((ord_less_nat N_1) (suc N_1))).
% Axiom fact_1060_Suc__mono:(forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat (suc M_1)) (suc N_1)))).
% Axiom fact_1061_zero__less__Suc:(forall (N_1:nat), ((ord_less_nat zero_zero_nat) (suc N_1))).
% Axiom fact_1062_Suc__inject:(forall (X:nat) (Y:nat), ((((eq nat) (suc X)) (suc Y))->(((eq nat) X) Y))).
% Axiom fact_1063_nat_Oinject:(forall (Nat:nat) (Nat_2:nat), ((iff (((eq nat) (suc Nat)) (suc Nat_2))) (((eq nat) Nat) Nat_2))).
% Axiom fact_1064_Suc__n__not__n:(forall (N_1:nat), (not (((eq nat) (suc N_1)) N_1))).
% Axiom fact_1065_n__not__Suc__n:(forall (N_1:nat), (not (((eq nat) N_1) (suc N_1)))).
% Axiom fact_1066_Suc__neq__Zero:(forall (M_1:nat), (not (((eq nat) (suc M_1)) zero_zero_nat))).
% Axiom fact_1067_Zero__neq__Suc:(forall (M_1:nat), (not (((eq nat) zero_zero_nat) (suc M_1)))).
% Axiom fact_1068_nat_Osimps_I3_J:(forall (Nat_3:nat), (not (((eq nat) (suc Nat_3)) zero_zero_nat))).
% Axiom fact_1069_Suc__not__Zero:(forall (M_1:nat), (not (((eq nat) (suc M_1)) zero_zero_nat))).
% Axiom fact_1070_nat_Osimps_I2_J:(forall (Nat_2:nat), (not (((eq nat) zero_zero_nat) (suc Nat_2)))).
% Axiom fact_1071_Zero__not__Suc:(forall (M_1:nat), (not (((eq nat) zero_zero_nat) (suc M_1)))).
% Axiom fact_1072_Suc__less__SucD:(forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc M_1)) (suc N_1))->((ord_less_nat M_1) N_1))).
% Axiom fact_1073_Suc__lessD:(forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc M_1)) N_1)->((ord_less_nat M_1) N_1))).
% Axiom fact_1074_less__SucE:(forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) (suc N_1))->((((ord_less_nat M_1) N_1)->False)->(((eq nat) M_1) N_1)))).
% Axiom fact_1075_less__trans__Suc:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat J) K)->((ord_less_nat (suc _TPTP_I)) K)))).
% Axiom fact_1076_Suc__lessI:(forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((not (((eq nat) (suc M_1)) N_1))->((ord_less_nat (suc M_1)) N_1)))).
% Axiom fact_1077_less__SucI:(forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat M_1) (suc N_1)))).
% Axiom fact_1078_less__antisym:(forall (N_1:nat) (M_1:nat), ((((ord_less_nat N_1) M_1)->False)->(((ord_less_nat N_1) (suc M_1))->(((eq nat) M_1) N_1)))).
% Axiom fact_1079_not__less__less__Suc__eq:(forall (N_1:nat) (M_1:nat), ((((ord_less_nat N_1) M_1)->False)->((iff ((ord_less_nat N_1) (suc M_1))) (((eq nat) N_1) M_1)))).
% Axiom fact_1080_Suc__less__eq:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat (suc M_1)) (suc N_1))) ((ord_less_nat M_1) N_1))).
% Axiom fact_1081_less__Suc__eq:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) (suc N_1))) ((or ((ord_less_nat M_1) N_1)) (((eq nat) M_1) N_1)))).
% Axiom fact_1082_not__less__eq:(forall (M_1:nat) (N_1:nat), ((iff (((ord_less_nat M_1) N_1)->False)) ((ord_less_nat N_1) (suc M_1)))).
% Axiom fact_1083_add__Suc__shift:(forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M_1)) N_1)) ((plus_plus_nat M_1) (suc N_1)))).
% Axiom fact_1084_add__Suc:(forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat (suc M_1)) N_1)) (suc ((plus_plus_nat M_1) N_1)))).
% Axiom fact_1085_add__Suc__right:(forall (M_1:nat) (N_1:nat), (((eq nat) ((plus_plus_nat M_1) (suc N_1))) (suc ((plus_plus_nat M_1) N_1)))).
% Axiom fact_1086_Suc__leD:(forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat (suc M_1)) N_1)->((ord_less_eq_nat M_1) N_1))).
% Axiom fact_1087_le__SucE:(forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) (suc N_1))->((((ord_less_eq_nat M_1) N_1)->False)->(((eq nat) M_1) (suc N_1))))).
% Axiom fact_1088_le__SucI:(forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((ord_less_eq_nat M_1) (suc N_1)))).
% Axiom fact_1089_Suc__le__mono:(forall (N_1:nat) (M_1:nat), ((iff ((ord_less_eq_nat (suc N_1)) (suc M_1))) ((ord_less_eq_nat N_1) M_1))).
% Axiom fact_1090_le__Suc__eq:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat M_1) (suc N_1))) ((or ((ord_less_eq_nat M_1) N_1)) (((eq nat) M_1) (suc N_1))))).
% Axiom fact_1091_not__less__eq__eq:(forall (M_1:nat) (N_1:nat), ((iff (((ord_less_eq_nat M_1) N_1)->False)) ((ord_less_eq_nat (suc N_1)) M_1))).
% Axiom fact_1092_Suc__n__not__le__n:(forall (N_1:nat), (((ord_less_eq_nat (suc N_1)) N_1)->False)).
% Axiom fact_1093_inj__Suc:(forall (N_2:(nat->Prop)), ((inj_on_nat_nat suc) N_2)).
% Axiom fact_1094_gr0__conv__Suc:(forall (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) N_1)) ((ex nat) (fun (M:nat)=> (((eq nat) N_1) (suc M)))))).
% Axiom fact_1095_less__Suc0:(forall (N_1:nat), ((iff ((ord_less_nat N_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))).
% Axiom fact_1096_less__Suc__eq__0__disj:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) (suc N_1))) ((or (((eq nat) M_1) zero_zero_nat)) ((ex nat) (fun (J_1:nat)=> ((and (((eq nat) M_1) (suc J_1))) ((ord_less_nat J_1) N_1))))))).
% Axiom fact_1097_add__is__1:(forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((plus_plus_nat M_1) N_1)) (suc zero_zero_nat))) ((or ((and (((eq nat) M_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat)))))).
% Axiom fact_1098_one__is__add:(forall (M_1:nat) (N_1:nat), ((iff (((eq nat) (suc zero_zero_nat)) ((plus_plus_nat M_1) N_1))) ((or ((and (((eq nat) M_1) (suc zero_zero_nat))) (((eq nat) N_1) zero_zero_nat))) ((and (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) (suc zero_zero_nat)))))).
% Axiom fact_1099_less__add__Suc1:(forall (_TPTP_I:nat) (M_1:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat _TPTP_I) M_1)))).
% Axiom fact_1100_less__add__Suc2:(forall (_TPTP_I:nat) (M_1:nat), ((ord_less_nat _TPTP_I) (suc ((plus_plus_nat M_1) _TPTP_I)))).
% Axiom fact_1101_less__iff__Suc__add:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) N_1)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N_1) (suc ((plus_plus_nat M_1) K_1))))))).
% Axiom fact_1102_less__eq__Suc__le:(forall (N_1:nat) (M_1:nat), ((iff ((ord_less_nat N_1) M_1)) ((ord_less_eq_nat (suc N_1)) M_1))).
% Axiom fact_1103_less__Suc__eq__le:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat M_1) (suc N_1))) ((ord_less_eq_nat M_1) N_1))).
% Axiom fact_1104_Suc__le__eq:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M_1)) N_1)) ((ord_less_nat M_1) N_1))).
% Axiom fact_1105_le__imp__less__Suc:(forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((ord_less_nat M_1) (suc N_1)))).
% Axiom fact_1106_Suc__leI:(forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_eq_nat (suc M_1)) N_1))).
% Axiom fact_1107_le__less__Suc__eq:(forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat M_1) N_1)->((iff ((ord_less_nat N_1) (suc M_1))) (((eq nat) N_1) M_1)))).
% Axiom fact_1108_Suc__le__lessD:(forall (M_1:nat) (N_1:nat), (((ord_less_eq_nat (suc M_1)) N_1)->((ord_less_nat M_1) N_1))).
% Axiom fact_1109_One__nat__def:(((eq nat) one_one_nat) (suc zero_zero_nat)).
% Axiom fact_1110_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_1111_card__Collect__le__nat:(forall (N_1:nat), (((eq nat) (finite_card_nat (collect_nat (fun (I_1:nat)=> ((ord_less_eq_nat I_1) N_1))))) (suc N_1))).
% Axiom fact_1112_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_1113_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_1114_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_1115_inc__induct:(forall (P:(nat->Prop)) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((P J)->((forall (I_1:nat), (((ord_less_nat I_1) J)->((P (suc I_1))->(P I_1))))->(P _TPTP_I))))).
% Axiom fact_1116_less__imp__Suc__add:(forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ex nat) (fun (K_1:nat)=> (((eq nat) N_1) (suc ((plus_plus_nat M_1) K_1))))))).
% Axiom fact_1117_gr0__implies__Suc:(forall (N_1:nat), (((ord_less_nat zero_zero_nat) N_1)->((ex nat) (fun (M:nat)=> (((eq nat) N_1) (suc M)))))).
% Axiom fact_1118_Suc__eq__plus1:(forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat N_1) one_one_nat))).
% Axiom fact_1119_Suc__eq__plus1__left:(forall (N_1:nat), (((eq nat) (suc N_1)) ((plus_plus_nat one_one_nat) N_1))).
% Axiom fact_1120_Suc__le__D:(forall (N_1:nat) (M_2:nat), (((ord_less_eq_nat (suc N_1)) M_2)->((ex nat) (fun (M:nat)=> (((eq nat) M_2) (suc M)))))).
% Axiom fact_1121_lessE:(forall (_TPTP_I:nat) (K:nat), (((ord_less_nat _TPTP_I) K)->((not (((eq nat) K) (suc _TPTP_I)))->((forall (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->(not (((eq nat) K) (suc J_1)))))->False)))).
% Axiom fact_1122_Suc__lessE:(forall (_TPTP_I:nat) (K:nat), (((ord_less_nat (suc _TPTP_I)) K)->((forall (J_1:nat), (((ord_less_nat _TPTP_I) J_1)->(not (((eq nat) K) (suc J_1)))))->False))).
% Axiom fact_1123_not0__implies__Suc:(forall (N_1:nat), ((not (((eq nat) N_1) zero_zero_nat))->((ex nat) (fun (M:nat)=> (((eq nat) N_1) (suc M)))))).
% Axiom fact_1124_nat_Oexhaust:(forall (Y:nat), ((not (((eq nat) Y) zero_zero_nat))->((forall (Nat_1:nat), (not (((eq nat) Y) (suc Nat_1))))->False))).
% Axiom fact_1125_zero__induct:(forall (P:(nat->Prop)) (K:nat), ((P K)->((forall (N:nat), ((P (suc N))->(P N)))->(P zero_zero_nat)))).
% Axiom fact_1126_nat__induct:(forall (N_1:nat) (P:(nat->Prop)), ((P zero_zero_nat)->((forall (N:nat), ((P N)->(P (suc N))))->(P N_1)))).
% Axiom fact_1127_surjh:(((eq (nat->Prop)) ((image_1011045538di_nat h) top_to54564308indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite2011930979e_indi top_to54564308indi_o))).
% Axiom fact_1128_finite__atLeastLessThan:(forall (L:nat) (U:nat), (finite_finite_nat ((ord_at4362885an_nat L) U))).
% Axiom fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12:((forall (H:(arrow_1196572341e_indi->nat)), (((inj_on1505595958di_nat H) top_to54564308indi_o)->(not (((eq (nat->Prop)) ((image_1011045538di_nat H) top_to54564308indi_o)) ((ord_at4362885an_nat zero_zero_nat) (finite2011930979e_indi top_to54564308indi_o))))))->False).
% Axiom fact_1130_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 fact_1131_image__Suc__atLeastLessThan:(forall (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat suc) ((ord_at4362885an_nat _TPTP_I) J))) ((ord_at4362885an_nat (suc _TPTP_I)) (suc J)))).
% Axiom fact_1132_image__add__atLeastLessThan:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat (fun (N:nat)=> ((plus_plus_nat N) K))) ((ord_at4362885an_nat _TPTP_I) J))) ((ord_at4362885an_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))).
% Axiom fact_1133_all__nat__less__eq:(forall (P:(nat->Prop)) (N_1:nat), ((iff (forall (M:nat), (((ord_less_nat M) N_1)->(P M)))) (forall (X_1:nat), (((member_nat X_1) ((ord_at4362885an_nat zero_zero_nat) N_1))->(P X_1))))).
% Axiom fact_1134_ex__nat__less__eq:(forall (P:(nat->Prop)) (N_1:nat), ((iff ((ex nat) (fun (M:nat)=> ((and ((ord_less_nat M) N_1)) (P M))))) ((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) ((ord_at4362885an_nat zero_zero_nat) N_1))) (P X_1)))))).
% Axiom fact_1135_greaterThan__0:(((eq (nat->Prop)) (ord_greaterThan_nat zero_zero_nat)) ((image_nat_nat suc) top_top_nat_o)).
% Axiom fact_1136_less__eq__nat_Osimps_I2_J:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc M_1)) N_1)) (((nat_case_o False) (ord_less_eq_nat M_1)) N_1))).
% Axiom fact_1137_finite__greaterThanAtMost:(forall (L:nat) (U:nat), (finite_finite_nat ((ord_gr375877188st_nat L) U))).
% Axiom fact_1138_finite__greaterThanLessThan:(forall (L:nat) (U:nat), (finite_finite_nat ((ord_gr660468384an_nat L) U))).
% Axiom fact_1139_atLeastSucLessThan__greaterThanLessThan:(forall (L:nat) (U:nat), (((eq (nat->Prop)) ((ord_at4362885an_nat (suc L)) U)) ((ord_gr660468384an_nat L) U))).
% Axiom fact_1140_le__square:(forall (M_1:nat), ((ord_less_eq_nat M_1) ((times_times_nat M_1) M_1))).
% Axiom fact_1141_le__cube:(forall (M_1:nat), ((ord_less_eq_nat M_1) ((times_times_nat M_1) ((times_times_nat M_1) M_1)))).
% Axiom fact_1142_mult__le__mono1:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((times_times_nat _TPTP_I) K)) ((times_times_nat J) K)))).
% Axiom fact_1143_mult__le__mono2:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((times_times_nat K) _TPTP_I)) ((times_times_nat K) J)))).
% Axiom fact_1144_mult__le__mono:(forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat _TPTP_I) K)) ((times_times_nat J) L))))).
% Axiom fact_1145_nat__mult__eq__1__iff:(forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) N_1)) one_one_nat)) ((and (((eq nat) M_1) one_one_nat)) (((eq nat) N_1) one_one_nat)))).
% Axiom fact_1146_nat__mult__1__right:(forall (N_1:nat), (((eq nat) ((times_times_nat N_1) one_one_nat)) N_1)).
% Axiom fact_1147_nat__1__eq__mult__iff:(forall (M_1:nat) (N_1:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M_1) N_1))) ((and (((eq nat) M_1) one_one_nat)) (((eq nat) N_1) one_one_nat)))).
% Axiom fact_1148_nat__mult__1:(forall (N_1:nat), (((eq nat) ((times_times_nat one_one_nat) N_1)) N_1)).
% Axiom fact_1149_add__mult__distrib:(forall (M_1:nat) (N_1:nat) (K:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M_1) N_1)) K)) ((plus_plus_nat ((times_times_nat M_1) K)) ((times_times_nat N_1) K)))).
% Axiom fact_1150_add__mult__distrib2:(forall (K:nat) (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat K) ((plus_plus_nat M_1) N_1))) ((plus_plus_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1)))).
% Axiom fact_1151_Suc__mult__cancel1:(forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat (suc K)) M_1)) ((times_times_nat (suc K)) N_1))) (((eq nat) M_1) N_1))).
% Axiom fact_1152_mult__cancel2:(forall (M_1:nat) (K:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) K)) ((times_times_nat N_1) K))) ((or (((eq nat) M_1) N_1)) (((eq nat) K) zero_zero_nat)))).
% Axiom fact_1153_mult__cancel1:(forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((or (((eq nat) M_1) N_1)) (((eq nat) K) zero_zero_nat)))).
% Axiom fact_1154_mult__is__0:(forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) N_1)) zero_zero_nat)) ((or (((eq nat) M_1) zero_zero_nat)) (((eq nat) N_1) zero_zero_nat)))).
% Axiom fact_1155_mult__0__right:(forall (M_1:nat), (((eq nat) ((times_times_nat M_1) zero_zero_nat)) zero_zero_nat)).
% Axiom fact_1156_mult__0:(forall (N_1:nat), (((eq nat) ((times_times_nat zero_zero_nat) N_1)) zero_zero_nat)).
% Axiom fact_1157_mult__eq__1__iff:(forall (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat M_1) N_1)) (suc zero_zero_nat))) ((and (((eq nat) M_1) (suc zero_zero_nat))) (((eq nat) N_1) (suc zero_zero_nat))))).
% Axiom fact_1158_mult__less__mono2:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) _TPTP_I)) ((times_times_nat K) J))))).
% Axiom fact_1159_mult__less__mono1:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat _TPTP_I) K)) ((times_times_nat J) K))))).
% Axiom fact_1160_mult__less__cancel2:(forall (M_1:nat) (K:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat M_1) K)) ((times_times_nat N_1) K))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M_1) N_1)))).
% Axiom fact_1161_mult__less__cancel1:(forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M_1) N_1)))).
% Axiom fact_1162_nat__0__less__mult__iff:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M_1) N_1))) ((and ((ord_less_nat zero_zero_nat) M_1)) ((ord_less_nat zero_zero_nat) N_1)))).
% Axiom fact_1163_Suc__mult__less__cancel1:(forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_nat ((times_times_nat (suc K)) M_1)) ((times_times_nat (suc K)) N_1))) ((ord_less_nat M_1) N_1))).
% Axiom fact_1164_mult__Suc__right:(forall (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat M_1) (suc N_1))) ((plus_plus_nat M_1) ((times_times_nat M_1) N_1)))).
% Axiom fact_1165_mult__Suc:(forall (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat (suc M_1)) N_1)) ((plus_plus_nat N_1) ((times_times_nat M_1) N_1)))).
% Axiom fact_1166_Suc__mult__le__cancel1:(forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat (suc K)) M_1)) ((times_times_nat (suc K)) N_1))) ((ord_less_eq_nat M_1) N_1))).
% Axiom fact_1167_mult__eq__self__implies__10:(forall (M_1:nat) (N_1:nat), ((((eq nat) M_1) ((times_times_nat M_1) N_1))->((or (((eq nat) N_1) one_one_nat)) (((eq nat) M_1) zero_zero_nat)))).
% Axiom fact_1168_n__less__m__mult__n:(forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc zero_zero_nat)) N_1)->(((ord_less_nat (suc zero_zero_nat)) M_1)->((ord_less_nat N_1) ((times_times_nat M_1) N_1))))).
% Axiom fact_1169_n__less__n__mult__m:(forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc zero_zero_nat)) N_1)->(((ord_less_nat (suc zero_zero_nat)) M_1)->((ord_less_nat N_1) ((times_times_nat N_1) M_1))))).
% Axiom fact_1170_one__less__mult:(forall (M_1:nat) (N_1:nat), (((ord_less_nat (suc zero_zero_nat)) N_1)->(((ord_less_nat (suc zero_zero_nat)) M_1)->((ord_less_nat (suc zero_zero_nat)) ((times_times_nat M_1) N_1))))).
% Axiom fact_1171_one__le__mult__iff:(forall (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat (suc zero_zero_nat)) ((times_times_nat M_1) N_1))) ((and ((ord_less_eq_nat (suc zero_zero_nat)) M_1)) ((ord_less_eq_nat (suc zero_zero_nat)) N_1)))).
% Axiom fact_1172_mult__le__cancel2:(forall (M_1:nat) (K:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat M_1) K)) ((times_times_nat N_1) K))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M_1) N_1)))).
% Axiom fact_1173_mult__le__cancel1:(forall (K:nat) (M_1:nat) (N_1:nat), ((iff ((ord_less_eq_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M_1) N_1)))).
% Axiom fact_1174_nat__mult__commute:(forall (M_1:nat) (N_1:nat), (((eq nat) ((times_times_nat M_1) N_1)) ((times_times_nat N_1) M_1))).
% Axiom fact_1175_nat__mult__assoc:(forall (M_1:nat) (N_1:nat) (K:nat), (((eq nat) ((times_times_nat ((times_times_nat M_1) N_1)) K)) ((times_times_nat M_1) ((times_times_nat N_1) K)))).
% Axiom fact_1176_nat__mult__le__cancel1:(forall (M_1:nat) (N_1:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_eq_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((ord_less_eq_nat M_1) N_1)))).
% Axiom fact_1177_nat__mult__less__cancel1:(forall (M_1:nat) (N_1:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_nat ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((ord_less_nat M_1) N_1)))).
% Axiom fact_1178_nat__mult__eq__cancel1:(forall (M_1:nat) (N_1:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff (((eq nat) ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) (((eq nat) M_1) N_1)))).
% Axiom fact_1179_nat__mult__eq__cancel__disj:(forall (K:nat) (M_1:nat) (N_1:nat), ((iff (((eq nat) ((times_times_nat K) M_1)) ((times_times_nat K) N_1))) ((or (((eq nat) K) zero_zero_nat)) (((eq nat) M_1) N_1)))).
% Axiom fact_1180_left__add__mult__distrib:(forall (_TPTP_I:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat _TPTP_I) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat _TPTP_I) J)) U)) K))).
% Axiom fact_1181_nat_Osize_I2_J:(forall (Nat:nat), (((eq nat) (nat_size (suc Nat))) ((plus_plus_nat (nat_size Nat)) (suc zero_zero_nat)))).
% Axiom fact_1182_nat_Osize_I1_J:(((eq nat) (nat_size zero_zero_nat)) zero_zero_nat).
% Axiom fact_1183_nat_Osize_I4_J:(forall (Nat:nat), (((eq nat) (size_size_nat (suc Nat))) ((plus_plus_nat (size_size_nat Nat)) (suc zero_zero_nat)))).
% Axiom fact_1184_nat__size:(forall (N_1:nat), (((eq nat) (size_size_nat N_1)) N_1)).
% Axiom fact_1185_nat_Osize_I3_J:(((eq nat) (size_size_nat zero_zero_nat)) zero_zero_nat).
% Axiom fact_1186_weak__decr__stable:(forall (F:(nat->nat)), ((forall (I_1:nat), ((ord_less_eq_nat (F (suc I_1))) (F I_1)))->((ex nat) (fun (I_1:nat)=> (forall (K_1:nat), (((eq nat) (F ((plus_plus_nat I_1) K_1))) (F I_1))))))).
% Axiom fact_1187_bool_Osize_I1_J:(((eq nat) (bool_size True)) zero_zero_nat).
% Axiom fact_1188_bool_Osize_I2_J:(((eq nat) (bool_size False)) zero_zero_nat).
% Axiom fact_1189_finite__atLeastAtMost:(forall (L:nat) (U:nat), (finite_finite_nat ((ord_at238088361st_nat L) U))).
% Axiom fact_1190_atLeastLessThanSuc__atLeastAtMost:(forall (L:nat) (U:nat), (((eq (nat->Prop)) ((ord_at4362885an_nat L) (suc U))) ((ord_at238088361st_nat L) U))).
% Axiom fact_1191_ex__nat__less:(forall (P:(nat->Prop)) (N_1:nat), ((iff ((ex nat) (fun (M:nat)=> ((and ((ord_less_eq_nat M) N_1)) (P M))))) ((ex nat) (fun (X_1:nat)=> ((and ((member_nat X_1) ((ord_at238088361st_nat zero_zero_nat) N_1))) (P X_1)))))).
% Axiom fact_1192_all__nat__less:(forall (P:(nat->Prop)) (N_1:nat), ((iff (forall (M:nat), (((ord_less_eq_nat M) N_1)->(P M)))) (forall (X_1:nat), (((member_nat X_1) ((ord_at238088361st_nat zero_zero_nat) N_1))->(P X_1))))).
% Axiom fact_1193_image__Suc__atLeastAtMost:(forall (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat suc) ((ord_at238088361st_nat _TPTP_I) J))) ((ord_at238088361st_nat (suc _TPTP_I)) (suc J)))).
% Axiom fact_1194_atLeastSucAtMost__greaterThanAtMost:(forall (L:nat) (U:nat), (((eq (nat->Prop)) ((ord_at238088361st_nat (suc L)) U)) ((ord_gr375877188st_nat L) U))).
% Axiom fact_1195_image__add__atLeastAtMost:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((eq (nat->Prop)) ((image_nat_nat (fun (N:nat)=> ((plus_plus_nat N) K))) ((ord_at238088361st_nat _TPTP_I) J))) ((ord_at238088361st_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))).
% Axiom fact_1196_atLeastLessThan__add__Un:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((eq (nat->Prop)) ((ord_at4362885an_nat _TPTP_I) ((plus_plus_nat J) K))) ((semila848761471_nat_o ((ord_at4362885an_nat _TPTP_I) J)) ((ord_at4362885an_nat J) ((plus_plus_nat J) K)))))).
% Axiom fact_1197_atLeast__0:(((eq (nat->Prop)) (ord_atLeast_nat zero_zero_nat)) top_top_nat_o).
% Axiom fact_1198_atLeast__Suc__greaterThan:(forall (K:nat), (((eq (nat->Prop)) (ord_atLeast_nat (suc K))) (ord_greaterThan_nat K))).
% Axiom fact_1199_setsum__shift__lb__Suc0__0:(forall (K:nat) (F:(nat->nat)), ((((eq nat) (F zero_zero_nat)) zero_zero_nat)->(((eq nat) ((big_co387207925at_nat F) ((ord_at238088361st_nat (suc zero_zero_nat)) K))) ((big_co387207925at_nat F) ((ord_at238088361st_nat zero_zero_nat) K))))).
% Axiom help_If_1_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_:(forall (X:(produc1572197287le_alt->Prop)) (Y:(produc1572197287le_alt->Prop)), (((eq (produc1572197287le_alt->Prop)) (((if_Pro278423000_alt_o True) X) Y)) X)).
% Axiom help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_:(forall (X:(produc1572197287le_alt->Prop)) (Y:(produc1572197287le_alt->Prop)), (((eq (produc1572197287le_alt->Prop)) (((if_Pro278423000_alt_o False) X) Y)) Y)).
% Axiom help_If_3_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____piyeccggrh_:(forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))).
% Trying to prove ((member285112084le_alt ((produc897867031le_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:((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_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 ((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_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 ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))
% Found (fun (x0:(((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_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 ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))
% Found (fun (x:(((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (x0:(((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_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 ((((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))
% Found (fun (x:(((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (x0:(((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_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 ((((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))->((((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p))))
% Found (and_rect00 (fun (x:(((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (x0:(((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_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 ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))
% Found ((and_rect0 ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))) (fun (x:(((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (x0:(((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_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 ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))
% Found (((fun (P:Type) (x:((((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))->((((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))) (fun (x:(((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (x0:(((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_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 ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))
% Found (((fun (P:Type) (x:((((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))->((((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))) (fun (x:(((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (x0:(((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_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 ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))
% Got proof (((fun (P:Type) (x:((((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))->((((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))) (fun (x:(((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (x0:(((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_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 = 9.629345s
% node=162 cost=894.000000 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:((((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))->((((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member285112084le_alt ((produc897867031le_alt c) d)) (f p))) (fun (x:(((member285112084le_alt ((produc897867031le_alt c) d)) (f p))->((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e)))))))) (x0:(((member285112084le_alt ((produc897867031le_alt c) d)) (f (fun (I_1:arrow_1196572341e_indi)=> (((if_Pro278423000_alt_o ((ord_less_nat (h I_1)) n)) ((arrow_1970123222_mktop (p I_1)) e)) (((if_Pro278423000_alt_o (((eq nat) (h I_1)) n)) (((arrow_556571452_above (p I_1)) c) e)) ((arrow_1821416136_mkbot (p I_1)) e))))))->((member285112084le_alt ((produc897867031le_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
%------------------------------------------------------------------------------