%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SCT170^1 : TPTP v6.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n179.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 13:29:45 EDT 2014

% Result   : Timeout 300.05s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SCT170^1 : TPTP v6.1.0. Released v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n179.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 08:25:51 CDT 2014
% % CPUTime  : 300.05 
% 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 0x9d43b0>, <kernel.Type object at 0x9d4200>) 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 0x811ef0>, <kernel.Type object at 0x9d4320>) 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 0x811ef0>, <kernel.Type object at 0x9d42d8>) of role type named ty_ty_tc__List__Olist_Itc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_J
% Using role type
% Declaring list_A1528105233le_alt:Type
% FOF formula (<kernel.Constant object at 0x9d4200>, <kernel.Type object at 0x9d40e0>) 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 0x9d4908>, <kernel.DependentProduct object at 0xc49b48>) of role type named sy_c_All
% Using role type
% Declaring all:((produc1832616231le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x9d45f0>, <kernel.DependentProduct object at 0x6df248>) 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 0xc49f38>, <kernel.DependentProduct object at 0x6df248>) 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 0xc49f38>, <kernel.DependentProduct object at 0x6df248>) 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 0x9d43f8>, <kernel.DependentProduct object at 0x9d4098>) 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 0x9d42d8>, <kernel.DependentProduct object at 0x9d4098>) of role type named sy_c_Arrow__Order__Mirabelle__sdiojnqkdh_Obelow
% Using role type
% Declaring arrow_1760938802_below:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(arrow_1346734812le_alt->(produc1832616231le_alt->Prop))))
% FOF formula (<kernel.Constant object at 0x9d43f8>, <kernel.DependentProduct object at 0x9f2758>) 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 0x9d4098>, <kernel.DependentProduct object at 0x6dfcb0>) 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 0x9d43f8>, <kernel.DependentProduct object at 0x9f29e0>) 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 0x9d43f8>, <kernel.DependentProduct object at 0x9f2758>) 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 0x6dfbd8>, <kernel.DependentProduct object at 0x9f27a0>) of role type named sy_c_Ex
% Using role type
% Declaring _TPTP_ex:((produc1832616231le_alt->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x6dfcb0>, <kernel.DependentProduct object at 0x9f29e0>) of role type named sy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt_000t
% Using role type
% Declaring in_rel895475842le_alt:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(arrow_1346734812le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x6dfbd8>, <kernel.DependentProduct object at 0x9f2560>) 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 0x6dfef0>, <kernel.DependentProduct object at 0x9f2560>) 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 0x6dfef0>, <kernel.DependentProduct object at 0x9f2248>) 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 0x9f29e0>, <kernel.DependentProduct object at 0x9f2680>) 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 0x9f25f0>, <kernel.DependentProduct object at 0x9f2758>) 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 0x9f27a0>, <kernel.DependentProduct object at 0x9f2440>) 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 0x9f24d0>, <kernel.DependentProduct object at 0x9f25f0>) 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 0x9f2290>, <kernel.DependentProduct object at 0x9f21b8>) 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 0x9f27a0>, <kernel.DependentProduct object at 0x9f25f0>) 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 0x9f24d0>, <kernel.DependentProduct object at 0x9f2878>) 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 0x9f2290>, <kernel.DependentProduct object at 0x9f2878>) 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 0x9f27a0>, <kernel.DependentProduct object at 0x9f22d8>) 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 0x9f25f0>, <kernel.DependentProduct object at 0x9f22d8>) 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 0x9f28c0>, <kernel.DependentProduct object at 0x9f24d0>) 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 0x9f29e0>, <kernel.DependentProduct object at 0x9f25f0>) 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 0x9f2638>, <kernel.DependentProduct object at 0x9f2c68>) 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 0x9f2a70>, <kernel.DependentProduct object at 0x9f29e0>) 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 0x9f22d8>, <kernel.DependentProduct object at 0x9f2c68>) of role type named sy_c_HOL_Oequal__class_Oequal_000tc__List__Olist_Itc__Arrow____Order____Mirabell
% Using role type
% Declaring equal_2044961839le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x9f23f8>, <kernel.DependentProduct object at 0x9f25f0>) of role type named sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring distin1107700095le_alt:(list_A1528105233le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x9f28c0>, <kernel.DependentProduct object at 0x9f2a28>) of role type named sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring insert844458914le_alt:(arrow_1346734812le_alt->(list_A1528105233le_alt->list_A1528105233le_alt))
% FOF formula (<kernel.Constant object at 0x9f2c68>, <kernel.DependentProduct object at 0x9f2320>) of role type named sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring cons_A1100118844le_alt:(arrow_1346734812le_alt->(list_A1528105233le_alt->list_A1528105233le_alt))
% FOF formula (<kernel.Constant object at 0x9f25f0>, <kernel.Constant object at 0x9f2320>) of role type named sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring nil_Ar10086284le_alt:list_A1528105233le_alt
% FOF formula (<kernel.Constant object at 0x9f28c0>, <kernel.DependentProduct object at 0x9f22d8>) of role type named sy_c_List_Onull_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring null_A244857236le_alt:(list_A1528105233le_alt->Prop)
% FOF formula (<kernel.Constant object at 0x9f2638>, <kernel.DependentProduct object at 0x9f2a28>) of role type named sy_c_List_Osplice_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring splice244790623le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->list_A1528105233le_alt))
% FOF formula (<kernel.Constant object at 0x9f2320>, <kernel.DependentProduct object at 0x9f20e0>) 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 0x9f22d8>, <kernel.DependentProduct object at 0x9f2638>) 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 0x9f27e8>, <kernel.DependentProduct object at 0x9f2a28>) 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 0x9f20e0>, <kernel.DependentProduct object at 0x9f2638>) 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 0x9f22d8>, <kernel.DependentProduct object at 0x9f2c20>) 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 0x9f2098>, <kernel.DependentProduct object at 0x9f2bd8>) 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 0x9f2638>, <kernel.Sort object at 0xaa4ef0>) 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 0x9f2a28>, <kernel.DependentProduct object at 0x9f22d8>) 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 0x9f25f0>, <kernel.DependentProduct object at 0x9f2d40>) of role type named sy_c_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____sdiojnqkdh__Oalt
% Using role type
% Declaring produc443407182_alt_o:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(arrow_1346734812le_alt->Prop)))
% FOF formula (<kernel.Constant object at 0x9f2098>, <kernel.DependentProduct object at 0x9f22d8>) 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 0x9f2908>, <kernel.DependentProduct object at 0x9f2b90>) 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 0x9f2950>, <kernel.DependentProduct object at 0x9f2a28>) 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 0x9f25f0>, <kernel.DependentProduct object at 0x9f2638>) 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 0x9f2d40>, <kernel.DependentProduct object at 0xc4b7a0>) 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 0x9f2908>, <kernel.DependentProduct object at 0xc4bb90>) 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 0x9f25f0>, <kernel.DependentProduct object at 0xc4bc68>) 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 0x9f2d40>, <kernel.DependentProduct object at 0xc4b830>) 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 0x9f25f0>, <kernel.DependentProduct object at 0xc4b248>) 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 0x9f2d40>, <kernel.DependentProduct object at 0xc4bb48>) 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 0x9f25f0>, <kernel.DependentProduct object at 0xc4b830>) 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 0x9f25f0>, <kernel.DependentProduct object at 0xc4b830>) 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 0xc4b248>, <kernel.DependentProduct object at 0xc4bfc8>) 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 0xc4b9e0>, <kernel.DependentProduct object at 0x9f3098>) 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 0xc4bbd8>, <kernel.DependentProduct object at 0x9f3e60>) 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 0xc4bfc8>, <kernel.DependentProduct object at 0x9f3950>) 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 0xc4b248>, <kernel.DependentProduct object at 0x9f3c68>) 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 0xc4bbd8>, <kernel.DependentProduct object at 0x9f3488>) 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 0xc4b9e0>, <kernel.DependentProduct object at 0x9f3950>) 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 0xc4bbd8>, <kernel.DependentProduct object at 0x9f3f38>) 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 0xc4b9e0>, <kernel.DependentProduct object at 0x9f3c68>) 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 0xc4b9e0>, <kernel.DependentProduct object at 0x9f3680>) 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 0x9f30e0>, <kernel.DependentProduct object at 0x9f3488>) 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 0x9f3f38>, <kernel.DependentProduct object at 0x9f3908>) 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 0x9f3680>, <kernel.DependentProduct object at 0x9f3b90>) 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 0x9f3488>, <kernel.DependentProduct object at 0x9f30e0>) 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 0x9f3908>, <kernel.DependentProduct object at 0x9f3b90>) of role type named sy_v_P_H____
% Using role type
% Declaring p_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x9f3f38>, <kernel.DependentProduct object at 0x7f6950>) of role type named sy_v_P____
% Using role type
% Declaring p:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))
% FOF formula (<kernel.Constant object at 0x9f3c20>, <kernel.Constant object at 0x9f3908>) of role type named sy_v_a____
% Using role type
% Declaring a:arrow_1346734812le_alt
% FOF formula (<kernel.Constant object at 0x9f3e60>, <kernel.Constant object at 0x9f3908>) of role type named sy_v_b____
% Using role type
% Declaring b:arrow_1346734812le_alt
% FOF formula (<kernel.Constant object at 0x9f3f38>, <kernel.Constant object at 0x9f3c20>) of role type named sy_v_c____
% Using role type
% Declaring c:arrow_1346734812le_alt
% FOF formula ((member1561882372_alt_o p) arrow_1605628760e_Prof) of role axiom named fact_0__096P_A_058_AProf_096
% A new axiom: ((member1561882372_alt_o p) arrow_1605628760e_Prof)
% FOF formula (arrow_1724561858le_IIA f) of role axiom named fact_1_assms_I3_J
% A new axiom: (arrow_1724561858le_IIA f)
% FOF formula (arrow_1889221221nimity f) of role axiom named fact_2_u
% A new axiom: (arrow_1889221221nimity f)
% FOF formula (not (((eq arrow_1346734812le_alt) a) b)) of role axiom named fact_3__096a_A_126_061_Ab_096
% A new axiom: (not (((eq arrow_1346734812le_alt) a) b))
% FOF formula (distin1107700095le_alt ((cons_A1100118844le_alt a) ((cons_A1100118844le_alt b) ((cons_A1100118844le_alt c) nil_Ar10086284le_alt)))) of role axiom named fact_4_dist
% A new axiom: (distin1107700095le_alt ((cons_A1100118844le_alt a) ((cons_A1100118844le_alt b) ((cons_A1100118844le_alt c) nil_Ar10086284le_alt))))
% FOF formula (forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt a) b)) (p _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt b) a)) (p_1 _TPTP_I)))) of role axiom named fact_5_iff
% A new axiom: (forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt a) b)) (p _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt b) a)) (p_1 _TPTP_I))))
% FOF formula ((forall (C:arrow_1346734812le_alt), ((distin1107700095le_alt ((cons_A1100118844le_alt a) ((cons_A1100118844le_alt b) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt))))->False))->False) of role axiom named fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_
% A new axiom: ((forall (C:arrow_1346734812le_alt), ((distin1107700095le_alt ((cons_A1100118844le_alt a) ((cons_A1100118844le_alt b) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt))))->False))->False)
% FOF formula ((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> (((arrow_1760938802_below (((arrow_1760938802_below (p P_4)) c) b)) b) a))) arrow_1605628760e_Prof) of role axiom named fact_7__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096
% A new axiom: ((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> (((arrow_1760938802_below (((arrow_1760938802_below (p P_4)) c) b)) b) a))) arrow_1605628760e_Prof)
% FOF formula ((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> (((arrow_1760938802_below (((arrow_1760938802_below (((arrow_1760938802_below (p P_4)) c) b)) b) a)) a) c))) arrow_1605628760e_Prof) of role axiom named fact_8__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_
% A new axiom: ((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> (((arrow_1760938802_below (((arrow_1760938802_below (((arrow_1760938802_below (p P_4)) c) b)) b) a)) a) c))) arrow_1605628760e_Prof)
% FOF formula ((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> (((arrow_1760938802_below (p P_4)) c) b))) arrow_1605628760e_Prof) of role axiom named fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096
% A new axiom: ((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> (((arrow_1760938802_below (p P_4)) c) b))) arrow_1605628760e_Prof)
% FOF formula (forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (Z:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) ((arrow_1717184938_mkbot L_1) Z))) ((and ((and (not (((eq arrow_1346734812le_alt) Y_5) Z))) ((((eq arrow_1346734812le_alt) X_14) Z)->(not (((eq arrow_1346734812le_alt) X_14) Y_5))))) ((not (((eq arrow_1346734812le_alt) X_14) Z))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1))))) of role axiom named fact_10_in__mkbot
% A new axiom: (forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (Z:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) ((arrow_1717184938_mkbot L_1) Z))) ((and ((and (not (((eq arrow_1346734812le_alt) Y_5) Z))) ((((eq arrow_1346734812le_alt) X_14) Z)->(not (((eq arrow_1346734812le_alt) X_14) Y_5))))) ((not (((eq arrow_1346734812le_alt) X_14) Z))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1)))))
% FOF formula (forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (Z:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) ((arrow_1865892024_mktop L_1) Z))) ((and ((and (not (((eq arrow_1346734812le_alt) X_14) Z))) ((((eq arrow_1346734812le_alt) Y_5) Z)->(not (((eq arrow_1346734812le_alt) X_14) Y_5))))) ((not (((eq arrow_1346734812le_alt) Y_5) Z))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1))))) of role axiom named fact_11_in__mktop
% A new axiom: (forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (Z:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) ((arrow_1865892024_mktop L_1) Z))) ((and ((and (not (((eq arrow_1346734812le_alt) X_14) Z))) ((((eq arrow_1346734812le_alt) Y_5) Z)->(not (((eq arrow_1346734812le_alt) X_14) Y_5))))) ((not (((eq arrow_1346734812le_alt) Y_5) Z))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1)))))
% FOF formula (forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) (((arrow_1760938802_below L_1) A_19) B_12))) ((and ((and (not (((eq arrow_1346734812le_alt) X_14) Y_5))) ((((eq arrow_1346734812le_alt) Y_5) A_19)->((member545531028le_alt ((produc990411159le_alt X_14) B_12)) L_1)))) ((not (((eq arrow_1346734812le_alt) Y_5) A_19))->((and ((((eq arrow_1346734812le_alt) X_14) A_19)->((or (((eq arrow_1346734812le_alt) Y_5) B_12)) ((member545531028le_alt ((produc990411159le_alt B_12) Y_5)) L_1)))) ((not (((eq arrow_1346734812le_alt) X_14) A_19))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1))))))))) of role axiom named fact_12_in__below
% A new axiom: (forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) (((arrow_1760938802_below L_1) A_19) B_12))) ((and ((and (not (((eq arrow_1346734812le_alt) X_14) Y_5))) ((((eq arrow_1346734812le_alt) Y_5) A_19)->((member545531028le_alt ((produc990411159le_alt X_14) B_12)) L_1)))) ((not (((eq arrow_1346734812le_alt) Y_5) A_19))->((and ((((eq arrow_1346734812le_alt) X_14) A_19)->((or (((eq arrow_1346734812le_alt) Y_5) B_12)) ((member545531028le_alt ((produc990411159le_alt B_12) Y_5)) L_1)))) ((not (((eq arrow_1346734812le_alt) X_14) A_19))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1)))))))))
% FOF formula (forall (P_7:(produc1832616231le_alt->Prop)), ((iff (all P_7)) (forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), (P_7 ((produc990411159le_alt A_7) B_4))))) of role axiom named fact_13_split__paired__All
% A new axiom: (forall (P_7:(produc1832616231le_alt->Prop)), ((iff (all P_7)) (forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), (P_7 ((produc990411159le_alt A_7) B_4)))))
% FOF formula (forall (A_25:arrow_1346734812le_alt) (B_18:arrow_1346734812le_alt) (A_24:arrow_1346734812le_alt) (B_17:arrow_1346734812le_alt), ((iff (((eq produc1832616231le_alt) ((produc990411159le_alt A_25) B_18)) ((produc990411159le_alt A_24) B_17))) ((and (((eq arrow_1346734812le_alt) A_25) A_24)) (((eq arrow_1346734812le_alt) B_18) B_17)))) of role axiom named fact_14_Pair__eq
% A new axiom: (forall (A_25:arrow_1346734812le_alt) (B_18:arrow_1346734812le_alt) (A_24:arrow_1346734812le_alt) (B_17:arrow_1346734812le_alt), ((iff (((eq produc1832616231le_alt) ((produc990411159le_alt A_25) B_18)) ((produc990411159le_alt A_24) B_17))) ((and (((eq arrow_1346734812le_alt) A_25) A_24)) (((eq arrow_1346734812le_alt) B_18) B_17))))
% FOF formula (forall (A_23:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_22:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((((eq produc1832616231le_alt) ((produc990411159le_alt A_23) B_16)) ((produc990411159le_alt A_22) B_15))->(((((eq arrow_1346734812le_alt) A_23) A_22)->(not (((eq arrow_1346734812le_alt) B_16) B_15)))->False))) of role axiom named fact_15_Pair__inject
% A new axiom: (forall (A_23:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_22:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((((eq produc1832616231le_alt) ((produc990411159le_alt A_23) B_16)) ((produc990411159le_alt A_22) B_15))->(((((eq arrow_1346734812le_alt) A_23) A_22)->(not (((eq arrow_1346734812le_alt) B_16) B_15)))->False)))
% FOF formula (forall (R_1:(produc1832616231le_alt->Prop)) (X_17:arrow_1346734812le_alt) (Y_6:arrow_1346734812le_alt), ((iff (((in_rel895475842le_alt R_1) X_17) Y_6)) ((member545531028le_alt ((produc990411159le_alt X_17) Y_6)) R_1))) of role axiom named fact_16_in__rel__def
% A new axiom: (forall (R_1:(produc1832616231le_alt->Prop)) (X_17:arrow_1346734812le_alt) (Y_6:arrow_1346734812le_alt), ((iff (((in_rel895475842le_alt R_1) X_17) Y_6)) ((member545531028le_alt ((produc990411159le_alt X_17) Y_6)) R_1)))
% FOF formula (forall (L_1:(produc1832616231le_alt->Prop)) (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) X_14) Y_5))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o (((arrow_1760938802_below L_1) X_14) Y_5)) arrow_1751445586le_Lin)))) of role axiom named fact_17_below__Lin
% A new axiom: (forall (L_1:(produc1832616231le_alt->Prop)) (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) X_14) Y_5))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o (((arrow_1760938802_below L_1) X_14) Y_5)) arrow_1751445586le_Lin))))
% FOF formula ((member1561882372_alt_o p_1) arrow_1605628760e_Prof) of role axiom named fact_18__096P_H_A_058_AProf_096
% A new axiom: ((member1561882372_alt_o p_1) arrow_1605628760e_Prof)
% FOF formula (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_21:arrow_1346734812le_alt) (B_14:arrow_1346734812le_alt) (A_20:arrow_1346734812le_alt) (B_13:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_20) B_13))->((not (((eq arrow_1346734812le_alt) A_21) B_14))->((not (((eq arrow_1346734812le_alt) A_20) B_14))->((not (((eq arrow_1346734812le_alt) B_13) A_21))->(((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_20) B_13)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (P_6 _TPTP_I))))->(((member545531028le_alt ((produc990411159le_alt A_20) B_13)) (f P_5))->((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (f P_6))))))))))) of role axiom named fact_19__C1_C
% A new axiom: (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_21:arrow_1346734812le_alt) (B_14:arrow_1346734812le_alt) (A_20:arrow_1346734812le_alt) (B_13:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_20) B_13))->((not (((eq arrow_1346734812le_alt) A_21) B_14))->((not (((eq arrow_1346734812le_alt) A_20) B_14))->((not (((eq arrow_1346734812le_alt) B_13) A_21))->(((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_20) B_13)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (P_6 _TPTP_I))))->(((member545531028le_alt ((produc990411159le_alt A_20) B_13)) (f P_5))->((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (f P_6)))))))))))
% FOF formula (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_21:arrow_1346734812le_alt) (B_14:arrow_1346734812le_alt) (A_20:arrow_1346734812le_alt) (B_13:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_20) B_13))->((not (((eq arrow_1346734812le_alt) A_21) B_14))->((not (((eq arrow_1346734812le_alt) A_20) B_14))->((not (((eq arrow_1346734812le_alt) B_13) A_21))->(((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_20) B_13)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_20) B_13)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (f P_6))))))))))) of role axiom named fact_20__C2_C
% A new axiom: (forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_21:arrow_1346734812le_alt) (B_14:arrow_1346734812le_alt) (A_20:arrow_1346734812le_alt) (B_13:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_20) B_13))->((not (((eq arrow_1346734812le_alt) A_21) B_14))->((not (((eq arrow_1346734812le_alt) A_20) B_14))->((not (((eq arrow_1346734812le_alt) B_13) A_21))->(((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_20) B_13)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_20) B_13)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (f P_6)))))))))))
% 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_21_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 (forall (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> L_1)) arrow_1605628760e_Prof))) of role axiom named fact_22_const__Lin__Prof
% A new axiom: (forall (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> L_1)) arrow_1605628760e_Prof)))
% FOF formula (forall (X_14:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1717184938_mkbot L_1) X_14)) arrow_1751445586le_Lin))) of role axiom named fact_23_mkbot__Lin
% A new axiom: (forall (X_14:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1717184938_mkbot L_1) X_14)) arrow_1751445586le_Lin)))
% FOF formula (forall (X_14:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1865892024_mktop L_1) X_14)) arrow_1751445586le_Lin))) of role axiom named fact_24_mktop__Lin
% A new axiom: (forall (X_14:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1865892024_mktop L_1) X_14)) arrow_1751445586le_Lin)))
% FOF formula (forall (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->(((member545531028le_alt ((produc990411159le_alt A_19) B_12)) L_1)->(((member545531028le_alt ((produc990411159le_alt B_12) A_19)) L_1)->False)))) of role axiom named fact_25_Lin__irrefl
% A new axiom: (forall (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->(((member545531028le_alt ((produc990411159le_alt A_19) B_12)) L_1)->(((member545531028le_alt ((produc990411159le_alt B_12) A_19)) L_1)->False))))
% FOF formula (forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((not (((eq arrow_1346734812le_alt) X_14) Y_5))->((iff (((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1)->False)) ((member545531028le_alt ((produc990411159le_alt Y_5) X_14)) L_1))))) of role axiom named fact_26_notin__Lin__iff
% A new axiom: (forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((not (((eq arrow_1346734812le_alt) X_14) Y_5))->((iff (((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1)->False)) ((member545531028le_alt ((produc990411159le_alt Y_5) X_14)) L_1)))))
% FOF formula (forall (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt A_19) ((cons_A1100118844le_alt B_12) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt)))))))) of role axiom named fact_27_third__alt
% A new axiom: (forall (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt A_19) ((cons_A1100118844le_alt B_12) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt))))))))
% FOF formula (forall (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1724561858le_IIA F_8)) (forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(forall (Xa:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o Xa) arrow_1605628760e_Prof)->(forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (X _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (Xa _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 X))) ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 Xa))))))))))) of role axiom named fact_28_IIA__def
% A new axiom: (forall (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1724561858le_IIA F_8)) (forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(forall (Xa:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o Xa) arrow_1605628760e_Prof)->(forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (X _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (Xa _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 X))) ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 Xa)))))))))))
% FOF formula (forall (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1889221221nimity F_8)) (forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (X _TPTP_I)))->((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 X)))))))) of role axiom named fact_29_unanimity__def
% A new axiom: (forall (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1889221221nimity F_8)) (forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (X _TPTP_I)))->((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 X))))))))
% FOF formula (forall (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->((ex (produc1832616231le_alt->Prop)) (fun (X:(produc1832616231le_alt->Prop))=> ((and ((member1362619835_alt_o X) arrow_1751445586le_Lin)) ((member545531028le_alt ((produc990411159le_alt A_19) B_12)) X)))))) of role axiom named fact_30_complete__Lin
% A new axiom: (forall (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->((ex (produc1832616231le_alt->Prop)) (fun (X:(produc1832616231le_alt->Prop))=> ((and ((member1362619835_alt_o X) arrow_1751445586le_Lin)) ((member545531028le_alt ((produc990411159le_alt A_19) B_12)) X))))))
% FOF formula (forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) (((arrow_452340254_above L_1) A_19) B_12))) ((and ((and (not (((eq arrow_1346734812le_alt) X_14) Y_5))) ((((eq arrow_1346734812le_alt) X_14) B_12)->((member545531028le_alt ((produc990411159le_alt A_19) Y_5)) L_1)))) ((not (((eq arrow_1346734812le_alt) X_14) B_12))->((and ((((eq arrow_1346734812le_alt) Y_5) B_12)->((or (((eq arrow_1346734812le_alt) X_14) A_19)) ((member545531028le_alt ((produc990411159le_alt X_14) A_19)) L_1)))) ((not (((eq arrow_1346734812le_alt) Y_5) B_12))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1))))))))) of role axiom named fact_31_in__above
% A new axiom: (forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) (((arrow_452340254_above L_1) A_19) B_12))) ((and ((and (not (((eq arrow_1346734812le_alt) X_14) Y_5))) ((((eq arrow_1346734812le_alt) X_14) B_12)->((member545531028le_alt ((produc990411159le_alt A_19) Y_5)) L_1)))) ((not (((eq arrow_1346734812le_alt) X_14) B_12))->((and ((((eq arrow_1346734812le_alt) Y_5) B_12)->((or (((eq arrow_1346734812le_alt) X_14) A_19)) ((member545531028le_alt ((produc990411159le_alt X_14) A_19)) L_1)))) ((not (((eq arrow_1346734812le_alt) Y_5) B_12))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1)))))))))
% FOF formula (distin1107700095le_alt nil_Ar10086284le_alt) of role axiom named fact_32_distinct_Osimps_I1_J
% A new axiom: (distin1107700095le_alt nil_Ar10086284le_alt)
% FOF formula (forall (A_18:arrow_1346734812le_alt) (List_4:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) ((cons_A1100118844le_alt A_18) List_4)))) of role axiom named fact_33_list_Osimps_I2_J
% A new axiom: (forall (A_18:arrow_1346734812le_alt) (List_4:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) ((cons_A1100118844le_alt A_18) List_4))))
% FOF formula (forall (A_17:arrow_1346734812le_alt) (List_3:list_A1528105233le_alt) (A_16:arrow_1346734812le_alt) (List_2:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_17) List_3)) ((cons_A1100118844le_alt A_16) List_2))) ((and (((eq arrow_1346734812le_alt) A_17) A_16)) (((eq list_A1528105233le_alt) List_3) List_2)))) of role axiom named fact_34_list_Oinject
% A new axiom: (forall (A_17:arrow_1346734812le_alt) (List_3:list_A1528105233le_alt) (A_16:arrow_1346734812le_alt) (List_2:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_17) List_3)) ((cons_A1100118844le_alt A_16) List_2))) ((and (((eq arrow_1346734812le_alt) A_17) A_16)) (((eq list_A1528105233le_alt) List_3) List_2))))
% FOF formula (forall (X_16:arrow_1346734812le_alt) (Xs_11:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_16) Xs_11)) Xs_11))) of role axiom named fact_35_not__Cons__self2
% A new axiom: (forall (X_16:arrow_1346734812le_alt) (Xs_11:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_16) Xs_11)) Xs_11)))
% FOF formula (forall (Xs_10:list_A1528105233le_alt) (X_15:arrow_1346734812le_alt), (not (((eq list_A1528105233le_alt) Xs_10) ((cons_A1100118844le_alt X_15) Xs_10)))) of role axiom named fact_36_not__Cons__self
% A new axiom: (forall (Xs_10:list_A1528105233le_alt) (X_15:arrow_1346734812le_alt), (not (((eq list_A1528105233le_alt) Xs_10) ((cons_A1100118844le_alt X_15) Xs_10))))
% FOF formula (forall (L_1:(produc1832616231le_alt->Prop)) (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) X_14) Y_5))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o (((arrow_452340254_above L_1) X_14) Y_5)) arrow_1751445586le_Lin)))) of role axiom named fact_37_above__Lin
% A new axiom: (forall (L_1:(produc1832616231le_alt->Prop)) (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) X_14) Y_5))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o (((arrow_452340254_above L_1) X_14) Y_5)) arrow_1751445586le_Lin))))
% FOF formula (forall (A_15:arrow_1346734812le_alt) (List_1:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_15) List_1)) nil_Ar10086284le_alt))) of role axiom named fact_38_list_Osimps_I3_J
% A new axiom: (forall (A_15:arrow_1346734812le_alt) (List_1:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_15) List_1)) nil_Ar10086284le_alt)))
% FOF formula (forall (I_1:arrow_1092341143e_indi) (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o F_8) ((pi_Arr1021537730_alt_o arrow_1605628760e_Prof) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> arrow_1751445586le_Lin)))->((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_7) B_4))->(((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (X I_1))->((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 X)))))))->((arrow_1098709355ctator F_8) I_1)))) of role axiom named fact_39_dictatorI
% A new axiom: (forall (I_1:arrow_1092341143e_indi) (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o F_8) ((pi_Arr1021537730_alt_o arrow_1605628760e_Prof) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> arrow_1751445586le_Lin)))->((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_7) B_4))->(((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (X I_1))->((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 X)))))))->((arrow_1098709355ctator F_8) I_1))))
% FOF formula (forall (X_13:produc1832616231le_alt) (F_11:(produc1832616231le_alt->Prop)) (A_14:(produc1832616231le_alt->Prop)) (B_11:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_11) ((pi_Pro539263375_alt_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member545531028le_alt X_13) A_14)->False)))) of role axiom named fact_40_PiE
% A new axiom: (forall (X_13:produc1832616231le_alt) (F_11:(produc1832616231le_alt->Prop)) (A_14:(produc1832616231le_alt->Prop)) (B_11:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_11) ((pi_Pro539263375_alt_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member545531028le_alt X_13) A_14)->False))))
% FOF formula (forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_11) ((pi_Arr1055270199le_alt A_14) B_11))->((((member545531028le_alt (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False)))) of role axiom named fact_41_PiE
% A new axiom: (forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_11) ((pi_Arr1055270199le_alt A_14) B_11))->((((member545531028le_alt (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False))))
% FOF formula (forall (X_13:Prop) (F_11:(Prop->produc1832616231le_alt)) (A_14:(Prop->Prop)) (B_11:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_11) ((pi_o_P988780107le_alt A_14) B_11))->((((member545531028le_alt (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False)))) of role axiom named fact_42_PiE
% A new axiom: (forall (X_13:Prop) (F_11:(Prop->produc1832616231le_alt)) (A_14:(Prop->Prop)) (B_11:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_11) ((pi_o_P988780107le_alt A_14) B_11))->((((member545531028le_alt (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False))))
% FOF formula (forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_11) ((pi_Arr651234977_alt_o A_14) B_11))->((((member1561882372_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False)))) of role axiom named fact_43_PiE
% A new axiom: (forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_11) ((pi_Arr651234977_alt_o A_14) B_11))->((((member1561882372_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False))))
% FOF formula (forall (X_13:Prop) (F_11:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_14:(Prop->Prop)) (B_11:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_11) ((pi_o_A71242893_alt_o A_14) B_11))->((((member1561882372_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False)))) of role axiom named fact_44_PiE
% A new axiom: (forall (X_13:Prop) (F_11:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_14:(Prop->Prop)) (B_11:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_11) ((pi_o_A71242893_alt_o A_14) B_11))->((((member1561882372_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False))))
% FOF formula (forall (X_13:Prop) (F_11:(Prop->(produc1832616231le_alt->Prop))) (A_14:(Prop->Prop)) (B_11:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_11) ((pi_o_P1538584260_alt_o A_14) B_11))->((((member1362619835_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False)))) of role axiom named fact_45_PiE
% A new axiom: (forall (X_13:Prop) (F_11:(Prop->(produc1832616231le_alt->Prop))) (A_14:(Prop->Prop)) (B_11:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_11) ((pi_o_P1538584260_alt_o A_14) B_11))->((((member1362619835_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False))))
% FOF formula (forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_11) ((pi_Arr1140519125_alt_o A_14) B_11))->((((member733327538_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False)))) of role axiom named fact_46_PiE
% A new axiom: (forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_11) ((pi_Arr1140519125_alt_o A_14) B_11))->((((member733327538_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False))))
% FOF formula (forall (X_13:Prop) (F_11:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_14:(Prop->Prop)) (B_11:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_11) ((pi_o_A1302557673_alt_o A_14) B_11))->((((member733327538_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False)))) of role axiom named fact_47_PiE
% A new axiom: (forall (X_13:Prop) (F_11:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_14:(Prop->Prop)) (B_11:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_11) ((pi_o_A1302557673_alt_o A_14) B_11))->((((member733327538_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False))))
% FOF formula (forall (X_13:produc1832616231le_alt) (F_11:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_14:(produc1832616231le_alt->Prop)) (B_11:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_11) ((pi_Pro1535452471e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member545531028le_alt X_13) A_14)->False)))) of role axiom named fact_48_PiE
% A new axiom: (forall (X_13:produc1832616231le_alt) (F_11:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_14:(produc1832616231le_alt->Prop)) (B_11:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_11) ((pi_Pro1535452471e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member545531028le_alt X_13) A_14)->False))))
% FOF formula (forall (X_13:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_14:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_11) ((pi_Arr170420797e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member1561882372_alt_o X_13) A_14)->False)))) of role axiom named fact_49_PiE
% A new axiom: (forall (X_13:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_14:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_11) ((pi_Arr170420797e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member1561882372_alt_o X_13) A_14)->False))))
% FOF formula (forall (X_13:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_14:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_11) ((pi_Arr1767527177lt_o_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member1561882372_alt_o X_13) A_14)->False)))) of role axiom named fact_50_PiE
% A new axiom: (forall (X_13:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_14:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_11) ((pi_Arr1767527177lt_o_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member1561882372_alt_o X_13) A_14)->False))))
% FOF formula (forall (X_13:(produc1832616231le_alt->Prop)) (F_11:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_14:((produc1832616231le_alt->Prop)->Prop)) (B_11:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_11) ((pi_Pro1340600692e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member1362619835_alt_o X_13) A_14)->False)))) of role axiom named fact_51_PiE
% A new axiom: (forall (X_13:(produc1832616231le_alt->Prop)) (F_11:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_14:((produc1832616231le_alt->Prop)->Prop)) (B_11:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_11) ((pi_Pro1340600692e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member1362619835_alt_o X_13) A_14)->False))))
% FOF formula (forall (X_13:(produc1832616231le_alt->Prop)) (F_11:((produc1832616231le_alt->Prop)->Prop)) (A_14:((produc1832616231le_alt->Prop)->Prop)) (B_11:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_11) ((pi_Pro410810898lt_o_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member1362619835_alt_o X_13) A_14)->False)))) of role axiom named fact_52_PiE
% A new axiom: (forall (X_13:(produc1832616231le_alt->Prop)) (F_11:((produc1832616231le_alt->Prop)->Prop)) (A_14:((produc1832616231le_alt->Prop)->Prop)) (B_11:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_11) ((pi_Pro410810898lt_o_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member1362619835_alt_o X_13) A_14)->False))))
% FOF formula (forall (X_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_14:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_11) ((pi_Arr1941314005e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member733327538_alt_o X_13) A_14)->False)))) of role axiom named fact_53_PiE
% A new axiom: (forall (X_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_14:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_11) ((pi_Arr1941314005e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member733327538_alt_o X_13) A_14)->False))))
% FOF formula (forall (X_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_14:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_11) ((pi_Arr1422400881lt_o_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member733327538_alt_o X_13) A_14)->False)))) of role axiom named fact_54_PiE
% A new axiom: (forall (X_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_14:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_11) ((pi_Arr1422400881lt_o_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member733327538_alt_o X_13) A_14)->False))))
% FOF formula (forall (X_13:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_14:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_11) ((pi_Arr1021537730_alt_o A_14) B_11))->((((member1362619835_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1561882372_alt_o X_13) A_14)->False)))) of role axiom named fact_55_PiE
% A new axiom: (forall (X_13:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_14:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_11) ((pi_Arr1021537730_alt_o A_14) B_11))->((((member1362619835_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1561882372_alt_o X_13) A_14)->False))))
% FOF formula (forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_11) ((pi_Arr418143960_alt_o A_14) B_11))->((((member1362619835_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False)))) of role axiom named fact_56_PiE
% A new axiom: (forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_11) ((pi_Arr418143960_alt_o A_14) B_11))->((((member1362619835_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False))))
% FOF formula (forall (Y_4:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Y_4) nil_Ar10086284le_alt))->((forall (A_7:arrow_1346734812le_alt) (List:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) Y_4) ((cons_A1100118844le_alt A_7) List))))->False))) of role axiom named fact_57_list_Oexhaust
% A new axiom: (forall (Y_4:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Y_4) nil_Ar10086284le_alt))->((forall (A_7:arrow_1346734812le_alt) (List:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) Y_4) ((cons_A1100118844le_alt A_7) List))))->False)))
% FOF formula (forall (Xs_9:list_A1528105233le_alt), ((iff (not (((eq list_A1528105233le_alt) Xs_9) nil_Ar10086284le_alt))) ((ex arrow_1346734812le_alt) (fun (Y_1:arrow_1346734812le_alt)=> ((ex list_A1528105233le_alt) (fun (Ys_2:list_A1528105233le_alt)=> (((eq list_A1528105233le_alt) Xs_9) ((cons_A1100118844le_alt Y_1) Ys_2)))))))) of role axiom named fact_58_neq__Nil__conv
% A new axiom: (forall (Xs_9:list_A1528105233le_alt), ((iff (not (((eq list_A1528105233le_alt) Xs_9) nil_Ar10086284le_alt))) ((ex arrow_1346734812le_alt) (fun (Y_1:arrow_1346734812le_alt)=> ((ex list_A1528105233le_alt) (fun (Ys_2:list_A1528105233le_alt)=> (((eq list_A1528105233le_alt) Xs_9) ((cons_A1100118844le_alt Y_1) Ys_2))))))))
% FOF formula ((ex arrow_1346734812le_alt) (fun (A_7:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (B_4:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt A_7) ((cons_A1100118844le_alt B_4) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt)))))))))) of role axiom named fact_59_alt3
% A new axiom: ((ex arrow_1346734812le_alt) (fun (A_7:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (B_4:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt A_7) ((cons_A1100118844le_alt B_4) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt))))))))))
% FOF formula (forall (X_12:produc1832616231le_alt) (F_10:(produc1832616231le_alt->Prop)) (A_13:(produc1832616231le_alt->Prop)) (B_10:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_10) ((pi_Pro539263375_alt_o A_13) B_10))->(((member545531028le_alt X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_60_Pi__mem
% A new axiom: (forall (X_12:produc1832616231le_alt) (F_10:(produc1832616231le_alt->Prop)) (A_13:(produc1832616231le_alt->Prop)) (B_10:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_10) ((pi_Pro539263375_alt_o A_13) B_10))->(((member545531028le_alt X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:produc1832616231le_alt) (F_10:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_13:(produc1832616231le_alt->Prop)) (B_10:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_10) ((pi_Pro1535452471e_indi A_13) B_10))->(((member545531028le_alt X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_61_Pi__mem
% A new axiom: (forall (X_12:produc1832616231le_alt) (F_10:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_13:(produc1832616231le_alt->Prop)) (B_10:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_10) ((pi_Pro1535452471e_indi A_13) B_10))->(((member545531028le_alt X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_10) ((pi_Arr170420797e_indi A_13) B_10))->(((member1561882372_alt_o X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_62_Pi__mem
% A new axiom: (forall (X_12:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_10) ((pi_Arr170420797e_indi A_13) B_10))->(((member1561882372_alt_o X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_10) ((pi_Arr1767527177lt_o_o A_13) B_10))->(((member1561882372_alt_o X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_63_Pi__mem
% A new axiom: (forall (X_12:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_10) ((pi_Arr1767527177lt_o_o A_13) B_10))->(((member1561882372_alt_o X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:(produc1832616231le_alt->Prop)) (F_10:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_13:((produc1832616231le_alt->Prop)->Prop)) (B_10:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_10) ((pi_Pro1340600692e_indi A_13) B_10))->(((member1362619835_alt_o X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_64_Pi__mem
% A new axiom: (forall (X_12:(produc1832616231le_alt->Prop)) (F_10:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_13:((produc1832616231le_alt->Prop)->Prop)) (B_10:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_10) ((pi_Pro1340600692e_indi A_13) B_10))->(((member1362619835_alt_o X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:(produc1832616231le_alt->Prop)) (F_10:((produc1832616231le_alt->Prop)->Prop)) (A_13:((produc1832616231le_alt->Prop)->Prop)) (B_10:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_10) ((pi_Pro410810898lt_o_o A_13) B_10))->(((member1362619835_alt_o X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_65_Pi__mem
% A new axiom: (forall (X_12:(produc1832616231le_alt->Prop)) (F_10:((produc1832616231le_alt->Prop)->Prop)) (A_13:((produc1832616231le_alt->Prop)->Prop)) (B_10:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_10) ((pi_Pro410810898lt_o_o A_13) B_10))->(((member1362619835_alt_o X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_13:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_10) ((pi_Arr1941314005e_indi A_13) B_10))->(((member733327538_alt_o X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_66_Pi__mem
% A new axiom: (forall (X_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_13:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_10) ((pi_Arr1941314005e_indi A_13) B_10))->(((member733327538_alt_o X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_13:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_10) ((pi_Arr1422400881lt_o_o A_13) B_10))->(((member733327538_alt_o X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_67_Pi__mem
% A new axiom: (forall (X_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_13:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_10) ((pi_Arr1422400881lt_o_o A_13) B_10))->(((member733327538_alt_o X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_10) ((pi_Arr1055270199le_alt A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member545531028le_alt (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_68_Pi__mem
% A new axiom: (forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_10) ((pi_Arr1055270199le_alt A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member545531028le_alt (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:Prop) (F_10:(Prop->produc1832616231le_alt)) (A_13:(Prop->Prop)) (B_10:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_10) ((pi_o_P988780107le_alt A_13) B_10))->(((member_o X_12) A_13)->((member545531028le_alt (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_69_Pi__mem
% A new axiom: (forall (X_12:Prop) (F_10:(Prop->produc1832616231le_alt)) (A_13:(Prop->Prop)) (B_10:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_10) ((pi_o_P988780107le_alt A_13) B_10))->(((member_o X_12) A_13)->((member545531028le_alt (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_10) ((pi_Arr651234977_alt_o A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member1561882372_alt_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_70_Pi__mem
% A new axiom: (forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_10) ((pi_Arr651234977_alt_o A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member1561882372_alt_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:Prop) (F_10:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_13:(Prop->Prop)) (B_10:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_10) ((pi_o_A71242893_alt_o A_13) B_10))->(((member_o X_12) A_13)->((member1561882372_alt_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_71_Pi__mem
% A new axiom: (forall (X_12:Prop) (F_10:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_13:(Prop->Prop)) (B_10:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_10) ((pi_o_A71242893_alt_o A_13) B_10))->(((member_o X_12) A_13)->((member1561882372_alt_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:Prop) (F_10:(Prop->(produc1832616231le_alt->Prop))) (A_13:(Prop->Prop)) (B_10:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_10) ((pi_o_P1538584260_alt_o A_13) B_10))->(((member_o X_12) A_13)->((member1362619835_alt_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_72_Pi__mem
% A new axiom: (forall (X_12:Prop) (F_10:(Prop->(produc1832616231le_alt->Prop))) (A_13:(Prop->Prop)) (B_10:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_10) ((pi_o_P1538584260_alt_o A_13) B_10))->(((member_o X_12) A_13)->((member1362619835_alt_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_10) ((pi_Arr1140519125_alt_o A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member733327538_alt_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_73_Pi__mem
% A new axiom: (forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_10) ((pi_Arr1140519125_alt_o A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member733327538_alt_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:Prop) (F_10:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_13:(Prop->Prop)) (B_10:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_10) ((pi_o_A1302557673_alt_o A_13) B_10))->(((member_o X_12) A_13)->((member733327538_alt_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_74_Pi__mem
% A new axiom: (forall (X_12:Prop) (F_10:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_13:(Prop->Prop)) (B_10:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_10) ((pi_o_A1302557673_alt_o A_13) B_10))->(((member_o X_12) A_13)->((member733327538_alt_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_10) ((pi_Arr1021537730_alt_o A_13) B_10))->(((member1561882372_alt_o X_12) A_13)->((member1362619835_alt_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_75_Pi__mem
% A new axiom: (forall (X_12:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_10) ((pi_Arr1021537730_alt_o A_13) B_10))->(((member1561882372_alt_o X_12) A_13)->((member1362619835_alt_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_10) ((pi_Arr418143960_alt_o A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member1362619835_alt_o (F_10 X_12)) (B_10 X_12))))) of role axiom named fact_76_Pi__mem
% A new axiom: (forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_10) ((pi_Arr418143960_alt_o A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member1362619835_alt_o (F_10 X_12)) (B_10 X_12)))))
% FOF formula (forall (X_11:produc1832616231le_alt) (F_9:(produc1832616231le_alt->Prop)) (A_12:(produc1832616231le_alt->Prop)) (B_9:(Prop->Prop)), (((member1362619835_alt_o F_9) ((pi_Pro539263375_alt_o A_12) (fun (Uu:produc1832616231le_alt)=> B_9)))->(((member545531028le_alt X_11) A_12)->((member_o (F_9 X_11)) B_9)))) of role axiom named fact_77_funcset__mem
% A new axiom: (forall (X_11:produc1832616231le_alt) (F_9:(produc1832616231le_alt->Prop)) (A_12:(produc1832616231le_alt->Prop)) (B_9:(Prop->Prop)), (((member1362619835_alt_o F_9) ((pi_Pro539263375_alt_o A_12) (fun (Uu:produc1832616231le_alt)=> B_9)))->(((member545531028le_alt X_11) A_12)->((member_o (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:produc1832616231le_alt) (F_9:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_12:(produc1832616231le_alt->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member1486844321e_indi F_9) ((pi_Pro1535452471e_indi A_12) (fun (Uu:produc1832616231le_alt)=> B_9)))->(((member545531028le_alt X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9)))) of role axiom named fact_78_funcset__mem
% A new axiom: (forall (X_11:produc1832616231le_alt) (F_9:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_12:(produc1832616231le_alt->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member1486844321e_indi F_9) ((pi_Pro1535452471e_indi A_12) (fun (Uu:produc1832616231le_alt)=> B_9)))->(((member545531028le_alt X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member1208133347e_indi F_9) ((pi_Arr170420797e_indi A_12) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_9)))->(((member1561882372_alt_o X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9)))) of role axiom named fact_79_funcset__mem
% A new axiom: (forall (X_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member1208133347e_indi F_9) ((pi_Arr170420797e_indi A_12) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_9)))->(((member1561882372_alt_o X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_9:(Prop->Prop)), (((member1754345465lt_o_o F_9) ((pi_Arr1767527177lt_o_o A_12) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_9)))->(((member1561882372_alt_o X_11) A_12)->((member_o (F_9 X_11)) B_9)))) of role axiom named fact_80_funcset__mem
% A new axiom: (forall (X_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_9:(Prop->Prop)), (((member1754345465lt_o_o F_9) ((pi_Arr1767527177lt_o_o A_12) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_9)))->(((member1561882372_alt_o X_11) A_12)->((member_o (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:(produc1832616231le_alt->Prop)) (F_9:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_12:((produc1832616231le_alt->Prop)->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member1255309082e_indi F_9) ((pi_Pro1340600692e_indi A_12) (fun (Uu:(produc1832616231le_alt->Prop))=> B_9)))->(((member1362619835_alt_o X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9)))) of role axiom named fact_81_funcset__mem
% A new axiom: (forall (X_11:(produc1832616231le_alt->Prop)) (F_9:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_12:((produc1832616231le_alt->Prop)->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member1255309082e_indi F_9) ((pi_Pro1340600692e_indi A_12) (fun (Uu:(produc1832616231le_alt->Prop))=> B_9)))->(((member1362619835_alt_o X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:(produc1832616231le_alt->Prop)) (F_9:((produc1832616231le_alt->Prop)->Prop)) (A_12:((produc1832616231le_alt->Prop)->Prop)) (B_9:(Prop->Prop)), (((member1949484546lt_o_o F_9) ((pi_Pro410810898lt_o_o A_12) (fun (Uu:(produc1832616231le_alt->Prop))=> B_9)))->(((member1362619835_alt_o X_11) A_12)->((member_o (F_9 X_11)) B_9)))) of role axiom named fact_82_funcset__mem
% A new axiom: (forall (X_11:(produc1832616231le_alt->Prop)) (F_9:((produc1832616231le_alt->Prop)->Prop)) (A_12:((produc1832616231le_alt->Prop)->Prop)) (B_9:(Prop->Prop)), (((member1949484546lt_o_o F_9) ((pi_Pro410810898lt_o_o A_12) (fun (Uu:(produc1832616231le_alt->Prop))=> B_9)))->(((member1362619835_alt_o X_11) A_12)->((member_o (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_12:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member986213183e_indi F_9) ((pi_Arr1941314005e_indi A_12) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_9)))->(((member733327538_alt_o X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9)))) of role axiom named fact_83_funcset__mem
% A new axiom: (forall (X_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_12:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member986213183e_indi F_9) ((pi_Arr1941314005e_indi A_12) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_9)))->(((member733327538_alt_o X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_12:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_9:(Prop->Prop)), (((member903234717lt_o_o F_9) ((pi_Arr1422400881lt_o_o A_12) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_9)))->(((member733327538_alt_o X_11) A_12)->((member_o (F_9 X_11)) B_9)))) of role axiom named fact_84_funcset__mem
% A new axiom: (forall (X_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_12:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_9:(Prop->Prop)), (((member903234717lt_o_o F_9) ((pi_Arr1422400881lt_o_o A_12) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_9)))->(((member733327538_alt_o X_11) A_12)->((member_o (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:(produc1832616231le_alt->Prop)), (((member1621875105le_alt F_9) ((pi_Arr1055270199le_alt A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member545531028le_alt (F_9 X_11)) B_9)))) of role axiom named fact_85_funcset__mem
% A new axiom: (forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:(produc1832616231le_alt->Prop)), (((member1621875105le_alt F_9) ((pi_Arr1055270199le_alt A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member545531028le_alt (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:Prop) (F_9:(Prop->produc1832616231le_alt)) (A_12:(Prop->Prop)) (B_9:(produc1832616231le_alt->Prop)), (((member1368218865le_alt F_9) ((pi_o_P988780107le_alt A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member545531028le_alt (F_9 X_11)) B_9)))) of role axiom named fact_86_funcset__mem
% A new axiom: (forall (X_11:Prop) (F_9:(Prop->produc1832616231le_alt)) (A_12:(Prop->Prop)) (B_9:(produc1832616231le_alt->Prop)), (((member1368218865le_alt F_9) ((pi_o_P988780107le_alt A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member545531028le_alt (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member1079651021_alt_o F_9) ((pi_Arr651234977_alt_o A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member1561882372_alt_o (F_9 X_11)) B_9)))) of role axiom named fact_87_funcset__mem
% A new axiom: (forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member1079651021_alt_o F_9) ((pi_Arr651234977_alt_o A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member1561882372_alt_o (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:Prop) (F_9:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_12:(Prop->Prop)) (B_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member537117565_alt_o F_9) ((pi_o_A71242893_alt_o A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member1561882372_alt_o (F_9 X_11)) B_9)))) of role axiom named fact_88_funcset__mem
% A new axiom: (forall (X_11:Prop) (F_9:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_12:(Prop->Prop)) (B_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member537117565_alt_o F_9) ((pi_o_A71242893_alt_o A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member1561882372_alt_o (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:Prop) (F_9:(Prop->(produc1832616231le_alt->Prop))) (A_12:(Prop->Prop)) (B_9:((produc1832616231le_alt->Prop)->Prop)), (((member1099673524_alt_o F_9) ((pi_o_P1538584260_alt_o A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member1362619835_alt_o (F_9 X_11)) B_9)))) of role axiom named fact_89_funcset__mem
% A new axiom: (forall (X_11:Prop) (F_9:(Prop->(produc1832616231le_alt->Prop))) (A_12:(Prop->Prop)) (B_9:((produc1832616231le_alt->Prop)->Prop)), (((member1099673524_alt_o F_9) ((pi_o_P1538584260_alt_o A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member1362619835_alt_o (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member24189887_alt_o F_9) ((pi_Arr1140519125_alt_o A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member733327538_alt_o (F_9 X_11)) B_9)))) of role axiom named fact_90_funcset__mem
% A new axiom: (forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member24189887_alt_o F_9) ((pi_Arr1140519125_alt_o A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member733327538_alt_o (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:Prop) (F_9:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_12:(Prop->Prop)) (B_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member1710515983_alt_o F_9) ((pi_o_A1302557673_alt_o A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member733327538_alt_o (F_9 X_11)) B_9)))) of role axiom named fact_91_funcset__mem
% A new axiom: (forall (X_11:Prop) (F_9:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_12:(Prop->Prop)) (B_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member1710515983_alt_o F_9) ((pi_o_A1302557673_alt_o A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member733327538_alt_o (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_9:((produc1832616231le_alt->Prop)->Prop)), (((member733327538_alt_o F_9) ((pi_Arr1021537730_alt_o A_12) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_9)))->(((member1561882372_alt_o X_11) A_12)->((member1362619835_alt_o (F_9 X_11)) B_9)))) of role axiom named fact_92_funcset__mem
% A new axiom: (forall (X_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_9:((produc1832616231le_alt->Prop)->Prop)), (((member733327538_alt_o F_9) ((pi_Arr1021537730_alt_o A_12) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_9)))->(((member1561882372_alt_o X_11) A_12)->((member1362619835_alt_o (F_9 X_11)) B_9))))
% FOF formula (forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:((produc1832616231le_alt->Prop)->Prop)), (((member1561882372_alt_o F_9) ((pi_Arr418143960_alt_o A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member1362619835_alt_o (F_9 X_11)) B_9)))) of role axiom named fact_93_funcset__mem
% A new axiom: (forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:((produc1832616231le_alt->Prop)->Prop)), (((member1561882372_alt_o F_9) ((pi_Arr418143960_alt_o A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member1362619835_alt_o (F_9 X_11)) B_9))))
% FOF formula (forall (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (I_1:arrow_1092341143e_indi), ((iff ((arrow_1098709355ctator F_8) I_1)) (forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(((eq (produc1832616231le_alt->Prop)) (F_8 X)) (X I_1)))))) of role axiom named fact_94_dictator__def
% A new axiom: (forall (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (I_1:arrow_1092341143e_indi), ((iff ((arrow_1098709355ctator F_8) I_1)) (forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(((eq (produc1832616231le_alt->Prop)) (F_8 X)) (X I_1))))))
% FOF formula (forall (F_7:(produc1832616231le_alt->arrow_1092341143e_indi)) (B_8:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))) (A_11:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member1486844321e_indi F_7) ((pi_Pro1535452471e_indi A_11) B_8)))) of role axiom named fact_95_Pi__I
% A new axiom: (forall (F_7:(produc1832616231le_alt->arrow_1092341143e_indi)) (B_8:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))) (A_11:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member1486844321e_indi F_7) ((pi_Pro1535452471e_indi A_11) B_8))))
% FOF formula (forall (F_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member1208133347e_indi F_7) ((pi_Arr170420797e_indi A_11) B_8)))) of role axiom named fact_96_Pi__I
% A new axiom: (forall (F_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member1208133347e_indi F_7) ((pi_Arr170420797e_indi A_11) B_8))))
% FOF formula (forall (F_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member1754345465lt_o_o F_7) ((pi_Arr1767527177lt_o_o A_11) B_8)))) of role axiom named fact_97_Pi__I
% A new axiom: (forall (F_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member1754345465lt_o_o F_7) ((pi_Arr1767527177lt_o_o A_11) B_8))))
% FOF formula (forall (F_7:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (B_8:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))) (A_11:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member1255309082e_indi F_7) ((pi_Pro1340600692e_indi A_11) B_8)))) of role axiom named fact_98_Pi__I
% A new axiom: (forall (F_7:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (B_8:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))) (A_11:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member1255309082e_indi F_7) ((pi_Pro1340600692e_indi A_11) B_8))))
% FOF formula (forall (F_7:((produc1832616231le_alt->Prop)->Prop)) (B_8:((produc1832616231le_alt->Prop)->(Prop->Prop))) (A_11:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member1949484546lt_o_o F_7) ((pi_Pro410810898lt_o_o A_11) B_8)))) of role axiom named fact_99_Pi__I
% A new axiom: (forall (F_7:((produc1832616231le_alt->Prop)->Prop)) (B_8:((produc1832616231le_alt->Prop)->(Prop->Prop))) (A_11:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member1949484546lt_o_o F_7) ((pi_Pro410810898lt_o_o A_11) B_8))))
% FOF formula (forall (F_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_8:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member986213183e_indi F_7) ((pi_Arr1941314005e_indi A_11) B_8)))) of role axiom named fact_100_Pi__I
% A new axiom: (forall (F_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_8:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member986213183e_indi F_7) ((pi_Arr1941314005e_indi A_11) B_8))))
% FOF formula (forall (F_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_8:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member903234717lt_o_o F_7) ((pi_Arr1422400881lt_o_o A_11) B_8)))) of role axiom named fact_101_Pi__I
% A new axiom: (forall (F_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_8:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member903234717lt_o_o F_7) ((pi_Arr1422400881lt_o_o A_11) B_8))))
% FOF formula (forall (F_7:(arrow_1092341143e_indi->produc1832616231le_alt)) (B_8:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member545531028le_alt (F_7 X)) (B_8 X))))->((member1621875105le_alt F_7) ((pi_Arr1055270199le_alt A_11) B_8)))) of role axiom named fact_102_Pi__I
% A new axiom: (forall (F_7:(arrow_1092341143e_indi->produc1832616231le_alt)) (B_8:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member545531028le_alt (F_7 X)) (B_8 X))))->((member1621875105le_alt F_7) ((pi_Arr1055270199le_alt A_11) B_8))))
% FOF formula (forall (F_7:(Prop->produc1832616231le_alt)) (B_8:(Prop->(produc1832616231le_alt->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member545531028le_alt (F_7 X)) (B_8 X))))->((member1368218865le_alt F_7) ((pi_o_P988780107le_alt A_11) B_8)))) of role axiom named fact_103_Pi__I
% A new axiom: (forall (F_7:(Prop->produc1832616231le_alt)) (B_8:(Prop->(produc1832616231le_alt->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member545531028le_alt (F_7 X)) (B_8 X))))->((member1368218865le_alt F_7) ((pi_o_P988780107le_alt A_11) B_8))))
% FOF formula (forall (F_7:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_8:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member1561882372_alt_o (F_7 X)) (B_8 X))))->((member1079651021_alt_o F_7) ((pi_Arr651234977_alt_o A_11) B_8)))) of role axiom named fact_104_Pi__I
% A new axiom: (forall (F_7:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_8:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member1561882372_alt_o (F_7 X)) (B_8 X))))->((member1079651021_alt_o F_7) ((pi_Arr651234977_alt_o A_11) B_8))))
% FOF formula (forall (F_7:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_8:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member1561882372_alt_o (F_7 X)) (B_8 X))))->((member537117565_alt_o F_7) ((pi_o_A71242893_alt_o A_11) B_8)))) of role axiom named fact_105_Pi__I
% A new axiom: (forall (F_7:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_8:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member1561882372_alt_o (F_7 X)) (B_8 X))))->((member537117565_alt_o F_7) ((pi_o_A71242893_alt_o A_11) B_8))))
% FOF formula (forall (F_7:(Prop->(produc1832616231le_alt->Prop))) (B_8:(Prop->((produc1832616231le_alt->Prop)->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member1362619835_alt_o (F_7 X)) (B_8 X))))->((member1099673524_alt_o F_7) ((pi_o_P1538584260_alt_o A_11) B_8)))) of role axiom named fact_106_Pi__I
% A new axiom: (forall (F_7:(Prop->(produc1832616231le_alt->Prop))) (B_8:(Prop->((produc1832616231le_alt->Prop)->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member1362619835_alt_o (F_7 X)) (B_8 X))))->((member1099673524_alt_o F_7) ((pi_o_P1538584260_alt_o A_11) B_8))))
% FOF formula (forall (F_7:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_8:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member733327538_alt_o (F_7 X)) (B_8 X))))->((member24189887_alt_o F_7) ((pi_Arr1140519125_alt_o A_11) B_8)))) of role axiom named fact_107_Pi__I
% A new axiom: (forall (F_7:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_8:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member733327538_alt_o (F_7 X)) (B_8 X))))->((member24189887_alt_o F_7) ((pi_Arr1140519125_alt_o A_11) B_8))))
% FOF formula (forall (F_7:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_8:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member733327538_alt_o (F_7 X)) (B_8 X))))->((member1710515983_alt_o F_7) ((pi_o_A1302557673_alt_o A_11) B_8)))) of role axiom named fact_108_Pi__I
% A new axiom: (forall (F_7:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_8:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member733327538_alt_o (F_7 X)) (B_8 X))))->((member1710515983_alt_o F_7) ((pi_o_A1302557673_alt_o A_11) B_8))))
% FOF formula (forall (F_7:(produc1832616231le_alt->Prop)) (B_8:(produc1832616231le_alt->(Prop->Prop))) (A_11:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member1362619835_alt_o F_7) ((pi_Pro539263375_alt_o A_11) B_8)))) of role axiom named fact_109_Pi__I
% A new axiom: (forall (F_7:(produc1832616231le_alt->Prop)) (B_8:(produc1832616231le_alt->(Prop->Prop))) (A_11:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member1362619835_alt_o F_7) ((pi_Pro539263375_alt_o A_11) B_8))))
% FOF formula (forall (F_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (B_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))) (A_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_11)->((member1362619835_alt_o (F_7 X)) (B_8 X))))->((member733327538_alt_o F_7) ((pi_Arr1021537730_alt_o A_11) B_8)))) of role axiom named fact_110_Pi__I
% A new axiom: (forall (F_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (B_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))) (A_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_11)->((member1362619835_alt_o (F_7 X)) (B_8 X))))->((member733327538_alt_o F_7) ((pi_Arr1021537730_alt_o A_11) B_8))))
% FOF formula (forall (F_7:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (B_8:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member1362619835_alt_o (F_7 X)) (B_8 X))))->((member1561882372_alt_o F_7) ((pi_Arr418143960_alt_o A_11) B_8)))) of role axiom named fact_111_Pi__I
% A new axiom: (forall (F_7:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (B_8:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member1362619835_alt_o (F_7 X)) (B_8 X))))->((member1561882372_alt_o F_7) ((pi_Arr418143960_alt_o A_11) B_8))))
% FOF formula (forall (F_6:(produc1832616231le_alt->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member1486844321e_indi F_6) ((pi_Pro1535452471e_indi A_10) (fun (Uu:produc1832616231le_alt)=> B_7))))) of role axiom named fact_112_funcsetI
% A new axiom: (forall (F_6:(produc1832616231le_alt->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member1486844321e_indi F_6) ((pi_Pro1535452471e_indi A_10) (fun (Uu:produc1832616231le_alt)=> B_7)))))
% FOF formula (forall (F_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member1208133347e_indi F_6) ((pi_Arr170420797e_indi A_10) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_7))))) of role axiom named fact_113_funcsetI
% A new axiom: (forall (F_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member1208133347e_indi F_6) ((pi_Arr170420797e_indi A_10) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_7)))))
% FOF formula (forall (F_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_7:(Prop->Prop)) (A_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_10)->((member_o (F_6 X)) B_7)))->((member1754345465lt_o_o F_6) ((pi_Arr1767527177lt_o_o A_10) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_7))))) of role axiom named fact_114_funcsetI
% A new axiom: (forall (F_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_7:(Prop->Prop)) (A_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_10)->((member_o (F_6 X)) B_7)))->((member1754345465lt_o_o F_6) ((pi_Arr1767527177lt_o_o A_10) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_7)))))
% FOF formula (forall (F_6:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member1255309082e_indi F_6) ((pi_Pro1340600692e_indi A_10) (fun (Uu:(produc1832616231le_alt->Prop))=> B_7))))) of role axiom named fact_115_funcsetI
% A new axiom: (forall (F_6:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member1255309082e_indi F_6) ((pi_Pro1340600692e_indi A_10) (fun (Uu:(produc1832616231le_alt->Prop))=> B_7)))))
% FOF formula (forall (F_6:((produc1832616231le_alt->Prop)->Prop)) (B_7:(Prop->Prop)) (A_10:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_10)->((member_o (F_6 X)) B_7)))->((member1949484546lt_o_o F_6) ((pi_Pro410810898lt_o_o A_10) (fun (Uu:(produc1832616231le_alt->Prop))=> B_7))))) of role axiom named fact_116_funcsetI
% A new axiom: (forall (F_6:((produc1832616231le_alt->Prop)->Prop)) (B_7:(Prop->Prop)) (A_10:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_10)->((member_o (F_6 X)) B_7)))->((member1949484546lt_o_o F_6) ((pi_Pro410810898lt_o_o A_10) (fun (Uu:(produc1832616231le_alt->Prop))=> B_7)))))
% FOF formula (forall (F_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member986213183e_indi F_6) ((pi_Arr1941314005e_indi A_10) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_7))))) of role axiom named fact_117_funcsetI
% A new axiom: (forall (F_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member986213183e_indi F_6) ((pi_Arr1941314005e_indi A_10) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_7)))))
% FOF formula (forall (F_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_7:(Prop->Prop)) (A_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_10)->((member_o (F_6 X)) B_7)))->((member903234717lt_o_o F_6) ((pi_Arr1422400881lt_o_o A_10) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_7))))) of role axiom named fact_118_funcsetI
% A new axiom: (forall (F_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_7:(Prop->Prop)) (A_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_10)->((member_o (F_6 X)) B_7)))->((member903234717lt_o_o F_6) ((pi_Arr1422400881lt_o_o A_10) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_7)))))
% FOF formula (forall (F_6:(arrow_1092341143e_indi->produc1832616231le_alt)) (B_7:(produc1832616231le_alt->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member545531028le_alt (F_6 X)) B_7)))->((member1621875105le_alt F_6) ((pi_Arr1055270199le_alt A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7))))) of role axiom named fact_119_funcsetI
% A new axiom: (forall (F_6:(arrow_1092341143e_indi->produc1832616231le_alt)) (B_7:(produc1832616231le_alt->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member545531028le_alt (F_6 X)) B_7)))->((member1621875105le_alt F_6) ((pi_Arr1055270199le_alt A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7)))))
% FOF formula (forall (F_6:(Prop->produc1832616231le_alt)) (B_7:(produc1832616231le_alt->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member545531028le_alt (F_6 X)) B_7)))->((member1368218865le_alt F_6) ((pi_o_P988780107le_alt A_10) (fun (Uu:Prop)=> B_7))))) of role axiom named fact_120_funcsetI
% A new axiom: (forall (F_6:(Prop->produc1832616231le_alt)) (B_7:(produc1832616231le_alt->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member545531028le_alt (F_6 X)) B_7)))->((member1368218865le_alt F_6) ((pi_o_P988780107le_alt A_10) (fun (Uu:Prop)=> B_7)))))
% FOF formula (forall (F_6:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member1561882372_alt_o (F_6 X)) B_7)))->((member1079651021_alt_o F_6) ((pi_Arr651234977_alt_o A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7))))) of role axiom named fact_121_funcsetI
% A new axiom: (forall (F_6:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member1561882372_alt_o (F_6 X)) B_7)))->((member1079651021_alt_o F_6) ((pi_Arr651234977_alt_o A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7)))))
% FOF formula (forall (F_6:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member1561882372_alt_o (F_6 X)) B_7)))->((member537117565_alt_o F_6) ((pi_o_A71242893_alt_o A_10) (fun (Uu:Prop)=> B_7))))) of role axiom named fact_122_funcsetI
% A new axiom: (forall (F_6:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member1561882372_alt_o (F_6 X)) B_7)))->((member537117565_alt_o F_6) ((pi_o_A71242893_alt_o A_10) (fun (Uu:Prop)=> B_7)))))
% FOF formula (forall (F_6:(Prop->(produc1832616231le_alt->Prop))) (B_7:((produc1832616231le_alt->Prop)->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member1362619835_alt_o (F_6 X)) B_7)))->((member1099673524_alt_o F_6) ((pi_o_P1538584260_alt_o A_10) (fun (Uu:Prop)=> B_7))))) of role axiom named fact_123_funcsetI
% A new axiom: (forall (F_6:(Prop->(produc1832616231le_alt->Prop))) (B_7:((produc1832616231le_alt->Prop)->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member1362619835_alt_o (F_6 X)) B_7)))->((member1099673524_alt_o F_6) ((pi_o_P1538584260_alt_o A_10) (fun (Uu:Prop)=> B_7)))))
% FOF formula (forall (F_6:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member733327538_alt_o (F_6 X)) B_7)))->((member24189887_alt_o F_6) ((pi_Arr1140519125_alt_o A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7))))) of role axiom named fact_124_funcsetI
% A new axiom: (forall (F_6:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member733327538_alt_o (F_6 X)) B_7)))->((member24189887_alt_o F_6) ((pi_Arr1140519125_alt_o A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7)))))
% FOF formula (forall (F_6:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member733327538_alt_o (F_6 X)) B_7)))->((member1710515983_alt_o F_6) ((pi_o_A1302557673_alt_o A_10) (fun (Uu:Prop)=> B_7))))) of role axiom named fact_125_funcsetI
% A new axiom: (forall (F_6:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member733327538_alt_o (F_6 X)) B_7)))->((member1710515983_alt_o F_6) ((pi_o_A1302557673_alt_o A_10) (fun (Uu:Prop)=> B_7)))))
% FOF formula (forall (F_6:(produc1832616231le_alt->Prop)) (B_7:(Prop->Prop)) (A_10:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_10)->((member_o (F_6 X)) B_7)))->((member1362619835_alt_o F_6) ((pi_Pro539263375_alt_o A_10) (fun (Uu:produc1832616231le_alt)=> B_7))))) of role axiom named fact_126_funcsetI
% A new axiom: (forall (F_6:(produc1832616231le_alt->Prop)) (B_7:(Prop->Prop)) (A_10:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_10)->((member_o (F_6 X)) B_7)))->((member1362619835_alt_o F_6) ((pi_Pro539263375_alt_o A_10) (fun (Uu:produc1832616231le_alt)=> B_7)))))
% FOF formula (forall (F_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (B_7:((produc1832616231le_alt->Prop)->Prop)) (A_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_10)->((member1362619835_alt_o (F_6 X)) B_7)))->((member733327538_alt_o F_6) ((pi_Arr1021537730_alt_o A_10) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_7))))) of role axiom named fact_127_funcsetI
% A new axiom: (forall (F_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (B_7:((produc1832616231le_alt->Prop)->Prop)) (A_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_10)->((member1362619835_alt_o (F_6 X)) B_7)))->((member733327538_alt_o F_6) ((pi_Arr1021537730_alt_o A_10) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_7)))))
% FOF formula (forall (F_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (B_7:((produc1832616231le_alt->Prop)->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member1362619835_alt_o (F_6 X)) B_7)))->((member1561882372_alt_o F_6) ((pi_Arr418143960_alt_o A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7))))) of role axiom named fact_128_funcsetI
% A new axiom: (forall (F_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (B_7:((produc1832616231le_alt->Prop)->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member1362619835_alt_o (F_6 X)) B_7)))->((member1561882372_alt_o F_6) ((pi_Arr418143960_alt_o A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7)))))
% FOF formula ((ex (produc1832616231le_alt->Prop)) (fun (L:(produc1832616231le_alt->Prop))=> ((member1362619835_alt_o L) arrow_1751445586le_Lin))) of role axiom named fact_129_linear__alt
% A new axiom: ((ex (produc1832616231le_alt->Prop)) (fun (L:(produc1832616231le_alt->Prop))=> ((member1362619835_alt_o L) arrow_1751445586le_Lin)))
% FOF formula (forall (F_5:(produc1832616231le_alt->arrow_1092341143e_indi)) (B_6:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))) (A_9:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member1486844321e_indi F_5) ((pi_Pro1535452471e_indi A_9) B_6)))) of role axiom named fact_130_Pi__I_H
% A new axiom: (forall (F_5:(produc1832616231le_alt->arrow_1092341143e_indi)) (B_6:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))) (A_9:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member1486844321e_indi F_5) ((pi_Pro1535452471e_indi A_9) B_6))))
% FOF formula (forall (F_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member1208133347e_indi F_5) ((pi_Arr170420797e_indi A_9) B_6)))) of role axiom named fact_131_Pi__I_H
% A new axiom: (forall (F_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member1208133347e_indi F_5) ((pi_Arr170420797e_indi A_9) B_6))))
% FOF formula (forall (F_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member1754345465lt_o_o F_5) ((pi_Arr1767527177lt_o_o A_9) B_6)))) of role axiom named fact_132_Pi__I_H
% A new axiom: (forall (F_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member1754345465lt_o_o F_5) ((pi_Arr1767527177lt_o_o A_9) B_6))))
% FOF formula (forall (F_5:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (B_6:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))) (A_9:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member1255309082e_indi F_5) ((pi_Pro1340600692e_indi A_9) B_6)))) of role axiom named fact_133_Pi__I_H
% A new axiom: (forall (F_5:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (B_6:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))) (A_9:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member1255309082e_indi F_5) ((pi_Pro1340600692e_indi A_9) B_6))))
% FOF formula (forall (F_5:((produc1832616231le_alt->Prop)->Prop)) (B_6:((produc1832616231le_alt->Prop)->(Prop->Prop))) (A_9:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member1949484546lt_o_o F_5) ((pi_Pro410810898lt_o_o A_9) B_6)))) of role axiom named fact_134_Pi__I_H
% A new axiom: (forall (F_5:((produc1832616231le_alt->Prop)->Prop)) (B_6:((produc1832616231le_alt->Prop)->(Prop->Prop))) (A_9:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member1949484546lt_o_o F_5) ((pi_Pro410810898lt_o_o A_9) B_6))))
% FOF formula (forall (F_5:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member986213183e_indi F_5) ((pi_Arr1941314005e_indi A_9) B_6)))) of role axiom named fact_135_Pi__I_H
% A new axiom: (forall (F_5:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member986213183e_indi F_5) ((pi_Arr1941314005e_indi A_9) B_6))))
% FOF formula (forall (F_5:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member903234717lt_o_o F_5) ((pi_Arr1422400881lt_o_o A_9) B_6)))) of role axiom named fact_136_Pi__I_H
% A new axiom: (forall (F_5:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member903234717lt_o_o F_5) ((pi_Arr1422400881lt_o_o A_9) B_6))))
% FOF formula (forall (F_5:(arrow_1092341143e_indi->produc1832616231le_alt)) (B_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member545531028le_alt (F_5 X)) (B_6 X))))->((member1621875105le_alt F_5) ((pi_Arr1055270199le_alt A_9) B_6)))) of role axiom named fact_137_Pi__I_H
% A new axiom: (forall (F_5:(arrow_1092341143e_indi->produc1832616231le_alt)) (B_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member545531028le_alt (F_5 X)) (B_6 X))))->((member1621875105le_alt F_5) ((pi_Arr1055270199le_alt A_9) B_6))))
% FOF formula (forall (F_5:(Prop->produc1832616231le_alt)) (B_6:(Prop->(produc1832616231le_alt->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member545531028le_alt (F_5 X)) (B_6 X))))->((member1368218865le_alt F_5) ((pi_o_P988780107le_alt A_9) B_6)))) of role axiom named fact_138_Pi__I_H
% A new axiom: (forall (F_5:(Prop->produc1832616231le_alt)) (B_6:(Prop->(produc1832616231le_alt->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member545531028le_alt (F_5 X)) (B_6 X))))->((member1368218865le_alt F_5) ((pi_o_P988780107le_alt A_9) B_6))))
% FOF formula (forall (F_5:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_6:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member1561882372_alt_o (F_5 X)) (B_6 X))))->((member1079651021_alt_o F_5) ((pi_Arr651234977_alt_o A_9) B_6)))) of role axiom named fact_139_Pi__I_H
% A new axiom: (forall (F_5:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_6:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member1561882372_alt_o (F_5 X)) (B_6 X))))->((member1079651021_alt_o F_5) ((pi_Arr651234977_alt_o A_9) B_6))))
% FOF formula (forall (F_5:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_6:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member1561882372_alt_o (F_5 X)) (B_6 X))))->((member537117565_alt_o F_5) ((pi_o_A71242893_alt_o A_9) B_6)))) of role axiom named fact_140_Pi__I_H
% A new axiom: (forall (F_5:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_6:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member1561882372_alt_o (F_5 X)) (B_6 X))))->((member537117565_alt_o F_5) ((pi_o_A71242893_alt_o A_9) B_6))))
% FOF formula (forall (F_5:(Prop->(produc1832616231le_alt->Prop))) (B_6:(Prop->((produc1832616231le_alt->Prop)->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member1362619835_alt_o (F_5 X)) (B_6 X))))->((member1099673524_alt_o F_5) ((pi_o_P1538584260_alt_o A_9) B_6)))) of role axiom named fact_141_Pi__I_H
% A new axiom: (forall (F_5:(Prop->(produc1832616231le_alt->Prop))) (B_6:(Prop->((produc1832616231le_alt->Prop)->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member1362619835_alt_o (F_5 X)) (B_6 X))))->((member1099673524_alt_o F_5) ((pi_o_P1538584260_alt_o A_9) B_6))))
% FOF formula (forall (F_5:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_6:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member733327538_alt_o (F_5 X)) (B_6 X))))->((member24189887_alt_o F_5) ((pi_Arr1140519125_alt_o A_9) B_6)))) of role axiom named fact_142_Pi__I_H
% A new axiom: (forall (F_5:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_6:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member733327538_alt_o (F_5 X)) (B_6 X))))->((member24189887_alt_o F_5) ((pi_Arr1140519125_alt_o A_9) B_6))))
% FOF formula (forall (F_5:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_6:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member733327538_alt_o (F_5 X)) (B_6 X))))->((member1710515983_alt_o F_5) ((pi_o_A1302557673_alt_o A_9) B_6)))) of role axiom named fact_143_Pi__I_H
% A new axiom: (forall (F_5:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_6:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member733327538_alt_o (F_5 X)) (B_6 X))))->((member1710515983_alt_o F_5) ((pi_o_A1302557673_alt_o A_9) B_6))))
% FOF formula (forall (F_5:(produc1832616231le_alt->Prop)) (B_6:(produc1832616231le_alt->(Prop->Prop))) (A_9:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member1362619835_alt_o F_5) ((pi_Pro539263375_alt_o A_9) B_6)))) of role axiom named fact_144_Pi__I_H
% A new axiom: (forall (F_5:(produc1832616231le_alt->Prop)) (B_6:(produc1832616231le_alt->(Prop->Prop))) (A_9:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member1362619835_alt_o F_5) ((pi_Pro539263375_alt_o A_9) B_6))))
% FOF formula (forall (F_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (B_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))) (A_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_9)->((member1362619835_alt_o (F_5 X)) (B_6 X))))->((member733327538_alt_o F_5) ((pi_Arr1021537730_alt_o A_9) B_6)))) of role axiom named fact_145_Pi__I_H
% A new axiom: (forall (F_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (B_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))) (A_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_9)->((member1362619835_alt_o (F_5 X)) (B_6 X))))->((member733327538_alt_o F_5) ((pi_Arr1021537730_alt_o A_9) B_6))))
% FOF formula (forall (F_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (B_6:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member1362619835_alt_o (F_5 X)) (B_6 X))))->((member1561882372_alt_o F_5) ((pi_Arr418143960_alt_o A_9) B_6)))) of role axiom named fact_146_Pi__I_H
% A new axiom: (forall (F_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (B_6:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member1362619835_alt_o (F_5 X)) (B_6 X))))->((member1561882372_alt_o F_5) ((pi_Arr418143960_alt_o A_9) B_6))))
% FOF formula (forall (B_5:(produc1832616231le_alt->(Prop->Prop))) (G:(produc1832616231le_alt->Prop)) (F_4:(produc1832616231le_alt->Prop)) (A_8:(produc1832616231le_alt->Prop)), ((forall (W:produc1832616231le_alt), (((member545531028le_alt W) A_8)->((iff (F_4 W)) (G W))))->((iff ((member1362619835_alt_o F_4) ((pi_Pro539263375_alt_o A_8) B_5))) ((member1362619835_alt_o G) ((pi_Pro539263375_alt_o A_8) B_5))))) of role axiom named fact_147_Pi__cong
% A new axiom: (forall (B_5:(produc1832616231le_alt->(Prop->Prop))) (G:(produc1832616231le_alt->Prop)) (F_4:(produc1832616231le_alt->Prop)) (A_8:(produc1832616231le_alt->Prop)), ((forall (W:produc1832616231le_alt), (((member545531028le_alt W) A_8)->((iff (F_4 W)) (G W))))->((iff ((member1362619835_alt_o F_4) ((pi_Pro539263375_alt_o A_8) B_5))) ((member1362619835_alt_o G) ((pi_Pro539263375_alt_o A_8) B_5)))))
% FOF formula (forall (B_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))) (F_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (G:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (W:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o W) A_8)->(((eq (produc1832616231le_alt->Prop)) (F_4 W)) (G W))))->((iff ((member733327538_alt_o F_4) ((pi_Arr1021537730_alt_o A_8) B_5))) ((member733327538_alt_o G) ((pi_Arr1021537730_alt_o A_8) B_5))))) of role axiom named fact_148_Pi__cong
% A new axiom: (forall (B_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))) (F_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (G:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (W:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o W) A_8)->(((eq (produc1832616231le_alt->Prop)) (F_4 W)) (G W))))->((iff ((member733327538_alt_o F_4) ((pi_Arr1021537730_alt_o A_8) B_5))) ((member733327538_alt_o G) ((pi_Arr1021537730_alt_o A_8) B_5)))))
% FOF formula (forall (B_5:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))) (F_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (G:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_8:(arrow_1092341143e_indi->Prop)), ((forall (W:arrow_1092341143e_indi), (((member1714766084e_indi W) A_8)->(((eq (produc1832616231le_alt->Prop)) (F_4 W)) (G W))))->((iff ((member1561882372_alt_o F_4) ((pi_Arr418143960_alt_o A_8) B_5))) ((member1561882372_alt_o G) ((pi_Arr418143960_alt_o A_8) B_5))))) of role axiom named fact_149_Pi__cong
% A new axiom: (forall (B_5:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))) (F_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (G:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_8:(arrow_1092341143e_indi->Prop)), ((forall (W:arrow_1092341143e_indi), (((member1714766084e_indi W) A_8)->(((eq (produc1832616231le_alt->Prop)) (F_4 W)) (G W))))->((iff ((member1561882372_alt_o F_4) ((pi_Arr418143960_alt_o A_8) B_5))) ((member1561882372_alt_o G) ((pi_Arr418143960_alt_o A_8) B_5)))))
% FOF formula (forall (V:arrow_1346734812le_alt) (Va:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt V) Va)) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt V) Va))) of role axiom named fact_150_splice_Osimps_I2_J
% A new axiom: (forall (V:arrow_1346734812le_alt) (Va:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt V) Va)) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt V) Va)))
% FOF formula (forall (X_10:arrow_1346734812le_alt) (Xs_8:list_A1528105233le_alt) (Y_3:arrow_1346734812le_alt) (Ys_1:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt X_10) Xs_8)) ((cons_A1100118844le_alt Y_3) Ys_1))) ((cons_A1100118844le_alt X_10) ((cons_A1100118844le_alt Y_3) ((splice244790623le_alt Xs_8) Ys_1))))) of role axiom named fact_151_splice_Osimps_I3_J
% A new axiom: (forall (X_10:arrow_1346734812le_alt) (Xs_8:list_A1528105233le_alt) (Y_3:arrow_1346734812le_alt) (Ys_1:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt X_10) Xs_8)) ((cons_A1100118844le_alt Y_3) Ys_1))) ((cons_A1100118844le_alt X_10) ((cons_A1100118844le_alt Y_3) ((splice244790623le_alt Xs_8) Ys_1)))))
% FOF formula (forall (Ys:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt nil_Ar10086284le_alt) Ys)) Ys)) of role axiom named fact_152_splice_Osimps_I1_J
% A new axiom: (forall (Ys:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt nil_Ar10086284le_alt) Ys)) Ys))
% FOF formula (forall (Xs_7:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt Xs_7) nil_Ar10086284le_alt)) Xs_7)) of role axiom named fact_153_splice__Nil2
% A new axiom: (forall (Xs_7:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt Xs_7) nil_Ar10086284le_alt)) Xs_7))
% FOF formula (forall (S:(produc1832616231le_alt->Prop)) (R:(produc1832616231le_alt->Prop)), ((iff (forall (X:arrow_1346734812le_alt) (Xa:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X) Xa)) R)) ((member545531028le_alt ((produc990411159le_alt X) Xa)) S)))) (((eq (produc1832616231le_alt->Prop)) R) S))) of role axiom named fact_154_pred__equals__eq2
% A new axiom: (forall (S:(produc1832616231le_alt->Prop)) (R:(produc1832616231le_alt->Prop)), ((iff (forall (X:arrow_1346734812le_alt) (Xa:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X) Xa)) R)) ((member545531028le_alt ((produc990411159le_alt X) Xa)) S)))) (((eq (produc1832616231le_alt->Prop)) R) S)))
% FOF formula (forall (Y_2:produc1832616231le_alt), ((forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), (not (((eq produc1832616231le_alt) Y_2) ((produc990411159le_alt A_7) B_4))))->False)) of role axiom named fact_155_prod_Oexhaust
% A new axiom: (forall (Y_2:produc1832616231le_alt), ((forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), (not (((eq produc1832616231le_alt) Y_2) ((produc990411159le_alt A_7) B_4))))->False))
% FOF formula (forall (P_3:produc1832616231le_alt), ((forall (X:arrow_1346734812le_alt) (Y_1:arrow_1346734812le_alt), (not (((eq produc1832616231le_alt) P_3) ((produc990411159le_alt X) Y_1))))->False)) of role axiom named fact_156_PairE
% A new axiom: (forall (P_3:produc1832616231le_alt), ((forall (X:arrow_1346734812le_alt) (Y_1:arrow_1346734812le_alt), (not (((eq produc1832616231le_alt) P_3) ((produc990411159le_alt X) Y_1))))->False))
% FOF formula (forall (P_2:(produc1832616231le_alt->Prop)), ((iff (_TPTP_ex P_2)) ((ex arrow_1346734812le_alt) (fun (A_7:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (B_4:arrow_1346734812le_alt)=> (P_2 ((produc990411159le_alt A_7) B_4)))))))) of role axiom named fact_157_split__paired__Ex
% A new axiom: (forall (P_2:(produc1832616231le_alt->Prop)), ((iff (_TPTP_ex P_2)) ((ex arrow_1346734812le_alt) (fun (A_7:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (B_4:arrow_1346734812le_alt)=> (P_2 ((produc990411159le_alt A_7) B_4))))))))
% FOF formula (forall (X_9:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) ((insert844458914le_alt X_9) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt X_9) nil_Ar10086284le_alt))) of role axiom named fact_158_insert__Nil
% A new axiom: (forall (X_9:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) ((insert844458914le_alt X_9) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt X_9) nil_Ar10086284le_alt)))
% FOF formula (forall (X_8:arrow_1346734812le_alt) (Xs_6:list_A1528105233le_alt), ((distin1107700095le_alt Xs_6)->(distin1107700095le_alt ((insert844458914le_alt X_8) Xs_6)))) of role axiom named fact_159_distinct__insert
% A new axiom: (forall (X_8:arrow_1346734812le_alt) (Xs_6:list_A1528105233le_alt), ((distin1107700095le_alt Xs_6)->(distin1107700095le_alt ((insert844458914le_alt X_8) Xs_6))))
% FOF formula (forall (X_7:arrow_1092341143e_indi) (A_6:(arrow_1092341143e_indi->Prop)), ((iff ((member1714766084e_indi X_7) A_6)) (A_6 X_7))) of role axiom named fact_160_mem__def
% A new axiom: (forall (X_7:arrow_1092341143e_indi) (A_6:(arrow_1092341143e_indi->Prop)), ((iff ((member1714766084e_indi X_7) A_6)) (A_6 X_7)))
% FOF formula (forall (X_7:Prop) (A_6:(Prop->Prop)), ((iff ((member_o X_7) A_6)) (A_6 X_7))) of role axiom named fact_161_mem__def
% A new axiom: (forall (X_7:Prop) (A_6:(Prop->Prop)), ((iff ((member_o X_7) A_6)) (A_6 X_7)))
% FOF formula (forall (X_7:produc1832616231le_alt) (A_6:(produc1832616231le_alt->Prop)), ((iff ((member545531028le_alt X_7) A_6)) (A_6 X_7))) of role axiom named fact_162_mem__def
% A new axiom: (forall (X_7:produc1832616231le_alt) (A_6:(produc1832616231le_alt->Prop)), ((iff ((member545531028le_alt X_7) A_6)) (A_6 X_7)))
% FOF formula (forall (X_7:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((iff ((member1561882372_alt_o X_7) A_6)) (A_6 X_7))) of role axiom named fact_163_mem__def
% A new axiom: (forall (X_7:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((iff ((member1561882372_alt_o X_7) A_6)) (A_6 X_7)))
% FOF formula (forall (X_7:(produc1832616231le_alt->Prop)) (A_6:((produc1832616231le_alt->Prop)->Prop)), ((iff ((member1362619835_alt_o X_7) A_6)) (A_6 X_7))) of role axiom named fact_164_mem__def
% A new axiom: (forall (X_7:(produc1832616231le_alt->Prop)) (A_6:((produc1832616231le_alt->Prop)->Prop)), ((iff ((member1362619835_alt_o X_7) A_6)) (A_6 X_7)))
% FOF formula (forall (X_7:((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_7) A_6)) (A_6 X_7))) of role axiom named fact_165_mem__def
% A new axiom: (forall (X_7:((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_7) A_6)) (A_6 X_7)))
% FOF formula (forall (P_1:(arrow_1092341143e_indi->Prop)), (((eq (arrow_1092341143e_indi->Prop)) (collec1832628290e_indi P_1)) P_1)) of role axiom named fact_166_Collect__def
% A new axiom: (forall (P_1:(arrow_1092341143e_indi->Prop)), (((eq (arrow_1092341143e_indi->Prop)) (collec1832628290e_indi P_1)) P_1))
% FOF formula (forall (P:(list_A1528105233le_alt->Prop)) (Xs_4:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_4) nil_Ar10086284le_alt))->((forall (X:arrow_1346734812le_alt), (P ((cons_A1100118844le_alt X) nil_Ar10086284le_alt)))->((forall (X:arrow_1346734812le_alt) (Xs_5:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_5) nil_Ar10086284le_alt))->((P Xs_5)->(P ((cons_A1100118844le_alt X) Xs_5)))))->(P Xs_4))))) of role axiom named fact_167_list__nonempty__induct
% A new axiom: (forall (P:(list_A1528105233le_alt->Prop)) (Xs_4:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_4) nil_Ar10086284le_alt))->((forall (X:arrow_1346734812le_alt), (P ((cons_A1100118844le_alt X) nil_Ar10086284le_alt)))->((forall (X:arrow_1346734812le_alt) (Xs_5:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_5) nil_Ar10086284le_alt))->((P Xs_5)->(P ((cons_A1100118844le_alt X) Xs_5)))))->(P Xs_4)))))
% FOF formula (forall (X:(produc1832616231le_alt->Prop)) (Xa:arrow_1346734812le_alt) (Xb:arrow_1346734812le_alt), ((iff (((produc443407182_alt_o X) Xa) Xb)) (X ((produc990411159le_alt Xa) Xb)))) of role axiom named fact_168_curry__def
% A new axiom: (forall (X:(produc1832616231le_alt->Prop)) (Xa:arrow_1346734812le_alt) (Xb:arrow_1346734812le_alt), ((iff (((produc443407182_alt_o X) Xa) Xb)) (X ((produc990411159le_alt Xa) Xb))))
% FOF formula (forall (F_3:(produc1832616231le_alt->Prop)) (A_5:arrow_1346734812le_alt) (B_3:arrow_1346734812le_alt), ((F_3 ((produc990411159le_alt A_5) B_3))->(((produc443407182_alt_o F_3) A_5) B_3))) of role axiom named fact_169_curryI
% A new axiom: (forall (F_3:(produc1832616231le_alt->Prop)) (A_5:arrow_1346734812le_alt) (B_3:arrow_1346734812le_alt), ((F_3 ((produc990411159le_alt A_5) B_3))->(((produc443407182_alt_o F_3) A_5) B_3)))
% FOF formula (forall (F_2:(produc1832616231le_alt->Prop)) (A_4:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt), ((((produc443407182_alt_o F_2) A_4) B_2)->(F_2 ((produc990411159le_alt A_4) B_2)))) of role axiom named fact_170_curryE
% A new axiom: (forall (F_2:(produc1832616231le_alt->Prop)) (A_4:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt), ((((produc443407182_alt_o F_2) A_4) B_2)->(F_2 ((produc990411159le_alt A_4) B_2))))
% FOF formula (forall (F_1:(produc1832616231le_alt->Prop)) (A_3:arrow_1346734812le_alt) (B_1:arrow_1346734812le_alt), ((((produc443407182_alt_o F_1) A_3) B_1)->(F_1 ((produc990411159le_alt A_3) B_1)))) of role axiom named fact_171_curryD
% A new axiom: (forall (F_1:(produc1832616231le_alt->Prop)) (A_3:arrow_1346734812le_alt) (B_1:arrow_1346734812le_alt), ((((produc443407182_alt_o F_1) A_3) B_1)->(F_1 ((produc990411159le_alt A_3) B_1))))
% FOF formula (forall (F:(produc1832616231le_alt->Prop)) (A_2:arrow_1346734812le_alt) (B:arrow_1346734812le_alt), ((iff (((produc443407182_alt_o F) A_2) B)) (F ((produc990411159le_alt A_2) B)))) of role axiom named fact_172_curry__conv
% A new axiom: (forall (F:(produc1832616231le_alt->Prop)) (A_2:arrow_1346734812le_alt) (B:arrow_1346734812le_alt), ((iff (((produc443407182_alt_o F) A_2) B)) (F ((produc990411159le_alt A_2) B))))
% FOF formula (forall (Xs_3:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Xs_3) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs_3))) of role axiom named fact_173_eq__Nil__null
% A new axiom: (forall (Xs_3:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Xs_3) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs_3)))
% FOF formula (forall (Xs_2:list_A1528105233le_alt), ((iff (null_A244857236le_alt Xs_2)) (((eq list_A1528105233le_alt) Xs_2) nil_Ar10086284le_alt))) of role axiom named fact_174_List_Onull__def
% A new axiom: (forall (Xs_2:list_A1528105233le_alt), ((iff (null_A244857236le_alt Xs_2)) (((eq list_A1528105233le_alt) Xs_2) nil_Ar10086284le_alt)))
% FOF formula (forall (X_6:arrow_1346734812le_alt) (Xs_1:list_A1528105233le_alt), ((null_A244857236le_alt ((cons_A1100118844le_alt X_6) Xs_1))->False)) of role axiom named fact_175_null__rec_I1_J
% A new axiom: (forall (X_6:arrow_1346734812le_alt) (Xs_1:list_A1528105233le_alt), ((null_A244857236le_alt ((cons_A1100118844le_alt X_6) Xs_1))->False))
% FOF formula (null_A244857236le_alt nil_Ar10086284le_alt) of role axiom named fact_176_null__rec_I2_J
% A new axiom: (null_A244857236le_alt nil_Ar10086284le_alt)
% FOF formula (forall (Xs:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt Xs) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs))) of role axiom named fact_177_equal__Nil__null
% A new axiom: (forall (Xs:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt Xs) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs)))
% 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_178_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_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (top_to1049332548lt_o_o X_5)) of role axiom named fact_179_top1I
% A new axiom: (forall (X_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (top_to1049332548lt_o_o X_5))
% FOF formula (forall (X_5:(produc1832616231le_alt->Prop)), (top_to1830848411lt_o_o X_5)) of role axiom named fact_180_top1I
% A new axiom: (forall (X_5:(produc1832616231le_alt->Prop)), (top_to1830848411lt_o_o X_5))
% FOF formula (forall (X_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (top_to790289938lt_o_o X_5)) of role axiom named fact_181_top1I
% A new axiom: (forall (X_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (top_to790289938lt_o_o X_5))
% FOF formula (forall (X_5:produc1832616231le_alt), (top_to679332578_alt_o X_5)) of role axiom named fact_182_top1I
% A new axiom: (forall (X_5:produc1832616231le_alt), (top_to679332578_alt_o X_5))
% FOF formula (forall (X_5:arrow_1092341143e_indi), (top_to527331954indi_o X_5)) of role axiom named fact_183_top1I
% A new axiom: (forall (X_5:arrow_1092341143e_indi), (top_to527331954indi_o X_5))
% FOF formula (forall (A_1:(produc1832616231le_alt->Prop)), (((eq ((produc1832616231le_alt->Prop)->Prop)) ((pi_Pro539263375_alt_o A_1) (fun (Uu:produc1832616231le_alt)=> top_top_o_o))) top_to1830848411lt_o_o)) of role axiom named fact_184_Pi__UNIV
% A new axiom: (forall (A_1:(produc1832616231le_alt->Prop)), (((eq ((produc1832616231le_alt->Prop)->Prop)) ((pi_Pro539263375_alt_o A_1) (fun (Uu:produc1832616231le_alt)=> top_top_o_o))) top_to1830848411lt_o_o))
% FOF formula (forall (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr1021537730_alt_o A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> top_to1830848411lt_o_o))) top_to1049332548lt_o_o)) of role axiom named fact_185_Pi__UNIV
% A new axiom: (forall (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr1021537730_alt_o A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> top_to1830848411lt_o_o))) top_to1049332548lt_o_o))
% FOF formula (forall (A_1:(arrow_1092341143e_indi->Prop)), (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr418143960_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> top_to1830848411lt_o_o))) top_to790289938lt_o_o)) of role axiom named fact_186_Pi__UNIV
% A new axiom: (forall (A_1:(arrow_1092341143e_indi->Prop)), (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr418143960_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> top_to1830848411lt_o_o))) top_to790289938lt_o_o))
% FOF formula (forall (X_4:list_A1528105233le_alt) (Y:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt X_4) Y)) (((eq list_A1528105233le_alt) X_4) Y))) of role axiom named fact_187_equal__list__def
% A new axiom: (forall (X_4:list_A1528105233le_alt) (Y:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt X_4) Y)) (((eq list_A1528105233le_alt) X_4) Y)))
% FOF formula (forall (X_3:Prop), ((member_o X_3) top_top_o_o)) of role axiom named fact_188_iso__tuple__UNIV__I
% A new axiom: (forall (X_3:Prop), ((member_o X_3) top_top_o_o))
% FOF formula (forall (X_3:arrow_1092341143e_indi), ((member1714766084e_indi X_3) top_to527331954indi_o)) of role axiom named fact_189_iso__tuple__UNIV__I
% A new axiom: (forall (X_3:arrow_1092341143e_indi), ((member1714766084e_indi X_3) top_to527331954indi_o))
% FOF formula (forall (X_3:produc1832616231le_alt), ((member545531028le_alt X_3) top_to679332578_alt_o)) of role axiom named fact_190_iso__tuple__UNIV__I
% A new axiom: (forall (X_3:produc1832616231le_alt), ((member545531028le_alt X_3) top_to679332578_alt_o))
% FOF formula (forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_3) top_to790289938lt_o_o)) of role axiom named fact_191_iso__tuple__UNIV__I
% A new axiom: (forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_3) top_to790289938lt_o_o))
% FOF formula (forall (X_3:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_3) top_to1830848411lt_o_o)) of role axiom named fact_192_iso__tuple__UNIV__I
% A new axiom: (forall (X_3:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_3) top_to1830848411lt_o_o))
% FOF formula (forall (X_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_3) top_to1049332548lt_o_o)) of role axiom named fact_193_iso__tuple__UNIV__I
% A new axiom: (forall (X_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_3) top_to1049332548lt_o_o))
% FOF formula (forall (X_2:Prop), ((member_o X_2) top_top_o_o)) of role axiom named fact_194_UNIV__I
% A new axiom: (forall (X_2:Prop), ((member_o X_2) top_top_o_o))
% FOF formula (forall (X_2:arrow_1092341143e_indi), ((member1714766084e_indi X_2) top_to527331954indi_o)) of role axiom named fact_195_UNIV__I
% A new axiom: (forall (X_2:arrow_1092341143e_indi), ((member1714766084e_indi X_2) top_to527331954indi_o))
% FOF formula (forall (X_2:produc1832616231le_alt), ((member545531028le_alt X_2) top_to679332578_alt_o)) of role axiom named fact_196_UNIV__I
% A new axiom: (forall (X_2:produc1832616231le_alt), ((member545531028le_alt X_2) top_to679332578_alt_o))
% FOF formula (forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_2) top_to790289938lt_o_o)) of role axiom named fact_197_UNIV__I
% A new axiom: (forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_2) top_to790289938lt_o_o))
% FOF formula (forall (X_2:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_2) top_to1830848411lt_o_o)) of role axiom named fact_198_UNIV__I
% A new axiom: (forall (X_2:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_2) top_to1830848411lt_o_o))
% FOF formula (forall (X_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_2) top_to1049332548lt_o_o)) of role axiom named fact_199_UNIV__I
% A new axiom: (forall (X_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_2) top_to1049332548lt_o_o))
% FOF formula (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) top_to1049332548lt_o_o) (collec2125720304_alt_o (fun (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> True))) of role axiom named fact_200_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:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> True)))
% FOF formula (((eq ((produc1832616231le_alt->Prop)->Prop)) top_to1830848411lt_o_o) (collec1079683069_alt_o (fun (X:(produc1832616231le_alt->Prop))=> True))) of role axiom named fact_201_UNIV__def
% A new axiom: (((eq ((produc1832616231le_alt->Prop)->Prop)) top_to1830848411lt_o_o) (collec1079683069_alt_o (fun (X:(produc1832616231le_alt->Prop))=> True)))
% FOF formula (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) top_to790289938lt_o_o) (collec1718651462_alt_o (fun (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> True))) of role axiom named fact_202_UNIV__def
% A new axiom: (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) top_to790289938lt_o_o) (collec1718651462_alt_o (fun (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> True)))
% FOF formula (((eq (produc1832616231le_alt->Prop)) top_to679332578_alt_o) (collec1201320914le_alt (fun (X:produc1832616231le_alt)=> True))) of role axiom named fact_203_UNIV__def
% A new axiom: (((eq (produc1832616231le_alt->Prop)) top_to679332578_alt_o) (collec1201320914le_alt (fun (X:produc1832616231le_alt)=> True)))
% FOF formula (((eq (arrow_1092341143e_indi->Prop)) top_to527331954indi_o) (collec1832628290e_indi (fun (X:arrow_1092341143e_indi)=> True))) of role axiom named fact_204_UNIV__def
% A new axiom: (((eq (arrow_1092341143e_indi->Prop)) top_to527331954indi_o) (collec1832628290e_indi (fun (X:arrow_1092341143e_indi)=> True)))
% FOF formula (forall (X_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (top_to1049332548lt_o_o X_1)) top_top_o)) of role axiom named fact_205_top__apply
% A new axiom: (forall (X_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (top_to1049332548lt_o_o X_1)) top_top_o))
% FOF formula (forall (X_1:(produc1832616231le_alt->Prop)), ((iff (top_to1830848411lt_o_o X_1)) top_top_o)) of role axiom named fact_206_top__apply
% A new axiom: (forall (X_1:(produc1832616231le_alt->Prop)), ((iff (top_to1830848411lt_o_o X_1)) top_top_o))
% FOF formula (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((iff (top_to790289938lt_o_o X_1)) top_top_o)) of role axiom named fact_207_top__apply
% A new axiom: (forall (X_1:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((iff (top_to790289938lt_o_o X_1)) top_top_o))
% FOF formula (forall (X_1:produc1832616231le_alt), ((iff (top_to679332578_alt_o X_1)) top_top_o)) of role axiom named fact_208_top__apply
% A new axiom: (forall (X_1:produc1832616231le_alt), ((iff (top_to679332578_alt_o X_1)) top_top_o))
% FOF formula (forall (X_1:arrow_1092341143e_indi), ((iff (top_to527331954indi_o X_1)) top_top_o)) of role axiom named fact_209_top__apply
% A new axiom: (forall (X_1:arrow_1092341143e_indi), ((iff (top_to527331954indi_o X_1)) top_top_o))
% FOF formula (forall (A:(Prop->Prop)), ((forall (X:Prop), ((member_o X) A))->(((eq (Prop->Prop)) top_top_o_o) A))) of role axiom named fact_210_UNIV__eq__I
% A new axiom: (forall (A:(Prop->Prop)), ((forall (X:Prop), ((member_o X) A))->(((eq (Prop->Prop)) top_top_o_o) A)))
% FOF formula (forall (A:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), ((member1714766084e_indi X) A))->(((eq (arrow_1092341143e_indi->Prop)) top_to527331954indi_o) A))) of role axiom named fact_211_UNIV__eq__I
% A new axiom: (forall (A:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), ((member1714766084e_indi X) A))->(((eq (arrow_1092341143e_indi->Prop)) top_to527331954indi_o) A)))
% FOF formula (forall (A:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), ((member545531028le_alt X) A))->(((eq (produc1832616231le_alt->Prop)) top_to679332578_alt_o) A))) of role axiom named fact_212_UNIV__eq__I
% A new axiom: (forall (A:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), ((member545531028le_alt X) A))->(((eq (produc1832616231le_alt->Prop)) top_to679332578_alt_o) A)))
% FOF formula (forall (A:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X) A))->(((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) top_to790289938lt_o_o) A))) of role axiom named fact_213_UNIV__eq__I
% A new axiom: (forall (A:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X) A))->(((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) top_to790289938lt_o_o) A)))
% FOF formula (forall (A:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X) A))->(((eq ((produc1832616231le_alt->Prop)->Prop)) top_to1830848411lt_o_o) A))) of role axiom named fact_214_UNIV__eq__I
% A new axiom: (forall (A:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X) A))->(((eq ((produc1832616231le_alt->Prop)->Prop)) top_to1830848411lt_o_o) A)))
% FOF formula (forall (A:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X) A))->(((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) top_to1049332548lt_o_o) A))) of role axiom named fact_215_UNIV__eq__I
% A new axiom: (forall (A:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X) A))->(((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) top_to1049332548lt_o_o) A)))
% FOF formula (forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt a) b)) (p _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt a) c)) (((arrow_1760938802_below (p _TPTP_I)) c) b)))) of role conjecture named conj_0
% Conjecture to prove = (forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt a) b)) (p _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt a) c)) (((arrow_1760938802_below (p _TPTP_I)) c) b)))):Prop
% Parameter arrow_1092341143e_indi_DUMMY:arrow_1092341143e_indi.
% Parameter produc1832616231le_alt_DUMMY:produc1832616231le_alt.
% We need to prove ['(forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt a) b)) (p _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt a) c)) (((arrow_1760938802_below (p _TPTP_I)) c) b))))']
% Parameter arrow_1346734812le_alt:Type.
% Parameter arrow_1092341143e_indi:Type.
% Parameter list_A1528105233le_alt: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_1760938802_below:((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 _TPTP_ex:((produc1832616231le_alt->Prop)->Prop).
% Parameter in_rel895475842le_alt:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(arrow_1346734812le_alt->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 equal_2044961839le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->Prop)).
% Parameter distin1107700095le_alt:(list_A1528105233le_alt->Prop).
% Parameter insert844458914le_alt:(arrow_1346734812le_alt->(list_A1528105233le_alt->list_A1528105233le_alt)).
% Parameter cons_A1100118844le_alt:(arrow_1346734812le_alt->(list_A1528105233le_alt->list_A1528105233le_alt)).
% Parameter nil_Ar10086284le_alt:list_A1528105233le_alt.
% Parameter null_A244857236le_alt:(list_A1528105233le_alt->Prop).
% Parameter splice244790623le_alt:(list_A1528105233le_alt->(list_A1528105233le_alt->list_A1528105233le_alt)).
% 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 produc443407182_alt_o:((produc1832616231le_alt->Prop)->(arrow_1346734812le_alt->(arrow_1346734812le_alt->Prop))).
% 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 p_1:(arrow_1092341143e_indi->(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.
% Axiom fact_0__096P_A_058_AProf_096:((member1561882372_alt_o p) arrow_1605628760e_Prof).
% Axiom fact_1_assms_I3_J:(arrow_1724561858le_IIA f).
% Axiom fact_2_u:(arrow_1889221221nimity f).
% Axiom fact_3__096a_A_126_061_Ab_096:(not (((eq arrow_1346734812le_alt) a) b)).
% Axiom fact_4_dist:(distin1107700095le_alt ((cons_A1100118844le_alt a) ((cons_A1100118844le_alt b) ((cons_A1100118844le_alt c) nil_Ar10086284le_alt)))).
% Axiom fact_5_iff:(forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt a) b)) (p _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt b) a)) (p_1 _TPTP_I)))).
% Axiom fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_:((forall (C:arrow_1346734812le_alt), ((distin1107700095le_alt ((cons_A1100118844le_alt a) ((cons_A1100118844le_alt b) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt))))->False))->False).
% Axiom fact_7__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096:((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> (((arrow_1760938802_below (((arrow_1760938802_below (p P_4)) c) b)) b) a))) arrow_1605628760e_Prof).
% Axiom fact_8__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_:((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> (((arrow_1760938802_below (((arrow_1760938802_below (((arrow_1760938802_below (p P_4)) c) b)) b) a)) a) c))) arrow_1605628760e_Prof).
% Axiom fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096:((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> (((arrow_1760938802_below (p P_4)) c) b))) arrow_1605628760e_Prof).
% Axiom fact_10_in__mkbot:(forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (Z:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) ((arrow_1717184938_mkbot L_1) Z))) ((and ((and (not (((eq arrow_1346734812le_alt) Y_5) Z))) ((((eq arrow_1346734812le_alt) X_14) Z)->(not (((eq arrow_1346734812le_alt) X_14) Y_5))))) ((not (((eq arrow_1346734812le_alt) X_14) Z))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1))))).
% Axiom fact_11_in__mktop:(forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (Z:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) ((arrow_1865892024_mktop L_1) Z))) ((and ((and (not (((eq arrow_1346734812le_alt) X_14) Z))) ((((eq arrow_1346734812le_alt) Y_5) Z)->(not (((eq arrow_1346734812le_alt) X_14) Y_5))))) ((not (((eq arrow_1346734812le_alt) Y_5) Z))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1))))).
% Axiom fact_12_in__below:(forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) (((arrow_1760938802_below L_1) A_19) B_12))) ((and ((and (not (((eq arrow_1346734812le_alt) X_14) Y_5))) ((((eq arrow_1346734812le_alt) Y_5) A_19)->((member545531028le_alt ((produc990411159le_alt X_14) B_12)) L_1)))) ((not (((eq arrow_1346734812le_alt) Y_5) A_19))->((and ((((eq arrow_1346734812le_alt) X_14) A_19)->((or (((eq arrow_1346734812le_alt) Y_5) B_12)) ((member545531028le_alt ((produc990411159le_alt B_12) Y_5)) L_1)))) ((not (((eq arrow_1346734812le_alt) X_14) A_19))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1))))))))).
% Axiom fact_13_split__paired__All:(forall (P_7:(produc1832616231le_alt->Prop)), ((iff (all P_7)) (forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), (P_7 ((produc990411159le_alt A_7) B_4))))).
% Axiom fact_14_Pair__eq:(forall (A_25:arrow_1346734812le_alt) (B_18:arrow_1346734812le_alt) (A_24:arrow_1346734812le_alt) (B_17:arrow_1346734812le_alt), ((iff (((eq produc1832616231le_alt) ((produc990411159le_alt A_25) B_18)) ((produc990411159le_alt A_24) B_17))) ((and (((eq arrow_1346734812le_alt) A_25) A_24)) (((eq arrow_1346734812le_alt) B_18) B_17)))).
% Axiom fact_15_Pair__inject:(forall (A_23:arrow_1346734812le_alt) (B_16:arrow_1346734812le_alt) (A_22:arrow_1346734812le_alt) (B_15:arrow_1346734812le_alt), ((((eq produc1832616231le_alt) ((produc990411159le_alt A_23) B_16)) ((produc990411159le_alt A_22) B_15))->(((((eq arrow_1346734812le_alt) A_23) A_22)->(not (((eq arrow_1346734812le_alt) B_16) B_15)))->False))).
% Axiom fact_16_in__rel__def:(forall (R_1:(produc1832616231le_alt->Prop)) (X_17:arrow_1346734812le_alt) (Y_6:arrow_1346734812le_alt), ((iff (((in_rel895475842le_alt R_1) X_17) Y_6)) ((member545531028le_alt ((produc990411159le_alt X_17) Y_6)) R_1))).
% Axiom fact_17_below__Lin:(forall (L_1:(produc1832616231le_alt->Prop)) (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) X_14) Y_5))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o (((arrow_1760938802_below L_1) X_14) Y_5)) arrow_1751445586le_Lin)))).
% Axiom fact_18__096P_H_A_058_AProf_096:((member1561882372_alt_o p_1) arrow_1605628760e_Prof).
% Axiom fact_19__C1_C:(forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_21:arrow_1346734812le_alt) (B_14:arrow_1346734812le_alt) (A_20:arrow_1346734812le_alt) (B_13:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_20) B_13))->((not (((eq arrow_1346734812le_alt) A_21) B_14))->((not (((eq arrow_1346734812le_alt) A_20) B_14))->((not (((eq arrow_1346734812le_alt) B_13) A_21))->(((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_20) B_13)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (P_6 _TPTP_I))))->(((member545531028le_alt ((produc990411159le_alt A_20) B_13)) (f P_5))->((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (f P_6))))))))))).
% Axiom fact_20__C2_C:(forall (P_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (P_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_21:arrow_1346734812le_alt) (B_14:arrow_1346734812le_alt) (A_20:arrow_1346734812le_alt) (B_13:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_20) B_13))->((not (((eq arrow_1346734812le_alt) A_21) B_14))->((not (((eq arrow_1346734812le_alt) A_20) B_14))->((not (((eq arrow_1346734812le_alt) B_13) A_21))->(((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_20) B_13)) (P_5 _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (P_6 _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_20) B_13)) (f P_5))) ((member545531028le_alt ((produc990411159le_alt A_21) B_14)) (f P_6))))))))))).
% Axiom fact_21_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_22_const__Lin__Prof:(forall (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1561882372_alt_o (fun (P_4:arrow_1092341143e_indi)=> L_1)) arrow_1605628760e_Prof))).
% Axiom fact_23_mkbot__Lin:(forall (X_14:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1717184938_mkbot L_1) X_14)) arrow_1751445586le_Lin))).
% Axiom fact_24_mktop__Lin:(forall (X_14:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o ((arrow_1865892024_mktop L_1) X_14)) arrow_1751445586le_Lin))).
% Axiom fact_25_Lin__irrefl:(forall (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->(((member545531028le_alt ((produc990411159le_alt A_19) B_12)) L_1)->(((member545531028le_alt ((produc990411159le_alt B_12) A_19)) L_1)->False)))).
% Axiom fact_26_notin__Lin__iff:(forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((not (((eq arrow_1346734812le_alt) X_14) Y_5))->((iff (((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1)->False)) ((member545531028le_alt ((produc990411159le_alt Y_5) X_14)) L_1))))).
% Axiom fact_27_third__alt:(forall (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt A_19) ((cons_A1100118844le_alt B_12) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt)))))))).
% Axiom fact_28_IIA__def:(forall (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1724561858le_IIA F_8)) (forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(forall (Xa:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o Xa) arrow_1605628760e_Prof)->(forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((iff ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (X _TPTP_I))) ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (Xa _TPTP_I))))->((iff ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 X))) ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 Xa))))))))))).
% Axiom fact_29_unanimity__def:(forall (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((iff (arrow_1889221221nimity F_8)) (forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((forall (_TPTP_I:arrow_1092341143e_indi), ((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (X _TPTP_I)))->((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 X)))))))).
% Axiom fact_30_complete__Lin:(forall (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->((ex (produc1832616231le_alt->Prop)) (fun (X:(produc1832616231le_alt->Prop))=> ((and ((member1362619835_alt_o X) arrow_1751445586le_Lin)) ((member545531028le_alt ((produc990411159le_alt A_19) B_12)) X)))))).
% Axiom fact_31_in__above:(forall (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt) (L_1:(produc1832616231le_alt->Prop)) (A_19:arrow_1346734812le_alt) (B_12:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_19) B_12))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((iff ((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) (((arrow_452340254_above L_1) A_19) B_12))) ((and ((and (not (((eq arrow_1346734812le_alt) X_14) Y_5))) ((((eq arrow_1346734812le_alt) X_14) B_12)->((member545531028le_alt ((produc990411159le_alt A_19) Y_5)) L_1)))) ((not (((eq arrow_1346734812le_alt) X_14) B_12))->((and ((((eq arrow_1346734812le_alt) Y_5) B_12)->((or (((eq arrow_1346734812le_alt) X_14) A_19)) ((member545531028le_alt ((produc990411159le_alt X_14) A_19)) L_1)))) ((not (((eq arrow_1346734812le_alt) Y_5) B_12))->((member545531028le_alt ((produc990411159le_alt X_14) Y_5)) L_1))))))))).
% Axiom fact_32_distinct_Osimps_I1_J:(distin1107700095le_alt nil_Ar10086284le_alt).
% Axiom fact_33_list_Osimps_I2_J:(forall (A_18:arrow_1346734812le_alt) (List_4:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) nil_Ar10086284le_alt) ((cons_A1100118844le_alt A_18) List_4)))).
% Axiom fact_34_list_Oinject:(forall (A_17:arrow_1346734812le_alt) (List_3:list_A1528105233le_alt) (A_16:arrow_1346734812le_alt) (List_2:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_17) List_3)) ((cons_A1100118844le_alt A_16) List_2))) ((and (((eq arrow_1346734812le_alt) A_17) A_16)) (((eq list_A1528105233le_alt) List_3) List_2)))).
% Axiom fact_35_not__Cons__self2:(forall (X_16:arrow_1346734812le_alt) (Xs_11:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt X_16) Xs_11)) Xs_11))).
% Axiom fact_36_not__Cons__self:(forall (Xs_10:list_A1528105233le_alt) (X_15:arrow_1346734812le_alt), (not (((eq list_A1528105233le_alt) Xs_10) ((cons_A1100118844le_alt X_15) Xs_10)))).
% Axiom fact_37_above__Lin:(forall (L_1:(produc1832616231le_alt->Prop)) (X_14:arrow_1346734812le_alt) (Y_5:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) X_14) Y_5))->(((member1362619835_alt_o L_1) arrow_1751445586le_Lin)->((member1362619835_alt_o (((arrow_452340254_above L_1) X_14) Y_5)) arrow_1751445586le_Lin)))).
% Axiom fact_38_list_Osimps_I3_J:(forall (A_15:arrow_1346734812le_alt) (List_1:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) ((cons_A1100118844le_alt A_15) List_1)) nil_Ar10086284le_alt))).
% Axiom fact_39_dictatorI:(forall (I_1:arrow_1092341143e_indi) (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o F_8) ((pi_Arr1021537730_alt_o arrow_1605628760e_Prof) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> arrow_1751445586le_Lin)))->((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), ((not (((eq arrow_1346734812le_alt) A_7) B_4))->(((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (X I_1))->((member545531028le_alt ((produc990411159le_alt A_7) B_4)) (F_8 X)))))))->((arrow_1098709355ctator F_8) I_1)))).
% Axiom fact_40_PiE:(forall (X_13:produc1832616231le_alt) (F_11:(produc1832616231le_alt->Prop)) (A_14:(produc1832616231le_alt->Prop)) (B_11:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_11) ((pi_Pro539263375_alt_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member545531028le_alt X_13) A_14)->False)))).
% Axiom fact_41_PiE:(forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_11) ((pi_Arr1055270199le_alt A_14) B_11))->((((member545531028le_alt (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False)))).
% Axiom fact_42_PiE:(forall (X_13:Prop) (F_11:(Prop->produc1832616231le_alt)) (A_14:(Prop->Prop)) (B_11:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_11) ((pi_o_P988780107le_alt A_14) B_11))->((((member545531028le_alt (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False)))).
% Axiom fact_43_PiE:(forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_11) ((pi_Arr651234977_alt_o A_14) B_11))->((((member1561882372_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False)))).
% Axiom fact_44_PiE:(forall (X_13:Prop) (F_11:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_14:(Prop->Prop)) (B_11:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_11) ((pi_o_A71242893_alt_o A_14) B_11))->((((member1561882372_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False)))).
% Axiom fact_45_PiE:(forall (X_13:Prop) (F_11:(Prop->(produc1832616231le_alt->Prop))) (A_14:(Prop->Prop)) (B_11:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_11) ((pi_o_P1538584260_alt_o A_14) B_11))->((((member1362619835_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False)))).
% Axiom fact_46_PiE:(forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_11) ((pi_Arr1140519125_alt_o A_14) B_11))->((((member733327538_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False)))).
% Axiom fact_47_PiE:(forall (X_13:Prop) (F_11:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_14:(Prop->Prop)) (B_11:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_11) ((pi_o_A1302557673_alt_o A_14) B_11))->((((member733327538_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member_o X_13) A_14)->False)))).
% Axiom fact_48_PiE:(forall (X_13:produc1832616231le_alt) (F_11:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_14:(produc1832616231le_alt->Prop)) (B_11:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_11) ((pi_Pro1535452471e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member545531028le_alt X_13) A_14)->False)))).
% Axiom fact_49_PiE:(forall (X_13:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_14:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_11) ((pi_Arr170420797e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member1561882372_alt_o X_13) A_14)->False)))).
% Axiom fact_50_PiE:(forall (X_13:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_14:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_11) ((pi_Arr1767527177lt_o_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member1561882372_alt_o X_13) A_14)->False)))).
% Axiom fact_51_PiE:(forall (X_13:(produc1832616231le_alt->Prop)) (F_11:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_14:((produc1832616231le_alt->Prop)->Prop)) (B_11:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_11) ((pi_Pro1340600692e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member1362619835_alt_o X_13) A_14)->False)))).
% Axiom fact_52_PiE:(forall (X_13:(produc1832616231le_alt->Prop)) (F_11:((produc1832616231le_alt->Prop)->Prop)) (A_14:((produc1832616231le_alt->Prop)->Prop)) (B_11:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_11) ((pi_Pro410810898lt_o_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member1362619835_alt_o X_13) A_14)->False)))).
% Axiom fact_53_PiE:(forall (X_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_14:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_11) ((pi_Arr1941314005e_indi A_14) B_11))->((((member1714766084e_indi (F_11 X_13)) (B_11 X_13))->False)->(((member733327538_alt_o X_13) A_14)->False)))).
% Axiom fact_54_PiE:(forall (X_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_14:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_11) ((pi_Arr1422400881lt_o_o A_14) B_11))->((((member_o (F_11 X_13)) (B_11 X_13))->False)->(((member733327538_alt_o X_13) A_14)->False)))).
% Axiom fact_55_PiE:(forall (X_13:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_14:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_11) ((pi_Arr1021537730_alt_o A_14) B_11))->((((member1362619835_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1561882372_alt_o X_13) A_14)->False)))).
% Axiom fact_56_PiE:(forall (X_13:arrow_1092341143e_indi) (F_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_14:(arrow_1092341143e_indi->Prop)) (B_11:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_11) ((pi_Arr418143960_alt_o A_14) B_11))->((((member1362619835_alt_o (F_11 X_13)) (B_11 X_13))->False)->(((member1714766084e_indi X_13) A_14)->False)))).
% Axiom fact_57_list_Oexhaust:(forall (Y_4:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Y_4) nil_Ar10086284le_alt))->((forall (A_7:arrow_1346734812le_alt) (List:list_A1528105233le_alt), (not (((eq list_A1528105233le_alt) Y_4) ((cons_A1100118844le_alt A_7) List))))->False))).
% Axiom fact_58_neq__Nil__conv:(forall (Xs_9:list_A1528105233le_alt), ((iff (not (((eq list_A1528105233le_alt) Xs_9) nil_Ar10086284le_alt))) ((ex arrow_1346734812le_alt) (fun (Y_1:arrow_1346734812le_alt)=> ((ex list_A1528105233le_alt) (fun (Ys_2:list_A1528105233le_alt)=> (((eq list_A1528105233le_alt) Xs_9) ((cons_A1100118844le_alt Y_1) Ys_2)))))))).
% Axiom fact_59_alt3:((ex arrow_1346734812le_alt) (fun (A_7:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (B_4:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (C:arrow_1346734812le_alt)=> (distin1107700095le_alt ((cons_A1100118844le_alt A_7) ((cons_A1100118844le_alt B_4) ((cons_A1100118844le_alt C) nil_Ar10086284le_alt)))))))))).
% Axiom fact_60_Pi__mem:(forall (X_12:produc1832616231le_alt) (F_10:(produc1832616231le_alt->Prop)) (A_13:(produc1832616231le_alt->Prop)) (B_10:(produc1832616231le_alt->(Prop->Prop))), (((member1362619835_alt_o F_10) ((pi_Pro539263375_alt_o A_13) B_10))->(((member545531028le_alt X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_61_Pi__mem:(forall (X_12:produc1832616231le_alt) (F_10:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_13:(produc1832616231le_alt->Prop)) (B_10:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))), (((member1486844321e_indi F_10) ((pi_Pro1535452471e_indi A_13) B_10))->(((member545531028le_alt X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_62_Pi__mem:(forall (X_12:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member1208133347e_indi F_10) ((pi_Arr170420797e_indi A_13) B_10))->(((member1561882372_alt_o X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_63_Pi__mem:(forall (X_12:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member1754345465lt_o_o F_10) ((pi_Arr1767527177lt_o_o A_13) B_10))->(((member1561882372_alt_o X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_64_Pi__mem:(forall (X_12:(produc1832616231le_alt->Prop)) (F_10:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_13:((produc1832616231le_alt->Prop)->Prop)) (B_10:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))), (((member1255309082e_indi F_10) ((pi_Pro1340600692e_indi A_13) B_10))->(((member1362619835_alt_o X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_65_Pi__mem:(forall (X_12:(produc1832616231le_alt->Prop)) (F_10:((produc1832616231le_alt->Prop)->Prop)) (A_13:((produc1832616231le_alt->Prop)->Prop)) (B_10:((produc1832616231le_alt->Prop)->(Prop->Prop))), (((member1949484546lt_o_o F_10) ((pi_Pro410810898lt_o_o A_13) B_10))->(((member1362619835_alt_o X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_66_Pi__mem:(forall (X_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_13:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))), (((member986213183e_indi F_10) ((pi_Arr1941314005e_indi A_13) B_10))->(((member733327538_alt_o X_12) A_13)->((member1714766084e_indi (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_67_Pi__mem:(forall (X_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_13:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))), (((member903234717lt_o_o F_10) ((pi_Arr1422400881lt_o_o A_13) B_10))->(((member733327538_alt_o X_12) A_13)->((member_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_68_Pi__mem:(forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1621875105le_alt F_10) ((pi_Arr1055270199le_alt A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member545531028le_alt (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_69_Pi__mem:(forall (X_12:Prop) (F_10:(Prop->produc1832616231le_alt)) (A_13:(Prop->Prop)) (B_10:(Prop->(produc1832616231le_alt->Prop))), (((member1368218865le_alt F_10) ((pi_o_P988780107le_alt A_13) B_10))->(((member_o X_12) A_13)->((member545531028le_alt (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_70_Pi__mem:(forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member1079651021_alt_o F_10) ((pi_Arr651234977_alt_o A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member1561882372_alt_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_71_Pi__mem:(forall (X_12:Prop) (F_10:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_13:(Prop->Prop)) (B_10:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))), (((member537117565_alt_o F_10) ((pi_o_A71242893_alt_o A_13) B_10))->(((member_o X_12) A_13)->((member1561882372_alt_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_72_Pi__mem:(forall (X_12:Prop) (F_10:(Prop->(produc1832616231le_alt->Prop))) (A_13:(Prop->Prop)) (B_10:(Prop->((produc1832616231le_alt->Prop)->Prop))), (((member1099673524_alt_o F_10) ((pi_o_P1538584260_alt_o A_13) B_10))->(((member_o X_12) A_13)->((member1362619835_alt_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_73_Pi__mem:(forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member24189887_alt_o F_10) ((pi_Arr1140519125_alt_o A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member733327538_alt_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_74_Pi__mem:(forall (X_12:Prop) (F_10:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_13:(Prop->Prop)) (B_10:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))), (((member1710515983_alt_o F_10) ((pi_o_A1302557673_alt_o A_13) B_10))->(((member_o X_12) A_13)->((member733327538_alt_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_75_Pi__mem:(forall (X_12:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_13:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))), (((member733327538_alt_o F_10) ((pi_Arr1021537730_alt_o A_13) B_10))->(((member1561882372_alt_o X_12) A_13)->((member1362619835_alt_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_76_Pi__mem:(forall (X_12:arrow_1092341143e_indi) (F_10:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_13:(arrow_1092341143e_indi->Prop)) (B_10:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))), (((member1561882372_alt_o F_10) ((pi_Arr418143960_alt_o A_13) B_10))->(((member1714766084e_indi X_12) A_13)->((member1362619835_alt_o (F_10 X_12)) (B_10 X_12))))).
% Axiom fact_77_funcset__mem:(forall (X_11:produc1832616231le_alt) (F_9:(produc1832616231le_alt->Prop)) (A_12:(produc1832616231le_alt->Prop)) (B_9:(Prop->Prop)), (((member1362619835_alt_o F_9) ((pi_Pro539263375_alt_o A_12) (fun (Uu:produc1832616231le_alt)=> B_9)))->(((member545531028le_alt X_11) A_12)->((member_o (F_9 X_11)) B_9)))).
% Axiom fact_78_funcset__mem:(forall (X_11:produc1832616231le_alt) (F_9:(produc1832616231le_alt->arrow_1092341143e_indi)) (A_12:(produc1832616231le_alt->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member1486844321e_indi F_9) ((pi_Pro1535452471e_indi A_12) (fun (Uu:produc1832616231le_alt)=> B_9)))->(((member545531028le_alt X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9)))).
% Axiom fact_79_funcset__mem:(forall (X_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member1208133347e_indi F_9) ((pi_Arr170420797e_indi A_12) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_9)))->(((member1561882372_alt_o X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9)))).
% Axiom fact_80_funcset__mem:(forall (X_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_9:(Prop->Prop)), (((member1754345465lt_o_o F_9) ((pi_Arr1767527177lt_o_o A_12) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_9)))->(((member1561882372_alt_o X_11) A_12)->((member_o (F_9 X_11)) B_9)))).
% Axiom fact_81_funcset__mem:(forall (X_11:(produc1832616231le_alt->Prop)) (F_9:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (A_12:((produc1832616231le_alt->Prop)->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member1255309082e_indi F_9) ((pi_Pro1340600692e_indi A_12) (fun (Uu:(produc1832616231le_alt->Prop))=> B_9)))->(((member1362619835_alt_o X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9)))).
% Axiom fact_82_funcset__mem:(forall (X_11:(produc1832616231le_alt->Prop)) (F_9:((produc1832616231le_alt->Prop)->Prop)) (A_12:((produc1832616231le_alt->Prop)->Prop)) (B_9:(Prop->Prop)), (((member1949484546lt_o_o F_9) ((pi_Pro410810898lt_o_o A_12) (fun (Uu:(produc1832616231le_alt->Prop))=> B_9)))->(((member1362619835_alt_o X_11) A_12)->((member_o (F_9 X_11)) B_9)))).
% Axiom fact_83_funcset__mem:(forall (X_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (A_12:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_9:(arrow_1092341143e_indi->Prop)), (((member986213183e_indi F_9) ((pi_Arr1941314005e_indi A_12) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_9)))->(((member733327538_alt_o X_11) A_12)->((member1714766084e_indi (F_9 X_11)) B_9)))).
% Axiom fact_84_funcset__mem:(forall (X_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (F_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_12:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_9:(Prop->Prop)), (((member903234717lt_o_o F_9) ((pi_Arr1422400881lt_o_o A_12) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_9)))->(((member733327538_alt_o X_11) A_12)->((member_o (F_9 X_11)) B_9)))).
% Axiom fact_85_funcset__mem:(forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->produc1832616231le_alt)) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:(produc1832616231le_alt->Prop)), (((member1621875105le_alt F_9) ((pi_Arr1055270199le_alt A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member545531028le_alt (F_9 X_11)) B_9)))).
% Axiom fact_86_funcset__mem:(forall (X_11:Prop) (F_9:(Prop->produc1832616231le_alt)) (A_12:(Prop->Prop)) (B_9:(produc1832616231le_alt->Prop)), (((member1368218865le_alt F_9) ((pi_o_P988780107le_alt A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member545531028le_alt (F_9 X_11)) B_9)))).
% Axiom fact_87_funcset__mem:(forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member1079651021_alt_o F_9) ((pi_Arr651234977_alt_o A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member1561882372_alt_o (F_9 X_11)) B_9)))).
% Axiom fact_88_funcset__mem:(forall (X_11:Prop) (F_9:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (A_12:(Prop->Prop)) (B_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((member537117565_alt_o F_9) ((pi_o_A71242893_alt_o A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member1561882372_alt_o (F_9 X_11)) B_9)))).
% Axiom fact_89_funcset__mem:(forall (X_11:Prop) (F_9:(Prop->(produc1832616231le_alt->Prop))) (A_12:(Prop->Prop)) (B_9:((produc1832616231le_alt->Prop)->Prop)), (((member1099673524_alt_o F_9) ((pi_o_P1538584260_alt_o A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member1362619835_alt_o (F_9 X_11)) B_9)))).
% Axiom fact_90_funcset__mem:(forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member24189887_alt_o F_9) ((pi_Arr1140519125_alt_o A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member733327538_alt_o (F_9 X_11)) B_9)))).
% Axiom fact_91_funcset__mem:(forall (X_11:Prop) (F_9:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (A_12:(Prop->Prop)) (B_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), (((member1710515983_alt_o F_9) ((pi_o_A1302557673_alt_o A_12) (fun (Uu:Prop)=> B_9)))->(((member_o X_11) A_12)->((member733327538_alt_o (F_9 X_11)) B_9)))).
% Axiom fact_92_funcset__mem:(forall (X_11:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (F_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_12:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_9:((produc1832616231le_alt->Prop)->Prop)), (((member733327538_alt_o F_9) ((pi_Arr1021537730_alt_o A_12) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_9)))->(((member1561882372_alt_o X_11) A_12)->((member1362619835_alt_o (F_9 X_11)) B_9)))).
% Axiom fact_93_funcset__mem:(forall (X_11:arrow_1092341143e_indi) (F_9:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_12:(arrow_1092341143e_indi->Prop)) (B_9:((produc1832616231le_alt->Prop)->Prop)), (((member1561882372_alt_o F_9) ((pi_Arr418143960_alt_o A_12) (fun (Uu:arrow_1092341143e_indi)=> B_9)))->(((member1714766084e_indi X_11) A_12)->((member1362619835_alt_o (F_9 X_11)) B_9)))).
% Axiom fact_94_dictator__def:(forall (F_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (I_1:arrow_1092341143e_indi), ((iff ((arrow_1098709355ctator F_8) I_1)) (forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) arrow_1605628760e_Prof)->(((eq (produc1832616231le_alt->Prop)) (F_8 X)) (X I_1)))))).
% Axiom fact_95_Pi__I:(forall (F_7:(produc1832616231le_alt->arrow_1092341143e_indi)) (B_8:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))) (A_11:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member1486844321e_indi F_7) ((pi_Pro1535452471e_indi A_11) B_8)))).
% Axiom fact_96_Pi__I:(forall (F_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member1208133347e_indi F_7) ((pi_Arr170420797e_indi A_11) B_8)))).
% Axiom fact_97_Pi__I:(forall (F_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member1754345465lt_o_o F_7) ((pi_Arr1767527177lt_o_o A_11) B_8)))).
% Axiom fact_98_Pi__I:(forall (F_7:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (B_8:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))) (A_11:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member1255309082e_indi F_7) ((pi_Pro1340600692e_indi A_11) B_8)))).
% Axiom fact_99_Pi__I:(forall (F_7:((produc1832616231le_alt->Prop)->Prop)) (B_8:((produc1832616231le_alt->Prop)->(Prop->Prop))) (A_11:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member1949484546lt_o_o F_7) ((pi_Pro410810898lt_o_o A_11) B_8)))).
% Axiom fact_100_Pi__I:(forall (F_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_8:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_11)->((member1714766084e_indi (F_7 X)) (B_8 X))))->((member986213183e_indi F_7) ((pi_Arr1941314005e_indi A_11) B_8)))).
% Axiom fact_101_Pi__I:(forall (F_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_8:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_11:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member903234717lt_o_o F_7) ((pi_Arr1422400881lt_o_o A_11) B_8)))).
% Axiom fact_102_Pi__I:(forall (F_7:(arrow_1092341143e_indi->produc1832616231le_alt)) (B_8:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member545531028le_alt (F_7 X)) (B_8 X))))->((member1621875105le_alt F_7) ((pi_Arr1055270199le_alt A_11) B_8)))).
% Axiom fact_103_Pi__I:(forall (F_7:(Prop->produc1832616231le_alt)) (B_8:(Prop->(produc1832616231le_alt->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member545531028le_alt (F_7 X)) (B_8 X))))->((member1368218865le_alt F_7) ((pi_o_P988780107le_alt A_11) B_8)))).
% Axiom fact_104_Pi__I:(forall (F_7:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_8:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member1561882372_alt_o (F_7 X)) (B_8 X))))->((member1079651021_alt_o F_7) ((pi_Arr651234977_alt_o A_11) B_8)))).
% Axiom fact_105_Pi__I:(forall (F_7:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_8:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member1561882372_alt_o (F_7 X)) (B_8 X))))->((member537117565_alt_o F_7) ((pi_o_A71242893_alt_o A_11) B_8)))).
% Axiom fact_106_Pi__I:(forall (F_7:(Prop->(produc1832616231le_alt->Prop))) (B_8:(Prop->((produc1832616231le_alt->Prop)->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member1362619835_alt_o (F_7 X)) (B_8 X))))->((member1099673524_alt_o F_7) ((pi_o_P1538584260_alt_o A_11) B_8)))).
% Axiom fact_107_Pi__I:(forall (F_7:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_8:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member733327538_alt_o (F_7 X)) (B_8 X))))->((member24189887_alt_o F_7) ((pi_Arr1140519125_alt_o A_11) B_8)))).
% Axiom fact_108_Pi__I:(forall (F_7:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_8:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_11:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_11)->((member733327538_alt_o (F_7 X)) (B_8 X))))->((member1710515983_alt_o F_7) ((pi_o_A1302557673_alt_o A_11) B_8)))).
% Axiom fact_109_Pi__I:(forall (F_7:(produc1832616231le_alt->Prop)) (B_8:(produc1832616231le_alt->(Prop->Prop))) (A_11:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_11)->((member_o (F_7 X)) (B_8 X))))->((member1362619835_alt_o F_7) ((pi_Pro539263375_alt_o A_11) B_8)))).
% Axiom fact_110_Pi__I:(forall (F_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (B_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))) (A_11:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_11)->((member1362619835_alt_o (F_7 X)) (B_8 X))))->((member733327538_alt_o F_7) ((pi_Arr1021537730_alt_o A_11) B_8)))).
% Axiom fact_111_Pi__I:(forall (F_7:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (B_8:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))) (A_11:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_11)->((member1362619835_alt_o (F_7 X)) (B_8 X))))->((member1561882372_alt_o F_7) ((pi_Arr418143960_alt_o A_11) B_8)))).
% Axiom fact_112_funcsetI:(forall (F_6:(produc1832616231le_alt->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member1486844321e_indi F_6) ((pi_Pro1535452471e_indi A_10) (fun (Uu:produc1832616231le_alt)=> B_7))))).
% Axiom fact_113_funcsetI:(forall (F_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member1208133347e_indi F_6) ((pi_Arr170420797e_indi A_10) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_7))))).
% Axiom fact_114_funcsetI:(forall (F_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_7:(Prop->Prop)) (A_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_10)->((member_o (F_6 X)) B_7)))->((member1754345465lt_o_o F_6) ((pi_Arr1767527177lt_o_o A_10) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_7))))).
% Axiom fact_115_funcsetI:(forall (F_6:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member1255309082e_indi F_6) ((pi_Pro1340600692e_indi A_10) (fun (Uu:(produc1832616231le_alt->Prop))=> B_7))))).
% Axiom fact_116_funcsetI:(forall (F_6:((produc1832616231le_alt->Prop)->Prop)) (B_7:(Prop->Prop)) (A_10:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_10)->((member_o (F_6 X)) B_7)))->((member1949484546lt_o_o F_6) ((pi_Pro410810898lt_o_o A_10) (fun (Uu:(produc1832616231le_alt->Prop))=> B_7))))).
% Axiom fact_117_funcsetI:(forall (F_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_7:(arrow_1092341143e_indi->Prop)) (A_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_10)->((member1714766084e_indi (F_6 X)) B_7)))->((member986213183e_indi F_6) ((pi_Arr1941314005e_indi A_10) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_7))))).
% Axiom fact_118_funcsetI:(forall (F_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_7:(Prop->Prop)) (A_10:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_10)->((member_o (F_6 X)) B_7)))->((member903234717lt_o_o F_6) ((pi_Arr1422400881lt_o_o A_10) (fun (Uu:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> B_7))))).
% Axiom fact_119_funcsetI:(forall (F_6:(arrow_1092341143e_indi->produc1832616231le_alt)) (B_7:(produc1832616231le_alt->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member545531028le_alt (F_6 X)) B_7)))->((member1621875105le_alt F_6) ((pi_Arr1055270199le_alt A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7))))).
% Axiom fact_120_funcsetI:(forall (F_6:(Prop->produc1832616231le_alt)) (B_7:(produc1832616231le_alt->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member545531028le_alt (F_6 X)) B_7)))->((member1368218865le_alt F_6) ((pi_o_P988780107le_alt A_10) (fun (Uu:Prop)=> B_7))))).
% Axiom fact_121_funcsetI:(forall (F_6:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member1561882372_alt_o (F_6 X)) B_7)))->((member1079651021_alt_o F_6) ((pi_Arr651234977_alt_o A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7))))).
% Axiom fact_122_funcsetI:(forall (F_6:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_7:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member1561882372_alt_o (F_6 X)) B_7)))->((member537117565_alt_o F_6) ((pi_o_A71242893_alt_o A_10) (fun (Uu:Prop)=> B_7))))).
% Axiom fact_123_funcsetI:(forall (F_6:(Prop->(produc1832616231le_alt->Prop))) (B_7:((produc1832616231le_alt->Prop)->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member1362619835_alt_o (F_6 X)) B_7)))->((member1099673524_alt_o F_6) ((pi_o_P1538584260_alt_o A_10) (fun (Uu:Prop)=> B_7))))).
% Axiom fact_124_funcsetI:(forall (F_6:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member733327538_alt_o (F_6 X)) B_7)))->((member24189887_alt_o F_6) ((pi_Arr1140519125_alt_o A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7))))).
% Axiom fact_125_funcsetI:(forall (F_6:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_7:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (A_10:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_10)->((member733327538_alt_o (F_6 X)) B_7)))->((member1710515983_alt_o F_6) ((pi_o_A1302557673_alt_o A_10) (fun (Uu:Prop)=> B_7))))).
% Axiom fact_126_funcsetI:(forall (F_6:(produc1832616231le_alt->Prop)) (B_7:(Prop->Prop)) (A_10:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_10)->((member_o (F_6 X)) B_7)))->((member1362619835_alt_o F_6) ((pi_Pro539263375_alt_o A_10) (fun (Uu:produc1832616231le_alt)=> B_7))))).
% Axiom fact_127_funcsetI:(forall (F_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (B_7:((produc1832616231le_alt->Prop)->Prop)) (A_10:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_10)->((member1362619835_alt_o (F_6 X)) B_7)))->((member733327538_alt_o F_6) ((pi_Arr1021537730_alt_o A_10) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> B_7))))).
% Axiom fact_128_funcsetI:(forall (F_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (B_7:((produc1832616231le_alt->Prop)->Prop)) (A_10:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_10)->((member1362619835_alt_o (F_6 X)) B_7)))->((member1561882372_alt_o F_6) ((pi_Arr418143960_alt_o A_10) (fun (Uu:arrow_1092341143e_indi)=> B_7))))).
% Axiom fact_129_linear__alt:((ex (produc1832616231le_alt->Prop)) (fun (L:(produc1832616231le_alt->Prop))=> ((member1362619835_alt_o L) arrow_1751445586le_Lin))).
% Axiom fact_130_Pi__I_H:(forall (F_5:(produc1832616231le_alt->arrow_1092341143e_indi)) (B_6:(produc1832616231le_alt->(arrow_1092341143e_indi->Prop))) (A_9:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member1486844321e_indi F_5) ((pi_Pro1535452471e_indi A_9) B_6)))).
% Axiom fact_131_Pi__I_H:(forall (F_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member1208133347e_indi F_5) ((pi_Arr170420797e_indi A_9) B_6)))).
% Axiom fact_132_Pi__I_H:(forall (F_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) (B_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member1754345465lt_o_o F_5) ((pi_Arr1767527177lt_o_o A_9) B_6)))).
% Axiom fact_133_Pi__I_H:(forall (F_5:((produc1832616231le_alt->Prop)->arrow_1092341143e_indi)) (B_6:((produc1832616231le_alt->Prop)->(arrow_1092341143e_indi->Prop))) (A_9:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member1255309082e_indi F_5) ((pi_Pro1340600692e_indi A_9) B_6)))).
% Axiom fact_134_Pi__I_H:(forall (F_5:((produc1832616231le_alt->Prop)->Prop)) (B_6:((produc1832616231le_alt->Prop)->(Prop->Prop))) (A_9:((produc1832616231le_alt->Prop)->Prop)), ((forall (X:(produc1832616231le_alt->Prop)), (((member1362619835_alt_o X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member1949484546lt_o_o F_5) ((pi_Pro410810898lt_o_o A_9) B_6)))).
% Axiom fact_135_Pi__I_H:(forall (F_5:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->arrow_1092341143e_indi)) (B_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(arrow_1092341143e_indi->Prop))) (A_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_9)->((member1714766084e_indi (F_5 X)) (B_6 X))))->((member986213183e_indi F_5) ((pi_Arr1941314005e_indi A_9) B_6)))).
% Axiom fact_136_Pi__I_H:(forall (F_5:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) (B_6:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->(Prop->Prop))) (A_9:(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (((member733327538_alt_o X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member903234717lt_o_o F_5) ((pi_Arr1422400881lt_o_o A_9) B_6)))).
% Axiom fact_137_Pi__I_H:(forall (F_5:(arrow_1092341143e_indi->produc1832616231le_alt)) (B_6:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member545531028le_alt (F_5 X)) (B_6 X))))->((member1621875105le_alt F_5) ((pi_Arr1055270199le_alt A_9) B_6)))).
% Axiom fact_138_Pi__I_H:(forall (F_5:(Prop->produc1832616231le_alt)) (B_6:(Prop->(produc1832616231le_alt->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member545531028le_alt (F_5 X)) (B_6 X))))->((member1368218865le_alt F_5) ((pi_o_P988780107le_alt A_9) B_6)))).
% Axiom fact_139_Pi__I_H:(forall (F_5:(arrow_1092341143e_indi->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_6:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member1561882372_alt_o (F_5 X)) (B_6 X))))->((member1079651021_alt_o F_5) ((pi_Arr651234977_alt_o A_9) B_6)))).
% Axiom fact_140_Pi__I_H:(forall (F_5:(Prop->(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))) (B_6:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member1561882372_alt_o (F_5 X)) (B_6 X))))->((member537117565_alt_o F_5) ((pi_o_A71242893_alt_o A_9) B_6)))).
% Axiom fact_141_Pi__I_H:(forall (F_5:(Prop->(produc1832616231le_alt->Prop))) (B_6:(Prop->((produc1832616231le_alt->Prop)->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member1362619835_alt_o (F_5 X)) (B_6 X))))->((member1099673524_alt_o F_5) ((pi_o_P1538584260_alt_o A_9) B_6)))).
% Axiom fact_142_Pi__I_H:(forall (F_5:(arrow_1092341143e_indi->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_6:(arrow_1092341143e_indi->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member733327538_alt_o (F_5 X)) (B_6 X))))->((member24189887_alt_o F_5) ((pi_Arr1140519125_alt_o A_9) B_6)))).
% Axiom fact_143_Pi__I_H:(forall (F_5:(Prop->((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))) (B_6:(Prop->(((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop))) (A_9:(Prop->Prop)), ((forall (X:Prop), (((member_o X) A_9)->((member733327538_alt_o (F_5 X)) (B_6 X))))->((member1710515983_alt_o F_5) ((pi_o_A1302557673_alt_o A_9) B_6)))).
% Axiom fact_144_Pi__I_H:(forall (F_5:(produc1832616231le_alt->Prop)) (B_6:(produc1832616231le_alt->(Prop->Prop))) (A_9:(produc1832616231le_alt->Prop)), ((forall (X:produc1832616231le_alt), (((member545531028le_alt X) A_9)->((member_o (F_5 X)) (B_6 X))))->((member1362619835_alt_o F_5) ((pi_Pro539263375_alt_o A_9) B_6)))).
% Axiom fact_145_Pi__I_H:(forall (F_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (B_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))) (A_9:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (X:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o X) A_9)->((member1362619835_alt_o (F_5 X)) (B_6 X))))->((member733327538_alt_o F_5) ((pi_Arr1021537730_alt_o A_9) B_6)))).
% Axiom fact_146_Pi__I_H:(forall (F_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (B_6:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))) (A_9:(arrow_1092341143e_indi->Prop)), ((forall (X:arrow_1092341143e_indi), (((member1714766084e_indi X) A_9)->((member1362619835_alt_o (F_5 X)) (B_6 X))))->((member1561882372_alt_o F_5) ((pi_Arr418143960_alt_o A_9) B_6)))).
% Axiom fact_147_Pi__cong:(forall (B_5:(produc1832616231le_alt->(Prop->Prop))) (G:(produc1832616231le_alt->Prop)) (F_4:(produc1832616231le_alt->Prop)) (A_8:(produc1832616231le_alt->Prop)), ((forall (W:produc1832616231le_alt), (((member545531028le_alt W) A_8)->((iff (F_4 W)) (G W))))->((iff ((member1362619835_alt_o F_4) ((pi_Pro539263375_alt_o A_8) B_5))) ((member1362619835_alt_o G) ((pi_Pro539263375_alt_o A_8) B_5))))).
% Axiom fact_148_Pi__cong:(forall (B_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->((produc1832616231le_alt->Prop)->Prop))) (F_4:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (G:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))) (A_8:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((forall (W:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (((member1561882372_alt_o W) A_8)->(((eq (produc1832616231le_alt->Prop)) (F_4 W)) (G W))))->((iff ((member733327538_alt_o F_4) ((pi_Arr1021537730_alt_o A_8) B_5))) ((member733327538_alt_o G) ((pi_Arr1021537730_alt_o A_8) B_5))))).
% Axiom fact_149_Pi__cong:(forall (B_5:(arrow_1092341143e_indi->((produc1832616231le_alt->Prop)->Prop))) (F_4:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (G:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_8:(arrow_1092341143e_indi->Prop)), ((forall (W:arrow_1092341143e_indi), (((member1714766084e_indi W) A_8)->(((eq (produc1832616231le_alt->Prop)) (F_4 W)) (G W))))->((iff ((member1561882372_alt_o F_4) ((pi_Arr418143960_alt_o A_8) B_5))) ((member1561882372_alt_o G) ((pi_Arr418143960_alt_o A_8) B_5))))).
% Axiom fact_150_splice_Osimps_I2_J:(forall (V:arrow_1346734812le_alt) (Va:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt V) Va)) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt V) Va))).
% Axiom fact_151_splice_Osimps_I3_J:(forall (X_10:arrow_1346734812le_alt) (Xs_8:list_A1528105233le_alt) (Y_3:arrow_1346734812le_alt) (Ys_1:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt ((cons_A1100118844le_alt X_10) Xs_8)) ((cons_A1100118844le_alt Y_3) Ys_1))) ((cons_A1100118844le_alt X_10) ((cons_A1100118844le_alt Y_3) ((splice244790623le_alt Xs_8) Ys_1))))).
% Axiom fact_152_splice_Osimps_I1_J:(forall (Ys:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt nil_Ar10086284le_alt) Ys)) Ys)).
% Axiom fact_153_splice__Nil2:(forall (Xs_7:list_A1528105233le_alt), (((eq list_A1528105233le_alt) ((splice244790623le_alt Xs_7) nil_Ar10086284le_alt)) Xs_7)).
% Axiom fact_154_pred__equals__eq2:(forall (S:(produc1832616231le_alt->Prop)) (R:(produc1832616231le_alt->Prop)), ((iff (forall (X:arrow_1346734812le_alt) (Xa:arrow_1346734812le_alt), ((iff ((member545531028le_alt ((produc990411159le_alt X) Xa)) R)) ((member545531028le_alt ((produc990411159le_alt X) Xa)) S)))) (((eq (produc1832616231le_alt->Prop)) R) S))).
% Axiom fact_155_prod_Oexhaust:(forall (Y_2:produc1832616231le_alt), ((forall (A_7:arrow_1346734812le_alt) (B_4:arrow_1346734812le_alt), (not (((eq produc1832616231le_alt) Y_2) ((produc990411159le_alt A_7) B_4))))->False)).
% Axiom fact_156_PairE:(forall (P_3:produc1832616231le_alt), ((forall (X:arrow_1346734812le_alt) (Y_1:arrow_1346734812le_alt), (not (((eq produc1832616231le_alt) P_3) ((produc990411159le_alt X) Y_1))))->False)).
% Axiom fact_157_split__paired__Ex:(forall (P_2:(produc1832616231le_alt->Prop)), ((iff (_TPTP_ex P_2)) ((ex arrow_1346734812le_alt) (fun (A_7:arrow_1346734812le_alt)=> ((ex arrow_1346734812le_alt) (fun (B_4:arrow_1346734812le_alt)=> (P_2 ((produc990411159le_alt A_7) B_4)))))))).
% Axiom fact_158_insert__Nil:(forall (X_9:arrow_1346734812le_alt), (((eq list_A1528105233le_alt) ((insert844458914le_alt X_9) nil_Ar10086284le_alt)) ((cons_A1100118844le_alt X_9) nil_Ar10086284le_alt))).
% Axiom fact_159_distinct__insert:(forall (X_8:arrow_1346734812le_alt) (Xs_6:list_A1528105233le_alt), ((distin1107700095le_alt Xs_6)->(distin1107700095le_alt ((insert844458914le_alt X_8) Xs_6)))).
% Axiom fact_160_mem__def:(forall (X_7:arrow_1092341143e_indi) (A_6:(arrow_1092341143e_indi->Prop)), ((iff ((member1714766084e_indi X_7) A_6)) (A_6 X_7))).
% Axiom fact_161_mem__def:(forall (X_7:Prop) (A_6:(Prop->Prop)), ((iff ((member_o X_7) A_6)) (A_6 X_7))).
% Axiom fact_162_mem__def:(forall (X_7:produc1832616231le_alt) (A_6:(produc1832616231le_alt->Prop)), ((iff ((member545531028le_alt X_7) A_6)) (A_6 X_7))).
% Axiom fact_163_mem__def:(forall (X_7:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))) (A_6:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), ((iff ((member1561882372_alt_o X_7) A_6)) (A_6 X_7))).
% Axiom fact_164_mem__def:(forall (X_7:(produc1832616231le_alt->Prop)) (A_6:((produc1832616231le_alt->Prop)->Prop)), ((iff ((member1362619835_alt_o X_7) A_6)) (A_6 X_7))).
% Axiom fact_165_mem__def:(forall (X_7:((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_7) A_6)) (A_6 X_7))).
% Axiom fact_166_Collect__def:(forall (P_1:(arrow_1092341143e_indi->Prop)), (((eq (arrow_1092341143e_indi->Prop)) (collec1832628290e_indi P_1)) P_1)).
% Axiom fact_167_list__nonempty__induct:(forall (P:(list_A1528105233le_alt->Prop)) (Xs_4:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_4) nil_Ar10086284le_alt))->((forall (X:arrow_1346734812le_alt), (P ((cons_A1100118844le_alt X) nil_Ar10086284le_alt)))->((forall (X:arrow_1346734812le_alt) (Xs_5:list_A1528105233le_alt), ((not (((eq list_A1528105233le_alt) Xs_5) nil_Ar10086284le_alt))->((P Xs_5)->(P ((cons_A1100118844le_alt X) Xs_5)))))->(P Xs_4))))).
% Axiom fact_168_curry__def:(forall (X:(produc1832616231le_alt->Prop)) (Xa:arrow_1346734812le_alt) (Xb:arrow_1346734812le_alt), ((iff (((produc443407182_alt_o X) Xa) Xb)) (X ((produc990411159le_alt Xa) Xb)))).
% Axiom fact_169_curryI:(forall (F_3:(produc1832616231le_alt->Prop)) (A_5:arrow_1346734812le_alt) (B_3:arrow_1346734812le_alt), ((F_3 ((produc990411159le_alt A_5) B_3))->(((produc443407182_alt_o F_3) A_5) B_3))).
% Axiom fact_170_curryE:(forall (F_2:(produc1832616231le_alt->Prop)) (A_4:arrow_1346734812le_alt) (B_2:arrow_1346734812le_alt), ((((produc443407182_alt_o F_2) A_4) B_2)->(F_2 ((produc990411159le_alt A_4) B_2)))).
% Axiom fact_171_curryD:(forall (F_1:(produc1832616231le_alt->Prop)) (A_3:arrow_1346734812le_alt) (B_1:arrow_1346734812le_alt), ((((produc443407182_alt_o F_1) A_3) B_1)->(F_1 ((produc990411159le_alt A_3) B_1)))).
% Axiom fact_172_curry__conv:(forall (F:(produc1832616231le_alt->Prop)) (A_2:arrow_1346734812le_alt) (B:arrow_1346734812le_alt), ((iff (((produc443407182_alt_o F) A_2) B)) (F ((produc990411159le_alt A_2) B)))).
% Axiom fact_173_eq__Nil__null:(forall (Xs_3:list_A1528105233le_alt), ((iff (((eq list_A1528105233le_alt) Xs_3) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs_3))).
% Axiom fact_174_List_Onull__def:(forall (Xs_2:list_A1528105233le_alt), ((iff (null_A244857236le_alt Xs_2)) (((eq list_A1528105233le_alt) Xs_2) nil_Ar10086284le_alt))).
% Axiom fact_175_null__rec_I1_J:(forall (X_6:arrow_1346734812le_alt) (Xs_1:list_A1528105233le_alt), ((null_A244857236le_alt ((cons_A1100118844le_alt X_6) Xs_1))->False)).
% Axiom fact_176_null__rec_I2_J:(null_A244857236le_alt nil_Ar10086284le_alt).
% Axiom fact_177_equal__Nil__null:(forall (Xs:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt Xs) nil_Ar10086284le_alt)) (null_A244857236le_alt Xs))).
% Axiom fact_178_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_179_top1I:(forall (X_5:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), (top_to1049332548lt_o_o X_5)).
% Axiom fact_180_top1I:(forall (X_5:(produc1832616231le_alt->Prop)), (top_to1830848411lt_o_o X_5)).
% Axiom fact_181_top1I:(forall (X_5:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), (top_to790289938lt_o_o X_5)).
% Axiom fact_182_top1I:(forall (X_5:produc1832616231le_alt), (top_to679332578_alt_o X_5)).
% Axiom fact_183_top1I:(forall (X_5:arrow_1092341143e_indi), (top_to527331954indi_o X_5)).
% Axiom fact_184_Pi__UNIV:(forall (A_1:(produc1832616231le_alt->Prop)), (((eq ((produc1832616231le_alt->Prop)->Prop)) ((pi_Pro539263375_alt_o A_1) (fun (Uu:produc1832616231le_alt)=> top_top_o_o))) top_to1830848411lt_o_o)).
% Axiom fact_185_Pi__UNIV:(forall (A_1:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)), (((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr1021537730_alt_o A_1) (fun (Uu:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop)))=> top_to1830848411lt_o_o))) top_to1049332548lt_o_o)).
% Axiom fact_186_Pi__UNIV:(forall (A_1:(arrow_1092341143e_indi->Prop)), (((eq ((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->Prop)) ((pi_Arr418143960_alt_o A_1) (fun (Uu:arrow_1092341143e_indi)=> top_to1830848411lt_o_o))) top_to790289938lt_o_o)).
% Axiom fact_187_equal__list__def:(forall (X_4:list_A1528105233le_alt) (Y:list_A1528105233le_alt), ((iff ((equal_2044961839le_alt X_4) Y)) (((eq list_A1528105233le_alt) X_4) Y))).
% Axiom fact_188_iso__tuple__UNIV__I:(forall (X_3:Prop), ((member_o X_3) top_top_o_o)).
% Axiom fact_189_iso__tuple__UNIV__I:(forall (X_3:arrow_1092341143e_indi), ((member1714766084e_indi X_3) top_to527331954indi_o)).
% Axiom fact_190_iso__tuple__UNIV__I:(forall (X_3:produc1832616231le_alt), ((member545531028le_alt X_3) top_to679332578_alt_o)).
% Axiom fact_191_iso__tuple__UNIV__I:(forall (X_3:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_3) top_to790289938lt_o_o)).
% Axiom fact_192_iso__tuple__UNIV__I:(forall (X_3:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_3) top_to1830848411lt_o_o)).
% Axiom fact_193_iso__tuple__UNIV__I:(forall (X_3:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_3) top_to1049332548lt_o_o)).
% Axiom fact_194_UNIV__I:(forall (X_2:Prop), ((member_o X_2) top_top_o_o)).
% Axiom fact_195_UNIV__I:(forall (X_2:arrow_1092341143e_indi), ((member1714766084e_indi X_2) top_to527331954indi_o)).
% Axiom fact_196_UNIV__I:(forall (X_2:produc1832616231le_alt), ((member545531028le_alt X_2) top_to679332578_alt_o)).
% Axiom fact_197_UNIV__I:(forall (X_2:(arrow_1092341143e_indi->(produc1832616231le_alt->Prop))), ((member1561882372_alt_o X_2) top_to790289938lt_o_o)).
% Axiom fact_198_UNIV__I:(forall (X_2:(produc1832616231le_alt->Prop)), ((member1362619835_alt_o X_2) top_to1830848411lt_o_o)).
% Axiom fact_199_UNIV__I:(forall (X_2:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))), ((member733327538_alt_o X_2) top_to1049332548lt_o_o)).
% Axiom fact_200_UNIV__def:(((eq (((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop))->Prop)) top_to1049332548lt_o_o) (collec2125720304_alt_o (fun (X:((arrow_1092341143e_indi->(produc1832616231le_alt->Prop))->(produc1832616231le_alt->Prop)))=> True))).
% Axiom fact_201_UNIV__def:(((eq ((produc1832616231le_alt->Prop)->Prop)) top_to1830848411lt_o_o) (collec
% EOF
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