cocATP---0.2.0.THM-Prf.s

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SCT171^1 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n092.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:29:46 EDT 2014

% Result   : Theorem 2.50s
% Output   : Proof 2.50s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SCT171^1 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n092.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 08:28:56 CDT 2014
% % CPUTime  : 2.50 
% 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 0xad76c8>, <kernel.Type object at 0xad7c20>) of role type named ty_ty_tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring arrow_1346734812le_alt:Type
% FOF formula (<kernel.Constant object at 0xcb5170>, <kernel.Type object at 0xad75f0>) of role type named ty_ty_tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi
% Using role type
% Declaring arrow_1092341143e_indi:Type
% FOF formula (<kernel.Constant object at 0xad7b90>, <kernel.Type object at 0xad77e8>) of role type named ty_ty_tc__Nat__Onat
% Using role type
% Declaring nat:Type
% FOF formula (<kernel.Constant object at 0xad7c20>, <kernel.Type object at 0xad74d0>) of role type named ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_Mtc__Arrow__
% Using role type
% Declaring produc1832616231le_alt:Type
% FOF formula (<kernel.Constant object at 0xad7cb0>, <kernel.DependentProduct object at 0xad7488>) of role type named sy_c_All
% Using role type
% Declaring all:((produc1832616231le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0xad7dd0>, <kernel.DependentProduct object at 0xad7368>) of role type named sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_OIIA
% Using role type
% Declaring arrow_1724561858le_IIA:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0xad7440>, <kernel.DependentProduct object at 0xad7560>) of role type named sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_OLin
% Using role type
% Declaring arrow_1751445586le_Lin:((produc1832616231le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0xad7758>, <kernel.DependentProduct object at 0xad7dd0>) of role type named sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_OProf
% Using role type
% Declaring arrow_1605628760e_Prof:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0xad7c20>, <kernel.DependentProduct object at 0xad7368>) of role type named sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Oabove
% Using role type
% Declaring arrow_452340254_above:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(arrow_1346734812le_alt->(produc1832616231le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0xad7560>, <kernel.DependentProduct object at 0xcd44d0>) of role type named sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Odictator
% Using role type
% Declaring arrow_1098709355ctator:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))
% FOF formula (<kernel.Constant object at 0xad7dd0>, <kernel.DependentProduct object at 0xcd4488>) of role type named sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Omkbot
% Using role type
% Declaring arrow_1717184938_mkbot:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(produc1832616231le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0xad7c20>, <kernel.DependentProduct object at 0xcd4518>) of role type named sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Omktop
% Using role type
% Declaring arrow_1865892024_mktop:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(produc1832616231le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0xad7560>, <kernel.DependentProduct object at 0xcd44d0>) of role type named sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Ounanimity
% Using role type
% Declaring arrow_1889221221nimity:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0xad7c20>, <kernel.DependentProduct object at 0xcd4f80>) of role type named sy_c_Finite__Set_Ocard_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi
% Using role type
% Declaring finite1907699781e_indi:((arrow_1092341143e_indi->Prop)->nat)
% FOF formula (<kernel.Constant object at 0xad7dd0>, <kernel.DependentProduct object at 0xcd41b8>) of role type named sy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000tc_
% Using role type
% Declaring inj_on945046484di_nat:((arrow_1092341143e_indi->nat)->((arrow_1092341143e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xad7c20>, <kernel.DependentProduct object at 0xcd4e18>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O
% Using role type
% Declaring pi_Arr1422400881lt_o_o:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0xad7c20>, <kernel.DependentProduct object at 0xcd4e18>) of role type named sy_c_FuncSet_OPi_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O_001
% Using role type
% Declaring pi_Arr1941314005e_indi:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0xcd40e0>, <kernel.DependentProduct object at 0xcd4170>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M
% Using role type
% Declaring pi_Arr1021537730_alt_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0xcd44d0>, <kernel.DependentProduct object at 0xcd4ef0>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_002
% Using role type
% Declaring pi_Arr1767527177lt_o_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0xcd41b8>, <kernel.DependentProduct object at 0xcd43f8>) of role type named sy_c_FuncSet_OPi_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_003
% Using role type
% Declaring pi_Arr170420797e_indi:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0xcd4560>, <kernel.DependentProduct object at 0xcd4050>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkd
% Using role type
% Declaring pi_Pro410810898lt_o_o:(((produc1832616231le_alt->Prop)->Prop)->(((produc1832616231le_alt->Prop)->(Prop->Prop))->(((produc1832616231le_alt->Prop)->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0xcd40e0>, <kernel.DependentProduct object at 0xcd41b8>) of role type named sy_c_FuncSet_OPi_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkd_004
% Using role type
% Declaring pi_Pro1340600692e_indi:(((produc1832616231le_alt->Prop)->Prop)->(((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))->(((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0xcd4710>, <kernel.DependentProduct object at 0xcd4ea8>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojn
% Using role type
% Declaring pi_o_A1302557673_alt_o:((Prop->Prop)->((Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))->((Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0xcd4560>, <kernel.DependentProduct object at 0xcd4ea8>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__
% Using role type
% Declaring pi_o_A71242893_alt_o:((Prop->Prop)->((Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))->((Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0xcd40e0>, <kernel.DependentProduct object at 0xcd4ea8>) of role type named sy_c_FuncSet_OPi_000_Eo_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sd
% Using role type
% Declaring pi_o_P1538584260_alt_o:((Prop->Prop)->((Prop->((produc1832616231le_alt->Prop)->Prop))->((Prop->(produc1832616231le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0xcd4710>, <kernel.DependentProduct object at 0xcd4ea8>) of role type named sy_c_FuncSet_OPi_000_Eo_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk
% Using role type
% Declaring pi_o_P988780107le_alt:((Prop->Prop)->((Prop->(produc1832616231le_alt->Prop))->((Prop->produc1832616231le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0xcd4560>, <kernel.DependentProduct object at 0xcd5b00>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000_062
% Using role type
% Declaring pi_Arr1140519125_alt_o:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))->((arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0xcd4f80>, <kernel.DependentProduct object at 0xcd5b00>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000_062_005
% Using role type
% Declaring pi_Arr651234977_alt_o:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))->((arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->Prop)))
% FOF formula (<kernel.Constant object at 0xcd55f0>, <kernel.DependentProduct object at 0xcd4f80>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000_062_006
% Using role type
% Declaring pi_Arr418143960_alt_o:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)))
% FOF formula (<kernel.Constant object at 0xcd5b00>, <kernel.DependentProduct object at 0xcd44d0>) of role type named sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_000tc__
% Using role type
% Declaring pi_Arr1055270199le_alt:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((arrow_1092341143e_indi->produc1832616231le_alt)->Prop)))
% FOF formula (<kernel.Constant object at 0xcd5638>, <kernel.DependentProduct object at 0xcd40e0>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oal
% Using role type
% Declaring pi_Pro539263375_alt_o:((produc1832616231le_alt->Prop)->((produc1832616231le_alt->(Prop->Prop))->((produc1832616231le_alt->Prop)->Prop)))
% FOF formula (<kernel.Constant object at 0xcd5638>, <kernel.DependentProduct object at 0xcd40e0>) of role type named sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oal_007
% Using role type
% Declaring pi_Pro1535452471e_indi:((produc1832616231le_alt->Prop)->((produc1832616231le_alt->(arrow_1092341143e_indi->Prop))->((produc1832616231le_alt->arrow_1092341143e_indi)->Prop)))
% FOF formula (<kernel.Constant object at 0xcd4f80>, <kernel.DependentProduct object at 0xaf2ef0>) of role type named sy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____sdiojnqkdh
% Using role type
% Declaring hilber564731065di_nat:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->nat)->(nat->arrow_1092341143e_indi)))
% FOF formula (<kernel.Constant object at 0xcd4368>, <kernel.DependentProduct object at 0xaf2d40>) of role type named sy_c_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_M
% Using role type
% Declaring if_Pro399136856_alt_o:(Prop->((produc1832616231le_alt->Prop)->((produc1832616231le_alt->Prop)->(produc1832616231le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0xcd44d0>, <kernel.DependentProduct object at 0xaf2ef0>) 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_le939309728lt_o_o:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xcd4f80>, <kernel.DependentProduct object at 0xaf2cb0>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__Arrow____Order____Mirabelle_
% Using role type
% Declaring ord_le972845494lt_o_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xcd40e0>, <kernel.DependentProduct object at 0xaf2d40>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_I_062_Itc__prod_Itc__Arrow____Order____
% Using role type
% Declaring ord_le898419007lt_o_o:(((produc1832616231le_alt->Prop)->Prop)->(((produc1832616231le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xcd4f80>, <kernel.DependentProduct object at 0xaf2e60>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__Arrow____Order____Mirabelle____sdi
% Using role type
% Declaring ord_le316791758indi_o:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xcd4368>, <kernel.DependentProduct object at 0xaf2b90>) of role type named sy_c_Orderings_Oord__class_Oless_000_062_Itc__prod_Itc__Arrow____Order____Mirabe
% Using role type
% Declaring ord_le1973646398_alt_o:((produc1832616231le_alt->Prop)->((produc1832616231le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xcd4368>, <kernel.DependentProduct object at 0xaf2ef0>) 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 0xaf2c20>, <kernel.DependentProduct object at 0xaf2dd0>) 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 0xaf2b90>, <kernel.DependentProduct object at 0xaf2a70>) 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_to1049332548lt_o_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0xaf2ef0>, <kernel.DependentProduct object at 0xaf2c20>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_I_062_Itc__Arrow____Order____Mirabelle__
% Using role type
% Declaring top_to790289938lt_o_o:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)
% FOF formula (<kernel.Constant object at 0xaf29e0>, <kernel.DependentProduct object at 0xaf2dd0>) 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_to1830848411lt_o_o:((produc1832616231le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0xaf2a70>, <kernel.DependentProduct object at 0xaf2c20>) 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 0xaf2ef0>, <kernel.DependentProduct object at 0xaf27a0>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__Arrow____Order____Mirabelle____sdio
% Using role type
% Declaring top_to527331954indi_o:(arrow_1092341143e_indi->Prop)
% FOF formula (<kernel.Constant object at 0xaf2638>, <kernel.DependentProduct object at 0xaf2830>) of role type named sy_c_Orderings_Otop__class_Otop_000_062_Itc__prod_Itc__Arrow____Order____Mirabel
% Using role type
% Declaring top_to679332578_alt_o:(produc1832616231le_alt->Prop)
% FOF formula (<kernel.Constant object at 0xaf2c20>, <kernel.Sort object at 0x9b8d88>) 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 0xaf2dd0>, <kernel.DependentProduct object at 0xaf2ef0>) of role type named sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_
% Using role type
% Declaring produc990411159le_alt:(arrow_1346734812le_alt->(arrow_1346734812le_alt->produc1832616231le_alt))
% FOF formula (<kernel.Constant object at 0xaf26c8>, <kernel.DependentProduct object at 0xaf24d0>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__
% Using role type
% Declaring collec2125720304_alt_o:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0xaf2638>, <kernel.DependentProduct object at 0xaf2c20>) of role type named sy_c_Set_OCollect_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_
% Using role type
% Declaring collec1718651462_alt_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))
% FOF formula (<kernel.Constant object at 0xaf23b0>, <kernel.DependentProduct object at 0xaf2710>) of role type named sy_c_Set_OCollect_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk
% Using role type
% Declaring collec1079683069_alt_o:(((produc1832616231le_alt->Prop)->Prop)->((produc1832616231le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xaf2dd0>, <kernel.DependentProduct object at 0xaf2560>) of role type named sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi
% Using role type
% Declaring collec1832628290e_indi:((arrow_1092341143e_indi->Prop)->(arrow_1092341143e_indi->Prop))
% FOF formula (<kernel.Constant object at 0xaf2680>, <kernel.DependentProduct object at 0xaf2710>) of role type named sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oa
% Using role type
% Declaring collec1201320914le_alt:((produc1832616231le_alt->Prop)->(produc1832616231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0xaf26c8>, <kernel.DependentProduct object at 0xaf2dd0>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__
% Using role type
% Declaring member903234717lt_o_o:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->(((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xaf27a0>, <kernel.DependentProduct object at 0xf2c5f0>) of role type named sy_c_member_000_062_I_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh___008
% Using role type
% Declaring member986213183e_indi:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->(((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xaf2ef0>, <kernel.DependentProduct object at 0xf2c8c0>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_
% Using role type
% Declaring member733327538_alt_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xaf26c8>, <kernel.DependentProduct object at 0xf2c3f8>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi__009
% Using role type
% Declaring member1754345465lt_o_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xaf27a0>, <kernel.DependentProduct object at 0xf2c7a0>) of role type named sy_c_member_000_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi__010
% Using role type
% Declaring member1208133347e_indi:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xaf26c8>, <kernel.DependentProduct object at 0xf2c3f8>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk
% Using role type
% Declaring member1949484546lt_o_o:(((produc1832616231le_alt->Prop)->Prop)->((((produc1832616231le_alt->Prop)->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xaf27a0>, <kernel.DependentProduct object at 0xf2c8c0>) of role type named sy_c_member_000_062_I_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqk_011
% Using role type
% Declaring member1255309082e_indi:(((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)->((((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xaf2ef0>, <kernel.DependentProduct object at 0xf2c170>) of role type named sy_c_member_000_062_I_Eo_M_062_I_062_Itc__Arrow____Order____Mirabelle____sdiojnq
% Using role type
% Declaring member1710515983_alt_o:((Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->(((Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xaf2ef0>, <kernel.DependentProduct object at 0xf2c7a0>) of role type named sy_c_member_000_062_I_Eo_M_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__O
% Using role type
% Declaring member537117565_alt_o:((Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->(((Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf2c3f8>, <kernel.DependentProduct object at 0xf2c170>) of role type named sy_c_member_000_062_I_Eo_M_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdi
% Using role type
% Declaring member1099673524_alt_o:((Prop->(produc1832616231le_alt->Prop))->(((Prop->(produc1832616231le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf2c7e8>, <kernel.DependentProduct object at 0xf2c320>) of role type named sy_c_member_000_062_I_Eo_Mtc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkd
% Using role type
% Declaring member1368218865le_alt:((Prop->produc1832616231le_alt)->(((Prop->produc1832616231le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf2c3b0>, <kernel.DependentProduct object at 0xae8950>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_062_
% Using role type
% Declaring member24189887_alt_o:((arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->(((arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf2c5f0>, <kernel.DependentProduct object at 0xae8830>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_062__012
% Using role type
% Declaring member1079651021_alt_o:((arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->(((arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf2c320>, <kernel.DependentProduct object at 0xae87e8>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_M_062__013
% Using role type
% Declaring member1561882372_alt_o:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf2c3b0>, <kernel.DependentProduct object at 0xae87a0>) of role type named sy_c_member_000_062_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi_Mtc__p
% Using role type
% Declaring member1621875105le_alt:((arrow_1092341143e_indi->produc1832616231le_alt)->(((arrow_1092341143e_indi->produc1832616231le_alt)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf2c5f0>, <kernel.DependentProduct object at 0xae8878>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oa
% Using role type
% Declaring member1362619835_alt_o:((produc1832616231le_alt->Prop)->(((produc1832616231le_alt->Prop)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf2c3b0>, <kernel.DependentProduct object at 0xae8758>) of role type named sy_c_member_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oa_014
% Using role type
% Declaring member1486844321e_indi:((produc1832616231le_alt->arrow_1092341143e_indi)->(((produc1832616231le_alt->arrow_1092341143e_indi)->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf2c320>, <kernel.DependentProduct object at 0xae8878>) 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 0xf2c3b0>, <kernel.DependentProduct object at 0xae8710>) of role type named sy_c_member_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oindi
% Using role type
% Declaring member1714766084e_indi:(arrow_1092341143e_indi->((arrow_1092341143e_indi->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xf2c3b0>, <kernel.DependentProduct object at 0xae8638>) of role type named sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_Mtc
% Using role type
% Declaring member545531028le_alt:(produc1832616231le_alt->((produc1832616231le_alt->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0xae8878>, <kernel.DependentProduct object at 0xae88c0>) of role type named sy_v_F
% Using role type
% Declaring f:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0xae8710>, <kernel.DependentProduct object at 0xae8908>) of role type named sy_v_Lab____
% Using role type
% Declaring lab:(produc1832616231le_alt->Prop)
% FOF formula (<kernel.Constant object at 0xae86c8>, <kernel.DependentProduct object at 0xae8680>) of role type named sy_v_Lba____
% Using role type
% Declaring lba:(produc1832616231le_alt->Prop)
% FOF formula (<kernel.Constant object at 0xae88c0>, <kernel.DependentProduct object at 0xae8638>) of role type named sy_v_P____
% Using role type
% Declaring p:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0xae8908>, <kernel.Constant object at 0xae8638>) of role type named sy_v_a____
% Using role type
% Declaring a:arrow_1346734812le_alt
% FOF formula (<kernel.Constant object at 0xae86c8>, <kernel.Constant object at 0xae8638>) of role type named sy_v_b____
% Using role type
% Declaring b:arrow_1346734812le_alt
% FOF formula (<kernel.Constant object at 0xae88c0>, <kernel.Constant object at 0xae8638>) of role type named sy_v_c____
% Using role type
% Declaring c:arrow_1346734812le_alt
% FOF formula (<kernel.Constant object at 0xae8908>, <kernel.Constant object at 0xae8638>) of role type named sy_v_d____
% Using role type
% Declaring d:arrow_1346734812le_alt
% FOF formula (<kernel.Constant object at 0xae86c8>, <kernel.Constant object at 0xae8638>) of role type named sy_v_e____
% Using role type
% Declaring e:arrow_1346734812le_alt
% FOF formula (<kernel.Constant object at 0xae88c0>, <kernel.DependentProduct object at 0xae8440>) of role type named sy_v_h____
% Using role type
% Declaring h:(arrow_1092341143e_indi->nat)
% FOF formula (<kernel.Constant object at 0xae8488>, <kernel.Constant object at 0xae8440>) of role type named sy_v_n____
% Using role type
% Declaring n:nat
% FOF formula (arrow_1724561858le_IIA f) of role axiom named fact_0_assms_I3_J
% A new axiom: (arrow_1724561858le_IIA f)
% FOF formula (arrow_1889221221nimity f) of role axiom named fact_1_u
% A new axiom: (arrow_1889221221nimity f)
% FOF formula (not (((eq arrow_1346734812le_alt) c) d)) of role axiom named fact_2__096c_A_126_061_Ad_096
% A new axiom: (not (((eq arrow_1346734812le_alt) c) d))
% FOF formula ((member1561882372_alt_o p) arrow_1605628760e_Prof) of role axiom named fact_3__096P_A_058_AProf_096
% A new axiom: ((member1561882372_alt_o p) arrow_1605628760e_Prof)
% FOF formula (forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)) (Z_2:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X) Y)) ((arrow_1717184938_mkbot L) Z_2))) ((and ((and (not (((eq arrow_1346734812le_alt) Y) Z_2))) ((((eq arrow_1346734812le_alt) X) Z_2)->(not (((eq arrow_1346734812le_alt) X) Y))))) ((not (((eq arrow_1346734812le_alt) X) Z_2))->((member545531028le_alt ((produc990411159le_alt X) Y)) L))))) of role axiom named fact_4_in__mkbot
% A new axiom: (forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)) (Z_2:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X) Y)) ((arrow_1717184938_mkbot L) Z_2))) ((and ((and (not (((eq arrow_1346734812le_alt) Y) Z_2))) ((((eq arrow_1346734812le_alt) X) Z_2)->(not (((eq arrow_1346734812le_alt) X) Y))))) ((not (((eq arrow_1346734812le_alt) X) Z_2))->((member545531028le_alt ((produc990411159le_alt X) Y)) L)))))
% FOF formula (forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)) (Z_2:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X) Y)) ((arrow_1865892024_mktop L) Z_2))) ((and ((and (not (((eq arrow_1346734812le_alt) X) Z_2))) ((((eq arrow_1346734812le_alt) Y) Z_2)->(not (((eq arrow_1346734812le_alt) X) Y))))) ((not (((eq arrow_1346734812le_alt) Y) Z_2))->((member545531028le_alt ((produc990411159le_alt X) Y)) L))))) of role axiom named fact_5_in__mktop
% A new axiom: (forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)) (Z_2:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X) Y)) ((arrow_1865892024_mktop L) Z_2))) ((and ((and (not (((eq arrow_1346734812le_alt) X) Z_2))) ((((eq arrow_1346734812le_alt) Y) Z_2)->(not (((eq arrow_1346734812le_alt) X) Y))))) ((not (((eq arrow_1346734812le_alt) Y) Z_2))->((member545531028le_alt ((produc990411159le_alt X) Y)) L)))))
% FOF formula (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_26:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) A_26) B_16))->((not (((eq arrow_1346734812le_alt) A_25) B_16))->((not (((eq arrow_1346734812le_alt) B_15) A_26))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (f P_6))))))))))) of role axiom named fact_6__C2_C
% A new axiom: (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_26:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) A_26) B_16))->((not (((eq arrow_1346734812le_alt) A_25) B_16))->((not (((eq arrow_1346734812le_alt) B_15) A_26))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (f P_6)))))))))))
% FOF formula (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_26:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) A_26) B_16))->((not (((eq arrow_1346734812le_alt) A_25) B_16))->((not (((eq arrow_1346734812le_alt) B_15) A_26))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (P_6 _TPTP_I))))->(((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))->((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (f P_6))))))))))) of role axiom named fact_7__C1_C
% A new axiom: (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_26:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) A_26) B_16))->((not (((eq arrow_1346734812le_alt) A_25) B_16))->((not (((eq arrow_1346734812le_alt) B_15) A_26))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (P_6 _TPTP_I))))->(((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))->((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (f P_6)))))))))))
% FOF formula (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (C_4:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) B_15) C_4))->((not (((eq arrow_1346734812le_alt) A_25) C_4))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt B_15) C_4)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt B_15) C_4)) (f P_6)))))))))) of role axiom named fact_8__C4_C
% A new axiom: (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (C_4:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) B_15) C_4))->((not (((eq arrow_1346734812le_alt) A_25) C_4))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt B_15) C_4)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt B_15) C_4)) (f P_6))))))))))
% FOF formula (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_26:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) A_26) B_16))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (f P_6))))))))) of role axiom named fact_9_pairwise__neutrality
% A new axiom: (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_26:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) A_26) B_16))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (f P_6)))))))))
% FOF formula (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt B_15) A_25)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt B_15) A_25)) (f P_6)))))))) of role axiom named fact_10__C3_C
% A new axiom: (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt B_15) A_25)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt B_15) A_25)) (f P_6))))))))
% FOF formula (forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt c) d)) (p _TPTP_I))) ((and (((ord_less_nat (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt c) d)) ((arrow_1865892024_mktop (p _TPTP_I)) e)))) ((((ord_less_nat (h _TPTP_I)) n)->False)->((and ((((eq nat) (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt c) d)) (((arrow_452340254_above (p _TPTP_I)) c) e)))) ((not (((eq nat) (h _TPTP_I)) n))->((member545531028le_alt ((produc990411159le_alt c) d)) ((arrow_1717184938_mkbot (p _TPTP_I)) 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 (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt c) d)) (p _TPTP_I))) ((and (((ord_less_nat (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt c) d)) ((arrow_1865892024_mktop (p _TPTP_I)) e)))) ((((ord_less_nat (h _TPTP_I)) n)->False)->((and ((((eq nat) (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt c) d)) (((arrow_452340254_above (p _TPTP_I)) c) e)))) ((not (((eq nat) (h _TPTP_I)) n))->((member545531028le_alt ((produc990411159le_alt c) d)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))))
% FOF formula ((member545531028le_alt ((produc990411159le_alt c) d)) (p (((hilber564731065di_nat top_to527331954indi_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: ((member545531028le_alt ((produc990411159le_alt c) d)) (p (((hilber564731065di_nat top_to527331954indi_o) h) n)))
% FOF formula ((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) 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: ((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))
% FOF formula ((iff ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))) ((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))) of role axiom named fact_14_PW
% A new axiom: ((iff ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))) ((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))
% FOF formula (forall (P_4:(produc1832616231le_alt->Prop)), ((iff (all P_4)) (forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), (P_4 ((produc990411159le_alt A_5) B_4))))) of role axiom named fact_15_split__paired__All
% A new axiom: (forall (P_4:(produc1832616231le_alt->Prop)), ((iff (all P_4)) (forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), (P_4 ((produc990411159le_alt A_5) B_4)))))
% FOF formula ((member1561882372_alt_o (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))) arrow_1605628760e_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: ((member1561882372_alt_o (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))) arrow_1605628760e_Prof)
% FOF formula ((member545531028le_alt ((produc990411159le_alt c) e)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) 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: ((member545531028le_alt ((produc990411159le_alt c) e)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))
% FOF formula ((member545531028le_alt ((produc990411159le_alt e) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) 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: ((member545531028le_alt ((produc990411159le_alt e) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))
% FOF formula ((ord_less_nat n) (finite1907699781e_indi top_to527331954indi_o)) of role axiom named fact_19_n_I1_J
% A new axiom: ((ord_less_nat n) (finite1907699781e_indi top_to527331954indi_o))
% FOF formula ((inj_on945046484di_nat h) top_to527331954indi_o) of role axiom named fact_20_injh
% A new axiom: ((inj_on945046484di_nat h) top_to527331954indi_o)
% FOF formula (forall (A_24:arrow_1346734812le_alt) (B_14:arrow_1346734812le_alt) (A_23:arrow_1346734812le_alt) (B_13:arrow_1346734812le_alt), ((((eq produc1832616231le_alt) ((produc990411159le_alt A_24) B_14)) ((produc990411159le_alt A_23) B_13))->(((((eq arrow_1346734812le_alt) A_24) A_23)->(not (((eq arrow_1346734812le_alt) B_14) B_13)))->False))) of role axiom named fact_21_Pair__inject
% A new axiom: (forall (A_24:arrow_1346734812le_alt) (B_14:arrow_1346734812le_alt) (A_23:arrow_1346734812le_alt) (B_13:arrow_1346734812le_alt), ((((eq produc1832616231le_alt) ((produc990411159le_alt A_24) B_14)) ((produc990411159le_alt A_23) B_13))->(((((eq arrow_1346734812le_alt) A_24) A_23)->(not (((eq arrow_1346734812le_alt) B_14) B_13)))->False)))
% FOF formula (forall (A_22:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt) (A_21:arrow_1346734812le_alt) (B_11:arrow_1346734812le_alt), ((iff (((eq produc1832616231le_alt) ((produc990411159le_alt A_22) B_12)) ((produc990411159le_alt A_21) B_11))) ((and (((eq arrow_1346734812le_alt) A_22) A_21)) (((eq arrow_1346734812le_alt) B_12) B_11)))) of role axiom named fact_22_Pair__eq
% A new axiom: (forall (A_22:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt) (A_21:arrow_1346734812le_alt) (B_11:arrow_1346734812le_alt), ((iff (((eq produc1832616231le_alt) ((produc990411159le_alt A_22) B_12)) ((produc990411159le_alt A_21) B_11))) ((and (((eq arrow_1346734812le_alt) A_22) A_21)) (((eq arrow_1346734812le_alt) B_12) B_11))))
% FOF formula (forall (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1724561858le_IIA F)) (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(forall (Xa:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o Xa) arrow_1605628760e_Prof)->(forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (X_1 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (Xa _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F X_1))) ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F Xa))))))))))) of role axiom named fact_23_IIA__def
% A new axiom: (forall (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1724561858le_IIA F)) (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(forall (Xa:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o Xa) arrow_1605628760e_Prof)->(forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (X_1 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (Xa _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F X_1))) ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F Xa)))))))))))
% FOF formula (forall (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1889221221nimity F)) (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (X_1 _TPTP_I)))->((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F X_1)))))))) of role axiom named fact_24_unanimity__def
% A new axiom: (forall (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1889221221nimity F)) (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (X_1 _TPTP_I)))->((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F X_1))))))))
% FOF formula (forall (X_34:(produc1832616231le_alt->Prop)), (top_to1830848411lt_o_o X_34)) of role axiom named fact_25_top1I
% A new axiom: (forall (X_34:(produc1832616231le_alt->Prop)), (top_to1830848411lt_o_o X_34))
% FOF formula (forall (X_34:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (top_to790289938lt_o_o X_34)) of role axiom named fact_26_top1I
% A new axiom: (forall (X_34:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (top_to790289938lt_o_o X_34))
% FOF formula (forall (X_34:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (top_to1049332548lt_o_o X_34)) of role axiom named fact_27_top1I
% A new axiom: (forall (X_34:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (top_to1049332548lt_o_o X_34))
% FOF formula (forall (X_34:produc1832616231le_alt), (top_to679332578_alt_o X_34)) of role axiom named fact_28_top1I
% A new axiom: (forall (X_34:produc1832616231le_alt), (top_to679332578_alt_o X_34))
% FOF formula (forall (X_34:arrow_1092341143e_indi), (top_to527331954indi_o X_34)) of role axiom named fact_29_top1I
% A new axiom: (forall (X_34:arrow_1092341143e_indi), (top_to527331954indi_o X_34))
% FOF formula (forall (X_33:Prop), ((member_o X_33) top_top_o_o)) of role axiom named fact_30_UNIV__I
% A new axiom: (forall (X_33:Prop), ((member_o X_33) top_top_o_o))
% FOF formula (forall (X_33:arrow_1092341143e_indi), ((member1714766084e_indi X_33) top_to527331954indi_o)) of role axiom named fact_31_UNIV__I
% A new axiom: (forall (X_33:arrow_1092341143e_indi), ((member1714766084e_indi X_33) top_to527331954indi_o))
% FOF formula (forall (X_33:produc1832616231le_alt), ((member545531028le_alt X_33) top_to679332578_alt_o)) of role axiom named fact_32_UNIV__I
% A new axiom: (forall (X_33:produc1832616231le_alt), ((member545531028le_alt X_33) top_to679332578_alt_o))
% FOF formula (forall (X_33:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_33) top_to790289938lt_o_o)) of role axiom named fact_33_UNIV__I
% A new axiom: (forall (X_33:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_33) top_to790289938lt_o_o))
% FOF formula (forall (X_33:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_33) top_to1049332548lt_o_o)) of role axiom named fact_34_UNIV__I
% A new axiom: (forall (X_33:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_33) top_to1049332548lt_o_o))
% FOF formula (forall (X_33:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_33) top_to1830848411lt_o_o)) of role axiom named fact_35_UNIV__I
% A new axiom: (forall (X_33:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_33) top_to1830848411lt_o_o))
% FOF formula (forall (X_32:Prop), ((member_o X_32) top_top_o_o)) of role axiom named fact_36_iso__tuple__UNIV__I
% A new axiom: (forall (X_32:Prop), ((member_o X_32) top_top_o_o))
% FOF formula (forall (X_32:arrow_1092341143e_indi), ((member1714766084e_indi X_32) top_to527331954indi_o)) of role axiom named fact_37_iso__tuple__UNIV__I
% A new axiom: (forall (X_32:arrow_1092341143e_indi), ((member1714766084e_indi X_32) top_to527331954indi_o))
% FOF formula (forall (X_32:produc1832616231le_alt), ((member545531028le_alt X_32) top_to679332578_alt_o)) of role axiom named fact_38_iso__tuple__UNIV__I
% A new axiom: (forall (X_32:produc1832616231le_alt), ((member545531028le_alt X_32) top_to679332578_alt_o))
% FOF formula (forall (X_32:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_32) top_to790289938lt_o_o)) of role axiom named fact_39_iso__tuple__UNIV__I
% A new axiom: (forall (X_32:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_32) top_to790289938lt_o_o))
% FOF formula (forall (X_32:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_32) top_to1049332548lt_o_o)) of role axiom named fact_40_iso__tuple__UNIV__I
% A new axiom: (forall (X_32:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_32) top_to1049332548lt_o_o))
% FOF formula (forall (X_32:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_32) top_to1830848411lt_o_o)) of role axiom named fact_41_iso__tuple__UNIV__I
% A new axiom: (forall (X_32:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_32) top_to1830848411lt_o_o))
% FOF formula (forall (X_31:(produc1832616231le_alt->Prop)), ((iff (top_to1830848411lt_o_o X_31)) top_top_o)) of role axiom named fact_42_top__apply
% A new axiom: (forall (X_31:(produc1832616231le_alt->Prop)), ((iff (top_to1830848411lt_o_o X_31)) top_top_o))
% FOF formula (forall (X_31:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((iff (top_to790289938lt_o_o X_31)) top_top_o)) of role axiom named fact_43_top__apply
% A new axiom: (forall (X_31:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((iff (top_to790289938lt_o_o X_31)) top_top_o))
% FOF formula (forall (X_31:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (top_to1049332548lt_o_o X_31)) top_top_o)) of role axiom named fact_44_top__apply
% A new axiom: (forall (X_31:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (top_to1049332548lt_o_o X_31)) top_top_o))
% FOF formula (forall (X_31:produc1832616231le_alt), ((iff (top_to679332578_alt_o X_31)) top_top_o)) of role axiom named fact_45_top__apply
% A new axiom: (forall (X_31:produc1832616231le_alt), ((iff (top_to679332578_alt_o X_31)) top_top_o))
% FOF formula (forall (X_31:arrow_1092341143e_indi), ((iff (top_to527331954indi_o X_31)) top_top_o)) of role axiom named fact_46_top__apply
% A new axiom: (forall (X_31:arrow_1092341143e_indi), ((iff (top_to527331954indi_o X_31)) top_top_o))
% FOF formula (forall (A_20:((produc1832616231le_alt->Prop)->Prop)), (((ord_le898419007lt_o_o top_to1830848411lt_o_o) A_20)->False)) of role axiom named fact_47_not__top__less
% A new axiom: (forall (A_20:((produc1832616231le_alt->Prop)->Prop)), (((ord_le898419007lt_o_o top_to1830848411lt_o_o) A_20)->False))
% FOF formula (forall (A_20:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((ord_le972845494lt_o_o top_to790289938lt_o_o) A_20)->False)) of role axiom named fact_48_not__top__less
% A new axiom: (forall (A_20:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((ord_le972845494lt_o_o top_to790289938lt_o_o) A_20)->False))
% FOF formula (forall (A_20:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((ord_le939309728lt_o_o top_to1049332548lt_o_o) A_20)->False)) of role axiom named fact_49_not__top__less
% A new axiom: (forall (A_20:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((ord_le939309728lt_o_o top_to1049332548lt_o_o) A_20)->False))
% FOF formula (forall (A_20:Prop), (((ord_less_o top_top_o) A_20)->False)) of role axiom named fact_50_not__top__less
% A new axiom: (forall (A_20:Prop), (((ord_less_o top_top_o) A_20)->False))
% FOF formula (forall (A_20:(produc1832616231le_alt->Prop)), (((ord_le1973646398_alt_o top_to679332578_alt_o) A_20)->False)) of role axiom named fact_51_not__top__less
% A new axiom: (forall (A_20:(produc1832616231le_alt->Prop)), (((ord_le1973646398_alt_o top_to679332578_alt_o) A_20)->False))
% FOF formula (forall (A_20:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o top_to527331954indi_o) A_20)->False)) of role axiom named fact_52_not__top__less
% A new axiom: (forall (A_20:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o top_to527331954indi_o) A_20)->False))
% FOF formula (forall (X_30:nat) (Y_23:nat), ((((ord_less_nat X_30) Y_23)->False)->((not (((eq nat) X_30) Y_23))->((ord_less_nat Y_23) X_30)))) of role axiom named fact_53_linorder__cases
% A new axiom: (forall (X_30:nat) (Y_23:nat), ((((ord_less_nat X_30) Y_23)->False)->((not (((eq nat) X_30) Y_23))->((ord_less_nat Y_23) X_30))))
% FOF formula (forall (X_29:(arrow_1092341143e_indi->Prop)) (Y_22:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_29) Y_22)->(((ord_le316791758indi_o Y_22) X_29)->False))) of role axiom named fact_54_order__less__asym
% A new axiom: (forall (X_29:(arrow_1092341143e_indi->Prop)) (Y_22:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_29) Y_22)->(((ord_le316791758indi_o Y_22) X_29)->False)))
% FOF formula (forall (X_29:nat) (Y_22:nat), (((ord_less_nat X_29) Y_22)->(((ord_less_nat Y_22) X_29)->False))) of role axiom named fact_55_order__less__asym
% A new axiom: (forall (X_29:nat) (Y_22:nat), (((ord_less_nat X_29) Y_22)->(((ord_less_nat Y_22) X_29)->False)))
% FOF formula (forall (Z_1:(arrow_1092341143e_indi->Prop)) (Y_21:(arrow_1092341143e_indi->Prop)) (X_28:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o Y_21) X_28)->(((ord_le316791758indi_o Z_1) Y_21)->((ord_le316791758indi_o Z_1) X_28)))) of role axiom named fact_56_xt1_I10_J
% A new axiom: (forall (Z_1:(arrow_1092341143e_indi->Prop)) (Y_21:(arrow_1092341143e_indi->Prop)) (X_28:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o Y_21) X_28)->(((ord_le316791758indi_o Z_1) Y_21)->((ord_le316791758indi_o Z_1) X_28))))
% FOF formula (forall (Z_1:nat) (Y_21:nat) (X_28:nat), (((ord_less_nat Y_21) X_28)->(((ord_less_nat Z_1) Y_21)->((ord_less_nat Z_1) X_28)))) of role axiom named fact_57_xt1_I10_J
% A new axiom: (forall (Z_1:nat) (Y_21:nat) (X_28:nat), (((ord_less_nat Y_21) X_28)->(((ord_less_nat Z_1) Y_21)->((ord_less_nat Z_1) X_28))))
% FOF formula (forall (Z:(arrow_1092341143e_indi->Prop)) (X_27:(arrow_1092341143e_indi->Prop)) (Y_20:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_27) Y_20)->(((ord_le316791758indi_o Y_20) Z)->((ord_le316791758indi_o X_27) Z)))) of role axiom named fact_58_order__less__trans
% A new axiom: (forall (Z:(arrow_1092341143e_indi->Prop)) (X_27:(arrow_1092341143e_indi->Prop)) (Y_20:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_27) Y_20)->(((ord_le316791758indi_o Y_20) Z)->((ord_le316791758indi_o X_27) Z))))
% FOF formula (forall (Z:nat) (X_27:nat) (Y_20:nat), (((ord_less_nat X_27) Y_20)->(((ord_less_nat Y_20) Z)->((ord_less_nat X_27) Z)))) of role axiom named fact_59_order__less__trans
% A new axiom: (forall (Z:nat) (X_27:nat) (Y_20:nat), (((ord_less_nat X_27) Y_20)->(((ord_less_nat Y_20) Z)->((ord_less_nat X_27) Z))))
% FOF formula (forall (C_3:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->Prop)) (A_19:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o B_10) A_19)->((((eq (arrow_1092341143e_indi->Prop)) B_10) C_3)->((ord_le316791758indi_o C_3) A_19)))) of role axiom named fact_60_xt1_I2_J
% A new axiom: (forall (C_3:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->Prop)) (A_19:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o B_10) A_19)->((((eq (arrow_1092341143e_indi->Prop)) B_10) C_3)->((ord_le316791758indi_o C_3) A_19))))
% FOF formula (forall (C_3:nat) (B_10:nat) (A_19:nat), (((ord_less_nat B_10) A_19)->((((eq nat) B_10) C_3)->((ord_less_nat C_3) A_19)))) of role axiom named fact_61_xt1_I2_J
% A new axiom: (forall (C_3:nat) (B_10:nat) (A_19:nat), (((ord_less_nat B_10) A_19)->((((eq nat) B_10) C_3)->((ord_less_nat C_3) A_19))))
% FOF formula (forall (C_2:(arrow_1092341143e_indi->Prop)) (A_18:(arrow_1092341143e_indi->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o A_18) B_9)->((((eq (arrow_1092341143e_indi->Prop)) B_9) C_2)->((ord_le316791758indi_o A_18) C_2)))) of role axiom named fact_62_ord__less__eq__trans
% A new axiom: (forall (C_2:(arrow_1092341143e_indi->Prop)) (A_18:(arrow_1092341143e_indi->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o A_18) B_9)->((((eq (arrow_1092341143e_indi->Prop)) B_9) C_2)->((ord_le316791758indi_o A_18) C_2))))
% FOF formula (forall (C_2:nat) (A_18:nat) (B_9:nat), (((ord_less_nat A_18) B_9)->((((eq nat) B_9) C_2)->((ord_less_nat A_18) C_2)))) of role axiom named fact_63_ord__less__eq__trans
% A new axiom: (forall (C_2:nat) (A_18:nat) (B_9:nat), (((ord_less_nat A_18) B_9)->((((eq nat) B_9) C_2)->((ord_less_nat A_18) C_2))))
% FOF formula (forall (C_1:(arrow_1092341143e_indi->Prop)) (A_17:(arrow_1092341143e_indi->Prop)) (B_8:(arrow_1092341143e_indi->Prop)), ((((eq (arrow_1092341143e_indi->Prop)) A_17) B_8)->(((ord_le316791758indi_o C_1) B_8)->((ord_le316791758indi_o C_1) A_17)))) of role axiom named fact_64_xt1_I1_J
% A new axiom: (forall (C_1:(arrow_1092341143e_indi->Prop)) (A_17:(arrow_1092341143e_indi->Prop)) (B_8:(arrow_1092341143e_indi->Prop)), ((((eq (arrow_1092341143e_indi->Prop)) A_17) B_8)->(((ord_le316791758indi_o C_1) B_8)->((ord_le316791758indi_o C_1) A_17))))
% FOF formula (forall (C_1:nat) (A_17:nat) (B_8:nat), ((((eq nat) A_17) B_8)->(((ord_less_nat C_1) B_8)->((ord_less_nat C_1) A_17)))) of role axiom named fact_65_xt1_I1_J
% A new axiom: (forall (C_1:nat) (A_17:nat) (B_8:nat), ((((eq nat) A_17) B_8)->(((ord_less_nat C_1) B_8)->((ord_less_nat C_1) A_17))))
% FOF formula (forall (C:(arrow_1092341143e_indi->Prop)) (A_16:(arrow_1092341143e_indi->Prop)) (B_7:(arrow_1092341143e_indi->Prop)), ((((eq (arrow_1092341143e_indi->Prop)) A_16) B_7)->(((ord_le316791758indi_o B_7) C)->((ord_le316791758indi_o A_16) C)))) of role axiom named fact_66_ord__eq__less__trans
% A new axiom: (forall (C:(arrow_1092341143e_indi->Prop)) (A_16:(arrow_1092341143e_indi->Prop)) (B_7:(arrow_1092341143e_indi->Prop)), ((((eq (arrow_1092341143e_indi->Prop)) A_16) B_7)->(((ord_le316791758indi_o B_7) C)->((ord_le316791758indi_o A_16) C))))
% FOF formula (forall (C:nat) (A_16:nat) (B_7:nat), ((((eq nat) A_16) B_7)->(((ord_less_nat B_7) C)->((ord_less_nat A_16) C)))) of role axiom named fact_67_ord__eq__less__trans
% A new axiom: (forall (C:nat) (A_16:nat) (B_7:nat), ((((eq nat) A_16) B_7)->(((ord_less_nat B_7) C)->((ord_less_nat A_16) C))))
% FOF formula (forall (B_6:(arrow_1092341143e_indi->Prop)) (A_15:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o B_6) A_15)->(((ord_le316791758indi_o A_15) B_6)->False))) of role axiom named fact_68_xt1_I9_J
% A new axiom: (forall (B_6:(arrow_1092341143e_indi->Prop)) (A_15:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o B_6) A_15)->(((ord_le316791758indi_o A_15) B_6)->False)))
% FOF formula (forall (B_6:nat) (A_15:nat), (((ord_less_nat B_6) A_15)->(((ord_less_nat A_15) B_6)->False))) of role axiom named fact_69_xt1_I9_J
% A new axiom: (forall (B_6:nat) (A_15:nat), (((ord_less_nat B_6) A_15)->(((ord_less_nat A_15) B_6)->False)))
% FOF formula (forall (A_14:(arrow_1092341143e_indi->Prop)) (B_5:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o A_14) B_5)->(((ord_le316791758indi_o B_5) A_14)->False))) of role axiom named fact_70_order__less__asym_H
% A new axiom: (forall (A_14:(arrow_1092341143e_indi->Prop)) (B_5:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o A_14) B_5)->(((ord_le316791758indi_o B_5) A_14)->False)))
% FOF formula (forall (A_14:nat) (B_5:nat), (((ord_less_nat A_14) B_5)->(((ord_less_nat B_5) A_14)->False))) of role axiom named fact_71_order__less__asym_H
% A new axiom: (forall (A_14:nat) (B_5:nat), (((ord_less_nat A_14) B_5)->(((ord_less_nat B_5) A_14)->False)))
% FOF formula (forall (P_3:Prop) (X_26:(arrow_1092341143e_indi->Prop)) (Y_19:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_26) Y_19)->(((ord_le316791758indi_o Y_19) X_26)->P_3))) of role axiom named fact_72_order__less__imp__triv
% A new axiom: (forall (P_3:Prop) (X_26:(arrow_1092341143e_indi->Prop)) (Y_19:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_26) Y_19)->(((ord_le316791758indi_o Y_19) X_26)->P_3)))
% FOF formula (forall (P_3:Prop) (X_26:nat) (Y_19:nat), (((ord_less_nat X_26) Y_19)->(((ord_less_nat Y_19) X_26)->P_3))) of role axiom named fact_73_order__less__imp__triv
% A new axiom: (forall (P_3:Prop) (X_26:nat) (Y_19:nat), (((ord_less_nat X_26) Y_19)->(((ord_less_nat Y_19) X_26)->P_3)))
% FOF formula (forall (X_25:(arrow_1092341143e_indi->Prop)) (Y_18:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_25) Y_18)->(not (((eq (arrow_1092341143e_indi->Prop)) Y_18) X_25)))) of role axiom named fact_74_order__less__imp__not__eq2
% A new axiom: (forall (X_25:(arrow_1092341143e_indi->Prop)) (Y_18:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_25) Y_18)->(not (((eq (arrow_1092341143e_indi->Prop)) Y_18) X_25))))
% FOF formula (forall (X_25:nat) (Y_18:nat), (((ord_less_nat X_25) Y_18)->(not (((eq nat) Y_18) X_25)))) of role axiom named fact_75_order__less__imp__not__eq2
% A new axiom: (forall (X_25:nat) (Y_18:nat), (((ord_less_nat X_25) Y_18)->(not (((eq nat) Y_18) X_25))))
% FOF formula (forall (X_24:(arrow_1092341143e_indi->Prop)) (Y_17:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_24) Y_17)->(not (((eq (arrow_1092341143e_indi->Prop)) X_24) Y_17)))) of role axiom named fact_76_order__less__imp__not__eq
% A new axiom: (forall (X_24:(arrow_1092341143e_indi->Prop)) (Y_17:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_24) Y_17)->(not (((eq (arrow_1092341143e_indi->Prop)) X_24) Y_17))))
% FOF formula (forall (X_24:nat) (Y_17:nat), (((ord_less_nat X_24) Y_17)->(not (((eq nat) X_24) Y_17)))) of role axiom named fact_77_order__less__imp__not__eq
% A new axiom: (forall (X_24:nat) (Y_17:nat), (((ord_less_nat X_24) Y_17)->(not (((eq nat) X_24) Y_17))))
% FOF formula (forall (X_23:(arrow_1092341143e_indi->Prop)) (Y_16:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_23) Y_16)->(((ord_le316791758indi_o Y_16) X_23)->False))) of role axiom named fact_78_order__less__imp__not__less
% A new axiom: (forall (X_23:(arrow_1092341143e_indi->Prop)) (Y_16:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_23) Y_16)->(((ord_le316791758indi_o Y_16) X_23)->False)))
% FOF formula (forall (X_23:nat) (Y_16:nat), (((ord_less_nat X_23) Y_16)->(((ord_less_nat Y_16) X_23)->False))) of role axiom named fact_79_order__less__imp__not__less
% A new axiom: (forall (X_23:nat) (Y_16:nat), (((ord_less_nat X_23) Y_16)->(((ord_less_nat Y_16) X_23)->False)))
% FOF formula (forall (X_22:(arrow_1092341143e_indi->Prop)) (Y_15:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_22) Y_15)->(((ord_le316791758indi_o Y_15) X_22)->False))) of role axiom named fact_80_order__less__not__sym
% A new axiom: (forall (X_22:(arrow_1092341143e_indi->Prop)) (Y_15:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_22) Y_15)->(((ord_le316791758indi_o Y_15) X_22)->False)))
% FOF formula (forall (X_22:nat) (Y_15:nat), (((ord_less_nat X_22) Y_15)->(((ord_less_nat Y_15) X_22)->False))) of role axiom named fact_81_order__less__not__sym
% A new axiom: (forall (X_22:nat) (Y_15:nat), (((ord_less_nat X_22) Y_15)->(((ord_less_nat Y_15) X_22)->False)))
% FOF formula (forall (X_21:(arrow_1092341143e_indi->Prop)) (Y_14:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_21) Y_14)->(not (((eq (arrow_1092341143e_indi->Prop)) X_21) Y_14)))) of role axiom named fact_82_less__imp__neq
% A new axiom: (forall (X_21:(arrow_1092341143e_indi->Prop)) (Y_14:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_21) Y_14)->(not (((eq (arrow_1092341143e_indi->Prop)) X_21) Y_14))))
% FOF formula (forall (X_21:nat) (Y_14:nat), (((ord_less_nat X_21) Y_14)->(not (((eq nat) X_21) Y_14)))) of role axiom named fact_83_less__imp__neq
% A new axiom: (forall (X_21:nat) (Y_14:nat), (((ord_less_nat X_21) Y_14)->(not (((eq nat) X_21) Y_14))))
% FOF formula (forall (X_20:nat) (Y_13:nat), ((not (((eq nat) X_20) Y_13))->((((ord_less_nat X_20) Y_13)->False)->((ord_less_nat Y_13) X_20)))) of role axiom named fact_84_linorder__neqE
% A new axiom: (forall (X_20:nat) (Y_13:nat), ((not (((eq nat) X_20) Y_13))->((((ord_less_nat X_20) Y_13)->False)->((ord_less_nat Y_13) X_20))))
% FOF formula (forall (Y_12:nat) (X_19:nat), ((((ord_less_nat Y_12) X_19)->False)->((iff (((ord_less_nat X_19) Y_12)->False)) (((eq nat) X_19) Y_12)))) of role axiom named fact_85_linorder__antisym__conv3
% A new axiom: (forall (Y_12:nat) (X_19:nat), ((((ord_less_nat Y_12) X_19)->False)->((iff (((ord_less_nat X_19) Y_12)->False)) (((eq nat) X_19) Y_12))))
% FOF formula (forall (X_18:nat) (Y_11:nat), ((or ((or ((ord_less_nat X_18) Y_11)) (((eq nat) X_18) Y_11))) ((ord_less_nat Y_11) X_18))) of role axiom named fact_86_linorder__less__linear
% A new axiom: (forall (X_18:nat) (Y_11:nat), ((or ((or ((ord_less_nat X_18) Y_11)) (((eq nat) X_18) Y_11))) ((ord_less_nat Y_11) X_18)))
% FOF formula (forall (X_17:nat) (Y_10:nat), ((iff (((ord_less_nat X_17) Y_10)->False)) ((or ((ord_less_nat Y_10) X_17)) (((eq nat) X_17) Y_10)))) of role axiom named fact_87_not__less__iff__gr__or__eq
% A new axiom: (forall (X_17:nat) (Y_10:nat), ((iff (((ord_less_nat X_17) Y_10)->False)) ((or ((ord_less_nat Y_10) X_17)) (((eq nat) X_17) Y_10))))
% FOF formula (forall (X_16:nat) (Y_9:nat), ((iff (not (((eq nat) X_16) Y_9))) ((or ((ord_less_nat X_16) Y_9)) ((ord_less_nat Y_9) X_16)))) of role axiom named fact_88_linorder__neq__iff
% A new axiom: (forall (X_16:nat) (Y_9:nat), ((iff (not (((eq nat) X_16) Y_9))) ((or ((ord_less_nat X_16) Y_9)) ((ord_less_nat Y_9) X_16))))
% FOF formula (forall (X_15:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_15) X_15)->False)) of role axiom named fact_89_order__less__irrefl
% A new axiom: (forall (X_15:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_15) X_15)->False))
% FOF formula (forall (X_15:nat), (((ord_less_nat X_15) X_15)->False)) of role axiom named fact_90_order__less__irrefl
% A new axiom: (forall (X_15:nat), (((ord_less_nat X_15) X_15)->False))
% FOF formula (((eq ((produc1832616231le_alt->Prop)->Prop)) top_to1830848411lt_o_o) (collec1079683069_alt_o (fun (X_1:(produc1832616231le_alt->Prop))=> True))) of role axiom named fact_91_UNIV__def
% A new axiom: (((eq ((produc1832616231le_alt->Prop)->Prop)) top_to1830848411lt_o_o) (collec1079683069_alt_o (fun (X_1:(produc1832616231le_alt->Prop))=> True)))
% FOF formula (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) top_to790289938lt_o_o) (collec1718651462_alt_o (fun (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> True))) of role axiom named fact_92_UNIV__def
% A new axiom: (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) top_to790289938lt_o_o) (collec1718651462_alt_o (fun (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> True)))
% FOF formula (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) top_to1049332548lt_o_o) (collec2125720304_alt_o (fun (X_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> True))) of role axiom named fact_93_UNIV__def
% A new axiom: (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) top_to1049332548lt_o_o) (collec2125720304_alt_o (fun (X_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> True)))
% FOF formula (((eq (produc1832616231le_alt->Prop)) top_to679332578_alt_o) (collec1201320914le_alt (fun (X_1:produc1832616231le_alt)=> True))) of role axiom named fact_94_UNIV__def
% A new axiom: (((eq (produc1832616231le_alt->Prop)) top_to679332578_alt_o) (collec1201320914le_alt (fun (X_1:produc1832616231le_alt)=> True)))
% FOF formula (((eq (arrow_1092341143e_indi->Prop)) top_to527331954indi_o) (collec1832628290e_indi (fun (X_1:arrow_1092341143e_indi)=> True))) of role axiom named fact_95_UNIV__def
% A new axiom: (((eq (arrow_1092341143e_indi->Prop)) top_to527331954indi_o) (collec1832628290e_indi (fun (X_1:arrow_1092341143e_indi)=> True)))
% FOF formula (forall (S:(produc1832616231le_alt->Prop)) (R:(produc1832616231le_alt->Prop)), ((iff (forall (X_1:arrow_1346734812le_alt) (Xa:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X_1) Xa)) R)) ((member545531028le_alt ((produc990411159le_alt X_1) Xa)) S)))) (((eq (produc1832616231le_alt->Prop)) R) S))) of role axiom named fact_96_pred__equals__eq2
% A new axiom: (forall (S:(produc1832616231le_alt->Prop)) (R:(produc1832616231le_alt->Prop)), ((iff (forall (X_1:arrow_1346734812le_alt) (Xa:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X_1) Xa)) R)) ((member545531028le_alt ((produc990411159le_alt X_1) Xa)) S)))) (((eq (produc1832616231le_alt->Prop)) R) S)))
% FOF formula (forall (A_13:((produc1832616231le_alt->Prop)->Prop)), ((iff (not (((eq ((produc1832616231le_alt->Prop)->Prop)) A_13) top_to1830848411lt_o_o))) ((ord_le898419007lt_o_o A_13) top_to1830848411lt_o_o))) of role axiom named fact_97_less__top
% A new axiom: (forall (A_13:((produc1832616231le_alt->Prop)->Prop)), ((iff (not (((eq ((produc1832616231le_alt->Prop)->Prop)) A_13) top_to1830848411lt_o_o))) ((ord_le898419007lt_o_o A_13) top_to1830848411lt_o_o)))
% FOF formula (forall (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((iff (not (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) A_13) top_to790289938lt_o_o))) ((ord_le972845494lt_o_o A_13) top_to790289938lt_o_o))) of role axiom named fact_98_less__top
% A new axiom: (forall (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((iff (not (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) A_13) top_to790289938lt_o_o))) ((ord_le972845494lt_o_o A_13) top_to790289938lt_o_o)))
% FOF formula (forall (A_13:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((iff (not (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) A_13) top_to1049332548lt_o_o))) ((ord_le939309728lt_o_o A_13) top_to1049332548lt_o_o))) of role axiom named fact_99_less__top
% A new axiom: (forall (A_13:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((iff (not (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) A_13) top_to1049332548lt_o_o))) ((ord_le939309728lt_o_o A_13) top_to1049332548lt_o_o)))
% FOF formula (forall (A_13:Prop), ((iff (((iff A_13) top_top_o)->False)) ((ord_less_o A_13) top_top_o))) of role axiom named fact_100_less__top
% A new axiom: (forall (A_13:Prop), ((iff (((iff A_13) top_top_o)->False)) ((ord_less_o A_13) top_top_o)))
% FOF formula (forall (A_13:(produc1832616231le_alt->Prop)), ((iff (not (((eq (produc1832616231le_alt->Prop)) A_13) top_to679332578_alt_o))) ((ord_le1973646398_alt_o A_13) top_to679332578_alt_o))) of role axiom named fact_101_less__top
% A new axiom: (forall (A_13:(produc1832616231le_alt->Prop)), ((iff (not (((eq (produc1832616231le_alt->Prop)) A_13) top_to679332578_alt_o))) ((ord_le1973646398_alt_o A_13) top_to679332578_alt_o)))
% FOF formula (forall (A_13:(arrow_1092341143e_indi->Prop)), ((iff (not (((eq (arrow_1092341143e_indi->Prop)) A_13) top_to527331954indi_o))) ((ord_le316791758indi_o A_13) top_to527331954indi_o))) of role axiom named fact_102_less__top
% A new axiom: (forall (A_13:(arrow_1092341143e_indi->Prop)), ((iff (not (((eq (arrow_1092341143e_indi->Prop)) A_13) top_to527331954indi_o))) ((ord_le316791758indi_o A_13) top_to527331954indi_o)))
% FOF formula (forall (X_14:arrow_1092341143e_indi) (Y_8:nat) (F_15:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_15) top_to527331954indi_o)->((((eq nat) (F_15 X_14)) Y_8)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat top_to527331954indi_o) F_15) Y_8)) X_14)))) of role axiom named fact_103_inv__f__eq
% A new axiom: (forall (X_14:arrow_1092341143e_indi) (Y_8:nat) (F_15:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_15) top_to527331954indi_o)->((((eq nat) (F_15 X_14)) Y_8)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat top_to527331954indi_o) F_15) Y_8)) X_14))))
% FOF formula (forall (X_13:arrow_1092341143e_indi) (F_14:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_14) top_to527331954indi_o)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat top_to527331954indi_o) F_14) (F_14 X_13))) X_13))) of role axiom named fact_104_inv__f__f
% A new axiom: (forall (X_13:arrow_1092341143e_indi) (F_14:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_14) top_to527331954indi_o)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat top_to527331954indi_o) F_14) (F_14 X_13))) X_13)))
% FOF formula (forall (X_12:arrow_1092341143e_indi) (F_13:(arrow_1092341143e_indi->nat)) (A_12:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_13) A_12)->(((member1714766084e_indi X_12) A_12)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat A_12) F_13) (F_13 X_12))) X_12)))) of role axiom named fact_105_inv__into__f__f
% A new axiom: (forall (X_12:arrow_1092341143e_indi) (F_13:(arrow_1092341143e_indi->nat)) (A_12:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_13) A_12)->(((member1714766084e_indi X_12) A_12)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat A_12) F_13) (F_13 X_12))) X_12))))
% FOF formula (forall (Y_7:nat) (X_11:arrow_1092341143e_indi) (F_12:(arrow_1092341143e_indi->nat)) (A_11:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_12) A_11)->(((member1714766084e_indi X_11) A_11)->((((eq nat) (F_12 X_11)) Y_7)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat A_11) F_12) Y_7)) X_11))))) of role axiom named fact_106_inv__into__f__eq
% A new axiom: (forall (Y_7:nat) (X_11:arrow_1092341143e_indi) (F_12:(arrow_1092341143e_indi->nat)) (A_11:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_12) A_11)->(((member1714766084e_indi X_11) A_11)->((((eq nat) (F_12 X_11)) Y_7)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat A_11) F_12) Y_7)) X_11)))))
% FOF formula (forall (X_10:arrow_1092341143e_indi) (Y_6:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_11) top_to527331954indi_o)->((iff (((eq nat) (F_11 X_10)) (F_11 Y_6))) (((eq arrow_1092341143e_indi) X_10) Y_6)))) of role axiom named fact_107_inj__eq
% A new axiom: (forall (X_10:arrow_1092341143e_indi) (Y_6:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_11) top_to527331954indi_o)->((iff (((eq nat) (F_11 X_10)) (F_11 Y_6))) (((eq arrow_1092341143e_indi) X_10) Y_6))))
% FOF formula (forall (F_10:(arrow_1092341143e_indi->nat)) (A_10:(arrow_1092341143e_indi->Prop)), ((iff ((inj_on945046484di_nat F_10) A_10)) (forall (X_1:arrow_1092341143e_indi), (((member1714766084e_indi X_1) A_10)->(forall (Xa:arrow_1092341143e_indi), (((member1714766084e_indi Xa) A_10)->((((eq nat) (F_10 X_1)) (F_10 Xa))->(((eq arrow_1092341143e_indi) X_1) Xa)))))))) of role axiom named fact_108_inj__on__def
% A new axiom: (forall (F_10:(arrow_1092341143e_indi->nat)) (A_10:(arrow_1092341143e_indi->Prop)), ((iff ((inj_on945046484di_nat F_10) A_10)) (forall (X_1:arrow_1092341143e_indi), (((member1714766084e_indi X_1) A_10)->(forall (Xa:arrow_1092341143e_indi), (((member1714766084e_indi Xa) A_10)->((((eq nat) (F_10 X_1)) (F_10 Xa))->(((eq arrow_1092341143e_indi) X_1) Xa))))))))
% FOF formula (forall (X_9:arrow_1092341143e_indi) (Y_5:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->nat)) (A_9:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_9) A_9)->((not (((eq arrow_1092341143e_indi) X_9) Y_5))->(((member1714766084e_indi X_9) A_9)->(((member1714766084e_indi Y_5) A_9)->(not (((eq nat) (F_9 X_9)) (F_9 Y_5)))))))) of role axiom named fact_109_inj__on__contraD
% A new axiom: (forall (X_9:arrow_1092341143e_indi) (Y_5:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->nat)) (A_9:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_9) A_9)->((not (((eq arrow_1092341143e_indi) X_9) Y_5))->(((member1714766084e_indi X_9) A_9)->(((member1714766084e_indi Y_5) A_9)->(not (((eq nat) (F_9 X_9)) (F_9 Y_5))))))))
% FOF formula (forall (Y_4:arrow_1092341143e_indi) (X_8:arrow_1092341143e_indi) (F_8:(arrow_1092341143e_indi->nat)) (A_8:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_8) A_8)->(((member1714766084e_indi X_8) A_8)->(((member1714766084e_indi Y_4) A_8)->((iff (((eq nat) (F_8 X_8)) (F_8 Y_4))) (((eq arrow_1092341143e_indi) X_8) Y_4)))))) of role axiom named fact_110_inj__on__iff
% A new axiom: (forall (Y_4:arrow_1092341143e_indi) (X_8:arrow_1092341143e_indi) (F_8:(arrow_1092341143e_indi->nat)) (A_8:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_8) A_8)->(((member1714766084e_indi X_8) A_8)->(((member1714766084e_indi Y_4) A_8)->((iff (((eq nat) (F_8 X_8)) (F_8 Y_4))) (((eq arrow_1092341143e_indi) X_8) Y_4))))))
% FOF formula (forall (X_7:arrow_1092341143e_indi) (Y_3:arrow_1092341143e_indi) (F_7:(arrow_1092341143e_indi->nat)) (A_7:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_7) A_7)->((((eq nat) (F_7 X_7)) (F_7 Y_3))->(((member1714766084e_indi X_7) A_7)->(((member1714766084e_indi Y_3) A_7)->(((eq arrow_1092341143e_indi) X_7) Y_3)))))) of role axiom named fact_111_inj__onD
% A new axiom: (forall (X_7:arrow_1092341143e_indi) (Y_3:arrow_1092341143e_indi) (F_7:(arrow_1092341143e_indi->nat)) (A_7:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_7) A_7)->((((eq nat) (F_7 X_7)) (F_7 Y_3))->(((member1714766084e_indi X_7) A_7)->(((member1714766084e_indi Y_3) A_7)->(((eq arrow_1092341143e_indi) X_7) Y_3))))))
% FOF formula (forall (X_6:arrow_1092341143e_indi) (Y_2:arrow_1092341143e_indi) (F_6:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_6) top_to527331954indi_o)->((((eq nat) (F_6 X_6)) (F_6 Y_2))->(((eq arrow_1092341143e_indi) X_6) Y_2)))) of role axiom named fact_112_injD
% A new axiom: (forall (X_6:arrow_1092341143e_indi) (Y_2:arrow_1092341143e_indi) (F_6:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_6) top_to527331954indi_o)->((((eq nat) (F_6 X_6)) (F_6 Y_2))->(((eq arrow_1092341143e_indi) X_6) Y_2))))
% FOF formula (forall (G:(nat->arrow_1092341143e_indi)) (F_5:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_5) top_to527331954indi_o)->((forall (X_1:nat), (((eq nat) (F_5 (G X_1))) X_1))->(((eq (nat->arrow_1092341143e_indi)) ((hilber564731065di_nat top_to527331954indi_o) F_5)) G)))) of role axiom named fact_113_inj__imp__inv__eq
% A new axiom: (forall (G:(nat->arrow_1092341143e_indi)) (F_5:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_5) top_to527331954indi_o)->((forall (X_1:nat), (((eq nat) (F_5 (G X_1))) X_1))->(((eq (nat->arrow_1092341143e_indi)) ((hilber564731065di_nat top_to527331954indi_o) F_5)) G))))
% FOF formula (forall (F_4:(arrow_1092341143e_indi->nat)), ((forall (X_1:arrow_1092341143e_indi) (Y_1:arrow_1092341143e_indi), ((((eq nat) (F_4 X_1)) (F_4 Y_1))->(((eq arrow_1092341143e_indi) X_1) Y_1)))->((inj_on945046484di_nat F_4) top_to527331954indi_o))) of role axiom named fact_114_injI
% A new axiom: (forall (F_4:(arrow_1092341143e_indi->nat)), ((forall (X_1:arrow_1092341143e_indi) (Y_1:arrow_1092341143e_indi), ((((eq nat) (F_4 X_1)) (F_4 Y_1))->(((eq arrow_1092341143e_indi) X_1) Y_1)))->((inj_on945046484di_nat F_4) top_to527331954indi_o)))
% FOF formula ((member733327538_alt_o f) ((pi_Arr1021537730_alt_o arrow_1605628760e_Prof) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> arrow_1751445586le_Lin))) of role axiom named fact_115_assms_I1_J
% A new axiom: ((member733327538_alt_o f) ((pi_Arr1021537730_alt_o arrow_1605628760e_Prof) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> arrow_1751445586le_Lin)))
% FOF formula ((member1362619835_alt_o lba) arrow_1751445586le_Lin) of role axiom named fact_116__096Lba_A_058_ALin_096
% A new axiom: ((member1362619835_alt_o lba) arrow_1751445586le_Lin)
% FOF formula ((member1362619835_alt_o lab) arrow_1751445586le_Lin) of role axiom named fact_117__096Lab_A_058_ALin_096
% A new axiom: ((member1362619835_alt_o lab) arrow_1751445586le_Lin)
% FOF formula (forall (A_3:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->(((member545531028le_alt ((produc990411159le_alt A_3) B_2)) L)->(((member545531028le_alt ((produc990411159le_alt B_2) A_3)) L)->False)))) of role axiom named fact_118_Lin__irrefl
% A new axiom: (forall (A_3:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->(((member545531028le_alt ((produc990411159le_alt A_3) B_2)) L)->(((member545531028le_alt ((produc990411159le_alt B_2) A_3)) L)->False))))
% FOF formula (forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((not (((eq arrow_1346734812le_alt) X) Y))->((iff (((member545531028le_alt ((produc990411159le_alt X) Y)) L)->False)) ((member545531028le_alt ((produc990411159le_alt Y) X)) L))))) of role axiom named fact_119_notin__Lin__iff
% A new axiom: (forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((not (((eq arrow_1346734812le_alt) X) Y))->((iff (((member545531028le_alt ((produc990411159le_alt X) Y)) L)->False)) ((member545531028le_alt ((produc990411159le_alt Y) X)) L)))))
% FOF formula (forall (X_5:arrow_1092341143e_indi) (A_6:(arrow_1092341143e_indi->Prop)), ((iff ((member1714766084e_indi X_5) A_6)) (A_6 X_5))) of role axiom named fact_120_mem__def
% A new axiom: (forall (X_5:arrow_1092341143e_indi) (A_6:(arrow_1092341143e_indi->Prop)), ((iff ((member1714766084e_indi X_5) A_6)) (A_6 X_5)))
% FOF formula (forall (X_5:Prop) (A_6:(Prop->Prop)), ((iff ((member_o X_5) A_6)) (A_6 X_5))) of role axiom named fact_121_mem__def
% A new axiom: (forall (X_5:Prop) (A_6:(Prop->Prop)), ((iff ((member_o X_5) A_6)) (A_6 X_5)))
% FOF formula (forall (X_5:produc1832616231le_alt) (A_6:(produc1832616231le_alt->Prop)), ((iff ((member545531028le_alt X_5) A_6)) (A_6 X_5))) of role axiom named fact_122_mem__def
% A new axiom: (forall (X_5:produc1832616231le_alt) (A_6:(produc1832616231le_alt->Prop)), ((iff ((member545531028le_alt X_5) A_6)) (A_6 X_5)))
% FOF formula (forall (X_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((iff ((member1561882372_alt_o X_5) A_6)) (A_6 X_5))) of role axiom named fact_123_mem__def
% A new axiom: (forall (X_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((iff ((member1561882372_alt_o X_5) A_6)) (A_6 X_5)))
% FOF formula (forall (X_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((iff ((member733327538_alt_o X_5) A_6)) (A_6 X_5))) of role axiom named fact_124_mem__def
% A new axiom: (forall (X_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((iff ((member733327538_alt_o X_5) A_6)) (A_6 X_5)))
% FOF formula (forall (X_5:(produc1832616231le_alt->Prop)) (A_6:((produc1832616231le_alt->Prop)->Prop)), ((iff ((member1362619835_alt_o X_5) A_6)) (A_6 X_5))) of role axiom named fact_125_mem__def
% A new axiom: (forall (X_5:(produc1832616231le_alt->Prop)) (A_6:((produc1832616231le_alt->Prop)->Prop)), ((iff ((member1362619835_alt_o X_5) A_6)) (A_6 X_5)))
% FOF formula (forall (P_2:(arrow_1092341143e_indi->Prop)), (((eq (arrow_1092341143e_indi->Prop)) (collec1832628290e_indi P_2)) P_2)) of role axiom named fact_126_Collect__def
% A new axiom: (forall (P_2:(arrow_1092341143e_indi->Prop)), (((eq (arrow_1092341143e_indi->Prop)) (collec1832628290e_indi P_2)) P_2))
% FOF formula (forall (X:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1865892024_mktop L) X)) arrow_1751445586le_Lin))) of role axiom named fact_127_mktop__Lin
% A new axiom: (forall (X:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1865892024_mktop L) X)) arrow_1751445586le_Lin)))
% FOF formula (forall (X:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1717184938_mkbot L) X)) arrow_1751445586le_Lin))) of role axiom named fact_128_mkbot__Lin
% A new axiom: (forall (X:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1717184938_mkbot L) X)) arrow_1751445586le_Lin)))
% FOF formula (forall (L:(produc1832616231le_alt->Prop)) (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) X) Y))->(((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1362619835_alt_o (((arrow_452340254_above L) X) Y)) arrow_1751445586le_Lin)))) of role axiom named fact_129_above__Lin
% A new axiom: (forall (L:(produc1832616231le_alt->Prop)) (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) X) Y))->(((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1362619835_alt_o (((arrow_452340254_above L) X) Y)) arrow_1751445586le_Lin))))
% FOF formula (forall (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1561882372_alt_o (fun (P_1:arrow_1092341143e_indi)=> L)) arrow_1605628760e_Prof))) of role axiom named fact_130_const__Lin__Prof
% A new axiom: (forall (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1561882372_alt_o (fun (P_1:arrow_1092341143e_indi)=> L)) arrow_1605628760e_Prof)))
% FOF formula (forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)) (A_3:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_3) B_2))->(((member1362619835_alt_o L) arrow_1751445586le_Lin)->((iff ((member545531028le_alt ((produc990411159le_alt X) Y)) (((arrow_452340254_above L) A_3) B_2))) ((and ((and (not (((eq arrow_1346734812le_alt) X) Y))) ((((eq arrow_1346734812le_alt) X) B_2)->((member545531028le_alt ((produc990411159le_alt A_3) Y)) L)))) ((not (((eq arrow_1346734812le_alt) X) B_2))->((and ((((eq arrow_1346734812le_alt) Y) B_2)->((or (((eq arrow_1346734812le_alt) X) A_3)) ((member545531028le_alt ((produc990411159le_alt X) A_3)) L)))) ((not (((eq arrow_1346734812le_alt) Y) B_2))->((member545531028le_alt ((produc990411159le_alt X) Y)) L))))))))) of role axiom named fact_131_in__above
% A new axiom: (forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)) (A_3:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_3) B_2))->(((member1362619835_alt_o L) arrow_1751445586le_Lin)->((iff ((member545531028le_alt ((produc990411159le_alt X) Y)) (((arrow_452340254_above L) A_3) B_2))) ((and ((and (not (((eq arrow_1346734812le_alt) X) Y))) ((((eq arrow_1346734812le_alt) X) B_2)->((member545531028le_alt ((produc990411159le_alt A_3) Y)) L)))) ((not (((eq arrow_1346734812le_alt) X) B_2))->((and ((((eq arrow_1346734812le_alt) Y) B_2)->((or (((eq arrow_1346734812le_alt) X) A_3)) ((member545531028le_alt ((produc990411159le_alt X) A_3)) L)))) ((not (((eq arrow_1346734812le_alt) Y) B_2))->((member545531028le_alt ((produc990411159le_alt X) Y)) L)))))))))
% FOF formula (forall (I_1:arrow_1092341143e_indi) (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o F) ((pi_Arr1021537730_alt_o arrow_1605628760e_Prof) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> arrow_1751445586le_Lin)))->((forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_5) B_4))->(((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (X_1 I_1))->((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F X_1)))))))->((arrow_1098709355ctator F) I_1)))) of role axiom named fact_132_dictatorI
% A new axiom: (forall (I_1:arrow_1092341143e_indi) (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o F) ((pi_Arr1021537730_alt_o arrow_1605628760e_Prof) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> arrow_1751445586le_Lin)))->((forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_5) B_4))->(((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (X_1 I_1))->((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F X_1)))))))->((arrow_1098709355ctator F) I_1))))
% FOF formula (forall (X_4:produc1832616231le_alt) (F_3:(produc1832616231le_alt->Prop)) (A_4:(produc1832616231le_alt->Prop)) (B_3:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_3) ((pi_Pro539263375_alt_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member545531028le_alt X_4) A_4)->False)))) of role axiom named fact_133_PiE
% A new axiom: (forall (X_4:produc1832616231le_alt) (F_3:(produc1832616231le_alt->Prop)) (A_4:(produc1832616231le_alt->Prop)) (B_3:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_3) ((pi_Pro539263375_alt_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member545531028le_alt X_4) A_4)->False))))
% FOF formula (forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_3) ((pi_Arr1055270199le_alt A_4) B_3))->((((member545531028le_alt (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False)))) of role axiom named fact_134_PiE
% A new axiom: (forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_3) ((pi_Arr1055270199le_alt A_4) B_3))->((((member545531028le_alt (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False))))
% FOF formula (forall (X_4:Prop) (F_3:(Prop->produc1832616231le_alt)) (A_4:(Prop->Prop)) (B_3:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_3) ((pi_o_P988780107le_alt A_4) B_3))->((((member545531028le_alt (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False)))) of role axiom named fact_135_PiE
% A new axiom: (forall (X_4:Prop) (F_3:(Prop->produc1832616231le_alt)) (A_4:(Prop->Prop)) (B_3:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_3) ((pi_o_P988780107le_alt A_4) B_3))->((((member545531028le_alt (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False))))
% FOF formula (forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_3) ((pi_Arr651234977_alt_o A_4) B_3))->((((member1561882372_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False)))) of role axiom named fact_136_PiE
% A new axiom: (forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_3) ((pi_Arr651234977_alt_o A_4) B_3))->((((member1561882372_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False))))
% FOF formula (forall (X_4:Prop) (F_3:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_4:(Prop->Prop)) (B_3:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_3) ((pi_o_A71242893_alt_o A_4) B_3))->((((member1561882372_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False)))) of role axiom named fact_137_PiE
% A new axiom: (forall (X_4:Prop) (F_3:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_4:(Prop->Prop)) (B_3:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_3) ((pi_o_A71242893_alt_o A_4) B_3))->((((member1561882372_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False))))
% FOF formula (forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_3) ((pi_Arr1140519125_alt_o A_4) B_3))->((((member733327538_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False)))) of role axiom named fact_138_PiE
% A new axiom: (forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_3) ((pi_Arr1140519125_alt_o A_4) B_3))->((((member733327538_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False))))
% FOF formula (forall (X_4:Prop) (F_3:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_4:(Prop->Prop)) (B_3:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_3) ((pi_o_A1302557673_alt_o A_4) B_3))->((((member733327538_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False)))) of role axiom named fact_139_PiE
% A new axiom: (forall (X_4:Prop) (F_3:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_4:(Prop->Prop)) (B_3:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_3) ((pi_o_A1302557673_alt_o A_4) B_3))->((((member733327538_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False))))
% FOF formula (forall (X_4:Prop) (F_3:(Prop->(produc1832616231le_alt->Prop))) (A_4:(Prop->Prop)) (B_3:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_3) ((pi_o_P1538584260_alt_o A_4) B_3))->((((member1362619835_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False)))) of role axiom named fact_140_PiE
% A new axiom: (forall (X_4:Prop) (F_3:(Prop->(produc1832616231le_alt->Prop))) (A_4:(Prop->Prop)) (B_3:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_3) ((pi_o_P1538584260_alt_o A_4) B_3))->((((member1362619835_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False))))
% FOF formula (forall (X_4:produc1832616231le_alt) (F_3:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_4:(produc1832616231le_alt->Prop)) (B_3:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_3) ((pi_Pro1535452471e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member545531028le_alt X_4) A_4)->False)))) of role axiom named fact_141_PiE
% A new axiom: (forall (X_4:produc1832616231le_alt) (F_3:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_4:(produc1832616231le_alt->Prop)) (B_3:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_3) ((pi_Pro1535452471e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member545531028le_alt X_4) A_4)->False))))
% FOF formula (forall (X_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_3) ((pi_Arr170420797e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member1561882372_alt_o X_4) A_4)->False)))) of role axiom named fact_142_PiE
% A new axiom: (forall (X_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_3) ((pi_Arr170420797e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member1561882372_alt_o X_4) A_4)->False))))
% FOF formula (forall (X_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_3) ((pi_Arr1767527177lt_o_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member1561882372_alt_o X_4) A_4)->False)))) of role axiom named fact_143_PiE
% A new axiom: (forall (X_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_3) ((pi_Arr1767527177lt_o_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member1561882372_alt_o X_4) A_4)->False))))
% FOF formula (forall (X_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_4:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_3) ((pi_Arr1941314005e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member733327538_alt_o X_4) A_4)->False)))) of role axiom named fact_144_PiE
% A new axiom: (forall (X_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_4:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_3) ((pi_Arr1941314005e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member733327538_alt_o X_4) A_4)->False))))
% FOF formula (forall (X_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_4:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_3) ((pi_Arr1422400881lt_o_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member733327538_alt_o X_4) A_4)->False)))) of role axiom named fact_145_PiE
% A new axiom: (forall (X_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_4:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_3) ((pi_Arr1422400881lt_o_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member733327538_alt_o X_4) A_4)->False))))
% FOF formula (forall (X_4:(produc1832616231le_alt->Prop)) (F_3:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_4:((produc1832616231le_alt->Prop)->Prop)) (B_3:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_3) ((pi_Pro1340600692e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member1362619835_alt_o X_4) A_4)->False)))) of role axiom named fact_146_PiE
% A new axiom: (forall (X_4:(produc1832616231le_alt->Prop)) (F_3:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_4:((produc1832616231le_alt->Prop)->Prop)) (B_3:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_3) ((pi_Pro1340600692e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member1362619835_alt_o X_4) A_4)->False))))
% FOF formula (forall (X_4:(produc1832616231le_alt->Prop)) (F_3:((produc1832616231le_alt->Prop)->Prop)) (A_4:((produc1832616231le_alt->Prop)->Prop)) (B_3:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_3) ((pi_Pro410810898lt_o_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member1362619835_alt_o X_4) A_4)->False)))) of role axiom named fact_147_PiE
% A new axiom: (forall (X_4:(produc1832616231le_alt->Prop)) (F_3:((produc1832616231le_alt->Prop)->Prop)) (A_4:((produc1832616231le_alt->Prop)->Prop)) (B_3:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_3) ((pi_Pro410810898lt_o_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member1362619835_alt_o X_4) A_4)->False))))
% FOF formula (forall (X_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_3) ((pi_Arr1021537730_alt_o A_4) B_3))->((((member1362619835_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1561882372_alt_o X_4) A_4)->False)))) of role axiom named fact_148_PiE
% A new axiom: (forall (X_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_3) ((pi_Arr1021537730_alt_o A_4) B_3))->((((member1362619835_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1561882372_alt_o X_4) A_4)->False))))
% FOF formula (forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_3) ((pi_Arr418143960_alt_o A_4) B_3))->((((member1362619835_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False)))) of role axiom named fact_149_PiE
% A new axiom: (forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_3) ((pi_Arr418143960_alt_o A_4) B_3))->((((member1362619835_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False))))
% FOF formula (forall (A_3:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_3) B_2))->((ex (produc1832616231le_alt->Prop)) (fun (X_1:(produc1832616231le_alt->Prop))=> ((and ((member1362619835_alt_o X_1) arrow_1751445586le_Lin)) ((member545531028le_alt ((produc990411159le_alt A_3) B_2)) X_1)))))) of role axiom named fact_150_complete__Lin
% A new axiom: (forall (A_3:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_3) B_2))->((ex (produc1832616231le_alt->Prop)) (fun (X_1:(produc1832616231le_alt->Prop))=> ((and ((member1362619835_alt_o X_1) arrow_1751445586le_Lin)) ((member545531028le_alt ((produc990411159le_alt A_3) B_2)) X_1))))))
% FOF formula (forall (N:nat), ((member1561882372_alt_o (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) N)) lab) lba))) arrow_1605628760e_Prof)) of role axiom named fact_151_PiProf
% A new axiom: (forall (N:nat), ((member1561882372_alt_o (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) N)) lab) lba))) arrow_1605628760e_Prof))
% FOF formula (forall (X_3:produc1832616231le_alt) (F_2:(produc1832616231le_alt->Prop)) (A_2:(produc1832616231le_alt->Prop)) (B_1:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_2) ((pi_Pro539263375_alt_o A_2) B_1))->(((member545531028le_alt X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_152_Pi__mem
% A new axiom: (forall (X_3:produc1832616231le_alt) (F_2:(produc1832616231le_alt->Prop)) (A_2:(produc1832616231le_alt->Prop)) (B_1:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_2) ((pi_Pro539263375_alt_o A_2) B_1))->(((member545531028le_alt X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:produc1832616231le_alt) (F_2:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_2:(produc1832616231le_alt->Prop)) (B_1:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_2) ((pi_Pro1535452471e_indi A_2) B_1))->(((member545531028le_alt X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_153_Pi__mem
% A new axiom: (forall (X_3:produc1832616231le_alt) (F_2:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_2:(produc1832616231le_alt->Prop)) (B_1:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_2) ((pi_Pro1535452471e_indi A_2) B_1))->(((member545531028le_alt X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_2) ((pi_Arr170420797e_indi A_2) B_1))->(((member1561882372_alt_o X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_154_Pi__mem
% A new axiom: (forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_2) ((pi_Arr170420797e_indi A_2) B_1))->(((member1561882372_alt_o X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_2) ((pi_Arr1767527177lt_o_o A_2) B_1))->(((member1561882372_alt_o X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_155_Pi__mem
% A new axiom: (forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_2) ((pi_Arr1767527177lt_o_o A_2) B_1))->(((member1561882372_alt_o X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_2) ((pi_Arr1941314005e_indi A_2) B_1))->(((member733327538_alt_o X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_156_Pi__mem
% A new axiom: (forall (X_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_2) ((pi_Arr1941314005e_indi A_2) B_1))->(((member733327538_alt_o X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_2) ((pi_Arr1422400881lt_o_o A_2) B_1))->(((member733327538_alt_o X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_157_Pi__mem
% A new axiom: (forall (X_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_2) ((pi_Arr1422400881lt_o_o A_2) B_1))->(((member733327538_alt_o X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:(produc1832616231le_alt->Prop)) (F_2:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_2:((produc1832616231le_alt->Prop)->Prop)) (B_1:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_2) ((pi_Pro1340600692e_indi A_2) B_1))->(((member1362619835_alt_o X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_158_Pi__mem
% A new axiom: (forall (X_3:(produc1832616231le_alt->Prop)) (F_2:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_2:((produc1832616231le_alt->Prop)->Prop)) (B_1:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_2) ((pi_Pro1340600692e_indi A_2) B_1))->(((member1362619835_alt_o X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:(produc1832616231le_alt->Prop)) (F_2:((produc1832616231le_alt->Prop)->Prop)) (A_2:((produc1832616231le_alt->Prop)->Prop)) (B_1:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_2) ((pi_Pro410810898lt_o_o A_2) B_1))->(((member1362619835_alt_o X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_159_Pi__mem
% A new axiom: (forall (X_3:(produc1832616231le_alt->Prop)) (F_2:((produc1832616231le_alt->Prop)->Prop)) (A_2:((produc1832616231le_alt->Prop)->Prop)) (B_1:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_2) ((pi_Pro410810898lt_o_o A_2) B_1))->(((member1362619835_alt_o X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_2) ((pi_Arr1055270199le_alt A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member545531028le_alt (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_160_Pi__mem
% A new axiom: (forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_2) ((pi_Arr1055270199le_alt A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member545531028le_alt (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:Prop) (F_2:(Prop->produc1832616231le_alt)) (A_2:(Prop->Prop)) (B_1:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_2) ((pi_o_P988780107le_alt A_2) B_1))->(((member_o X_3) A_2)->((member545531028le_alt (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_161_Pi__mem
% A new axiom: (forall (X_3:Prop) (F_2:(Prop->produc1832616231le_alt)) (A_2:(Prop->Prop)) (B_1:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_2) ((pi_o_P988780107le_alt A_2) B_1))->(((member_o X_3) A_2)->((member545531028le_alt (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_2) ((pi_Arr651234977_alt_o A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member1561882372_alt_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_162_Pi__mem
% A new axiom: (forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_2) ((pi_Arr651234977_alt_o A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member1561882372_alt_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:Prop) (F_2:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_2:(Prop->Prop)) (B_1:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_2) ((pi_o_A71242893_alt_o A_2) B_1))->(((member_o X_3) A_2)->((member1561882372_alt_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_163_Pi__mem
% A new axiom: (forall (X_3:Prop) (F_2:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_2:(Prop->Prop)) (B_1:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_2) ((pi_o_A71242893_alt_o A_2) B_1))->(((member_o X_3) A_2)->((member1561882372_alt_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_2) ((pi_Arr1140519125_alt_o A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member733327538_alt_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_164_Pi__mem
% A new axiom: (forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_2) ((pi_Arr1140519125_alt_o A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member733327538_alt_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:Prop) (F_2:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_2:(Prop->Prop)) (B_1:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_2) ((pi_o_A1302557673_alt_o A_2) B_1))->(((member_o X_3) A_2)->((member733327538_alt_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_165_Pi__mem
% A new axiom: (forall (X_3:Prop) (F_2:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_2:(Prop->Prop)) (B_1:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_2) ((pi_o_A1302557673_alt_o A_2) B_1))->(((member_o X_3) A_2)->((member733327538_alt_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:Prop) (F_2:(Prop->(produc1832616231le_alt->Prop))) (A_2:(Prop->Prop)) (B_1:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_2) ((pi_o_P1538584260_alt_o A_2) B_1))->(((member_o X_3) A_2)->((member1362619835_alt_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_166_Pi__mem
% A new axiom: (forall (X_3:Prop) (F_2:(Prop->(produc1832616231le_alt->Prop))) (A_2:(Prop->Prop)) (B_1:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_2) ((pi_o_P1538584260_alt_o A_2) B_1))->(((member_o X_3) A_2)->((member1362619835_alt_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_2) ((pi_Arr1021537730_alt_o A_2) B_1))->(((member1561882372_alt_o X_3) A_2)->((member1362619835_alt_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_167_Pi__mem
% A new axiom: (forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_2) ((pi_Arr1021537730_alt_o A_2) B_1))->(((member1561882372_alt_o X_3) A_2)->((member1362619835_alt_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_2) ((pi_Arr418143960_alt_o A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member1362619835_alt_o (F_2 X_3)) (B_1 X_3))))) of role axiom named fact_168_Pi__mem
% A new axiom: (forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_2) ((pi_Arr418143960_alt_o A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member1362619835_alt_o (F_2 X_3)) (B_1 X_3)))))
% FOF formula (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) arrow_1605628760e_Prof) ((pi_Arr418143960_alt_o top_to527331954indi_o) (fun (Uu:arrow_1092341143e_indi)=> arrow_1751445586le_Lin))) of role axiom named fact_169_Prof__def
% A new axiom: (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) arrow_1605628760e_Prof) ((pi_Arr418143960_alt_o top_to527331954indi_o) (fun (Uu:arrow_1092341143e_indi)=> arrow_1751445586le_Lin)))
% FOF formula (forall (X_2:produc1832616231le_alt) (F_1:(produc1832616231le_alt->Prop)) (A_1:(produc1832616231le_alt->Prop)) (B:(Prop->Prop)), (((member1362619835_alt_o F_1) ((pi_Pro539263375_alt_o A_1) (fun (Uu:produc1832616231le_alt)=> B)))->(((member545531028le_alt X_2) A_1)->((member_o (F_1 X_2)) B)))) of role axiom named fact_170_funcset__mem
% A new axiom: (forall (X_2:produc1832616231le_alt) (F_1:(produc1832616231le_alt->Prop)) (A_1:(produc1832616231le_alt->Prop)) (B:(Prop->Prop)), (((member1362619835_alt_o F_1) ((pi_Pro539263375_alt_o A_1) (fun (Uu:produc1832616231le_alt)=> B)))->(((member545531028le_alt X_2) A_1)->((member_o (F_1 X_2)) B))))
% FOF formula (forall (X_2:produc1832616231le_alt) (F_1:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_1:(produc1832616231le_alt->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member1486844321e_indi F_1) ((pi_Pro1535452471e_indi A_1) (fun (Uu:produc1832616231le_alt)=> B)))->(((member545531028le_alt X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B)))) of role axiom named fact_171_funcset__mem
% A new axiom: (forall (X_2:produc1832616231le_alt) (F_1:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_1:(produc1832616231le_alt->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member1486844321e_indi F_1) ((pi_Pro1535452471e_indi A_1) (fun (Uu:produc1832616231le_alt)=> B)))->(((member545531028le_alt X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B))))
% FOF formula (forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member1208133347e_indi F_1) ((pi_Arr170420797e_indi A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B)))->(((member1561882372_alt_o X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B)))) of role axiom named fact_172_funcset__mem
% A new axiom: (forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member1208133347e_indi F_1) ((pi_Arr170420797e_indi A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B)))->(((member1561882372_alt_o X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B))))
% FOF formula (forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B:(Prop->Prop)), (((member1754345465lt_o_o F_1) ((pi_Arr1767527177lt_o_o A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B)))->(((member1561882372_alt_o X_2) A_1)->((member_o (F_1 X_2)) B)))) of role axiom named fact_173_funcset__mem
% A new axiom: (forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B:(Prop->Prop)), (((member1754345465lt_o_o F_1) ((pi_Arr1767527177lt_o_o A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B)))->(((member1561882372_alt_o X_2) A_1)->((member_o (F_1 X_2)) B))))
% FOF formula (forall (X_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member986213183e_indi F_1) ((pi_Arr1941314005e_indi A_1) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B)))->(((member733327538_alt_o X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B)))) of role axiom named fact_174_funcset__mem
% A new axiom: (forall (X_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member986213183e_indi F_1) ((pi_Arr1941314005e_indi A_1) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B)))->(((member733327538_alt_o X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B))))
% FOF formula (forall (X_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B:(Prop->Prop)), (((member903234717lt_o_o F_1) ((pi_Arr1422400881lt_o_o A_1) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B)))->(((member733327538_alt_o X_2) A_1)->((member_o (F_1 X_2)) B)))) of role axiom named fact_175_funcset__mem
% A new axiom: (forall (X_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B:(Prop->Prop)), (((member903234717lt_o_o F_1) ((pi_Arr1422400881lt_o_o A_1) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B)))->(((member733327538_alt_o X_2) A_1)->((member_o (F_1 X_2)) B))))
% FOF formula (forall (X_2:(produc1832616231le_alt->Prop)) (F_1:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_1:((produc1832616231le_alt->Prop)->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member1255309082e_indi F_1) ((pi_Pro1340600692e_indi A_1) (fun (Uu:(produc1832616231le_alt->Prop))=> B)))->(((member1362619835_alt_o X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B)))) of role axiom named fact_176_funcset__mem
% A new axiom: (forall (X_2:(produc1832616231le_alt->Prop)) (F_1:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_1:((produc1832616231le_alt->Prop)->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member1255309082e_indi F_1) ((pi_Pro1340600692e_indi A_1) (fun (Uu:(produc1832616231le_alt->Prop))=> B)))->(((member1362619835_alt_o X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B))))
% FOF formula (forall (X_2:(produc1832616231le_alt->Prop)) (F_1:((produc1832616231le_alt->Prop)->Prop)) (A_1:((produc1832616231le_alt->Prop)->Prop)) (B:(Prop->Prop)), (((member1949484546lt_o_o F_1) ((pi_Pro410810898lt_o_o A_1) (fun (Uu:(produc1832616231le_alt->Prop))=> B)))->(((member1362619835_alt_o X_2) A_1)->((member_o (F_1 X_2)) B)))) of role axiom named fact_177_funcset__mem
% A new axiom: (forall (X_2:(produc1832616231le_alt->Prop)) (F_1:((produc1832616231le_alt->Prop)->Prop)) (A_1:((produc1832616231le_alt->Prop)->Prop)) (B:(Prop->Prop)), (((member1949484546lt_o_o F_1) ((pi_Pro410810898lt_o_o A_1) (fun (Uu:(produc1832616231le_alt->Prop))=> B)))->(((member1362619835_alt_o X_2) A_1)->((member_o (F_1 X_2)) B))))
% FOF formula (forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_1:(arrow_1092341143e_indi->Prop)) (B:(produc1832616231le_alt->Prop)), (((member1621875105le_alt F_1) ((pi_Arr1055270199le_alt A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member545531028le_alt (F_1 X_2)) B)))) of role axiom named fact_178_funcset__mem
% A new axiom: (forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_1:(arrow_1092341143e_indi->Prop)) (B:(produc1832616231le_alt->Prop)), (((member1621875105le_alt F_1) ((pi_Arr1055270199le_alt A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member545531028le_alt (F_1 X_2)) B))))
% FOF formula (forall (X_2:Prop) (F_1:(Prop->produc1832616231le_alt)) (A_1:(Prop->Prop)) (B:(produc1832616231le_alt->Prop)), (((member1368218865le_alt F_1) ((pi_o_P988780107le_alt A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member545531028le_alt (F_1 X_2)) B)))) of role axiom named fact_179_funcset__mem
% A new axiom: (forall (X_2:Prop) (F_1:(Prop->produc1832616231le_alt)) (A_1:(Prop->Prop)) (B:(produc1832616231le_alt->Prop)), (((member1368218865le_alt F_1) ((pi_o_P988780107le_alt A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member545531028le_alt (F_1 X_2)) B))))
% FOF formula (forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_1:(arrow_1092341143e_indi->Prop)) (B:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member1079651021_alt_o F_1) ((pi_Arr651234977_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member1561882372_alt_o (F_1 X_2)) B)))) of role axiom named fact_180_funcset__mem
% A new axiom: (forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_1:(arrow_1092341143e_indi->Prop)) (B:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member1079651021_alt_o F_1) ((pi_Arr651234977_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member1561882372_alt_o (F_1 X_2)) B))))
% FOF formula (forall (X_2:Prop) (F_1:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_1:(Prop->Prop)) (B:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member537117565_alt_o F_1) ((pi_o_A71242893_alt_o A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member1561882372_alt_o (F_1 X_2)) B)))) of role axiom named fact_181_funcset__mem
% A new axiom: (forall (X_2:Prop) (F_1:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_1:(Prop->Prop)) (B:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member537117565_alt_o F_1) ((pi_o_A71242893_alt_o A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member1561882372_alt_o (F_1 X_2)) B))))
% FOF formula (forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_1:(arrow_1092341143e_indi->Prop)) (B:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member24189887_alt_o F_1) ((pi_Arr1140519125_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member733327538_alt_o (F_1 X_2)) B)))) of role axiom named fact_182_funcset__mem
% A new axiom: (forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_1:(arrow_1092341143e_indi->Prop)) (B:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member24189887_alt_o F_1) ((pi_Arr1140519125_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member733327538_alt_o (F_1 X_2)) B))))
% FOF formula (forall (X_2:Prop) (F_1:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_1:(Prop->Prop)) (B:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member1710515983_alt_o F_1) ((pi_o_A1302557673_alt_o A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member733327538_alt_o (F_1 X_2)) B)))) of role axiom named fact_183_funcset__mem
% A new axiom: (forall (X_2:Prop) (F_1:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_1:(Prop->Prop)) (B:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member1710515983_alt_o F_1) ((pi_o_A1302557673_alt_o A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member733327538_alt_o (F_1 X_2)) B))))
% FOF formula (forall (X_2:Prop) (F_1:(Prop->(produc1832616231le_alt->Prop))) (A_1:(Prop->Prop)) (B:((produc1832616231le_alt->Prop)->Prop)), (((member1099673524_alt_o F_1) ((pi_o_P1538584260_alt_o A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member1362619835_alt_o (F_1 X_2)) B)))) of role axiom named fact_184_funcset__mem
% A new axiom: (forall (X_2:Prop) (F_1:(Prop->(produc1832616231le_alt->Prop))) (A_1:(Prop->Prop)) (B:((produc1832616231le_alt->Prop)->Prop)), (((member1099673524_alt_o F_1) ((pi_o_P1538584260_alt_o A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member1362619835_alt_o (F_1 X_2)) B))))
% FOF formula (forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B:((produc1832616231le_alt->Prop)->Prop)), (((member733327538_alt_o F_1) ((pi_Arr1021537730_alt_o A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B)))->(((member1561882372_alt_o X_2) A_1)->((member1362619835_alt_o (F_1 X_2)) B)))) of role axiom named fact_185_funcset__mem
% A new axiom: (forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B:((produc1832616231le_alt->Prop)->Prop)), (((member733327538_alt_o F_1) ((pi_Arr1021537730_alt_o A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B)))->(((member1561882372_alt_o X_2) A_1)->((member1362619835_alt_o (F_1 X_2)) B))))
% FOF formula (forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_1:(arrow_1092341143e_indi->Prop)) (B:((produc1832616231le_alt->Prop)->Prop)), (((member1561882372_alt_o F_1) ((pi_Arr418143960_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member1362619835_alt_o (F_1 X_2)) B)))) of role axiom named fact_186_funcset__mem
% A new axiom: (forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_1:(arrow_1092341143e_indi->Prop)) (B:((produc1832616231le_alt->Prop)->Prop)), (((member1561882372_alt_o F_1) ((pi_Arr418143960_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member1362619835_alt_o (F_1 X_2)) B))))
% FOF formula (forall (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (I_1:arrow_1092341143e_indi), ((iff ((arrow_1098709355ctator F) I_1)) (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(((eq (produc1832616231le_alt->Prop)) (F X_1)) (X_1 I_1)))))) of role axiom named fact_187_dictator__def
% A new axiom: (forall (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (I_1:arrow_1092341143e_indi), ((iff ((arrow_1098709355ctator F) I_1)) (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(((eq (produc1832616231le_alt->Prop)) (F X_1)) (X_1 I_1))))))
% FOF formula (forall (A:(produc1832616231le_alt->Prop)), (((eq ((produc1832616231le_alt->Prop)->Prop)) ((pi_Pro539263375_alt_o A) (fun (Uu:produc1832616231le_alt)=> top_top_o_o))) top_to1830848411lt_o_o)) of role axiom named fact_188_Pi__UNIV
% A new axiom: (forall (A:(produc1832616231le_alt->Prop)), (((eq ((produc1832616231le_alt->Prop)->Prop)) ((pi_Pro539263375_alt_o A) (fun (Uu:produc1832616231le_alt)=> top_top_o_o))) top_to1830848411lt_o_o))
% FOF formula (forall (A:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr1021537730_alt_o A) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> top_to1830848411lt_o_o))) top_to1049332548lt_o_o)) of role axiom named fact_189_Pi__UNIV
% A new axiom: (forall (A:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr1021537730_alt_o A) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> top_to1830848411lt_o_o))) top_to1049332548lt_o_o))
% FOF formula (forall (A:(arrow_1092341143e_indi->Prop)), (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr418143960_alt_o A) (fun (Uu:arrow_1092341143e_indi)=> top_to1830848411lt_o_o))) top_to790289938lt_o_o)) of role axiom named fact_190_Pi__UNIV
% A new axiom: (forall (A:(arrow_1092341143e_indi->Prop)), (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr418143960_alt_o A) (fun (Uu:arrow_1092341143e_indi)=> top_to1830848411lt_o_o))) top_to790289938lt_o_o))
% FOF formula ((iff ((member545531028le_alt ((produc990411159le_alt e) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))) ((member545531028le_alt ((produc990411159le_alt b) a)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) lab) lba))))) of role axiom named fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am
% A new axiom: ((iff ((member545531028le_alt ((produc990411159le_alt e) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))) ((member545531028le_alt ((produc990411159le_alt b) a)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) lab) lba)))))
% FOF formula (forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((and (((ord_less_nat (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt e) d)) ((arrow_1865892024_mktop (p _TPTP_I)) e)))) ((((ord_less_nat (h _TPTP_I)) n)->False)->((and ((((eq nat) (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt e) d)) (((arrow_452340254_above (p _TPTP_I)) c) e)))) ((not (((eq nat) (h _TPTP_I)) n))->((member545531028le_alt ((produc990411159le_alt e) d)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))) ((and (((ord_less_nat (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt b) a)) lab))) ((((ord_less_nat (h _TPTP_I)) n)->False)->((member545531028le_alt ((produc990411159le_alt b) a)) lba))))) of role axiom named fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am
% A new axiom: (forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((and (((ord_less_nat (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt e) d)) ((arrow_1865892024_mktop (p _TPTP_I)) e)))) ((((ord_less_nat (h _TPTP_I)) n)->False)->((and ((((eq nat) (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt e) d)) (((arrow_452340254_above (p _TPTP_I)) c) e)))) ((not (((eq nat) (h _TPTP_I)) n))->((member545531028le_alt ((produc990411159le_alt e) d)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))) ((and (((ord_less_nat (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt b) a)) lab))) ((((ord_less_nat (h _TPTP_I)) n)->False)->((member545531028le_alt ((produc990411159le_alt b) a)) lba)))))
% FOF formula (not (((eq arrow_1346734812le_alt) a) b)) of role axiom named fact_193__096a_A_126_061_Ab_096
% A new axiom: (not (((eq arrow_1346734812le_alt) a) b))
% FOF formula ((member545531028le_alt ((produc990411159le_alt b) a)) lba) of role axiom named fact_194__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096
% A new axiom: ((member545531028le_alt ((produc990411159le_alt b) a)) lba)
% FOF formula ((member545531028le_alt ((produc990411159le_alt a) b)) lab) of role axiom named fact_195__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096
% A new axiom: ((member545531028le_alt ((produc990411159le_alt a) b)) lab)
% FOF formula (((member545531028le_alt ((produc990411159le_alt a) b)) lba)->False) of role axiom named fact_196__096_Ia_M_Ab_J_A_126_058_ALba_096
% A new axiom: (((member545531028le_alt ((produc990411159le_alt a) b)) lba)->False)
% FOF formula (((member545531028le_alt ((produc990411159le_alt b) a)) lab)->False) of role axiom named fact_197__096_Ib_M_Aa_J_A_126_058_ALab_096
% A new axiom: (((member545531028le_alt ((produc990411159le_alt b) a)) lab)->False)
% FOF formula (forall (X:(produc1832616231le_alt->Prop)) (Y:(produc1832616231le_alt->Prop)), (((eq (produc1832616231le_alt->Prop)) (((if_Pro399136856_alt_o True) X) Y)) X)) of role axiom named help_If_1_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_
% A new axiom: (forall (X:(produc1832616231le_alt->Prop)) (Y:(produc1832616231le_alt->Prop)), (((eq (produc1832616231le_alt->Prop)) (((if_Pro399136856_alt_o True) X) Y)) X))
% FOF formula (forall (X:(produc1832616231le_alt->Prop)) (Y:(produc1832616231le_alt->Prop)), (((eq (produc1832616231le_alt->Prop)) (((if_Pro399136856_alt_o False) X) Y)) Y)) of role axiom named help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_
% A new axiom: (forall (X:(produc1832616231le_alt->Prop)) (Y:(produc1832616231le_alt->Prop)), (((eq (produc1832616231le_alt->Prop)) (((if_Pro399136856_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____sdiojnqkdh_
% A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% FOF formula ((member545531028le_alt ((produc990411159le_alt c) d)) (f p)) of role conjecture named conj_0
% Conjecture to prove = ((member545531028le_alt ((produc990411159le_alt c) d)) (f p)):Prop
% Parameter arrow_1092341143e_indi_DUMMY:arrow_1092341143e_indi.
% Parameter produc1832616231le_alt_DUMMY:produc1832616231le_alt.
% We need to prove ['((member545531028le_alt ((produc990411159le_alt c) d)) (f p))']
% Parameter arrow_1346734812le_alt:Type.
% Parameter arrow_1092341143e_indi:Type.
% Parameter nat:Type.
% Parameter produc1832616231le_alt:Type.
% Parameter all:((produc1832616231le_alt->Prop)->Prop).
% Parameter arrow_1724561858le_IIA:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop).
% Parameter arrow_1751445586le_Lin:((produc1832616231le_alt->Prop)->Prop).
% Parameter arrow_1605628760e_Prof:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop).
% Parameter arrow_452340254_above:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(arrow_1346734812le_alt->(produc1832616231le_alt->Prop)))).
% Parameter arrow_1098709355ctator:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop)).
% Parameter arrow_1717184938_mkbot:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(produc1832616231le_alt->Prop))).
% Parameter arrow_1865892024_mktop:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(produc1832616231le_alt->Prop))).
% Parameter arrow_1889221221nimity:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop).
% Parameter finite1907699781e_indi:((arrow_1092341143e_indi->Prop)->nat).
% Parameter inj_on945046484di_nat:((arrow_1092341143e_indi->nat)->((arrow_1092341143e_indi->Prop)->Prop)).
% Parameter pi_Arr1422400881lt_o_o:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->Prop))).
% Parameter pi_Arr1941314005e_indi:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->Prop))).
% Parameter pi_Arr1021537730_alt_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))).
% Parameter pi_Arr1767527177lt_o_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->Prop))).
% Parameter pi_Arr170420797e_indi:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->Prop))).
% Parameter pi_Pro410810898lt_o_o:(((produc1832616231le_alt->Prop)->Prop)->(((produc1832616231le_alt->Prop)->(Prop->Prop))->(((produc1832616231le_alt->Prop)->Prop)->Prop))).
% Parameter pi_Pro1340600692e_indi:(((produc1832616231le_alt->Prop)->Prop)->(((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))->(((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)->Prop))).
% Parameter pi_o_A1302557673_alt_o:((Prop->Prop)->((Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))->((Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->Prop))).
% Parameter pi_o_A71242893_alt_o:((Prop->Prop)->((Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))->((Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->Prop))).
% Parameter pi_o_P1538584260_alt_o:((Prop->Prop)->((Prop->((produc1832616231le_alt->Prop)->Prop))->((Prop->(produc1832616231le_alt->Prop))->Prop))).
% Parameter pi_o_P988780107le_alt:((Prop->Prop)->((Prop->(produc1832616231le_alt->Prop))->((Prop->produc1832616231le_alt)->Prop))).
% Parameter pi_Arr1140519125_alt_o:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))->((arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->Prop))).
% Parameter pi_Arr651234977_alt_o:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))->((arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->Prop))).
% Parameter pi_Arr418143960_alt_o:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))).
% Parameter pi_Arr1055270199le_alt:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((arrow_1092341143e_indi->produc1832616231le_alt)->Prop))).
% Parameter pi_Pro539263375_alt_o:((produc1832616231le_alt->Prop)->((produc1832616231le_alt->(Prop->Prop))->((produc1832616231le_alt->Prop)->Prop))).
% Parameter pi_Pro1535452471e_indi:((produc1832616231le_alt->Prop)->((produc1832616231le_alt->(arrow_1092341143e_indi->Prop))->((produc1832616231le_alt->arrow_1092341143e_indi)->Prop))).
% Parameter hilber564731065di_nat:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->nat)->(nat->arrow_1092341143e_indi))).
% Parameter if_Pro399136856_alt_o:(Prop->((produc1832616231le_alt->Prop)->((produc1832616231le_alt->Prop)->(produc1832616231le_alt->Prop)))).
% Parameter ord_le939309728lt_o_o:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->Prop)).
% Parameter ord_le972845494lt_o_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->Prop)).
% Parameter ord_le898419007lt_o_o:(((produc1832616231le_alt->Prop)->Prop)->(((produc1832616231le_alt->Prop)->Prop)->Prop)).
% Parameter ord_le316791758indi_o:((arrow_1092341143e_indi->Prop)->((arrow_1092341143e_indi->Prop)->Prop)).
% Parameter ord_le1973646398_alt_o:((produc1832616231le_alt->Prop)->((produc1832616231le_alt->Prop)->Prop)).
% Parameter ord_less_o:(Prop->(Prop->Prop)).
% Parameter ord_less_nat:(nat->(nat->Prop)).
% Parameter top_to1049332548lt_o_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop).
% Parameter top_to790289938lt_o_o:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop).
% Parameter top_to1830848411lt_o_o:((produc1832616231le_alt->Prop)->Prop).
% Parameter top_top_o_o:(Prop->Prop).
% Parameter top_to527331954indi_o:(arrow_1092341143e_indi->Prop).
% Parameter top_to679332578_alt_o:(produc1832616231le_alt->Prop).
% Parameter top_top_o:Prop.
% Parameter produc990411159le_alt:(arrow_1346734812le_alt->(arrow_1346734812le_alt->produc1832616231le_alt)).
% Parameter collec2125720304_alt_o:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)).
% Parameter collec1718651462_alt_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)).
% Parameter collec1079683069_alt_o:(((produc1832616231le_alt->Prop)->Prop)->((produc1832616231le_alt->Prop)->Prop)).
% Parameter collec1832628290e_indi:((arrow_1092341143e_indi->Prop)->(arrow_1092341143e_indi->Prop)).
% Parameter collec1201320914le_alt:((produc1832616231le_alt->Prop)->(produc1832616231le_alt->Prop)).
% Parameter member903234717lt_o_o:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->(((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->Prop)->Prop)).
% Parameter member986213183e_indi:((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->(((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->Prop)->Prop)).
% Parameter member733327538_alt_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)->Prop)).
% Parameter member1754345465lt_o_o:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->Prop)->Prop)).
% Parameter member1208133347e_indi:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->((((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)->Prop)->Prop)).
% Parameter member1949484546lt_o_o:(((produc1832616231le_alt->Prop)->Prop)->((((produc1832616231le_alt->Prop)->Prop)->Prop)->Prop)).
% Parameter member1255309082e_indi:(((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)->((((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)->Prop)->Prop)).
% Parameter member1710515983_alt_o:((Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->(((Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->Prop)->Prop)).
% Parameter member537117565_alt_o:((Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->(((Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->Prop)->Prop)).
% Parameter member1099673524_alt_o:((Prop->(produc1832616231le_alt->Prop))->(((Prop->(produc1832616231le_alt->Prop))->Prop)->Prop)).
% Parameter member1368218865le_alt:((Prop->produc1832616231le_alt)->(((Prop->produc1832616231le_alt)->Prop)->Prop)).
% Parameter member24189887_alt_o:((arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->(((arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))->Prop)->Prop)).
% Parameter member1079651021_alt_o:((arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->(((arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))->Prop)->Prop)).
% Parameter member1561882372_alt_o:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)->Prop)).
% Parameter member1621875105le_alt:((arrow_1092341143e_indi->produc1832616231le_alt)->(((arrow_1092341143e_indi->produc1832616231le_alt)->Prop)->Prop)).
% Parameter member1362619835_alt_o:((produc1832616231le_alt->Prop)->(((produc1832616231le_alt->Prop)->Prop)->Prop)).
% Parameter member1486844321e_indi:((produc1832616231le_alt->arrow_1092341143e_indi)->(((produc1832616231le_alt->arrow_1092341143e_indi)->Prop)->Prop)).
% Parameter member_o:(Prop->((Prop->Prop)->Prop)).
% Parameter member1714766084e_indi:(arrow_1092341143e_indi->((arrow_1092341143e_indi->Prop)->Prop)).
% Parameter member545531028le_alt:(produc1832616231le_alt->((produc1832616231le_alt->Prop)->Prop)).
% Parameter f:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)).
% Parameter lab:(produc1832616231le_alt->Prop).
% Parameter lba:(produc1832616231le_alt->Prop).
% Parameter p:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)).
% Parameter a:arrow_1346734812le_alt.
% Parameter b:arrow_1346734812le_alt.
% Parameter c:arrow_1346734812le_alt.
% Parameter d:arrow_1346734812le_alt.
% Parameter e:arrow_1346734812le_alt.
% Parameter h:(arrow_1092341143e_indi->nat).
% Parameter n:nat.
% Axiom fact_0_assms_I3_J:(arrow_1724561858le_IIA f).
% Axiom fact_1_u:(arrow_1889221221nimity f).
% Axiom fact_2__096c_A_126_061_Ad_096:(not (((eq arrow_1346734812le_alt) c) d)).
% Axiom fact_3__096P_A_058_AProf_096:((member1561882372_alt_o p) arrow_1605628760e_Prof).
% Axiom fact_4_in__mkbot:(forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)) (Z_2:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X) Y)) ((arrow_1717184938_mkbot L) Z_2))) ((and ((and (not (((eq arrow_1346734812le_alt) Y) Z_2))) ((((eq arrow_1346734812le_alt) X) Z_2)->(not (((eq arrow_1346734812le_alt) X) Y))))) ((not (((eq arrow_1346734812le_alt) X) Z_2))->((member545531028le_alt ((produc990411159le_alt X) Y)) L))))).
% Axiom fact_5_in__mktop:(forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)) (Z_2:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X) Y)) ((arrow_1865892024_mktop L) Z_2))) ((and ((and (not (((eq arrow_1346734812le_alt) X) Z_2))) ((((eq arrow_1346734812le_alt) Y) Z_2)->(not (((eq arrow_1346734812le_alt) X) Y))))) ((not (((eq arrow_1346734812le_alt) Y) Z_2))->((member545531028le_alt ((produc990411159le_alt X) Y)) L))))).
% Axiom fact_6__C2_C:(forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_26:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) A_26) B_16))->((not (((eq arrow_1346734812le_alt) A_25) B_16))->((not (((eq arrow_1346734812le_alt) B_15) A_26))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (f P_6))))))))))).
% Axiom fact_7__C1_C:(forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_26:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) A_26) B_16))->((not (((eq arrow_1346734812le_alt) A_25) B_16))->((not (((eq arrow_1346734812le_alt) B_15) A_26))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (P_6 _TPTP_I))))->(((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))->((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (f P_6))))))))))).
% Axiom fact_8__C4_C:(forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (C_4:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) B_15) C_4))->((not (((eq arrow_1346734812le_alt) A_25) C_4))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt B_15) C_4)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt B_15) C_4)) (f P_6)))))))))).
% Axiom fact_9_pairwise__neutrality:(forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_26:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->((not (((eq arrow_1346734812le_alt) A_26) B_16))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt A_26) B_16)) (f P_6))))))))).
% Axiom fact_10__C3_C:(forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_25:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_25) B_15))->(((member1561882372_alt_o P_5) arrow_1605628760e_Prof)->(((member1561882372_alt_o P_6) arrow_1605628760e_Prof)->((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt B_15) A_25)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_25) B_15)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt B_15) A_25)) (f P_6)))))))).
% Axiom fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J:(forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt c) d)) (p _TPTP_I))) ((and (((ord_less_nat (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt c) d)) ((arrow_1865892024_mktop (p _TPTP_I)) e)))) ((((ord_less_nat (h _TPTP_I)) n)->False)->((and ((((eq nat) (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt c) d)) (((arrow_452340254_above (p _TPTP_I)) c) e)))) ((not (((eq nat) (h _TPTP_I)) n))->((member545531028le_alt ((produc990411159le_alt c) d)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))).
% Axiom fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0:((member545531028le_alt ((produc990411159le_alt c) d)) (p (((hilber564731065di_nat top_to527331954indi_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:((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))).
% Axiom fact_14_PW:((iff ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))) ((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))).
% Axiom fact_15_split__paired__All:(forall (P_4:(produc1832616231le_alt->Prop)), ((iff (all P_4)) (forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), (P_4 ((produc990411159le_alt A_5) B_4))))).
% Axiom fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai:((member1561882372_alt_o (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))) arrow_1605628760e_Prof).
% Axiom fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto:((member545531028le_alt ((produc990411159le_alt c) e)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))).
% Axiom fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto:((member545531028le_alt ((produc990411159le_alt e) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))).
% Axiom fact_19_n_I1_J:((ord_less_nat n) (finite1907699781e_indi top_to527331954indi_o)).
% Axiom fact_20_injh:((inj_on945046484di_nat h) top_to527331954indi_o).
% Axiom fact_21_Pair__inject:(forall (A_24:arrow_1346734812le_alt) (B_14:arrow_1346734812le_alt) (A_23:arrow_1346734812le_alt) (B_13:arrow_1346734812le_alt), ((((eq produc1832616231le_alt) ((produc990411159le_alt A_24) B_14)) ((produc990411159le_alt A_23) B_13))->(((((eq arrow_1346734812le_alt) A_24) A_23)->(not (((eq arrow_1346734812le_alt) B_14) B_13)))->False))).
% Axiom fact_22_Pair__eq:(forall (A_22:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt) (A_21:arrow_1346734812le_alt) (B_11:arrow_1346734812le_alt), ((iff (((eq produc1832616231le_alt) ((produc990411159le_alt A_22) B_12)) ((produc990411159le_alt A_21) B_11))) ((and (((eq arrow_1346734812le_alt) A_22) A_21)) (((eq arrow_1346734812le_alt) B_12) B_11)))).
% Axiom fact_23_IIA__def:(forall (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1724561858le_IIA F)) (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(forall (Xa:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o Xa) arrow_1605628760e_Prof)->(forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (X_1 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (Xa _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F X_1))) ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F Xa))))))))))).
% Axiom fact_24_unanimity__def:(forall (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1889221221nimity F)) (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (X_1 _TPTP_I)))->((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F X_1)))))))).
% Axiom fact_25_top1I:(forall (X_34:(produc1832616231le_alt->Prop)), (top_to1830848411lt_o_o X_34)).
% Axiom fact_26_top1I:(forall (X_34:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (top_to790289938lt_o_o X_34)).
% Axiom fact_27_top1I:(forall (X_34:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (top_to1049332548lt_o_o X_34)).
% Axiom fact_28_top1I:(forall (X_34:produc1832616231le_alt), (top_to679332578_alt_o X_34)).
% Axiom fact_29_top1I:(forall (X_34:arrow_1092341143e_indi), (top_to527331954indi_o X_34)).
% Axiom fact_30_UNIV__I:(forall (X_33:Prop), ((member_o X_33) top_top_o_o)).
% Axiom fact_31_UNIV__I:(forall (X_33:arrow_1092341143e_indi), ((member1714766084e_indi X_33) top_to527331954indi_o)).
% Axiom fact_32_UNIV__I:(forall (X_33:produc1832616231le_alt), ((member545531028le_alt X_33) top_to679332578_alt_o)).
% Axiom fact_33_UNIV__I:(forall (X_33:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_33) top_to790289938lt_o_o)).
% Axiom fact_34_UNIV__I:(forall (X_33:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_33) top_to1049332548lt_o_o)).
% Axiom fact_35_UNIV__I:(forall (X_33:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_33) top_to1830848411lt_o_o)).
% Axiom fact_36_iso__tuple__UNIV__I:(forall (X_32:Prop), ((member_o X_32) top_top_o_o)).
% Axiom fact_37_iso__tuple__UNIV__I:(forall (X_32:arrow_1092341143e_indi), ((member1714766084e_indi X_32) top_to527331954indi_o)).
% Axiom fact_38_iso__tuple__UNIV__I:(forall (X_32:produc1832616231le_alt), ((member545531028le_alt X_32) top_to679332578_alt_o)).
% Axiom fact_39_iso__tuple__UNIV__I:(forall (X_32:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_32) top_to790289938lt_o_o)).
% Axiom fact_40_iso__tuple__UNIV__I:(forall (X_32:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_32) top_to1049332548lt_o_o)).
% Axiom fact_41_iso__tuple__UNIV__I:(forall (X_32:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_32) top_to1830848411lt_o_o)).
% Axiom fact_42_top__apply:(forall (X_31:(produc1832616231le_alt->Prop)), ((iff (top_to1830848411lt_o_o X_31)) top_top_o)).
% Axiom fact_43_top__apply:(forall (X_31:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((iff (top_to790289938lt_o_o X_31)) top_top_o)).
% Axiom fact_44_top__apply:(forall (X_31:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (top_to1049332548lt_o_o X_31)) top_top_o)).
% Axiom fact_45_top__apply:(forall (X_31:produc1832616231le_alt), ((iff (top_to679332578_alt_o X_31)) top_top_o)).
% Axiom fact_46_top__apply:(forall (X_31:arrow_1092341143e_indi), ((iff (top_to527331954indi_o X_31)) top_top_o)).
% Axiom fact_47_not__top__less:(forall (A_20:((produc1832616231le_alt->Prop)->Prop)), (((ord_le898419007lt_o_o top_to1830848411lt_o_o) A_20)->False)).
% Axiom fact_48_not__top__less:(forall (A_20:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((ord_le972845494lt_o_o top_to790289938lt_o_o) A_20)->False)).
% Axiom fact_49_not__top__less:(forall (A_20:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((ord_le939309728lt_o_o top_to1049332548lt_o_o) A_20)->False)).
% Axiom fact_50_not__top__less:(forall (A_20:Prop), (((ord_less_o top_top_o) A_20)->False)).
% Axiom fact_51_not__top__less:(forall (A_20:(produc1832616231le_alt->Prop)), (((ord_le1973646398_alt_o top_to679332578_alt_o) A_20)->False)).
% Axiom fact_52_not__top__less:(forall (A_20:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o top_to527331954indi_o) A_20)->False)).
% Axiom fact_53_linorder__cases:(forall (X_30:nat) (Y_23:nat), ((((ord_less_nat X_30) Y_23)->False)->((not (((eq nat) X_30) Y_23))->((ord_less_nat Y_23) X_30)))).
% Axiom fact_54_order__less__asym:(forall (X_29:(arrow_1092341143e_indi->Prop)) (Y_22:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_29) Y_22)->(((ord_le316791758indi_o Y_22) X_29)->False))).
% Axiom fact_55_order__less__asym:(forall (X_29:nat) (Y_22:nat), (((ord_less_nat X_29) Y_22)->(((ord_less_nat Y_22) X_29)->False))).
% Axiom fact_56_xt1_I10_J:(forall (Z_1:(arrow_1092341143e_indi->Prop)) (Y_21:(arrow_1092341143e_indi->Prop)) (X_28:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o Y_21) X_28)->(((ord_le316791758indi_o Z_1) Y_21)->((ord_le316791758indi_o Z_1) X_28)))).
% Axiom fact_57_xt1_I10_J:(forall (Z_1:nat) (Y_21:nat) (X_28:nat), (((ord_less_nat Y_21) X_28)->(((ord_less_nat Z_1) Y_21)->((ord_less_nat Z_1) X_28)))).
% Axiom fact_58_order__less__trans:(forall (Z:(arrow_1092341143e_indi->Prop)) (X_27:(arrow_1092341143e_indi->Prop)) (Y_20:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_27) Y_20)->(((ord_le316791758indi_o Y_20) Z)->((ord_le316791758indi_o X_27) Z)))).
% Axiom fact_59_order__less__trans:(forall (Z:nat) (X_27:nat) (Y_20:nat), (((ord_less_nat X_27) Y_20)->(((ord_less_nat Y_20) Z)->((ord_less_nat X_27) Z)))).
% Axiom fact_60_xt1_I2_J:(forall (C_3:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->Prop)) (A_19:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o B_10) A_19)->((((eq (arrow_1092341143e_indi->Prop)) B_10) C_3)->((ord_le316791758indi_o C_3) A_19)))).
% Axiom fact_61_xt1_I2_J:(forall (C_3:nat) (B_10:nat) (A_19:nat), (((ord_less_nat B_10) A_19)->((((eq nat) B_10) C_3)->((ord_less_nat C_3) A_19)))).
% Axiom fact_62_ord__less__eq__trans:(forall (C_2:(arrow_1092341143e_indi->Prop)) (A_18:(arrow_1092341143e_indi->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o A_18) B_9)->((((eq (arrow_1092341143e_indi->Prop)) B_9) C_2)->((ord_le316791758indi_o A_18) C_2)))).
% Axiom fact_63_ord__less__eq__trans:(forall (C_2:nat) (A_18:nat) (B_9:nat), (((ord_less_nat A_18) B_9)->((((eq nat) B_9) C_2)->((ord_less_nat A_18) C_2)))).
% Axiom fact_64_xt1_I1_J:(forall (C_1:(arrow_1092341143e_indi->Prop)) (A_17:(arrow_1092341143e_indi->Prop)) (B_8:(arrow_1092341143e_indi->Prop)), ((((eq (arrow_1092341143e_indi->Prop)) A_17) B_8)->(((ord_le316791758indi_o C_1) B_8)->((ord_le316791758indi_o C_1) A_17)))).
% Axiom fact_65_xt1_I1_J:(forall (C_1:nat) (A_17:nat) (B_8:nat), ((((eq nat) A_17) B_8)->(((ord_less_nat C_1) B_8)->((ord_less_nat C_1) A_17)))).
% Axiom fact_66_ord__eq__less__trans:(forall (C:(arrow_1092341143e_indi->Prop)) (A_16:(arrow_1092341143e_indi->Prop)) (B_7:(arrow_1092341143e_indi->Prop)), ((((eq (arrow_1092341143e_indi->Prop)) A_16) B_7)->(((ord_le316791758indi_o B_7) C)->((ord_le316791758indi_o A_16) C)))).
% Axiom fact_67_ord__eq__less__trans:(forall (C:nat) (A_16:nat) (B_7:nat), ((((eq nat) A_16) B_7)->(((ord_less_nat B_7) C)->((ord_less_nat A_16) C)))).
% Axiom fact_68_xt1_I9_J:(forall (B_6:(arrow_1092341143e_indi->Prop)) (A_15:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o B_6) A_15)->(((ord_le316791758indi_o A_15) B_6)->False))).
% Axiom fact_69_xt1_I9_J:(forall (B_6:nat) (A_15:nat), (((ord_less_nat B_6) A_15)->(((ord_less_nat A_15) B_6)->False))).
% Axiom fact_70_order__less__asym_H:(forall (A_14:(arrow_1092341143e_indi->Prop)) (B_5:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o A_14) B_5)->(((ord_le316791758indi_o B_5) A_14)->False))).
% Axiom fact_71_order__less__asym_H:(forall (A_14:nat) (B_5:nat), (((ord_less_nat A_14) B_5)->(((ord_less_nat B_5) A_14)->False))).
% Axiom fact_72_order__less__imp__triv:(forall (P_3:Prop) (X_26:(arrow_1092341143e_indi->Prop)) (Y_19:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_26) Y_19)->(((ord_le316791758indi_o Y_19) X_26)->P_3))).
% Axiom fact_73_order__less__imp__triv:(forall (P_3:Prop) (X_26:nat) (Y_19:nat), (((ord_less_nat X_26) Y_19)->(((ord_less_nat Y_19) X_26)->P_3))).
% Axiom fact_74_order__less__imp__not__eq2:(forall (X_25:(arrow_1092341143e_indi->Prop)) (Y_18:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_25) Y_18)->(not (((eq (arrow_1092341143e_indi->Prop)) Y_18) X_25)))).
% Axiom fact_75_order__less__imp__not__eq2:(forall (X_25:nat) (Y_18:nat), (((ord_less_nat X_25) Y_18)->(not (((eq nat) Y_18) X_25)))).
% Axiom fact_76_order__less__imp__not__eq:(forall (X_24:(arrow_1092341143e_indi->Prop)) (Y_17:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_24) Y_17)->(not (((eq (arrow_1092341143e_indi->Prop)) X_24) Y_17)))).
% Axiom fact_77_order__less__imp__not__eq:(forall (X_24:nat) (Y_17:nat), (((ord_less_nat X_24) Y_17)->(not (((eq nat) X_24) Y_17)))).
% Axiom fact_78_order__less__imp__not__less:(forall (X_23:(arrow_1092341143e_indi->Prop)) (Y_16:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_23) Y_16)->(((ord_le316791758indi_o Y_16) X_23)->False))).
% Axiom fact_79_order__less__imp__not__less:(forall (X_23:nat) (Y_16:nat), (((ord_less_nat X_23) Y_16)->(((ord_less_nat Y_16) X_23)->False))).
% Axiom fact_80_order__less__not__sym:(forall (X_22:(arrow_1092341143e_indi->Prop)) (Y_15:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_22) Y_15)->(((ord_le316791758indi_o Y_15) X_22)->False))).
% Axiom fact_81_order__less__not__sym:(forall (X_22:nat) (Y_15:nat), (((ord_less_nat X_22) Y_15)->(((ord_less_nat Y_15) X_22)->False))).
% Axiom fact_82_less__imp__neq:(forall (X_21:(arrow_1092341143e_indi->Prop)) (Y_14:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_21) Y_14)->(not (((eq (arrow_1092341143e_indi->Prop)) X_21) Y_14)))).
% Axiom fact_83_less__imp__neq:(forall (X_21:nat) (Y_14:nat), (((ord_less_nat X_21) Y_14)->(not (((eq nat) X_21) Y_14)))).
% Axiom fact_84_linorder__neqE:(forall (X_20:nat) (Y_13:nat), ((not (((eq nat) X_20) Y_13))->((((ord_less_nat X_20) Y_13)->False)->((ord_less_nat Y_13) X_20)))).
% Axiom fact_85_linorder__antisym__conv3:(forall (Y_12:nat) (X_19:nat), ((((ord_less_nat Y_12) X_19)->False)->((iff (((ord_less_nat X_19) Y_12)->False)) (((eq nat) X_19) Y_12)))).
% Axiom fact_86_linorder__less__linear:(forall (X_18:nat) (Y_11:nat), ((or ((or ((ord_less_nat X_18) Y_11)) (((eq nat) X_18) Y_11))) ((ord_less_nat Y_11) X_18))).
% Axiom fact_87_not__less__iff__gr__or__eq:(forall (X_17:nat) (Y_10:nat), ((iff (((ord_less_nat X_17) Y_10)->False)) ((or ((ord_less_nat Y_10) X_17)) (((eq nat) X_17) Y_10)))).
% Axiom fact_88_linorder__neq__iff:(forall (X_16:nat) (Y_9:nat), ((iff (not (((eq nat) X_16) Y_9))) ((or ((ord_less_nat X_16) Y_9)) ((ord_less_nat Y_9) X_16)))).
% Axiom fact_89_order__less__irrefl:(forall (X_15:(arrow_1092341143e_indi->Prop)), (((ord_le316791758indi_o X_15) X_15)->False)).
% Axiom fact_90_order__less__irrefl:(forall (X_15:nat), (((ord_less_nat X_15) X_15)->False)).
% Axiom fact_91_UNIV__def:(((eq ((produc1832616231le_alt->Prop)->Prop)) top_to1830848411lt_o_o) (collec1079683069_alt_o (fun (X_1:(produc1832616231le_alt->Prop))=> True))).
% Axiom fact_92_UNIV__def:(((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) top_to790289938lt_o_o) (collec1718651462_alt_o (fun (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> True))).
% Axiom fact_93_UNIV__def:(((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) top_to1049332548lt_o_o) (collec2125720304_alt_o (fun (X_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> True))).
% Axiom fact_94_UNIV__def:(((eq (produc1832616231le_alt->Prop)) top_to679332578_alt_o) (collec1201320914le_alt (fun (X_1:produc1832616231le_alt)=> True))).
% Axiom fact_95_UNIV__def:(((eq (arrow_1092341143e_indi->Prop)) top_to527331954indi_o) (collec1832628290e_indi (fun (X_1:arrow_1092341143e_indi)=> True))).
% Axiom fact_96_pred__equals__eq2:(forall (S:(produc1832616231le_alt->Prop)) (R:(produc1832616231le_alt->Prop)), ((iff (forall (X_1:arrow_1346734812le_alt) (Xa:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X_1) Xa)) R)) ((member545531028le_alt ((produc990411159le_alt X_1) Xa)) S)))) (((eq (produc1832616231le_alt->Prop)) R) S))).
% Axiom fact_97_less__top:(forall (A_13:((produc1832616231le_alt->Prop)->Prop)), ((iff (not (((eq ((produc1832616231le_alt->Prop)->Prop)) A_13) top_to1830848411lt_o_o))) ((ord_le898419007lt_o_o A_13) top_to1830848411lt_o_o))).
% Axiom fact_98_less__top:(forall (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((iff (not (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) A_13) top_to790289938lt_o_o))) ((ord_le972845494lt_o_o A_13) top_to790289938lt_o_o))).
% Axiom fact_99_less__top:(forall (A_13:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((iff (not (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) A_13) top_to1049332548lt_o_o))) ((ord_le939309728lt_o_o A_13) top_to1049332548lt_o_o))).
% Axiom fact_100_less__top:(forall (A_13:Prop), ((iff (((iff A_13) top_top_o)->False)) ((ord_less_o A_13) top_top_o))).
% Axiom fact_101_less__top:(forall (A_13:(produc1832616231le_alt->Prop)), ((iff (not (((eq (produc1832616231le_alt->Prop)) A_13) top_to679332578_alt_o))) ((ord_le1973646398_alt_o A_13) top_to679332578_alt_o))).
% Axiom fact_102_less__top:(forall (A_13:(arrow_1092341143e_indi->Prop)), ((iff (not (((eq (arrow_1092341143e_indi->Prop)) A_13) top_to527331954indi_o))) ((ord_le316791758indi_o A_13) top_to527331954indi_o))).
% Axiom fact_103_inv__f__eq:(forall (X_14:arrow_1092341143e_indi) (Y_8:nat) (F_15:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_15) top_to527331954indi_o)->((((eq nat) (F_15 X_14)) Y_8)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat top_to527331954indi_o) F_15) Y_8)) X_14)))).
% Axiom fact_104_inv__f__f:(forall (X_13:arrow_1092341143e_indi) (F_14:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_14) top_to527331954indi_o)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat top_to527331954indi_o) F_14) (F_14 X_13))) X_13))).
% Axiom fact_105_inv__into__f__f:(forall (X_12:arrow_1092341143e_indi) (F_13:(arrow_1092341143e_indi->nat)) (A_12:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_13) A_12)->(((member1714766084e_indi X_12) A_12)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat A_12) F_13) (F_13 X_12))) X_12)))).
% Axiom fact_106_inv__into__f__eq:(forall (Y_7:nat) (X_11:arrow_1092341143e_indi) (F_12:(arrow_1092341143e_indi->nat)) (A_11:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_12) A_11)->(((member1714766084e_indi X_11) A_11)->((((eq nat) (F_12 X_11)) Y_7)->(((eq arrow_1092341143e_indi) (((hilber564731065di_nat A_11) F_12) Y_7)) X_11))))).
% Axiom fact_107_inj__eq:(forall (X_10:arrow_1092341143e_indi) (Y_6:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_11) top_to527331954indi_o)->((iff (((eq nat) (F_11 X_10)) (F_11 Y_6))) (((eq arrow_1092341143e_indi) X_10) Y_6)))).
% Axiom fact_108_inj__on__def:(forall (F_10:(arrow_1092341143e_indi->nat)) (A_10:(arrow_1092341143e_indi->Prop)), ((iff ((inj_on945046484di_nat F_10) A_10)) (forall (X_1:arrow_1092341143e_indi), (((member1714766084e_indi X_1) A_10)->(forall (Xa:arrow_1092341143e_indi), (((member1714766084e_indi Xa) A_10)->((((eq nat) (F_10 X_1)) (F_10 Xa))->(((eq arrow_1092341143e_indi) X_1) Xa)))))))).
% Axiom fact_109_inj__on__contraD:(forall (X_9:arrow_1092341143e_indi) (Y_5:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->nat)) (A_9:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_9) A_9)->((not (((eq arrow_1092341143e_indi) X_9) Y_5))->(((member1714766084e_indi X_9) A_9)->(((member1714766084e_indi Y_5) A_9)->(not (((eq nat) (F_9 X_9)) (F_9 Y_5)))))))).
% Axiom fact_110_inj__on__iff:(forall (Y_4:arrow_1092341143e_indi) (X_8:arrow_1092341143e_indi) (F_8:(arrow_1092341143e_indi->nat)) (A_8:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_8) A_8)->(((member1714766084e_indi X_8) A_8)->(((member1714766084e_indi Y_4) A_8)->((iff (((eq nat) (F_8 X_8)) (F_8 Y_4))) (((eq arrow_1092341143e_indi) X_8) Y_4)))))).
% Axiom fact_111_inj__onD:(forall (X_7:arrow_1092341143e_indi) (Y_3:arrow_1092341143e_indi) (F_7:(arrow_1092341143e_indi->nat)) (A_7:(arrow_1092341143e_indi->Prop)), (((inj_on945046484di_nat F_7) A_7)->((((eq nat) (F_7 X_7)) (F_7 Y_3))->(((member1714766084e_indi X_7) A_7)->(((member1714766084e_indi Y_3) A_7)->(((eq arrow_1092341143e_indi) X_7) Y_3)))))).
% Axiom fact_112_injD:(forall (X_6:arrow_1092341143e_indi) (Y_2:arrow_1092341143e_indi) (F_6:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_6) top_to527331954indi_o)->((((eq nat) (F_6 X_6)) (F_6 Y_2))->(((eq arrow_1092341143e_indi) X_6) Y_2)))).
% Axiom fact_113_inj__imp__inv__eq:(forall (G:(nat->arrow_1092341143e_indi)) (F_5:(arrow_1092341143e_indi->nat)), (((inj_on945046484di_nat F_5) top_to527331954indi_o)->((forall (X_1:nat), (((eq nat) (F_5 (G X_1))) X_1))->(((eq (nat->arrow_1092341143e_indi)) ((hilber564731065di_nat top_to527331954indi_o) F_5)) G)))).
% Axiom fact_114_injI:(forall (F_4:(arrow_1092341143e_indi->nat)), ((forall (X_1:arrow_1092341143e_indi) (Y_1:arrow_1092341143e_indi), ((((eq nat) (F_4 X_1)) (F_4 Y_1))->(((eq arrow_1092341143e_indi) X_1) Y_1)))->((inj_on945046484di_nat F_4) top_to527331954indi_o))).
% Axiom fact_115_assms_I1_J:((member733327538_alt_o f) ((pi_Arr1021537730_alt_o arrow_1605628760e_Prof) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> arrow_1751445586le_Lin))).
% Axiom fact_116__096Lba_A_058_ALin_096:((member1362619835_alt_o lba) arrow_1751445586le_Lin).
% Axiom fact_117__096Lab_A_058_ALin_096:((member1362619835_alt_o lab) arrow_1751445586le_Lin).
% Axiom fact_118_Lin__irrefl:(forall (A_3:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->(((member545531028le_alt ((produc990411159le_alt A_3) B_2)) L)->(((member545531028le_alt ((produc990411159le_alt B_2) A_3)) L)->False)))).
% Axiom fact_119_notin__Lin__iff:(forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((not (((eq arrow_1346734812le_alt) X) Y))->((iff (((member545531028le_alt ((produc990411159le_alt X) Y)) L)->False)) ((member545531028le_alt ((produc990411159le_alt Y) X)) L))))).
% Axiom fact_120_mem__def:(forall (X_5:arrow_1092341143e_indi) (A_6:(arrow_1092341143e_indi->Prop)), ((iff ((member1714766084e_indi X_5) A_6)) (A_6 X_5))).
% Axiom fact_121_mem__def:(forall (X_5:Prop) (A_6:(Prop->Prop)), ((iff ((member_o X_5) A_6)) (A_6 X_5))).
% Axiom fact_122_mem__def:(forall (X_5:produc1832616231le_alt) (A_6:(produc1832616231le_alt->Prop)), ((iff ((member545531028le_alt X_5) A_6)) (A_6 X_5))).
% Axiom fact_123_mem__def:(forall (X_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((iff ((member1561882372_alt_o X_5) A_6)) (A_6 X_5))).
% Axiom fact_124_mem__def:(forall (X_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((iff ((member733327538_alt_o X_5) A_6)) (A_6 X_5))).
% Axiom fact_125_mem__def:(forall (X_5:(produc1832616231le_alt->Prop)) (A_6:((produc1832616231le_alt->Prop)->Prop)), ((iff ((member1362619835_alt_o X_5) A_6)) (A_6 X_5))).
% Axiom fact_126_Collect__def:(forall (P_2:(arrow_1092341143e_indi->Prop)), (((eq (arrow_1092341143e_indi->Prop)) (collec1832628290e_indi P_2)) P_2)).
% Axiom fact_127_mktop__Lin:(forall (X:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1865892024_mktop L) X)) arrow_1751445586le_Lin))).
% Axiom fact_128_mkbot__Lin:(forall (X:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1717184938_mkbot L) X)) arrow_1751445586le_Lin))).
% Axiom fact_129_above__Lin:(forall (L:(produc1832616231le_alt->Prop)) (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) X) Y))->(((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1362619835_alt_o (((arrow_452340254_above L) X) Y)) arrow_1751445586le_Lin)))).
% Axiom fact_130_const__Lin__Prof:(forall (L:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L) arrow_1751445586le_Lin)->((member1561882372_alt_o (fun (P_1:arrow_1092341143e_indi)=> L)) arrow_1605628760e_Prof))).
% Axiom fact_131_in__above:(forall (X:arrow_1346734812le_alt) (Y:arrow_1346734812le_alt) (L:(produc1832616231le_alt->Prop)) (A_3:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_3) B_2))->(((member1362619835_alt_o L) arrow_1751445586le_Lin)->((iff ((member545531028le_alt ((produc990411159le_alt X) Y)) (((arrow_452340254_above L) A_3) B_2))) ((and ((and (not (((eq arrow_1346734812le_alt) X) Y))) ((((eq arrow_1346734812le_alt) X) B_2)->((member545531028le_alt ((produc990411159le_alt A_3) Y)) L)))) ((not (((eq arrow_1346734812le_alt) X) B_2))->((and ((((eq arrow_1346734812le_alt) Y) B_2)->((or (((eq arrow_1346734812le_alt) X) A_3)) ((member545531028le_alt ((produc990411159le_alt X) A_3)) L)))) ((not (((eq arrow_1346734812le_alt) Y) B_2))->((member545531028le_alt ((produc990411159le_alt X) Y)) L))))))))).
% Axiom fact_132_dictatorI:(forall (I_1:arrow_1092341143e_indi) (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o F) ((pi_Arr1021537730_alt_o arrow_1605628760e_Prof) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> arrow_1751445586le_Lin)))->((forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(forall (A_5:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_5) B_4))->(((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (X_1 I_1))->((member545531028le_alt ((produc990411159le_alt A_5) B_4)) (F X_1)))))))->((arrow_1098709355ctator F) I_1)))).
% Axiom fact_133_PiE:(forall (X_4:produc1832616231le_alt) (F_3:(produc1832616231le_alt->Prop)) (A_4:(produc1832616231le_alt->Prop)) (B_3:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_3) ((pi_Pro539263375_alt_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member545531028le_alt X_4) A_4)->False)))).
% Axiom fact_134_PiE:(forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_3) ((pi_Arr1055270199le_alt A_4) B_3))->((((member545531028le_alt (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False)))).
% Axiom fact_135_PiE:(forall (X_4:Prop) (F_3:(Prop->produc1832616231le_alt)) (A_4:(Prop->Prop)) (B_3:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_3) ((pi_o_P988780107le_alt A_4) B_3))->((((member545531028le_alt (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False)))).
% Axiom fact_136_PiE:(forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_3) ((pi_Arr651234977_alt_o A_4) B_3))->((((member1561882372_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False)))).
% Axiom fact_137_PiE:(forall (X_4:Prop) (F_3:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_4:(Prop->Prop)) (B_3:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_3) ((pi_o_A71242893_alt_o A_4) B_3))->((((member1561882372_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False)))).
% Axiom fact_138_PiE:(forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_3) ((pi_Arr1140519125_alt_o A_4) B_3))->((((member733327538_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False)))).
% Axiom fact_139_PiE:(forall (X_4:Prop) (F_3:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_4:(Prop->Prop)) (B_3:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_3) ((pi_o_A1302557673_alt_o A_4) B_3))->((((member733327538_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False)))).
% Axiom fact_140_PiE:(forall (X_4:Prop) (F_3:(Prop->(produc1832616231le_alt->Prop))) (A_4:(Prop->Prop)) (B_3:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_3) ((pi_o_P1538584260_alt_o A_4) B_3))->((((member1362619835_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member_o X_4) A_4)->False)))).
% Axiom fact_141_PiE:(forall (X_4:produc1832616231le_alt) (F_3:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_4:(produc1832616231le_alt->Prop)) (B_3:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_3) ((pi_Pro1535452471e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member545531028le_alt X_4) A_4)->False)))).
% Axiom fact_142_PiE:(forall (X_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_3) ((pi_Arr170420797e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member1561882372_alt_o X_4) A_4)->False)))).
% Axiom fact_143_PiE:(forall (X_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_3) ((pi_Arr1767527177lt_o_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member1561882372_alt_o X_4) A_4)->False)))).
% Axiom fact_144_PiE:(forall (X_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_4:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_3) ((pi_Arr1941314005e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member733327538_alt_o X_4) A_4)->False)))).
% Axiom fact_145_PiE:(forall (X_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_4:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_3:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_3) ((pi_Arr1422400881lt_o_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member733327538_alt_o X_4) A_4)->False)))).
% Axiom fact_146_PiE:(forall (X_4:(produc1832616231le_alt->Prop)) (F_3:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_4:((produc1832616231le_alt->Prop)->Prop)) (B_3:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_3) ((pi_Pro1340600692e_indi A_4) B_3))->((((member1714766084e_indi (F_3 X_4)) (B_3 X_4))->False)->(((member1362619835_alt_o X_4) A_4)->False)))).
% Axiom fact_147_PiE:(forall (X_4:(produc1832616231le_alt->Prop)) (F_3:((produc1832616231le_alt->Prop)->Prop)) (A_4:((produc1832616231le_alt->Prop)->Prop)) (B_3:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_3) ((pi_Pro410810898lt_o_o A_4) B_3))->((((member_o (F_3 X_4)) (B_3 X_4))->False)->(((member1362619835_alt_o X_4) A_4)->False)))).
% Axiom fact_148_PiE:(forall (X_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_3) ((pi_Arr1021537730_alt_o A_4) B_3))->((((member1362619835_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1561882372_alt_o X_4) A_4)->False)))).
% Axiom fact_149_PiE:(forall (X_4:arrow_1092341143e_indi) (F_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_4:(arrow_1092341143e_indi->Prop)) (B_3:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_3) ((pi_Arr418143960_alt_o A_4) B_3))->((((member1362619835_alt_o (F_3 X_4)) (B_3 X_4))->False)->(((member1714766084e_indi X_4) A_4)->False)))).
% Axiom fact_150_complete__Lin:(forall (A_3:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_3) B_2))->((ex (produc1832616231le_alt->Prop)) (fun (X_1:(produc1832616231le_alt->Prop))=> ((and ((member1362619835_alt_o X_1) arrow_1751445586le_Lin)) ((member545531028le_alt ((produc990411159le_alt A_3) B_2)) X_1)))))).
% Axiom fact_151_PiProf:(forall (N:nat), ((member1561882372_alt_o (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) N)) lab) lba))) arrow_1605628760e_Prof)).
% Axiom fact_152_Pi__mem:(forall (X_3:produc1832616231le_alt) (F_2:(produc1832616231le_alt->Prop)) (A_2:(produc1832616231le_alt->Prop)) (B_1:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_2) ((pi_Pro539263375_alt_o A_2) B_1))->(((member545531028le_alt X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_153_Pi__mem:(forall (X_3:produc1832616231le_alt) (F_2:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_2:(produc1832616231le_alt->Prop)) (B_1:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_2) ((pi_Pro1535452471e_indi A_2) B_1))->(((member545531028le_alt X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_154_Pi__mem:(forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_2) ((pi_Arr170420797e_indi A_2) B_1))->(((member1561882372_alt_o X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_155_Pi__mem:(forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_2) ((pi_Arr1767527177lt_o_o A_2) B_1))->(((member1561882372_alt_o X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_156_Pi__mem:(forall (X_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_2) ((pi_Arr1941314005e_indi A_2) B_1))->(((member733327538_alt_o X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_157_Pi__mem:(forall (X_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_2:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_2) ((pi_Arr1422400881lt_o_o A_2) B_1))->(((member733327538_alt_o X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_158_Pi__mem:(forall (X_3:(produc1832616231le_alt->Prop)) (F_2:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_2:((produc1832616231le_alt->Prop)->Prop)) (B_1:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_2) ((pi_Pro1340600692e_indi A_2) B_1))->(((member1362619835_alt_o X_3) A_2)->((member1714766084e_indi (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_159_Pi__mem:(forall (X_3:(produc1832616231le_alt->Prop)) (F_2:((produc1832616231le_alt->Prop)->Prop)) (A_2:((produc1832616231le_alt->Prop)->Prop)) (B_1:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_2) ((pi_Pro410810898lt_o_o A_2) B_1))->(((member1362619835_alt_o X_3) A_2)->((member_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_160_Pi__mem:(forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_2) ((pi_Arr1055270199le_alt A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member545531028le_alt (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_161_Pi__mem:(forall (X_3:Prop) (F_2:(Prop->produc1832616231le_alt)) (A_2:(Prop->Prop)) (B_1:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_2) ((pi_o_P988780107le_alt A_2) B_1))->(((member_o X_3) A_2)->((member545531028le_alt (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_162_Pi__mem:(forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_2) ((pi_Arr651234977_alt_o A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member1561882372_alt_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_163_Pi__mem:(forall (X_3:Prop) (F_2:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_2:(Prop->Prop)) (B_1:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_2) ((pi_o_A71242893_alt_o A_2) B_1))->(((member_o X_3) A_2)->((member1561882372_alt_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_164_Pi__mem:(forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_2) ((pi_Arr1140519125_alt_o A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member733327538_alt_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_165_Pi__mem:(forall (X_3:Prop) (F_2:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_2:(Prop->Prop)) (B_1:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_2) ((pi_o_A1302557673_alt_o A_2) B_1))->(((member_o X_3) A_2)->((member733327538_alt_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_166_Pi__mem:(forall (X_3:Prop) (F_2:(Prop->(produc1832616231le_alt->Prop))) (A_2:(Prop->Prop)) (B_1:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_2) ((pi_o_P1538584260_alt_o A_2) B_1))->(((member_o X_3) A_2)->((member1362619835_alt_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_167_Pi__mem:(forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_2) ((pi_Arr1021537730_alt_o A_2) B_1))->(((member1561882372_alt_o X_3) A_2)->((member1362619835_alt_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_168_Pi__mem:(forall (X_3:arrow_1092341143e_indi) (F_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_2:(arrow_1092341143e_indi->Prop)) (B_1:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_2) ((pi_Arr418143960_alt_o A_2) B_1))->(((member1714766084e_indi X_3) A_2)->((member1362619835_alt_o (F_2 X_3)) (B_1 X_3))))).
% Axiom fact_169_Prof__def:(((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) arrow_1605628760e_Prof) ((pi_Arr418143960_alt_o top_to527331954indi_o) (fun (Uu:arrow_1092341143e_indi)=> arrow_1751445586le_Lin))).
% Axiom fact_170_funcset__mem:(forall (X_2:produc1832616231le_alt) (F_1:(produc1832616231le_alt->Prop)) (A_1:(produc1832616231le_alt->Prop)) (B:(Prop->Prop)), (((member1362619835_alt_o F_1) ((pi_Pro539263375_alt_o A_1) (fun (Uu:produc1832616231le_alt)=> B)))->(((member545531028le_alt X_2) A_1)->((member_o (F_1 X_2)) B)))).
% Axiom fact_171_funcset__mem:(forall (X_2:produc1832616231le_alt) (F_1:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_1:(produc1832616231le_alt->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member1486844321e_indi F_1) ((pi_Pro1535452471e_indi A_1) (fun (Uu:produc1832616231le_alt)=> B)))->(((member545531028le_alt X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B)))).
% Axiom fact_172_funcset__mem:(forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member1208133347e_indi F_1) ((pi_Arr170420797e_indi A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B)))->(((member1561882372_alt_o X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B)))).
% Axiom fact_173_funcset__mem:(forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B:(Prop->Prop)), (((member1754345465lt_o_o F_1) ((pi_Arr1767527177lt_o_o A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B)))->(((member1561882372_alt_o X_2) A_1)->((member_o (F_1 X_2)) B)))).
% Axiom fact_174_funcset__mem:(forall (X_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member986213183e_indi F_1) ((pi_Arr1941314005e_indi A_1) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B)))->(((member733327538_alt_o X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B)))).
% Axiom fact_175_funcset__mem:(forall (X_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_1:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B:(Prop->Prop)), (((member903234717lt_o_o F_1) ((pi_Arr1422400881lt_o_o A_1) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B)))->(((member733327538_alt_o X_2) A_1)->((member_o (F_1 X_2)) B)))).
% Axiom fact_176_funcset__mem:(forall (X_2:(produc1832616231le_alt->Prop)) (F_1:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_1:((produc1832616231le_alt->Prop)->Prop)) (B:(arrow_1092341143e_indi->Prop)), (((member1255309082e_indi F_1) ((pi_Pro1340600692e_indi A_1) (fun (Uu:(produc1832616231le_alt->Prop))=> B)))->(((member1362619835_alt_o X_2) A_1)->((member1714766084e_indi (F_1 X_2)) B)))).
% Axiom fact_177_funcset__mem:(forall (X_2:(produc1832616231le_alt->Prop)) (F_1:((produc1832616231le_alt->Prop)->Prop)) (A_1:((produc1832616231le_alt->Prop)->Prop)) (B:(Prop->Prop)), (((member1949484546lt_o_o F_1) ((pi_Pro410810898lt_o_o A_1) (fun (Uu:(produc1832616231le_alt->Prop))=> B)))->(((member1362619835_alt_o X_2) A_1)->((member_o (F_1 X_2)) B)))).
% Axiom fact_178_funcset__mem:(forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_1:(arrow_1092341143e_indi->Prop)) (B:(produc1832616231le_alt->Prop)), (((member1621875105le_alt F_1) ((pi_Arr1055270199le_alt A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member545531028le_alt (F_1 X_2)) B)))).
% Axiom fact_179_funcset__mem:(forall (X_2:Prop) (F_1:(Prop->produc1832616231le_alt)) (A_1:(Prop->Prop)) (B:(produc1832616231le_alt->Prop)), (((member1368218865le_alt F_1) ((pi_o_P988780107le_alt A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member545531028le_alt (F_1 X_2)) B)))).
% Axiom fact_180_funcset__mem:(forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_1:(arrow_1092341143e_indi->Prop)) (B:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member1079651021_alt_o F_1) ((pi_Arr651234977_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member1561882372_alt_o (F_1 X_2)) B)))).
% Axiom fact_181_funcset__mem:(forall (X_2:Prop) (F_1:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_1:(Prop->Prop)) (B:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member537117565_alt_o F_1) ((pi_o_A71242893_alt_o A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member1561882372_alt_o (F_1 X_2)) B)))).
% Axiom fact_182_funcset__mem:(forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_1:(arrow_1092341143e_indi->Prop)) (B:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member24189887_alt_o F_1) ((pi_Arr1140519125_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member733327538_alt_o (F_1 X_2)) B)))).
% Axiom fact_183_funcset__mem:(forall (X_2:Prop) (F_1:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_1:(Prop->Prop)) (B:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member1710515983_alt_o F_1) ((pi_o_A1302557673_alt_o A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member733327538_alt_o (F_1 X_2)) B)))).
% Axiom fact_184_funcset__mem:(forall (X_2:Prop) (F_1:(Prop->(produc1832616231le_alt->Prop))) (A_1:(Prop->Prop)) (B:((produc1832616231le_alt->Prop)->Prop)), (((member1099673524_alt_o F_1) ((pi_o_P1538584260_alt_o A_1) (fun (Uu:Prop)=> B)))->(((member_o X_2) A_1)->((member1362619835_alt_o (F_1 X_2)) B)))).
% Axiom fact_185_funcset__mem:(forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B:((produc1832616231le_alt->Prop)->Prop)), (((member733327538_alt_o F_1) ((pi_Arr1021537730_alt_o A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B)))->(((member1561882372_alt_o X_2) A_1)->((member1362619835_alt_o (F_1 X_2)) B)))).
% Axiom fact_186_funcset__mem:(forall (X_2:arrow_1092341143e_indi) (F_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_1:(arrow_1092341143e_indi->Prop)) (B:((produc1832616231le_alt->Prop)->Prop)), (((member1561882372_alt_o F_1) ((pi_Arr418143960_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> B)))->(((member1714766084e_indi X_2) A_1)->((member1362619835_alt_o (F_1 X_2)) B)))).
% Axiom fact_187_dictator__def:(forall (F:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (I_1:arrow_1092341143e_indi), ((iff ((arrow_1098709355ctator F) I_1)) (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X_1) arrow_1605628760e_Prof)->(((eq (produc1832616231le_alt->Prop)) (F X_1)) (X_1 I_1)))))).
% Axiom fact_188_Pi__UNIV:(forall (A:(produc1832616231le_alt->Prop)), (((eq ((produc1832616231le_alt->Prop)->Prop)) ((pi_Pro539263375_alt_o A) (fun (Uu:produc1832616231le_alt)=> top_top_o_o))) top_to1830848411lt_o_o)).
% Axiom fact_189_Pi__UNIV:(forall (A:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr1021537730_alt_o A) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> top_to1830848411lt_o_o))) top_to1049332548lt_o_o)).
% Axiom fact_190_Pi__UNIV:(forall (A:(arrow_1092341143e_indi->Prop)), (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr418143960_alt_o A) (fun (Uu:arrow_1092341143e_indi)=> top_to1830848411lt_o_o))) top_to790289938lt_o_o)).
% Axiom fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am:((iff ((member545531028le_alt ((produc990411159le_alt e) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))) ((member545531028le_alt ((produc990411159le_alt b) a)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) lab) lba))))).
% Axiom fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am:(forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((and (((ord_less_nat (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt e) d)) ((arrow_1865892024_mktop (p _TPTP_I)) e)))) ((((ord_less_nat (h _TPTP_I)) n)->False)->((and ((((eq nat) (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt e) d)) (((arrow_452340254_above (p _TPTP_I)) c) e)))) ((not (((eq nat) (h _TPTP_I)) n))->((member545531028le_alt ((produc990411159le_alt e) d)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))) ((and (((ord_less_nat (h _TPTP_I)) n)->((member545531028le_alt ((produc990411159le_alt b) a)) lab))) ((((ord_less_nat (h _TPTP_I)) n)->False)->((member545531028le_alt ((produc990411159le_alt b) a)) lba))))).
% Axiom fact_193__096a_A_126_061_Ab_096:(not (((eq arrow_1346734812le_alt) a) b)).
% Axiom fact_194__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096:((member545531028le_alt ((produc990411159le_alt b) a)) lba).
% Axiom fact_195__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096:((member545531028le_alt ((produc990411159le_alt a) b)) lab).
% Axiom fact_196__096_Ia_M_Ab_J_A_126_058_ALba_096:(((member545531028le_alt ((produc990411159le_alt a) b)) lba)->False).
% Axiom fact_197__096_Ib_M_Aa_J_A_126_058_ALab_096:(((member545531028le_alt ((produc990411159le_alt b) a)) lab)->False).
% Axiom help_If_1_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_:(forall (X:(produc1832616231le_alt->Prop)) (Y:(produc1832616231le_alt->Prop)), (((eq (produc1832616231le_alt->Prop)) (((if_Pro399136856_alt_o True) X) Y)) X)).
% Axiom help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_:(forall (X:(produc1832616231le_alt->Prop)) (Y:(produc1832616231le_alt->Prop)), (((eq (produc1832616231le_alt->Prop)) (((if_Pro399136856_alt_o False) X) Y)) Y)).
% Axiom help_If_3_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____sdiojnqkdh_:(forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))).
% Trying to prove ((member545531028le_alt ((produc990411159le_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:((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) 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 ((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) 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 ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))
% Found (fun (x0:(((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_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 ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))
% Found (fun (x:(((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (x0:(((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_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 ((((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))
% Found (fun (x:(((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (x0:(((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_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 ((((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))->((((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p))))
% Found (and_rect00 (fun (x:(((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (x0:(((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_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 ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))
% Found ((and_rect0 ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))) (fun (x:(((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (x0:(((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_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 ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))
% Found (((fun (P:Type) (x:((((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))->((((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))) (fun (x:(((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (x0:(((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_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 ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))
% Found (((fun (P:Type) (x:((((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))->((((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))) (fun (x:(((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (x0:(((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_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 ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))
% Got proof (((fun (P:Type) (x:((((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))->((((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))) (fun (x:(((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (x0:(((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_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 = 1.583704s
% node=43 cost=795.000000 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:((((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))->((((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))->P)))=> (((((and_rect (((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_alt c) d)) (f p)))) P) x) fact_14_PW)) ((member545531028le_alt ((produc990411159le_alt c) d)) (f p))) (fun (x:(((member545531028le_alt ((produc990411159le_alt c) d)) (f p))->((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e)))))))) (x0:(((member545531028le_alt ((produc990411159le_alt c) d)) (f (fun (_TPTP_I:arrow_1092341143e_indi)=> (((if_Pro399136856_alt_o ((ord_less_nat (h _TPTP_I)) n)) ((arrow_1865892024_mktop (p _TPTP_I)) e)) (((if_Pro399136856_alt_o (((eq nat) (h _TPTP_I)) n)) (((arrow_452340254_above (p _TPTP_I)) c) e)) ((arrow_1717184938_mkbot (p _TPTP_I)) e))))))->((member545531028le_alt ((produc990411159le_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
%------------------------------------------------------------------------------